MECHANICAL CHARACTERIZATION OF THE HARD PALATE
By
JENNIFER LANE HOTZMAN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2010
1
© 2010 Jennifer Lane Hotzman
2
To my family and friends
3
ACKNOWLEDGMENTS
Many individuals have contributed to the success of my dissertation. First, I would like to
thank my advisor, Dr. David Daegling, for all of his assistance throughout this entire experience.
I would have never been able to complete this undertaking without all of his patience and
guidance. I would also like to thank my parents who were unfailing in their support of my dream
to accomplish this goal. I give general thanks to Kaki York and Chris Ward who helped answer
questions regarding statistics throughout the entire process. There are also specific individuals
and organizations I would like to thank for providing help with particular portions of my project.
Dr. Gerald Bourne assited with granting access to both the nanoindenter and
microindenter. The nanoindentater is in the Major Analytical Instrumentation Center,
Department of Materials Science and Engineering, University of Florida. I would like to thank
Dr. Andrew Rapoff for providing guidance on how to best prepare the specimens for indentation.
Laurel Freas assisted with the initial sawing of the palate that was completed in order to prepare
the specimens for indentation.
SCANCO USA, Inc. conducted the micro-computed tomography scanning of the macaque
skull. I would like to thank Dr. Rasheesh Kapadia for coordinating the scanning and providing the data to me. I would also like to thank Casey Self for packaging the specimen and shipping it to the company to be scanned.
I would like to thank Eileen Westwig at the American Museum of Natural History and
Linda Gordon at the Smithsonian National Museum of Natural History for coordinating my visits
and allowing me access the museum collections to gather my comparative data. I also wish to
thank Laura Regan for providing me room and board when I collected my data at the
Smithsonian Museum.
4
The wood block experiment also required some assistance during the preparation phase. I
would like to thank Andy Thon and Anna Vick for helping me to procure the wood necessary for the experiment as well as the tools. Traci van Deest also helped preparing the wood block by assisting with sawing it to the correct dimensions.
Finally, I would like to thank Chris Ayers for his computer support and more importantly his moral support. Without his help, this project would have been even more difficult to accomplish. I want to extend my gratitude to all of the individuals who helped me to complete my project.
5
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...... 4
LIST OF TABLES...... 7
LIST OF FIGURES ...... 9
CHAPTER
1 PROBLEM INTRODUCTION...... 17
Research Statement...... 17 Hypotheses...... 18
2 BACKGROUND INFORMATION...... 22
Mechanics in Bone Growth ...... 22 Palatal Growth ...... 33 Sutures ...... 38 Structure and Function of the Periodontal Ligament...... 45 Biomechanics of Mastication ...... 47
3 METHODS...... 61
4 RESULTS...... 91
5 DISCUSSION...... 250
Comparing the Material Properties of the Maxillae and Mandible ...... 250 Modeling the Palate ...... 259 Sutural Complexity and Loading...... 266 Allometry of the Palate...... 271 Implications of Research for Understanding the Functional Morphology of the Skull ...... 275 Unresolved Questions...... 277
6 CONCLUSIONS ...... 287
LIST OF REFERENCES...... 292
BIOGRAPHICAL SKETCH ...... 303
6
LIST OF TABLES
Table page
3-1 Samples sizes for comparative study ...... 83
3-2 Definitions of measurements collected...... 84
4-1 Descriptive statistics for elastic moduli (GPa) values from the nanoindentation section...... 130
4-2 Elastic moduli values from section 1 calculated from microindentation...... 137
4-3 Elastic moduli values from section 2 calculated from microindentation...... 138
4-4 Elastic moduli values from section 3 calculated from microindentation...... 139
4-5 Elastic moduli values from section 4 calculated from microindentation...... 140
4-6 Elastic moduli values from section 5 calculated from microindentation...... 141
4-7 Elastic moduli values from section 6 calculated from microindentation...... 142
4-8 Elastic moduli values from section 7 calculated from microindentation...... 143
4-9 Maximum strain at different gage locations in the pigs...... 146
4-10 Position 1 predictions and observed strain...... 150
4-11 Position 2 predictions and observed strain...... 150
4-12 Position 3 predictions and observed strain...... 150
4-13 Predicted stress and strain values from hand calculated moment of inertia ...... 151
4-14 Expected versus observed strain ratios during macaque bending...... 152
4-15 Shear and principal strain ratios for pig specimens in torsion...... 152
4-16 Position 1 shear predictions for the macaque cranium during twisting...... 158
4-17 Position 2 shear predictions for the macaque cranium during twisting...... 158
4-18 Shear strains and principal strain ratios for the macaque during twisting ...... 158
4-19 Reduced major axis results for papionins...... 162
4-20 Reduced major axis results for colobines...... 164
7
4-21 Reduced major axis results for hominoids...... 166
4-22 Significance (alpha) values for phylogenetic group comparisons from RMA2*...... 168
4-23 Ratio averages for palatal dimensions versus size...... 169
4-24 Descriptive statistics of fractal dimensions for species by sex...... 237
4-25 Descriptive statistics of suture length ratio for species by sex ...... 238
4-26 Mann-Whitney U P values for the sexes of each species ...... 239
4-27 Mann-Whitney U tests significance values for species versus fractal dimension (FD) ..240
4-28 Mann-Whitney U tests significance values for species versus suture length ratio...... 243
4-29 Mann-Whitney U tests significance values for phylogenetic groups versus suture measurement ...... 246
4-30 Mann-Whitney U tests significance values for dietary contrasts...... 246
4-31 Reduced major axis (RMA) regression results for colobines ...... 247
4-32 Reduced major axis (RMA) regression results for papionins...... 248
4-33 Reduced major axis (RMA) regression results for hominoids...... 249
5-1 Predicted versus observed strains during cantilever bending of wood block ...... 284
5-2 Expected versus observed strain ratios at gage locations in the wood block experiment...... 284
5-3 Maximum strain at common loads (32-33N) during bending and twisting of the macaque ...... 285
5-4 Number of specimens whose mid-palatal suture is fused for each species...... 286
8
LIST OF FIGURES
Figure page
2-1 “V” principle of facial growth ...... 54
2-2 Transverse view of palate during molar biting ...... 55
2-3 Lateral view of working side molar biting...... 56
2-4 Lateral view of balancing side molar biting...... 57
2-5 Lateral view of incisor biting...... 58
2-6 Frontal view of incisor biting...... 59
2-7 Frontal view of molar biting ...... 60
3-1 Original position of skull in the µCT scanner...... 85
3-2 Strain gage locations on Sus domesticus...... 86
3-3 Schematic of torsional pig loading regime...... 87
3-4 Strain gage locations for the Macaca fascicularis specimen...... 88
3-5 Molar loading set-up for the macaque ...... 89
3-6 Incisor loading set-up for the macaque...... 89
3-7 Twisting set-up for the macaque experiment...... 90
4-1 Density gradient from mid-palatal suture to tooth for representative coronal section. ...129
4-2 Microindented specimen 1...... 130
4-3 Microindented specimen 2...... 131
4-4 Microindented specimen 3...... 132
4-5 Microindented specimen 4...... 133
4-6 Microindented specimen 5...... 134
4-7 Microindented specimen 6...... 135
4-8 Microindented specimen 7...... 136
4-9 Regression of bone density versus elastic modulus from section 5...... 144
9
4-10 Regression of bone density versus elastic modulus from section 7...... 145
4-11 Theoretical versus observed strains in the pig specimens during bending...... 147
4-12 Maximum principal strain directions for all pig specimens during bending...... 148
4-13 Idealized geometries used to calculate predicted stress for macaque loading...... 149
4-14 Gage classification by positions...... 149
4-15 Predicted stress at each gage position in for each idealized geometry...... 150
4-16 Five µCT scans of macaque skull used to estimate moment of inertia...... 151
4-17 Maximum principal strain directions during incisor loading...... 152
4-18 Tension versus load for right molar loading...... 153
4-19 Tension versus load for left molar loading...... 154
4-20 Theoretical versus observed strain during torsion for the pig specimens...... 155
4-21 Maximum principal strain direction during torsion...... 156
4-22 Shear versus load for the macaque cranium during clockwise twisting...... 157
4-23 Maximum principal strain direction from clockwise twisting...... 158
4-24 Strain at the suture versus bone on a pig cranium...... 159
4-25 Strain at the mid-palatal suture and adjacent bone in the pig cranium...... 159
4-26 Tensile strain versus load in the macaque during bending...... 160
4-27 Shear at each tooth during vertical loading at 20N...... 161
4-28 Papionin regression of facial width versus external palate breadth...... 170
4-29 Papionin regression of facial width versus internal palate breadth...... 171
4-30 Papionin regression of facial width versus palate depth...... 172
4-31 Papionin regression of facial width versus palatine palate length...... 173
4-32 Papionin regression of facial width versus palate width...... 174
4-33 Papionin regression of facial width versus internal palate breadth...... 175
4-34 Papionin regression of facial width versus total palatine length...... 176
10
4-35 Colobine regression of facial width versus palate width...... 177
4-36 Colobine regression of facial width versus maxillary palate length...... 177
4-37 Colobine regression of facial width versus total palate length...... 178
4-38 Colobine regression of facial width versus external palate breadth...... 178
4-39 Colobine regression of facial width versus palate depth...... 179
4-40 Colobine regression of facial width versus internal palate breadth...... 179
4-41 Colobine regression of facial width versus palatine palate length...... 180
4-42 Hominoid regression of facial width versus palatine palate length...... 180
4-43 Hominoid regression of facial width versus maxillary palate length...... 181
4-44 Hominoid regression of facial width versus internal palate breadth...... 181
4-45 Hominoid regression of facial width versus total palate length...... 182
4-46 Hominoid regression of facial width versus external palate breadth...... 182
4-47 Hominoid regression of facial width versus palate width...... 183
4-48 Hominoid regression of facial width versus palate depth...... 183
4-49 Papionin regression of upper facial height versus total palate length...... 184
4-50 Papionin regression of upper facial height versus palatine palate length...... 185
4-51 Papionin regression of upper facial height versus maxillary palate length...... 186
4-52 Papionin regression of upper facial height versus palate width...... 187
4-53 Papionin regression of upper facial height versus external palate breadth...... 188
4-54 Papionin regression of upper facial height versus internal palate breadth...... 189
4-55 Papionin regression of upper facial height versus palate depth...... 190
4-56 Colobine regression of upper facial height versus maxillary palate length...... 191
4-57 Colobine regression of upper facial height versus total palate length...... 191
4-58 Colobine regression of upper facial height versus palate width...... 192
4-59 Colobine regression of upper facial height versus internal palate breadth...... 192
11
4-60 Colobine regression of upper facial height versus external palate breadth...... 193
4-61 Colobine regression of upper facial height versus palate depth...... 193
4-62 Colobine regression of upper facial height versus palatine palate length...... 194
4-63 Hominoid regression of upper facial height versus palatine palate length...... 194
4-64 Hominoid regression of upper facial height versus maxillary palate length...... 195
4-65 Hominoid regression of upper facial height versus total palate length...... 195
4-66 Hominoid regression of upper facial height versus palate width...... 196
4-67 Hominoid regression of upper facial height versus external palate breadth...... 196
4-68 Hominoid regression of upper facial height versus internal palate breadth...... 197
4-69 Hominoid regression of upper facial height versus palate depth...... 197
4-70 Papionin regression of upper facial height versus maxillary palate length...... 198
4-71 Papionin regression of upper facial height versus palatine palate length...... 199
4-72 Papionin regression of upper facial height versus total palate length...... 200
4-73 Papionin regression of upper facial height versus palate depth...... 201
4-74 Papionin regression of upper facial height versus palate width...... 202
4-75 Papionin regression of upper facial height versus external palate breadth...... 203
4-76 Papionin regression of upper facial height versus internal palate breadth...... 204
4-77 Colobine regression of total facial height versus palate width...... 205
4-78 Colobine regression of total facial height versus palate depth...... 205
4-79 Colobine regression of total facial height versus external palate breadth...... 206
4-80 Colobine regression of total facial height versus internal palate breadth...... 206
4-81 Colobine regression of total facial height versus palatine palate length...... 207
4-82 Colobine regression of total facial height versus maxillary palate length...... 207
4-83 Colobine regression of total facial height versus total palate length...... 208
4-84 Hominoid regression of total facial height versus internal palate breadth...... 208
12
4-85 Papionin regression of skull length versus maxillary palate length...... 209
4-86 Papionin regression of skull length versus total palate length...... 210
4-87 Papionin regression of skull length versus palatine palate length...... 211
4-88 Papionin regression of skull length versus palate width...... 212
4-89 Papionin regression of skull length versus palate depth...... 213
4-90 Papionin regression of skull length versus external palate breadth...... 214
4-91 Papionin regression of skull length versus internal palate breadth...... 215
4-92 Colobine regression of skull length versus palate width...... 216
4-93 Colobine regression of skull length versus external palate breadth...... 216
4-94 Colobine regression of skull length versus internal palate breadth...... 217
4-95 Colobine regression of skull length versus maxillary palate length...... 217
4-96 Colobine regression of skull length versus total palate length...... 218
4-97 Colobine regression of skull length versus palatine palate length...... 218
4-98 Colobine regression of skull length versus palate depth...... 219
4-99 Hominoid regression of skull length versus palate depth...... 219
4-100 Hominoid regression of skull length versus palate width...... 220
4-101 Hominoid regression of skull length versus maxillary palate length...... 220
4-102 Hominoid regression of skull length versus external palate breadth...... 221
4-103 Hominoid regression of skull length versus internal palate breadth...... 221
4-104 Hominoid regression of skull length versus total palate length...... 222
4-105 Hominoid regression of skull length versus palatine palate length...... 222
4-106 Papionin regression of bipterygoid breadth versus external palate breadth...... 223
4-107 Papionin regression of bipterygoid breadth versus internal palate breadth...... 224
4-108 Papionin regression of bipterygoid breadth versus palate depth...... 225
4-109 Papionin regression of bipterygoid breadth versus palatine palate length...... 226
13
4-110 Papionin regression of bipterygoid breadth versus palate width...... 227
4-111 Papionin regression of bipterygoid breadth versus maxillary palate length...... 228
4-112 Papionin regression of bipterygoid breadth versus total palate length...... 229
4-113 Colobine regression of bipterygoid breadth versus total palate length...... 230
4-114 Colobine regression of bipterygoid breadth versus palate depth...... 230
4-115 Colobine regression of bipterygoid breadth versus external palate breadth...... 231
4-116 Colobine regression of bipterygoid breadth versus internal palate breadth...... 231
4-117 Colobine regression of bipterygoid breadth versus palatine palate length...... 232
4-118 Colobine regression of bipterygoid breadth versus maxillary palate length...... 232
4-119 Colobine regression of bipterygoid breadth versus total palate length...... 233
4-120 Hominoid regression of bipterygoid breadth versus palate depth...... 233
4-121 Hominoid regression of bipterygoid breadth versus palate width...... 234
4-122 Hominoid regression of bipterygoid breadth versus maxillary palate length...... 234
4-123 Hominoid regression of bipterygoid breadth versus external palate breadth...... 235
4-124 Hominoid regression of bipterygoid breadth versus internal palate breadth...... 235
4-125 Hominoid regression of bipterygoid breadth versus total palate length...... 236
4-126 Hominoid regression of bipterygoid breadth versus palatine palate length...... 236
5-1 Elastic moduli values from the anterior to posterior palate in the transverse section...... 281
5-2 Elastic moduli versus density regression at a regional level of comparison...... 282
5-3 Expectations of stress (σ) prediction based on the change in moment of inertia and bending moment...... 283
5-4 Span and depth of the macaque skull...... 283
5-5 Wood block set-up to simulate the macaque skull...... 284
5-6 Regression of fractal dimension and suture length ratio...... 285
14
Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
MECHANICAL CHARACTERIZATION OF THE HARD PALATE
By
Jennifer Lane Hotzman
May 2010
Chair: David Daegling Major: Anthropology
Masticatory studies have typically focused on the mandible, but the maxillae are also involved in mastication and incision. The morphology and material properties of the hard palate are examined to help characterize the mechanical environment to determine the evolutionary significance of palatal morphology in terms of biomechanics. Both sets of variables have a significant impact on what types of stresses are present and how the loads are distributed throughout the hard palate. This information is important for assessing how palatal bone responds to force. This knowledge can contribute to the overall understanding and possible treatment and/or prevention of certain craniofacial disorders. An additional objective is to determine the functional significance of these skeletal elements when found in the fossil record.
Material properties were collected through indentation experiments and micro-computed tomography scans on a female Macaca fascicularis cranium. The scans allowed grayscale variation to be collected which was used to calculate bone density. For the indentation study, hardness data were collected and converted into elastic moduli, which is a measure of structural stiffness. These data were compared to known data from the mandible. Elastic moduli values illustrated that mandubular bone is overall stiffer than maxillary bone, suggesting that the mandible is subjected to greater stress during mastication and incision.
15
Strain experimentation was performed on the macaque specimen to determine bone
deformation under load cases, such as incisor and molar loading, and twisting of the snout.
Different geometrical models were used to formulate predictions to determine which model
would be most appropriate for the palate. Unfortunately, none of the models used accurately
predicted the strains observed during the experiments. Therefore, due to the structural
complexity of the rostrum, different theoretical approaches were explored.
Finally, a comparative analysis was performed to collect sutural complexity data and palatal and facial measurements from representative species of Old World monkeys and apes.
The measurements collected were used to conduct an allometric analysis to determine scaling effects. No discernible patterns were observed based on species phylogeny. Sutural complexity analysis did support the idea that sutures become more complex when subjected to greater loads.
16
CHAPTER 1 PROBLEM INTRODUCTION
Research Statement
Determining the mechanical significance of morphology in the fossil record is one of the many challenges facing paleoanthropologists. Inferring function from structure is necessary when studying fossil taxa since there are no extant members to directly observe. Care must be taken, however, when making this inference since there is not always a tight link between function and structure (Lauder, 1995). Paleontologists often employ one of two methods to make these inferences. The phylogenetic method relies on comparative studies of extant taxa that are related to the extinct organism, while the paradigm method requires the development of several mechanical models that are used to predict what a structure should look like considering the constraints employed in the model (Lauder, 1995). Both approaches have strengths and weaknesses and variations of each of these approaches are utilized in this dissertation.
The jaw apparatus, i.e. the mandible and/or the maxilla, are frequently recovered elements in the fossil record. The goal of this research is to assess the evolutionary significance of the morphological aspects of the hard palate from the perspective of biomechanics.
Mastication and incision generate the majority of force experienced by the palate and both are strongly influenced by dietary consistency (Saijo and Sugimuro, 1993; Peterson et al., 2006).
Food consistencies can vary dramatically with harder food items requiring more force to breakdown than softer items (Bouvier and Hylander, 1984). Therefore, dietary differences are integral to the assessment of different palatal morphologies in terms of biomechanics. The geometry of the palate varies interspecifically. Consequently, data on palatal dimensions
(length, width, depth, etc.) provide a foundation for assessing the mechanical and allometric consequences of this variation.
17
Determining a generalized model of the stress and strain field of the palate may help researchers to infer the functional significance of different palatal morphologies as well as to compare the stress field of the palate to other craniofacial regions. Assessing the stress field includes determining the types, magnitude, frequency, and distribution of stress throughout the structure. Mechanobiology is a growing area of research that studies the interaction between mechanical signals and biological processes in cells and tissues (Mao, 2002). In order to effectively understand craniofacial anomalies such as cleft lip and palate, an understanding of the relationship between mechanics and craniofacial growth is necessary (Mao and Nah, 2004). If the mechanical environment of the maxilla, particularly the palate, can be characterized, then the influence of the mechanical environment on growth and development of the upper jaw can be better understood.
The emphasis of my research is to explore the biomechanical consequences of palatal morphology in a sample of Old World primates. This study will contribute towards understanding of how biomechanical factors influence metabolic activity in bone tissue. Loads have long been recognized as having a significant influence on bone modeling and remodeling.
In the context of paleoanthropology and the study of fossil primate craniodental morphology, this research will help determine which mechanical variables are important in regulating bone mass.
This is vital if credible functional linkages are to be made between masticatory activities and palatal morphology. My research is intended to aid in the determination of the functional significance of skeletal elements found in the fossil record and to provide an increased understanding of how the strain field in the palate relates to masticatory activities.
Hypotheses
Accomplishing the goals listed above requires the consideration of four major hypotheses. 1) Does the functional environment of the masticatory apparatus determine that the
18
maxillae will be morphologically responsive to force magnitudes in a similar manner as the mandible? Morphologically the mandible and the palate are very different, but they share the same masticatory function. Given this functional similarity, a reasonable assumption is that the loads experienced by the maxillae, specifically the palate, during masticatory activities will be comparable to what the mandible experiences during biting and chewing. Similar loading environments would suggest similar responsiveness of palatal tissues to the mechanical consequences of allometric or dietary variation.
Strain experimentation, micro-computed tomography (µCT), and microindentation on a representative Old World monkey, Macaca fascicularis, were used to address this hypothesis.
Strain gage experimentation provides strain data for specific locations on the palate which can be compared to the bone density in that location as determined by µCT. The elastic moduli data
(via hardness values) gathered through microindentation can be related to the strain and density data, thus providing the means to compare maxillary and mandibular data.
2) Do sutures influence the biomechanical environment of the palate? If sutures function to reduce stresses transmitted throughout the facial skeleton, then the bone at the sutural margins should show more deflection, up to an order of magnitude greater, than the surrounding bone
(Herring, 2000). One major structural difference between the anthropoid mandible and the palate is the presence of sutures in the palate. Sutures have several functions, including acting as a site for bone growth and the ability to act as shock absorbers (Jaslow, 1990; Herring and Teng,
2000).
Sutural morphology is also thought to reflect the loading conditions under which the suture is subjected. The complexity of sutural interdigitations increase as the magnitude of the load increases which may be a reflection of the greater amounts of deflection the suture
19
experiences (Herring, 2000). Sutures are thought to become more interdigitated in areas of high
stress in order to prevent the bones from becoming disarticulated (Herring, 1993). A
comparative study of Old World monkeys and apes was conducted to address this issue of
sutural complexity. Data generated through the strain experiments provided insight into how much deformation palatal sutures undergo during loading.
3) Is the geometry of the palate correlated with the types and magnitudes of loads that the palate experiences? a) Specialized primate diets such as folivory and seed predation will be reflected by localized increases in bone mass to bring stress and strain to levels comparable to those primates with more generalized diets. b) Allometric changes seen in palatal length and breadth may significantly affect the degree of palatal curvature, i.e. palatal depth, and therefore
the distribution and amount of stress in the palate. c) Upper jaw proportions and jaw muscle
efficiency is simply a function of somatic size rather than specifically related to diet.
The distribution of bone throughout the palate is expected to vary depending upon the
overall size and shape of the palate. For example, longer palates will have thicker bone than shorter palates because longer palates will be subjected to greater bending moments. The differences in palatal geometry among various species, however, may simply be related to their
overall body size and have no predictable relationship with their different dietary habits. The
comparative study tested whether or not this hypothesis concerning the relationship between
palatal geometry and diet is supported or rejected.
4) Idealized geometric models are used to approximate the behavior of complicated
structures such as the palate, but the type of model most appropriate for analyzing the palate is
unknown. Based on palatal geometry, should the palate be modeled as a shell, beam or plate?
The importance of this question is due to the fact that computations differ depending upon how
20
the palate is modeled. Plates, shells, and beams assume different morphologies, therefore, they will deform differently under the “same” force. Plates are thin pieces of flat material, while shells are thin pieces of material that are not planar (i.e. exhibiting varying degrees of curvature in three dimensions). Beams are structural members that have a tendency to bend when subjected to loads. Modeling the palate will be more accurate once the behavior of this structure is determined.
The results from these approaches employed in this project accomplish several goals.
First, the mechanical behavior of the rostrum, specifically the hard palate, is modeled to determine how the palate responds during different loading scenarios, e.g. incisor biting, molar biting, and twisting. Second, the effects of diet on the morphology of the structure as a whole as well as the mid-palatal suture are explored. The main question raised is whether or not palatal morphology can be understood through the mechanobiological perspective.
21
CHAPTER 2 BACKGROUND INFORMATION
Mechanics in Bone Growth
Craniofacial growth and development is influenced by many factors, including mechanical environment (Herring, 1993). The maxillae, in particular the bones of the hard palate, are likely exposed to different types of loads throughout the earliest stages of growth, e.g. human infants first suckle then masticate their food. These diverse activities likely result in a variety of load types and magnitudes of stress, which elicit a morphogenetic response from the bone (Herring,
1993; Martin et al., 1998). When mastication begins, the consistency of the diet has been shown experimentally to affect craniofacial growth and development (Beecher et al., 1983; Kiliaridis et al., 1985; Yamamoto, 1996; Ciochon et al., 1997).
Wolff’s Law
The idea that bone adapts to its mechanical environment has existed for centuries. Julius
Wolff is often credited with formulating this idea in the late 1800s, but the idea has been traced as far back as Galileo in the 1600s (Martin et al., 1998). Wolff’s law states that the architecture of living bone continuously adapts to changes in the mechanical environment to which bone is subjected. Although Wolff’s law is generally accepted as true, the biological aspects of the law that he formulated have proven to be false (Dibbets, 1992). Three main biases exist in his arguments: his theory on interstitial bone growth, the role of heredity in bone growth, and his concept of function (Dibbets, 1992).
Wolff was convinced that bone growth underwent the same mechanisms as soft tissue growth, which is bone growth consisted solely of cell division and the accumulation of intracellular material. He discounted the process of remodeling because he did not believe that bone actually resorbed. Dibbets (1992) points out that the reason Wolff held so firmly to this
22
concept of interstitial bone growth was because, in Wolff’s view, the trabecular architecture preexisted in the compacta (cortical bone) and was not formed as the result of a dynamic process.
This idea that trabecular bone architecture was inherited was based on Wolff’s observation of distinct trabecular patterns observed in the fetus, which could not have been exposed to significant load in utero (Dibbets, 1992). However, the fetus is exposed to mechanical forces in utero. Forces are intermittently imposed on the fetus by skeletal tissue stresses that are caused by muscular contractions from the increasingly active developing muscular system
(Carter and Beaupre, 2001).
Wolff’s concept of function is the third bias because the definition he provided differs greatly from how function is usually defined today. If researchers were asked to define function today, they would probably define it as changing structure, i.e. a dynamic process requiring action (Wainwright, 1988). Wolff defined function as a static requirement to meet a specific need (Dibbets, 1992). Unfortunately, the term function is often not explicitly defined by researchers, which causes ambiguity as to exactly which definition of function is being applied.
If Wolff defined function completely differently than it is defined by most today, where did the modern day definition develop? The answer is from one of Wolff’s contemporaries,
Wilhelm Roux. Roux saw function as a dynamic interaction as opposed to a static constraint and recognized that information for the developing bone was partially provided by loading and unloading (Dibbets, 1992). He referred to the physicochemical processes that aid development as “Entwicklungsmechanik” or “developmental mechanics” (Carter et al., 1998).
The forces that affect skeletogenesis can be studied at different scales of analysis, including the molecular, cellular, tissue, and organ levels (Carter and Beaupre, 2001). In the time period in which Wolff and Roux worked, the analyses generally took place on the tissue
23
level due to lack of technology. As technological advances were made, more studies were
conducted at the molecular and cellular levels (Carter et al., 1998). Molecular level studies have
begun to study the role of integrins, which are cell surface receptors involved in cell adhesion to
other cells and the extracellular matrix, and the cytoskeleton. Cellular studies have shown that
hydrostatic pressure and shear loading of cells have a direct influence on gene expression and
cell biosynthesis (Carter et al., 1998). The tissue level, however, is still the scale at which most
analyses occur. One reason for this is because the technology needed to conduct tissue level
analyses is generally more accessible than the technology needed for cellular and molecular
studies. Analyses can also be conducted at the organ level, but they provide little insight into the
underlying mechanisms of how bone responds to different mechanical conditions (Carter and
Beaupre, 2001). Only when the organs are broken down into smaller units, e.g. tissues, can we
begin to evaluate and understand the physical conditions of connective tissue cells (Carter and
Beaupre, 2001).
Concepts of Stress and Strain
Two important concepts for studying mechanical forces at the tissue level are stress and strain. When discussing stress and strain in biological materials, in this case bone, the terms are defined as if the tissue under study was a homogenous material (Carter et al., 1998). In this
“continuum model” representation, the fact that bone consists of molecules, discrete atoms, and crystals interacting with one another is ignored (Carter and Beaupre, 2001). This means that the material properties represent average properties over some volume that is large in comparison to the microstructural features of the tissue (Carter and Beaupre, 2001).
Stress is a measure of normalized intensity of a force and is the load per unit area, while strain is a measure of normalized load deformation. Strain, in simple terms, is defined as the
24
fractional change in dimension of a loaded body (Martin et al., 1998). Both stress and strain are tensor quantities, so they have a magnitude and direction. The stress state can also be represented with scalar quantities referred to as invariants. Scalar quantities have a magnitude, but no direction. The two most common stress invariants are referred to as hydrostatic stress and octahedral shear stress. Hydrostatic stress can either be positive (hydrostatic tension) or negative
(hydrostatic compression or pressure) and is calculated as the average value of the three principal stresses. Octahedral stress can only be a positive number and will only change the shape and not the volume of the material in question (Carter and Beaupre, 2001). These two stress invariants affect cartilage growth and ossification differently. Octahedral shear stress causes an acceleration of cartilage growth and ossification, while hydrostatic compressive stress slows it down (Carter and Beaupre, 2001).
Primary and Secondary Cartilages
Primary and secondary cartilages are both important to skull growth. These two cartilages are distinguished based on the timing of their formation. Primary cartilage precedes the development of the replacement bones that form the primary skeleton. Secondary cartilage is different because it does not form on dermal bones until after intramembranous ossification has begun (Hall, 1984). Unlike most of the bones in the human skeleton, dermal bones are not preformed in cartilage, but arise directly from connective tissue membranes. When studying the influence of mechanics on craniofacial growth, the secondary cartilage is important because it does not develop in the absence of mechanical stimulation (Herring, 1993). Secondary cartilage only differentiates from progenitor cells in response to mechanical stimulation (Hall, 1984). This cartilage is found in association with many cranial bones, sutures, and the upper and lower alveolar processes in mammals. These locations are sites of either articulations or muscle
25
attachments, which provides support for the idea that mechanical stimulation is necessary for the differentiation of secondary cartilage (Herring, 1993).
The mandibular condyle is the only major growth site of secondary cartilage anywhere in the mammalian skeleton (Herring, 1993); therefore most of the studies on jaws have been on the condyle (Simon, 1977; Copray, 1985; Throckmorton and Dechow, 1994). However, the condyle is not the only secondary cartilage that is sensitive to mechanical changes in the environment. Hinton (1988) studied the response of cartilage present in the mid-palatal suture to changes in masticatory function. He divided rats into separate groups based on dietary consistency and/or incisor amputation, then performed biochemical and histological analyses.
Dietary consistency and/or incisor amputation did alter the morphology and the metabolism of the mid-palatal suture to varying degrees. The group of rats that were fed a soft diet and had their incisors amputated were affected the most, with their sutures becoming largely fibrous.
Bone Modeling and Remodeling
Consensus exists that mechanical environment affects bone growth, but the details as to how this happens is debated. Several factors determine the overall mechanical environment, such as frequency of loading and types of loads applied. Bone growth and modeling are not the only processes that loading conditions may affect. Bone remodeling is also heavily influenced by mechanical conditions. Bone modeling and remodeling both refer to the actions of osteoblasts and osteoclasts in reshaping and replacing portions of the skeleton (Martin et al.,
1998). However, these are two distinct processes.
Martin et al. (1998) provide a list of differences that exist between the processes of modeling and remodeling. Although both modeling and remodeling involve osteoblasts and osteoclasts, in modeling these two cell types work independently while in remodeling their
26
actions are coupled, i.e. sequential. Modeling affects the size and/or shape of the bone, while remodeling typically does not affect either size or shape. Modeling and remodeling are both most active before skeletal maturity is reached, however, their rates differ after skeletal maturity.
Unlike modeling, remodeling occurs throughout life. Finally when modeling occurs at a particular site the process is continuous and prolonged while remodeling is episodic and has a definite beginning and ending.
Although both modeling and remodeling are affected by mechanical conditions, most of the experimental studies have only focused on the process of remodeling (Lanyon et al., 1982;
O’Connor et al., 1982; Carter, 1984; Lanyon, 1984; Lanyon and Rubin, 1984; Meade et al.,
1984; Burr et al., 1985; Rubin and Lanyon, 1985). The reason for this is that mature experimental animals are used to try to eliminate as many unknown variables as possible.
Controlling the many variables influencing bone growth, such as hormones, genes, mechanics, etc., is difficult, if not impossible.
Three important variables that are known to influence remodeling include strain
magnitude, strain rate, and strain distribution (Lanyon, 1984). Lanyon et al. (1982) conducted an
experiment using mature sheep that involved excising a portion of a sheep’s ulna and then
measured peak principal strains during walking. They found that the bone adapted to produce
strains that were lower than before the osteotomy, which is not consistent with the view that
bone reacts to control strain magnitude. Instead, they concluded that adaptive remodeling of periosteal bone is influenced by alterations in strain distribution rather than peak strains alone.
Rubin and Lanyon (1985) conducted a similar study using turkeys and came to a comparable conclusion that bone remodeling is sensitive to both strain distribution as well as strain magnitude.
27
Strain rate is also an influential variable in bone remodeling. In order to evaluate how strain rate affects remodeling, O’Connor et al. (1982) chronically inserted implants into the radius and ulna of mature sheep. These implants were subjected to both bending and compressive loads while varying the peak strains and strain rates. Their conclusion was that in order for remodeling to occur, sufficiently high strains and appropriate strain rates must be present. This leads to the question of whether or not the frequency of the loads, i.e. static and dynamic loads, affect bone remodeling.
Lanyon and Rubin (1984) conducted experiments on avian ulnae in order to address the question of whether or not both static and dynamic loads affect bone remodeling. Remodeling activity was assessed under three different conditions: disuse alone, disuse with a superimposed continuous compressive load, and disuse interrupted by a short daily period of intermittent loading. From this experiment, Lanyon and Rubin (1984) concluded that remodeling occurs under both dynamic and static loads when the bone is exposed to strains within the functional strain range, but the remodeling is more effective under dynamic loading conditions. Meade et al. (1984) conducted a similar experiment by exposing the femora of adult dogs to continuously applied loads and noted that there was an outward movement of the periosteal surface, but little or no effect was seen on the endosteal surface of the bone.
In addition to the changes in strain distribution, strain magnitude, and strain rate, bone also initiates remodeling as a response to fatigue microdamage (Burr et al., 1985). Burr et al.
(1985) tested the validity of the theory that osteonal remodeling is triggered by microdamage by conducting several different experiments on adult dogs. The data that were collected support the idea that fatigue microdamage is a significant factor in the initiation of remodeling.
28
According to Herring (1993), characterization of the in vivo loading regime of skeletal elements is needed to determine the functional influences of bone growth. Although computer models and strain gage technology have been helpful in trying to determine stress distributions, both have limitations. The major limitation of the computer models is that all local effects must be ignored or modeled precisely, which is currently impractical. Strain gage technology helps to overcome this problem, but it is limited to a specific area of the structure being studied. Even though there are technological difficulties when trying to determine the loading regime of skeletal elements, successful strain gage experiments have been conducted that have yielded useful information.
Lanyon (1973, 1974) performed experiments on the calcaneus of sheep using rosette strain gages and demonstrated that the trabecular orientation corresponded with the principal compressive and tensile strain directions. This experiment was able to confirm Wolff's idea about principal stress directions coinciding with trabecular orientation (Martin et al., 1998).
Once this was confirmed, attention turned to the question of what type of load is responsible for apposition and resorption. Herring (1993) argues that resorption occurs in the direction of compression, while periosteal bone growth corresponds generally to areas under tension. Of course, as mentioned earlier, it is not only the type of force applied, but also the frequency and magnitude that determine whether or not bone is deposited or resorbed.
Effect of Dietary Consistency on Bone Growth
Several studies conducted over the years support the idea that dietary consistency affects craniofacial bone growth and development. Many of these studies were initiated in an attempt to determine why Western societies had such high rates of malocclusion compared to non-industrial societies (Beecher et al., 1983; Ciochon et al., 1997). The theory that forceful chewing was
29
necessary for proper growth became one avenue of exploration. Beecher et al. (1983) examined
this hypothesis by raising two groups of squirrel monkeys, one given a naturally tough diet while
the other was given a diet of artificially softened foods. Significant differences were noted
between the two groups and the authors concluded that there is a minimum threshold of stress
needed for proper craniofacial development to occur.
The animals given the soft diet in the study of Beecher et al. (1983) exhibited maxillary
arch narrowing and increased palatal height. These two characteristics occurring simultaneously suggests that maxillary arch collapse (maxillary arch narrowing), the most common occlusal problem in American youths in 1983, probably occurs because of differences in the growth of the mid-palatal suture and the fact that teeth situated in the maxillary alveolar process are not correctly aligned with the mandibular teeth. Other cranial sutures were also affected by dietary consistency. Distinct differences in calcification were seen in the lambdoid and sagittal sutures through the use of radiographs. The soft diet group of monkeys exhibited a much broader radiolucent area at the sutures than was observed in the hard diet group, which means that the sutures in the soft diet area are more patent and less calcified (Beecher et al., 1983).
Squirrel monkeys are not the only experimental animals that have supported the idea that craniofacial growth and development is affected by the consistency of diet. Experiments have also been conducted using rats (Beecher and Corruccini, 1981; Bouvier and Hylander, 1984;
Kiliaridis et al., 1985; Yamamoto, 1996) and minipigs (Ciochon et al., 1997). Differences were found in the mandibles of Yucatan minipigs raised on diets of varying consistencies (Ciochon et al., 1997). In addition to examining the bones, Ciochon et al. (1997) also examined the weight of the muscles involved in mastication. They found that the weights for the superficial masseter, deep masseter, and temporalis muscles were all significantly higher in the hard diet group. The
30
frontal profiles of the cranium also differed between the two groups; the hard diet group displayed a steep profile while the soft diet group displayed an overall more horizontally oriented profile. Morphological differences in the shape of the mandible between the two groups were also noted. Unfortunately, the maxilla was not the main focus of this study so little information concerning the hard palate was presented. However, Ciochon et al. (1997) did note that the palate was relatively longer in the soft diet group. They also took measurements of the maxillary arch breadth and unlike the results reported by Beecher et al. (1983) in the squirrel monkeys, there was no difference found between the groups of the Yucatan minipigs.
Rats have served as another common experimental animal for pursuing the effects of dietary consistency on craniofacial growth and development. Beecher and Corruccini (1981) conducted a study using rats that consisted of two groups, a soft diet group and a hard diet group.
They reported that the rats fed a soft diet had a significantly narrower maxillary arch breadth compared to the hard diet group. The animals in the soft diet group weighed approximately 13% less than the animals in the hard diet group at the end of the experiment, however, the weight difference was not considered an important factor. Bouvier and Hylander (1984) disagree with
Beecher and Corruccini (1981) about the weight differences not being important. Bouvier and
Hylander (1984) conducted a similar experiment and found that maxillary arch length was significantly different between the animals raised on different diets, but once corrections were made for weight difference, the maxillary arch differences were not significant.
Kiliaridis et al. (1985) used cephalometric longitudinal analysis for growing rats using a normal diet group and a group fed a soft diet. Differences were noted in the growth patterns of both the neurocranium and the viscerocranium between the two groups. The viscerocranium of the soft diet group showed a more orthocranial position, which refers to the skull being of
31
medium height relative to length, with the most noticeable changes occurring in the nasal area.
Changes were also noted in the incisors of the upper jaw as well as the mandible. The incisors of
the upper jaw showed a greater proclination in relation to occlusal and palatal planes in the soft
diet group, while the gonial angle of the mandible showed a decreased appositional rate.
As seen in a comparison of the studies by Beecher and Corruccini (1981) and Bouvier
and Hylander (1984), no consensus exists on the effect of dietary consistency on the growth of
the palate. Yamamoto (1996) examined how food consistency effects the growth of the palatal
region of the maxillary complex through the use of bone histomorphometry to try to resolve
this issue. Specifically, the goal was to investigate how the consistency of the diet affected the
pattern of bone apposition at the growth site of the palatal region. As with the previous studies,
the rats were divided into two groups; one was fed a hard (solid) diet while the other was fed a
soft (liquid) diet. There were significant differences found between the two groups.
Yamamoto’s (1996) results agreed with those of Kiliaridis et al. (1985) in that the vertical
growth of the palate differed between the two groups and there was a more anteriorly directed
growth rotation of the palate in the soft diet group. Other studies that examine the underlying
mechanism for this difference have noted a marked decrease in the bone appositional rate in the
areas of muscle insertion in the anterior part of the viscerocranium (Engstrom et al., 1986),
however, the area under consideration in Yamamoto’s (1996) study was not an area of muscle
insertion. This implies that the changes in the palatal region of the maxilla cannot be caused
directly by activities such as muscle action; however, muscle action can have large effects due to mechanical activities such as bending and twisting so there may be an indirect effect.
As mentioned previously with the study of Ciochon et al. (1997), the growth of the mandible has also been explored in relation to dietary consistency. One line of reasoning is if an
32
animal has a diet that consists of hard items, then their mandible would be more massive in terms
of bone than a similar sized animal with a softer diet (Bouvier, 1986; Jablonski et al., 1998).
Similar to the previous studies whose results differed concerning the effect of dietary hardness on maxillary arch breadth, differences also exist on this issue concerning the mandible. Several studies that support the link between dietary consistency and mandibular morphology are Cole
(1992), Daegling (1992), and Hylander (1979a,b). A more recent study that does not support the line of reasoning expressed above was conducted by Daegling and McGraw (2001). They
examined the mandibles from two different species of colobus monkeys that are similar in size
and sympatric, but one of the species (Colobus polykomos) has a diet containing hard food items.
The expectation was that C. polykomos would have a more robust mandible than the other
species (Procolobus badius), but this was not the case. In fact, mandibular morphology did not
reflect the differences in diet in these two species.
The studies mentioned so far have been concerned with mastication, but this is not the
only process that mammals use for oral food intake. Infant mammals engage in a unique form of
feeding referred to as suckling. Although the mechanism of suckling has been explored (German et al., 1992) as well as the transition from suckling to drinking at weaning (Thexton et al., 1998), there have been no studies conducted on the types of loads this mechanism produces and whether or not these loads also affect craniofacial growth and development.
Palatal Growth
Embryological Growth and Development in Humans
Facial development begins around the third week of gestation with the development of five facial swellings, or primordia, in the frontonasal and visceral arch regions. These five primordia
consist of the frontonasal prominence, which forms the forehead and nose, two maxillary
prominences that form the lateral stomodeum, or primitive mouth, and two mandibular
33
prominences, which form the caudal stomodeum (Bender, 2000; Scheuer and Black, 2000).
Within each of these prominences, neural crest cells differentiate into fibrous connective tissue, all the dental tissues except enamel, and skeletal and connective tissue of the face, cartilage, and bone. By the end of the fourth week, the lower aspect of the frontonasal prominences develop bilateral oval thickenings of the surface ectoderm known as nasal placodes, which will produce
the medial and lateral nasal prominences (Kirschner and LaRossa, 2000; Moore and Persaud,
2003). The intermaxillary segment of the maxilla forms when the medial nasal prominences
merge. This segment gives rise to the philtrum of the upper lip, the premaxillary part of the
maxilla, and the primary palate (Moore and Persaud, 2003). The maxillary prominences enlarge
during the fifth week and connect with the lateral nasal prominences to establish continuity
between the nose and the cheek while the maxillary prominences fuse with the medial nasal
prominences to complete the lip.
Palatogenesis begins at the end of the fifth week and continues until the twelfth week. The
median palatine process develops from the intermaxillary segment during the sixth week (Moore
and Persaud, 2003). This process forms the primary palate, which gives rise to the premaxillary
part of the maxilla. In the adult hard palate, the premaxilla represents only a small portion of the
hard palate anterior to the incisive foramen forming the part of the maxillary alveolus that bears
the incisors.
During the sixth week, the secondary palate develops from the paired lateral palatine processes also known as the palatal shelves. The lateral palatine processes are two mesenchymal projections that extend from the internal aspects of the maxillary prominences (Moore and
Persaud, 2003). Initially both palatal shelves are oriented vertically on either side of the developing tongue. As the tongue descends, the palatal shelves gradually move to a horizontal
34
position where they will meet and fuse at the midline. An intrinsic shelf elevating force is
believed to be responsible for the movement of the palatal shelves. This force is generated by the
hydration of hyaluronic acid in the mesenchymal cells within the palatal processes (Moore and
Persaud, 2003). Hyaluronic acid acts as a water barrier and provides “tissue turgor” that moves
the palatal shelves (Brinkley and Morris-Wiman, 1984). The movement of the palatal shelves
begins in the seventh week, but fusion is not completed until the twelfth week. Fusion of the
palatal shelves results in the formation of the uvula, soft palate, and hard palate posterior to the
incisive foramen (Kirschner and LaRossa, 2000).
For nonhuman primates such as baboons and macaques, palatogenesis occurs
approximately at the same stage as humans (Hendrickx and Peterson, 1997). The underlying
mechanisms for palatal closure are also thought to be the same between these primate species
and humans (Bollert and Hendrickx, 1971; King and Schneiderman, 1993). Since the timing and the underlying mechanisms of palatal closure are similar in baboons, macaques, and humans, then catarrhine primates may be appropriate animals to use in order to explore orofacial teratogenesis in humans (Bollert and Hendrickx, 1971).
Postnatal Growth and Development
Growth refers to a structure, in this case bone, changing in magnitude (Enlow and Hans,
1996). Contrary to prior belief, there are no centralized and self-contained growth centers; instead all portions of the bone surfaces play a role in the growth of the structure (Enlow and
Hans, 1996). As opposed to growth centers, the functional matrix is the determinant of the skeletal growth processes. The functional matrix is all the tissues and spaces that work together to fulfill a particular function (Moss, 1969). This concept provides an explanation of what
35
happens during craniofacial growth, but not how the cellular and molecular mechanisms
underlying growth work.
Remodeling and displacement are two basic kinds of growth movements involved in
facial growth. Remodeling serves five main functions that are outlined by Enlow and Hans
(1996): 1) progressively changes the size of the whole bone, 2) sequentially relocates the
component regions of the whole bone to allow for overall enlargement, 3) shapes the bone for its
functions, 4) fine-tunes the outline of separate bones to each other and their surrounding soft tissues, and 5) carries out structural adaptations to the intrinsic and extrinsic changes in conditions. This remodeling is not synonymous with the type of remodeling discussed earlier.
Unlike Martin et al. (1998), Enlow and Hans (1996) do not make a distinction between the processes of modeling and remodeling. Instead, Enlow and Hans (1996) make a distinction between remodeling (as defined above) and displacement. Displacement is the process of the physical movement of the whole bone and occurs when remodeling is simultaneously resorbing and depositing bone.
Palatal remodeling occurs through a process known as the “V” principle. This concept is based on the fact that many cranial and facial bones, including the palate, have a V-shaped configuration (Enlow and Hans, 1996). Bone deposition takes place on the inner side of the V while resorption takes place on the outer side of the V (Figure 2-1, adapted from Enlow and
Hans, 1996). In the case of the maxillae, the superior side of the anterior part of the maxillary arch is resorbed while bone is deposited on the inferior side of the arch. This process increases the width of the arch causing the palate to become wider (Enlow and Hans, 1996). Growth along the mid-palatal suture also adds to the progressive widening of the palate and maxillary
36
(alveolar) arch (Friede, 1998). Widening of the palate continues into adulthood (Scheuer and
Black, 2000).
Lengthening of the hard palate occurs partly in the transverse suture and partly by the apposition of bone to the posterior margin (Melsen, 1975). The growth in the transverse suture continues until puberty, but the appositional activity continues until approximately 18 years of age. Disagreement exists concerning the appositional activity on the posterior margin of the palate. According to Sejrsen et al. (1996), little growth occurs at the posterior border of the hard palate, a conclusion reached by studying archaeological samples that show a constant distance between the greater palatine foramen and the posterior margin of the palatine bone at various dental stages. Sejrsen et al. (1996) attribute lengthening of the hard palate almost solely to growth in the transverse suture. Although the amount of apposition that occurs on the posterior margin is controversial, consensus exists that little to no apposition occurs on the anterior margin.
The palatal growth rates of several nonhuman primates, specifically Macaca nemestrina and Papio cynocephalus, were investigated to determine differences between the two genera
(Swindler and Sirianni, 1973). Although the absolute size of these primates is different, the growth of the palate occurred at similar rates with both gradually decelerating with age. The deceleration of the growth rate is also characteristic of humans. Another significant finding from this study is that no sexual dimorphism exists in the rate of growth of the palate within either species (Swindler and Sirianni, 1973); therefore time, not rate, is responsible for the differences observed.
As previously noted, both the mid-palatal and transverse palatine sutures play a role in the growth of the palate. In the embryonic stage, the incisive suture separates the premaxilla
37
and the maxilla, but this suture fuses before birth; a slight visible suture line may appear on the lingual surface of the palate and persist into adulthood (Mann et al., 1987). The mid-palatal and transverse palatine sutures fuse erratically, but they usually remain open well into adulthood.
The morphology of these two sutures changes throughout different stages of growth. The transverse suture begins broad and slightly sinuous at birth and later develops into a typical squamous suture (Melsen, 1975). The mid-palatal suture progresses through three stages; in the first stage the suture is short, broad, and Y-shaped, with the vomer bone in the groove of the Y between the two maxilla halves; in the second stage the suture is more sinuous; and in the third stage the suture is heavily interdigitated (Melsen, 1975). The change in sutural morphology may be attributed to changes in the mechanical environment.
Sutures
Functions of Sutures
Sutures are any articulation between dermal bones of the skull (Herring, 2000). These articulations are usually fibrous but sometimes contain cartilage or fibrocartilage.
Evolutionarily, the earliest sutures developed in the armored jawless fish and consisted simply of the skin that remained between the dermal plates. The properties that are typically associated with sutures, mobility, growth, and the potential for synostosis (closure), were already present in these armored jawless fish (Herring, 2000). Mammals show no evolutionary progression of sutures; in fact, they have lost some of the sutural diversity in terms of structure.
All taxonomic groups that have sutures show a complete range of sutural morphology, from loose connective tissue to elaborate interdigitations joined by a well-defined ligament (Herring,
2000).
Three main biological functions are associated with sutures: to unite bones while still allowing slight movement, to act as growth areas, and to absorb mechanical stress (Persson,
38
1995; Cohen, 2000). Two types of movements typically take place at the sutures. At birth is
when the first type of movement occurs, which entails the displacement of the calvaria bones as
the human head is compressed through the birth canal (Persson, 1995). This causes a molding of
the head that resolves during the first week of life through cranial re-expansion and widening of
the sutural areas (Cohen, 2000). The other type of movement at the sutures is caused by the
displacement of bones relative to one another as the skull grows (Persson, 1995).
The amount of growth that occurs at the sutures is debated, but sutures do play a role in
craniofacial growth. Sarnat (2003) conducted experiments on macaques that involved surgically
producing clefts of the palate on one side only. The severity in the clefts varied from a narrow
slit to almost the entire half of the palate excised. No significant differences were noted in the
growth and development of the hard palate or maxillary arch between the operated and
unoperated sides or between the experimental (operated) and control (not operated) macaques.
Sarnat (2003) postulated two possible conclusions; either the transverse palatine and mid-palatal
sutures do not make a primary contribution to growth or other areas of growth compensated for
the altered condition. From this particular experiment there is no way to decide which
conclusion is correct, but other researchers have postulated that the palatal sutures only
secondarily contribute to growth (Melsen, 1975). Not only does the same suture grow differentially at various times, but the rate and the amount of growth varies for different sutures
at different times (Persson, 1970; Sarnat, 2003). The problem with intervention studies is that
they create a situation not found in nature, so the results cannot be applied to animals under
normal physiological conditions.
Persson (1970) conducted a study on the postnatal growth of facial sutures in the rat that
revealed different growth patterns in individual sutures as well as in the bony margins of the
39
same suture. Four different growth patterns were observed. The first pattern was appositional growth against both sutural margins, which was observed in the premaxillary part of the mid- palatal suture. Another type of pattern observed was appositional growth against only one sutural margin while the other remained inactive. This pattern was found in the main part of the naso-premaxillary suture. The palatomaxillary suture showed appositional growth against one sutural margin, while the other margin showed resorption. This finding contradicts that of Sarnat
(2003), who stated that sutural growth is only through apposition with no resorption involved.
The final growth pattern observed by Persson (1970) is perichondral growth in the maxillary part of the mid-palatal suture. This suture is an example of cartilage being present in the articulation as opposed to just collagenous fibers (Herring, 2000).
Mechanical environment also affects sutural growth and development. Mao (2002) concluded that sutural growth is accelerated when exposed to tension and compression. Another potential stimulus for sutural growth is the oscillatory component of cyclic force. Kopher and
Mao (2003) demonstrated that small doses of oscillatory mechanical stimuli can affect sutural growth by either accelerating osteogenesis of the suture or initiating net sutural bone resorption.
This information can potentially affect therapeutic goals in craniofacial disorders.
The third biological function of sutures is that they act either as a shock absorber for mechanical stress or serve to transmit force across the sutures (Herring, 1972; Persson, 1995).
Although Herring and Persson did not define what they meant by “shock-absorber,” Jaslow
(1990) clarifies that the sutures absorb more energy than cranial bone alone. The majority of mechanical stress in the suture areas is associated with mastication (Persson, 1995). Sutural morphology has been postulated to reflect the loading environment under which the suture is
40
subjected (Herring, 1972; Wagemans et al., 1988; Herring and Teng, 2000). Whether or not this is true will be explored in the following sections.
Sutural Biology and Morphology
Pritchard et al. (1956) outlined the development of cranial and facial sutures based on six different species: humans, sheep, pigs, cats, rabbits and rats. At all stages of development, sutures exhibit five intervening layers as well as two uniting layers between the adjoining bones.
The five intervening layers consist of a pair of cambial layers, a pair of periosteal fibrous capsular layers, and a middle looser layer of cellular mesenchymal tissue. The cambial layers are the sites of active osteogenesis producing woven bone, but the capsular layers must also expand in order to keep pace with the growing bone. The two uniting layers occur when the fibrous capsules are joined by means of two fibrous laminae, an external and an internal. The extremities of the fibrous capsules retain their separate identities due to the intervening layer of loose mesenchymal tissue.
The facial and cranial sutures have the same structure, but they arise somewhat differently. Before the sutures are formed in the face, the cambial and capsular layers are already present with the middle and uniting layers being derived from the mesenchyme between the approaching bone territories. The bones in the cranial vault approach each other within an already differentiated fibrous membrane referred to as the ectomeninx. The capsular layers do not form in the cranium until the cambial layers have almost met and the middle and uniting layers are derived from the delamination of the ectomeninx between the bones (Pritchard et al.,
1956).
The histological structure of sutures, however, is not agreed upon. Pirelli et al. (1999) conducted a study using biopsy samples of the mid-palatal suture obtained from patients ranging
41
in age from 10 years old to 30 years old. They reported that the capsular and cambial layers reported by Pritchard et al. (1956) were not detected in any of their samples nor were the cells typically associated with these layers, osteoblasts and osteoclasts. The absence of osteoblasts and osteoclasts suggest that the bone was in a resting period at the time of the sample. Unlike the woven bone detected by Pritchard et al. (1956), Pirelli et al. (1999) stated that all the sutures were formed by lamellar and bundle bone. Bundle bone is the term used to describe bone in the suture that closely resembles the alveolar bone lining the periodontal ligament with a high
turnover rate (Pirelli et al., 1999). Although the functional significance of the lamellar bone in the sutures is unclear, Pirelli et al. (1999) stated that the lamellar bone may progressively replace the bundle bone when the suture is no longer active in growth and remodeling. If this is the case, the lamellar bone may represent the structural basis of the physiological process of synostosis
(Pirelli et al., 1999). The discrepancies in the sutural structures between Pritchard et al. (1956) and Pirelli et al. (1999) may be attributed to the differences in the ages of the samples examined.
The functional significance of the presence of cartilage in some of the postnatal sutures is
heavily debated. The cartilage is only present for a limited time and usually only appears in the
midline sutures, i.e. the sagittal and mid-palatal sutures. The function of this cartilage seems to
be linked to changes in the mechanical environment (Wagemans et al., 1988). Sutures are
normally under tension, but during growth the sutures may be exposed to particularly strong
pressure and shearing stresses (Pritchard et al., 1956). The secondary cartilage that is present in
these sutures is mainly found in rapidly growing areas (Perssons, 1995). Pritchard et al. (1956)
recommend that the effect of masticatory forces should be considered in relation to the
development of sutures.
42
The morphology of sutures not only varies between different sutures, but the morphology of a single suture can vary throughout the life of the individual. Melsen (1975) identified three morphological stages in the development of the mid-palatal suture: Y-shaped, slightly sinuous at birth, and interdigitated at puberty. Del Santo et al. (1998) conducted a study of the morphological aspects of the mid-palatal suture in the human fetus that partially confirmed the changes in morphology described by Melsen (1975). The first group of fetuses (16-23 weeks) in this study showed a mid-palatal suture that was rectilinear in nature with a wide zone of intense cellular proliferation. The second (24-31 weeks) and third groups (32-39 weeks) displayed a sinuous form with a narrower cellular proliferation zone.
The complex morphology of sutures is thought to reflect their functional environment
(Rafferty and Herring, 1999). Oudhof (1982) found that although sutural tissue has hereditary characteristics that determine the specific differentiation, certain environmental influences are necessary for the manifestation and development of qualities associated with sutures. For example, in the transplantation experiments conducted by Oudhof (1982), when a portion of a suture was relocated to an area of little or unspecified growth, the suture gradually lost its specific structure. On the other hand, when a suture was transplanted to an area of active growth, the suture adapts to its surroundings. This was witnessed when a portion of the sagittal suture of a rat was transplanted into a coronal suture. The sagittal suture adapted by developing a more intensive formation of fibers as well as more lingulae, which were longer (Oudhof, 1982). The influence of the mechanical environment on sutures is discussed next.
Sutures and Loads
Suture morphology is geometrically complex and several researchers have postulated that the mechanical environment is one factor that influences their morphology (Linge, 1970;
43
Herring, 1972; Oudhof, 1982; Wagemans et al., 1988; Herring and Teng, 2000; Mao, 2002).
Herring (1972) examined sutural morphology in suoids to explore the use of cranial sutures as
indicators for the amount and direction of stress in the skull. She assessed sutural morphology
in two ways: first she examined disarticulated sutural surfaces for six specimens, and second
she examined dried articulated suoid skulls and subjectively categorized them as straight,
slightly interdigitated, interdigitated, and very interdigitated. Another way to classify sutures is
as either beveled or butt-ended.
One tentative conclusion that Herring (1972) drew from her research was that the
beveling of sutures may allow adjustive movements or stress reductions during forceful
operations, like rooting in pigs. Another conclusion was that interdigitations were instrumental in
the transmission of force from one bone to another and to resist shear loads. Generally speaking,
the interdigitations of the sutures will be either perpendicular or parallel to the main force
applied and these interdigitations serve to increase the surface area for collagen fibers to attach
(Herring, 1972; Jaslow, 1990; Rafferty and Herring, 1999). Jaslow (1990) examined the
mechanical properties of sutures and concluded that during rapid displacement increased
interdigitations do improve the bending strength of suture specimens but pure cranial bone was
still almost twice as strong. Only when the most interdigitated sutures experienced slow loads
did their bending strengths become comparable to cranial bone alone.
Jaslow (1990) was also able to provide support for the hypothesis that sutures act as
shock absorbers in the skull. This is based on the discovery that cranial bone with a suture
present was able to absorb more energy, regardless of the sutural morphology, than the pure
cranial bone. The sutural morphology also influences the amount of energy absorbed. Energy absorption increased as the complexity of sutural interdigitation increased. Interdigitation also
44
seems to be correlated with the degree of compressive strain. The more compressive strain a suture is exposed to, the higher the degree of interdigitation (Rafferty and Herring, 1999).
Adjacent sutures also seem to experience large magnitude strains of opposite polarity during normal mastication, at least in pigs (Rafferty and Herring, 1999). This result is intuitive because
tension and compression are orthogonal to one another.
Structure and Function of the Periodontal Ligament
The periodontal ligament is composed of soft, highly vascular and cellular connective
tissue that connects the root cementum of the tooth to the surrounding alveolar bone (Rees and
Jacobsen, 1997; McCulloch et al., 2000). This structure is often overlooked in studies
concerning mastication and jaw form; however this ligament plays important roles such as
providing support, protection and provision of sensory input to the masticatory system.
Structurally the periodontal ligament is complex containing several cell populations and several types of fibers in the extracellular matrix (Beertsen et al., 1997; McCulloch et al., 2000). The unique structural composite of the periodontal ligament is what provides its unique (and essential) function in the masticatory system.
The majority of fibers found in the periodontal ligament are collagenous and the most abundant is specifically type I collagen. These fibers form a meshwork that resembles a stretched fishing net between the tooth root and the alveolar bone (McCulloch et al., 2000). The
arrangement of these fibers as well as their molecular composition is what provides the ligament
with its mechanical strength. In addition to anchoring the tooth, the oblique orientation of these fibers also serve as a suspensory ligament which allows vertical forces to be transmitted to the
alveolar wall as lateral tension (Atmaram and Mohammed, 1981). The fibers seen on the
interdigitated endocranial portions of sutures are analogous to the arrangements of fibers in the
periodontal ligament (Herring and Teng, 2000). The interaction between bone, suture, and bone
45
is not unlike the interaction between bone, periodontal ligament, and tooth, which suggests that
there may be similar principles that govern how fibrous tissue respond to mechanical stimuli
(Henderson et al., 2004).
Type I is not the only collagen present; about 20 percent of the collagen is type III and
much smaller percentages of type V, VI, and XII are also present (Berkovitz, 1990; Beertsen et
al., 1997). The functional significance of these other minor collagens in the periodontal ligament
is not well understood (Berkovitz, 1990; Beertsen et al., 1997).
Several populations of cells are present in healthy periodontal ligaments including
fibroblasts (predominant), epithelial cell rests of Malassez, sensory cells, osteogenic, osteoclastic
and cementoblasts (Beertsen et al., 1997). (Epithelial cell rests of Malassez are remnant cells of
a sheath of epithelial cells that formed the root during tooth development.) The fibroblast cell
population does not appear to be homogenous. Instead a variety of fibroblast populations with
varying functions are present within the periodontal ligament. The fibroblasts located in closest
proximity to the bone exhibit a larger quantity of alkaline phosphatase than the fibroblasts
located on the tooth side (McCulloch et al., 2000). Mechanoreceptor cells in the periodontal
ligament respond to imposed loads in order to regulate the resorption and formation of the bone
matrix (Henderson et al., 2004).
In addition to simply anchoring the tooth to the bone, the periodontal ligament also has
some important mechanical functions. One function is distributing applied forces to the alveolar bone (Beertsen et al., 1997; McCulloch et al., 2000). Alveolar bone has natural holes, i.e. the tooth sockets, which could potentially cause this bone to be weaker than bone elsewhere in the mandible and maxilla. The periodontal ligament seems to play an important role alleviating some of the forces that the alveolar bone experiences. Another function is that the direction,
46
frequency, duration and size of the forces determines in part the extent of bone remodeling as
well as how quickly remodeling takes place (Beertsen et al., 1997; McCulloch et al., 2000). This function is supported by the fact that when forces are applied to teeth that are lacking a periodontal ligament, the rate and degree of bone remodeling is limited. These functions indicate
that the periodontal ligament is important for both load transmission and in alveolar bone
remodeling (Beertsen et al., 1997; McCulloch et al., 2000).
Biomechanics of Mastication
Overview
Understanding the biomechanics of mastication is necessary since this activity is the
primary source of loading for the facial skeleton. Extensive research has been conducted on the
mandible to determine the forces experienced during mastication (e.g. Hylander, 1975; Hylander,
1979a,b,c, 1984, 1985; Smith, 1978; Walker, 1978). Hylander (1975) determined that the
mandible functions like a lever during mastication and behaves more or less like a beam.
Modeling the lower jaw in this manner as opposed to a “link” (Gingerich, 1971; Robinson,
1946), implies that the temporomandibular joint is reactively loaded instead of not loaded at all
(Herring, 1993). Hylander (1979c) also explored the functional significance of the primate
mandibular form and concluded that symphseal fusion does appear to be an adaptive response to
multiple forces produced during mastication.
Unfortunately the upper and lower jaws do not function in the same manner. Due to the
structural nature of the maxilla, modeling the upper jaw experimentally has been difficult to date.
One assumption made is that the maxilla does not experience bending and twisting like the
mandible due to the presence of the hard palate, but no experimental evidence exists that states
what type of stresses the maxilla does experience during mastication (Daegling and Hylander,
47
1997). Nevertheless, the forces generated by mastication are still of particular interest when
examining the palate since this structure plays a pivotal role in masticatory activities.
Two basic types of masticatory activities are incision (tearing) and mastication (grinding
and crushing). Incision mostly involves the incisors and canines, while the molars and premolars
are predominantly involved in mastication. Both activities involve three basic phases: opening
stroke, power stroke, and closing stroke, which collectively constitute one chewing cycle
(Walker, 1978; Hylander, 1992). These movements involve both the upper and lower jaw; however, the mandible is the element that moves in relation to the maxilla. For this reason analyzing the forces involved in the mandible is less complicated because it is more easily considered in isolation from the rest of the skull.
Forces
Since the maxilla is not an isolated element, the entire cranium needs to be considered for determining loading during chewing. In addition to mastication, the skull as a whole may experience load from several other sources including forces from the inertia and weight of the skull itself, joint reaction forces, forces caused by muscle actions, and trauma (Russell and
Thomason, 1993). If these forces act directly on the structure, then shearing stresses will result.
Other loads the skull may experience include bending and torsion. Preuschoft (1989) stated that the bite forces inside the upper jaw evoke shearing forces, torsional moments, and bending moments, although the sources or nature of these different loading conditions are not specified.
The concept of dynamic strain similarity states that certain load-bearing skeletal elements experience similar peak functional strains during habitual loading regardless of body size (Rubin and Lanyon, 1984; Vinyard and Ravosa, 1998). Since facial bones experience variable amounts of stress during mastication, this suggests that not every facial bone is specifically designed for
48
countering masticatory loads (Hylander et al., 1991; Hylander and Johnson, 1997). In other words, the facial areas that experience low stress are not important for resisting forces generated during this activity.
Static versus Dynamic Considerations
Static analysis refers to the study of loads within a physical system that is in static equilibrium, which means that the system is either at rest or its center of mass is moving at a constant velocity. Dynamic analysis refers to the study of accelerating bodies. Due to the relative simplicity of static analysis versus dynamic analysis, many of the masticatory studies are static. Free body analysis is one method employed to evaluate how a structure is statically loaded. Free body analysis is used to determine how the palate is loaded. Unfortunately this problem is statically indeterminate, which means that it does not have a unique solution. There are too many unknowns to solve the equilibrium equations for this static analysis. However, a general idea of the forces affecting the palate and their role in producing specific loads can be determined.
Free Body Analysis
The hard palate presents a unique challenge when determining the forces that act upon this structure. To construct a free body diagram, all the forces that act directly on the structure must be considered. As stated above, typical forces involved in modeling masticatory skeletal elements are bite force, muscle force, and joint reaction force. Bite force is a direct force for the maxilla, but there are no direct muscle forces (i.e. no muscles directly attach to the palate) and the palate (and the maxilla as a whole) has no direct articulation at the temporomandibular joint
(TMJ) either. Due to these factors, the following free body analysis is a static analysis of the
49
cranium with an emphasis on what is occurring at the palate. This allows easier visualization of the forces involved in mastication than if the palate was isolated for this analysis.
Masticatory muscles can be categorized as elevators and depressors. Elevators function during jaw closing and the power stroke of the chewing cycle, while depressors function during jaw opening. Most of the major muscles involved in mastication function as elevators including
the temporalis, masseter, and medial pterygoid muscles. The lateral pterygoid has two
functionally distinct heads; the superior head stabilizes the mandibular condyle against the
articular eminence while the inferior head functions as a depressor (Hylander, 1992; Koolstra,
2002). Other depressor muscles that play a smaller role in mastication are located in the floor of
the mouth including the geniohyoid, the mylohyoid, and digastric muscles (Koolstra, 2002). An
important caveat from a comparative perspective is that muscles are named based on where they
attach so the same muscle may not be functionally comparable in different species (Herring,
2007). This does not appear to be an issue for the comparison of humans and macaques, i.e. the
same muscles involved in mastication appear to be functionally similar.
Fiber orientation is indicative of the line of action that occurs during contraction of the
muscle fibers. The elevator muscles have a wide range of attachment so their fibers are heavily
pennate causing a relatively large physiological cross section (Koolstra, 2002). This indicates
that the elevator muscles are suited for the generation of large forces although their short fibers
limit their capacity for active shortening during contraction (Koolstra, 2002). However muscle
size is not the only determinant of muscle force; the stretching of the sarcomeres and the speed
of contraction also influence the amount of muscle force generated (Herring, 1993). Compared
to the elevator muscles, the depressors have more parallel fibers with a relatively smaller
physiological cross section. Therefore, these muscles generate less force but can contract over a
50
longer distance (Koolstra, 2002). Individual muscle forces can be divided into both horizontal and vertical components (Smith, 1978). In the free body analysis, the vertical components of muscle force are represented since these influence the loading of the maxilla more so than the horizontal components which are negligible (Smith, 1978).
Similar to the muscle forces, only the vertical component of the bite force will be modeled as well. The precise direction of the bite force in primates is unknown and although both medial and lateral components most likely exist during mastication these force components are negligible (Hylander, 1979a). Figure 2-2 shows the medial component of the molar bite force on the palate; since these forces are negligible, they will not be represented in the other free body diagrams.
The last external force modeled on the free body diagrams is the joint reaction force at the TMJ. Differential loading of the TMJ occurs on the ipsilateral (working) and contralateral
(balancing) sides of the jaw due to the relative amount of muscle force from the ipsilateral and contralateral sides (Hylander, 1992). For example, if the muscle force on the ipsilateral side is twice the muscle force on the contralateral side, then the joint reaction force on the ipsilateral side will be about 1.4 times that found on the contralateral side (Hylander, 1992). Several scenarios are possible concerning the ratio of ipsilateral to contralateral muscle force since it varies with the mechanical property of the food items being chewed (Hylander, 1992).
Experimental evidence has shown that among macaques the TMJ is loaded by a compressive reaction force with the contralateral TMJ reaction force being larger than the ipsilateral TMJ during mastication and incision (Hylander, 1979b). However, during isometric biting, the bite position did elicit different loading patterns in the TMJ. When biting was on the premolars and first two molars, a compressive reaction force was observed while biting on the
51
third molar elicited very little compressive stress, no stress, or tension at the ipsilateral TMJ
(Hylander, 1979b).
The free body analysis conducted here consists of two loading scenarios, incisor and molar biting, represented by three lateral projection diagrams and two frontal projection diagrams (Figures 2-3 through 2-7). The lateral projections include the working and balancing side for the molar biting loading scenario since both cannot be included in a single diagram. The frontal projection will allow a simultaneous examination of both TMJs.
Figure 2-3 is a lateral projection of the working side of the skull during molar biting
while Figure 2-4 shows the balancing side. Only the vertical components of the forces are
considered. The external forces represented in the diagram include the force of the muscles
which is positioned immediately posterior to the tooth row, the joint reaction force at the TMJ,
and on the working side, the bite force at the second molar. Internal shearing force at the anterior maxilla is also represented as it is likely to occur during molar biting. Figure 2-5 shows
a lateral projection of incision. Since biting occurs in the mid-sagittal plane the
temporomandibular joints cannot be differentiated into balancing and working sides.
When analyzing the skull in the frontal projection, both temporomandibular joints may be
represented simultaneously. Figure 2-6 illustrates incisal biting which occurs roughly in the
midline; therefore the two TMJs cannot be differentiated into working and balancing. The
reaction muscle forces would also be located in the mid-sagittal plane because the muscle forces
probably act close to a 1:1 ratio (Smith, 1978). This loading scenario suggests that the skull is
being bent. Figure 2-7 shows a frontal projection of molar biting. This scenario is more
complicated than incisal biting because the diagram illustrates that the skull experiences both
bending and twisting. The muscle force would be displaced more toward the working side as
52
opposed to the midline, and the twisting of the snout would suggest that the balancing side TMJ
would be more compressed than the working side TMJ. As stated above, this has been observed
experimentally in macaques (Hylander, 1979b).
Although these free body diagrams are far from representing a detailed view of the
mechanical environment of the maxilla, they do provide a generalization of the forces expected
during these activities. These diagrams contribute to the analysis of the strain gage experiments conducted on the macaque skull by helping to elucidate the general patterns observed during mastication and incision.
During masticatory activities, the face is likely to experience both bending and twisting
(Ross, 2008). In most loading scenarios of the face, these two load cases, i.e. bending and twisting, are likely to be superimposed meaning that both are occurring simultaneously. The rostrum, specifically the palate, will likely experience a large amount of shear compared to the mandible. Although shearing stresses do occur in the mandible, the shearing stresses will be a larger factor in the palate due to its geometry. The macaque face in particular has a rather short snout compared to the height of the face and this arrangement will cause predominately shearing stresses within the structure.
53
Figure 2-1. “V” principle of facial growth. As the V moves from position A to position B, the structure increases in overall dimensions. The + marks indicate bone deposition on the inner side of the V, while the – marks indicate bone resorption on the outside surface.
54
Figure 2-2. Transverse view of palate during molar biting. FB represents the medial component of the bite force on the second molar. FJM represents the medial components of the muscle and joint reaction forces. These forces do not act directly on the palate so they have been resolved into one moment represented by the curved arrow. This moment is necessary to counteract the medial bite force so that the diagram is in equilibrium.
55
Figure 2-3. Lateral view of working side molar biting. FS represents the internal shearing force (the resultant of balancing side muscle and joint forces) during molar biting. FB represents the bite force on the second molar. FM represents the muscle reaction force. FJ represents the joint reaction force at the TMJ. According to Hylander (1979c, 1992), the TMJ is loaded less on the working side compared to the balancing side and the muscles on the working side are most likely generating 1.5 times as much force as the balancing side muscles.
56
Figure 2-4. Lateral view of balancing side molar biting. FS represents the internal shearing stress during molar biting. FM represents the muscle reaction force. FJ represents the joint reaction force at the TMJ. According to Hylander (1979c, 1992), the TMJ is loaded more on the balancing side compared to the working side and the muscles on the balancing side are most likely generating less force compared to the working side muscles.
57
Figure 2-5. Lateral view of incisor biting. FB represents the bite force on the incisors. FM represents the muscle force. FJ represents the joint reaction force at the TMJ. There is no differentiation between working and balancing sides in incision.
58
Figure 2-6. Frontal view of incisor biting. FB represents the bite force on the incisors. FM represents the muscle reaction force. FJ represents the joint reaction force at the TMJ. Since biting is in the mid-sagittal plane both joints are theoretically worked equally; therefore, there is no differentiation between working and balancing sides. This scenario illustrates bending only in this projection; there is no twisting moment.
59
Figure 2-7. Frontal view of molar biting. FB represents the bite force on the second molar. FM represents the muscle reaction force. FJW represents the joint reaction force at the working side TMJ. FJB represents the joint reaction force at the balancing side TMJ. The white arrow represents the twisting moment. This scenario illustrates that the face is twisted and bent. According to Hylander (1992), the working side muscles are slightly more active than the muscles on the balancing side causing the resultant muscle force to be located more toward the working side as opposed to the mid- sagittal plane. This load case also results in more compression on the balancing side TMJ compared the working side.
60
CHAPTER 3 METHODS
Theoretical Modeling and Experimentation
For theoretical modeling and experimentation several methodologies were employed to elucidate how the hard palate responds to varying loads due to incision and mastication. Micro- computed tomography (µCT) was performed on the skull of an adult female macaque (Macaca fascicularis) in order to gain a better understanding of cross-sectional geometry and to obtain grayscale values that can be correlated to bone density. In vitro strain gage experiments were conducted on this specimen to determine how specific areas of the maxillae, and the palate in particular, deform when subjected to controlled loading scenarios. Pig crania (Sus domesticus) also underwent in vitro strain experimentation to determine the strain profile on the palate during bending and twisting. The pig crania were chosen because they have a larger surface area for placing strain gages on the palate surface compared to the macaque. Finally, microindentation was then performed on the same macaque skull which underwent µCT and strain experimentation in order to obtain material properties, specifically elastic (Young’s) modulus, via hardness.
Micro-Computed Tomography
Micro-computed tomography (µCT) has become a widely used method in conducting skeletal research (Ruegsegger et al., 1996; Muller et al., 1998). This noninvasive technique has provided researchers with a way to capture the geometry of their study specimens without causing any damage to the bones. The main difference between micro-computed tomography and computed tomography (CT) is pixel size, i.e. the resolution of the images produced by the scanners. As the name suggests, µCT produces higher resolution images compared to the CT scanner.
61
A computed tomography scanner is a device that can produce a precise mapping of the attenuation properties of the object being scanned (Marshall, 1982). This method is routinely used in clinical settings and is becoming increasingly popular in anthropological and paleontological research. Although this technique is different from conventional x-ray, the principles involved are the same.
Computed tomography uses a series of x-ray beams that take thin cross-sectional slices of the object being scanned. CT uses the attenuation of the x-ray as it passes through an object to reconstruct an image of the object (Ruff and Leo, 1986). Attenuation is a term that refers to any reduction in the strength of the signal. In terms of CT scanning, attenuation means the absorption and the scattering of the x-ray beam. In this context, absorption refers to the ratio of the intensity of x-rays at the source and x-ray intensity at the detector located beyond the object being scanned (Daegling, 1990). One of the uncontrollable limitations of computed tomography is the random nature of the attenuation process, but this can be addressed by expressing the attenuation numbers of a material relative to the linear coefficient of water at the same energy levels (Ruff and Leo, 1986).
Two distinct advantages exist with the use of CT over conventional roentgenography.
First, the CT scanner only takes cross section slices and reconstructs them into two-dimensional images for display (Takahashi, 1981). This provides a distinct advantage over conventional x- ray because it eliminates the overlap redundant shadows. Second, since CT uses one or more thin x-ray beams the amount of scattered radiation is reduced (Takahashi, 1981).
In using CT technology for skeletal research, the recommendation is to use the smallest available slice width and pixel size possible during scanning and image reconstruction (Ruff and
Leo, 1986). The display settings (window width and window length) must also be appropriately
62
set since they have a major influence on the image output. Once these settings have been
determined, then the object is ready to be scanned. Most CT scanners are set up so that there is
an adjustable platform that moves through a stationary gantry that contains the x-ray source and detectors (Ruff and Leo, 1986). The object being scanned should be stable on the platform so there is no movement during the scanning process. The object should also be placed so that it is near the center of the gantry opening since this is the location where quality control calibrations are typically performed (Ruff and Leo, 1986).
Although CT scanning offers advantages over other methods, there are some limitations.
Two factors that are beyond the control of the investigator but should still be recognized are the inherent uncertainty of the attenuation process and the regional variations within tissues
(Daegling, 1990). These factors only pose difficulty if minute variations in the attenuation coefficients are necessary to the analysis. Other factors that affect the quality of CT images include machine drift, camera drift, size and shape of the object being scanned, and artifacts
(Daegling, 1990). Machine drift refers to attenuation values drifting from their calibrated values, but this is rarely a problem since CT scanners are calibrated regularly. Camera drift is when the photographic production of the hard copy distorts the images. This is a serious concern in skeletal research since the main objective is often geometric reconstruction. If the image is distorted then the geometric reconstruction will be inaccurate. The size and shape of the object can be problematic if the window settings are incorrect. Finally, artifacts refer to inaccuracies in the CT image not caused by any of the above factors (Daegling, 1990). The majority of the limitations can be overcome with the proper knowledge of how the CT scanner functions.
In my project one female Macaca fascicularis skull was sent to Scanco USA, Inc.
(Southeastern, PA) for µCT scanning. A µCT 80 machine was used with a resolution of 74
63
microns, energy setting of 70Kvp and a 1024 x 1024 matrix with 1000 projections/360 degrees.
The skull was positioned in the scanner as seen in Figure 3-1.
Since the skull was not in anatomical position, the images were imported into a program
called Drishti (Lamaye, 2006) for reconstruction. From the reconstructed rendering of the skull,
coronal sections were taken through the palate. The reconstructed images were used to take
measurements to calculate the moment of inertia at each section, which was used to make
predictions of stress using formulas that correspond to the idealized geometries that may
characterize the maxillae.
The original scans were imported into a program called ImageJ (Rasband, 1997-2009) to
collect grayscale values at specific locations. These locations correspond to the areas that were
microindented. The grayscale value (gv) was then used to calculate density (d) in mg/cm3 using the following equation.
d = (gv * 389.04) - 227 (3-1)
These data were collected for two main reasons: 1) to determine whether or not grayscale values, i.e. density, could be correlated to hardness values, i.e. elastic modulus, and 2) to determine if there were differences in bone density between various regions. To address the first reason, density and elastic modulus were regressed against each other at the same location in the palate and the correlation coefficient was examined. For determining regional differences in bone density, one-way ANOVAs were conducted. The regions of analytical interest included the bone adjacent to the suture (within 1 mm), the bone on the medial alveolar process and lateral alveolar process, the bone on the hard palate (more than 1mm from suture), and the bone in the zygomatic region as a control. Unless otherwise noted, all statistical tests were conducted using SPSS software.
64
Microindentation
Indentation is a tool employed to determine material properties, specifically hardness, of
a substance. Two levels of indentation used for bone studies include nanoindentation and microindentation. As the names imply, the main difference between the two techniques involve the scale of analysis. The principle involved in both techniques is basically the same. A machine is used to lower a specific mass (indenter tip) into the specimen at a known load and for a predetermined duration. The residual impression on the specimen is then measured and those measurements are used to derive hardness at that specific site (Johnson and Rapoff, 2007).
In microindentation hardness testing the user has a choice between two different tips to
indent the material: the Vickers indenter or the Knoop indenter. The Vickers indenter is a
square-based diamond pyramid indenter while the Knoop is a rhombo-hedral shaped indenter
(Vander Voort and Lucas, 1998). The main advantage of the Knoop indenter is that the
measurements taken are slightly quicker than the Vickers and it is particularly good for very thin
layers. The Vickers indenter yields more constant hardness values over a wide range of loads
which is not true of the Knoop indenter (Vander Voort and Lucas, 1998). For the
microindentation conducted in my study a Vickers indenter was used.
According to Johnson and Rapoff (2007), five independent variables need to be
considered before completing microindentation. The first variable is applied mass, which refers
to the amount of mass used for the indenter tip to contact the specimen. Previous studies had
found that there is a lower end of applied mass which yields unreliable hardness measurements
(Ramrakhiani et al., 1979). Johnson and Rapoff (1997) recommend a minimum applied mass of
0.1kg. The second variable is dwell time, or the duration which the indenter contacts the
65
specimen. Johnson and Rapoff”s (2007) study showed no significant difference between values ranging from 5 seconds to 60 seconds. For convenience they suggest a dwell time of 10 seconds.
The third variable is drying time which is only applicable to wet specimens. This applies to bone since studies have indicated a difference in material properties between dried and fresh
(wet) bone (Rho and Pharr, 1999). To get the most accurate depiction of the material properties of bone, microindentation needs to be performed on wet specimens. In order to actually perform the microindentation, it is necessary to remove the bone specimen from the wet environment in which it has been stored in order to secure it to the stage of the microindenter for testing.
Johnson and Rapoff (2007) evaluated the amount of time a specimen can be out of the water solution before affecting the hardness values. They found a specimen could be out of the wet environment for up to 105 minutes before statistically significance differences in hardness measurements were observed. They recommend a maximum of no more than 30 minutes out of the water solution during testing.
The fourth variable is the time between indentation and measurement while the fifth variable is the distance between indentation and pore. Johnson and Rapoff (2007) did not find any statistically significant differences between the time the indentation was made and the indentation was measured, up to 30 minutes, so they arbitrarily chose 10 minutes as a standard.
Distance between the indentation and pores within the bones have to be considered because the material properties change within the vicinity of pores. An effect is seen starting at a distance of
73µm from the center of the indentation to the edge of the pore. Due to this effect, Johnson and
Rapoff (2007) recommend a distance of at least 100µm between the indentation center and the edge of a pore or any neighboring indentation.
66
The specimens for indentation were sectioned from the same female Macaca fascicularis skull that was µCT scanned. For the indentation, the samples were prepared from the maxillae, specifically the hard palate. A hacksaw was used to cut transversely through the nasal cavity to separate the hard palate from the rest of the skull. Then an isomet saw was used to make a parasagittal cut through the palate starting anteriorly at the left central incisor. The right half of the palate included the mid-palatal suture.
The first sample was cut coronally from the left side of the palate just posterior to the edge of the lateral incisor root. This sample was subjected to nanoindentation. For nanoindentation, the sample was embedded in epoxy. To prepare a surface for indentation, it must be polished to remove the kerfs generated by sawing the bone in order to produce a smooth, even surface for indenting. The polishing protocol for this sample started with 120 grit paper for
10 minutes, followed by approximately 3 minutes for the following grit sizes: 240, 320, 400, and
600. Next the sample was polished with suspension solutions for approximately 3 minutes each, starting with 15µm, 5 µm, 1 µm, 0.3 µm, and finishing with 0.05 µm. A 15mm mounting disc was affixed to the bottom of the epoxyed sample underneath the area that was to be indented.
Once the polishing was complete and the disc was affixed, the sample was ready for nanoindentation.
A Hysitron Triboindenter (Minneapolis, MN) with a Berkovitch indenter tip was used for the nanoindentation. The parameters were a load of 4mN at a rate of 800µN/s and a dwell time of 5 s. The indents were spaced 20 µm apart. A total of 500 indents were completed in a grid pattern with 100 indents in the x direction and 5 indents in the y direction. One major disadvantage of nanoindentation is since this process is automated and you cannot see the residual impression of the indenter, there is no way to avoid indenting voids. Datum points must
67
be analyzed individually to determine whether or not bone was indented. Only this sample was
nanoindented. The remaining samples were microindented since it was determined that this was more appropriate for the level of analysis of my project.
To determine the orthrotropic nature of the bone, sections of the palate were taken from
three different planes for analysis. The Vickers indenter, which was used in this project, assumes
transverse isotropy of the material. A study involving the mandibular bone of this macaque
specimen could not falsify this hypothesis of transverse isotropy (Rapoff et al., 2008). The
second sample was a sagittal section from the left side of the palate. Unfortunately this section
proved to be too porous to yield any reliable hardness values. The third sample was a transverse
section, which was also cut from the left side of the palate. The remaining samples were coronal
sections from the right side of the palate moving from an anterior position starting at the fourth
premolar and moving posteriorly. The last sample was taken through the second molar. The
microindented samples were numbered 1-7, with sample 2 being the transverse section and the
remaining sections all coronal. Since no reliable data were generated from the sagittal section
that specimen was not included in the analysis.
Each sample was mounted to glass slides with cyanoacrylate and then the side to be
indented was polished. The polishing protocol for the microindentation samples differed from the nanoindentation. This protocol involved polishing the samples at 3 different grits, starting with 6µm, followed by 3 µm, and then 0.05 µm, for 10 minutes at each stage. The samples were then wrapped in saline soaked cheesecloth and placed under refrigeration until microindentation was performed.
The parameters for the microindentation were a load time of 10 seconds, a load of 100 gram-force, and a dwell time of 10 seconds. A Vickers indenter tip was used for all indentations.
68
Both diagonals were measured, and then the average was taken and used in the following formula to determine hardness:
3 F HV *10*854.1 (3-2) d 2
HV stands for hardness, F is the load used (in this case 100 gram-force) and d2 is the average of the diagonals measured from the residual impression of the Vickers indenter.
Ultimately what is desired from the indentation data collected is not hardness, per se, but elastic modulus. Elastic modulus is the material stiffness during normal loading (tension and compression) (Martin et al., 1998). The hardness value can be used in the following regression formula to determine the elastic modulus (E):
E = 0.36 * HV + 0.58 (3-3)
This formula was taken from the study conducted by Rapoff et al. (2008). Once the elastic modulus was calculated, it was regressed against the density values determined from the grayscale values in the µCT scans at the same locations. The goal of this regression was to determine whether or not density and elastic modulus is correlated.
Strain Gage Experiments
The first set of strain gage experiments were conducted on three fresh (previously frozen) juvenile Sus domesticus crania. A total of four rosette gages, five single element gages, and a strip gage consisting of five elements were bonded to the palate (Figure 3-2). For the rosette gages, three were bonded on the right side of the palate between the alveolar process and the mid-palatal suture and one was bonded across the mid-palatal suture. Three single element gages were bonded to the left side of the palate between the mid-palatal suture and the alveolar process, and two single element gages were bonded across the transverse palatine suture on the left side. The 5-element strip gage was bonded horizontally across the mid-palatal suture such
69
that element 3 was aligned on the suture. The posterior portion of each cranium was secured in a block of epoxy resin, while loads were applied using the MTS mechanical testing system at the premaxilla via a sleeve of commercial polyester resin. Cantilever loads were applied at a rate of
0.2 mm/second in a vertical superior direction, and twisting loads were applied bilaterally with a force transducer along one side with a reaction force imposed contralaterally (Figure 3-3). The main objectives for the pig experiments were to 1) assess the magnitude of sutural strains relative to adjacent bone strain under controlled loading regimes of cantilever bending and axial twisting and 2) to characterize strain patterns arising from these two loading scenarios and evaluate observed gradients against the predictions from the geometric model of a thin-walled tube
(Greaves, 1985; Rafferty et al., 2003; Ross, 2008).
The next set of strain experiments were conducted on a female Macaca fascicularis skull after it was µCT scanned. The skull was embedded in epoxy resin posterior to the external auditory meatus so it could be gripped in the vise for the experiments. Experiments were conducted using an MTS mechanical testing system with the exception of experiments 1 and 5 which used a manual transducer. Data were collected using an instrument built in SuperScope software (Somerville, MA). The duration of each experiment performed was 100 seconds. A total of 6 rosette gages and 3 single element gages were affixed using cyanoacrylate to various points in the skull. One single element gage was bonded to the zygomatic region while the other
2 single element gages were affixed across the transverse palatine suture on the right and left sides. Four rosette gages were affixed to the hard palate; 2 on either side of the mid-palatal suture. One rosette gage was attached to the right maxilla just superior to the tooth roots between the first and second molars. The remaining rosette gage was attached midline on the nasal bones in the interorbital region. Figure 3-4 shows the gage locations as just described.
70
A series of loads were performed on this specimen. In experiment 1 a manual transducer was used to apply a vertical load to each tooth starting at the left third molar and moving sequentially to the right third molar. The loading scenario of experiment 2 was a point load on the right first and second molars (Figure 3-5). The load was applied at a rate of 0.2mm/s until
30N was reached and then the load was held for the remainder of the experiment. Experiment 3 was similar to experiment 2 with the only difference being that the left first and second molars were loaded. Experiment 4 consisted of a point load on the central incisors (Figure 3-6). The load for this experiment was also applied at a rate of 0.2mm/s until 30 N was reached and then the load was held for the remainder of the experiment. The final loading scenario, experiment 5, involved twisting the snout of the skull. A metal grip was screwed onto the snout and then a manual transducer was used to apply pressure at the inferior portion of the grip (Figure 3-7).
Strain predictions were calculated based on the coronal cross sectional geometry of the specimens. Conventional beam theory assumes the beam is prismatic which means that the moment of inertia is constant throughout the entire structure. The macaque face clearly does not have a constant geometry and therefore the moment of inertia will differ at each section of the face. To take the tapering of the face into account, moment of inertias were calculated separately for each section of interest. The theoretical cross sectional geometries were chosen based on the closest approximations to the facial geometry (in a coronal cross section). The formulas used for the predictions were from Young and Budynas (2002). These formulas do not take into account the presence of the sutures although two of the theoretical models used do accommodate for the presence of the nasal cavity and the paranasal sinuses, at least in part. Predictions were also calculated based on the actual cortical contours using the parallel axis theorem. The theoretical predictions were compared to the observed strains, and strain profiles in each of the loading
71
scenarios were analyzed. The strain observed at the sutures for both the pigs and the macaque were compared to the strain observed at the adjacent bone to determine if the sutures experienced at least one order of magnitude higher strains than the adjacent bone.
Comparative Analysis
The comparative analysis was conducted to examine palatal dimensions and sutural complexity of cercopithecines and apes to determine if these variables could be functionally related to dietary consistency. The skulls of 23 species of cercopithecines and hominoids were examined from collections housed at the Smithsonian National Museum of Natural History
(Washington D.C.) and the American Museum of Natural History (New York City, NY) (Table
3-1). These species were classified into three major phylogenetic groups: papionins, colobines, and hominoids (Table 3-1). Thirteen measurements were taken from each skull to control for allometric scaling (Table 3-2). With the exception of palate depth, the osteometric points are defined in Bass (1995). Palate depth was measured using an instrument that is colloquially referred to as a carpenter’s or contouring tool. The contour that corresponds to palate depth was traced from the edge of the alveolar ridge of the second molar to the level of the mid-palatal suture. The height of the contoured tracings was then measured resulting in the depth of the palate. The palate of each specimen was photographed to examine the complexity of the mid- palatal suture through the use of fractal analysis and suture length ratio.
Diet and Ecology of Study Samples
The species were chosen based on phylogenetic relationships and dietary contrasts.
Phylogeny needs to be considered because evolutionary relationships between species may account for the similarities and differences observed rather than mechanical factors resulting from dietary differences. Therefore, the ecologies and diets of the species were examined to
72
develop the dietary contrasts used in the analysis. Although the diets are complex in terms of the food items ingested, for the purpose of my analysis, the dietary consistencies of the species are simplified as hard versus soft diets.
Papionin ecology
The papionin species have a wide range of geographic distributions and dietary habits.
They were divided into the following taxonomic subgroups for discussion: macaques (Macaca), common baboons (Papio), gelada baboons (Therapithecus), mangabeys (Lophocebus and
Cercocebus), and mandrills (Mandrillus).
Macaques are one of the most successful primate radiations with species residing in
Africa and Asia, representing the largest geographic distribution of primates except for humans
(Thierry, 2007). Phylogenetically, macaques can be divided into three lineages: Silenus- sylvanus, Sinica-arctoides, and Fascicularis (Thierry, 2007). The four macaque species used in my study are from 2 of the lineages. M. sylvanus is a member of the Silenus-sylvanus lineage while the remaining 3 species (M. fascicularis, M. mulatta, and M. fuscata) are members of the
Fascicularis lineage. No members of the Sinica-arctoides lineage were analyzed in the current study.
Due to the large geographic distribution, classifying the macaques as one type of feeder does not provide an accurate representation of their diets. M. mulatta (rhesus macaques), M. fuscata (Japanese macaques), and M. sylvanus (Barbary macaques) are often described as non- specialized feeders although certain patterns have been observed based on habitat (Thierry,
2007). Of the 4 macaque species involved in my study, M. fascicularis (long-tailed macaques) is the most frugivorous as they inhabit principally tropical and equatorial regions. They are often found in riverine and secondary forests in low altitudes. M. fuscata is confined to islands but
73
their environments can vary. In warm-temperate areas, Japanese macaques are mainly frugivorous while in cool-temperate areas they are mostly granivorous (Menard, 2004; Thierry,
2007). The Barbary macaques reside predominantly in the montane forests of North Africa where their diets are mainly granivorous or folivorous depending on the season (Menard, 2004;
Thierry, 2007). The final species of macaque, M. mulatta, has a wide geographic range and is mainly folivorous or frugivorous depending on their habitat (Menard, 2004; Thierry, 2007).
Rhesus macaques also rely heavily on agricultural crops and food from humans throughout much of their range (Thierry, 2007).
Common baboons have very flexible diets that include a wide range of food items. They are basically generalized omnivores that feed opportunistically (Whiten et al., 1991; Jolly, 2007).
Common baboons have a wide geographic distribution and habitat range having the ability to survive in all tropical, sub-tropical, and temperate-zone vegetation types within sub-Saharan
Africa as long as they can find adequate food and water (Jolly, 2007).
Gelada baboons live mostly in open, high plateau habitats in the highlands of Ethiopia which provide few resources from arboreal sources. Geladas are primarily herbivores and they derive much of their diet from plants such as the blades of grasses and clovers, as well as seeds and roots (Fleagle, 1999; Jolly, 2007).
L. albigena (gray-cheeked mangabeys) extend from Nigeria to Uganda inhabiting mostly continuous evergreen forests. They feed mainly in the forest canopy consisting mostly of fruits where available but falling back on hard-shelled fruits and seeds when necessary (Jolly, 2007).
Cercocebus mangabeys are divided into two main groups: C. agilis (agile mangabey) occupies one group (galeritus) while C. torquatus (capped mangabey) and C.atys (sooty mangabey) occupies the other group (torquatus) (Jolly, 2007). The galeritus group is distributed in forested
74
areas from Gabon to the coast of Kenya while the torquatus group is located entirely in West
Africa. Mangabeys are predominantly frugivorous specializing in fallen fruit, fungi, and invertebrates found on the forest floor (Fleagle, 1999; Jolly, 2007).
Mandrills (M. sphinx) are particularly well-adapted for a frugivorous diet that includes tough-shelled fruits and seeds (Caldecott et al., 1996; Fleagle, 1999; Jolly, 2007). These papionins are predominantly confined to arboreal habitats within the equatorial rain forest of the west-central African coast (Jolly, 2007).
Colobine ecology
Historically, researchers have classified colobus monkeys as specialists, based on the amount of leaves in their diets. The origin of this belief seems to stem from an early paper by
Booth (1956) that refers to colobus monkeys as ‘purely leaf-eating.’ Casual observations and the study of the contents of the stomach formed the basis of this assumption. Anatomical features such as the large complex stomach and high-crowned molars and premolars also support the notion that colobus monkeys are largely leaf-eaters (Campbell and Loy, 2000). Recent evidence, however, suggests that this initial view of colobines is not accurate, at least not for all species and/or groups (Maisels et al., 1994). Leaves do make up a large portion of most, if not all, colobus monkey diets, but seeds, fruits, and flowers also contribute significantly to their diets.
The original belief that colobines were specialists was based on studies conducted on groups of colobines in east Africa (Dasilva, 1994). Research at sites such as Tiwai Island in western Africa has shown that seasonal variability exists in their diets, including seeds, fruits, and both young and mature leaves (Dasilva, 1994; Davies et al., 1999).
Feeding techniques do not vary much between different species of colobines. The type of food eaten affects the technique used, but regardless of the food type, there is very little manual
75
manipulation involved (Clutton-Brock, 1975). Colobus monkeys have reduced thumbs, which may explain the little amount of manipulation. The reduced pollex does not provide them with the grip of other primates who have larger thumbs that allow more precise gripping. Clutton-
Brock (1975) did observe some manipulation, though, such as stripping the pinnules off of the leaf stem by gripping the stem in their teeth and dragging the stem through their clenched fists.
He states that he never saw them use their hands to strip or break open fruit; if the covering was removed from a fruit they opted to use their teeth instead (Clutton-Brock, 1975).
One difference between red colobus (Procolobus badius) and king colobus (Colobus polykomos) is their preference for location of feeding. The former usually acquires a large portion of their food from some of the largest trees in the upper canopy of their habitat, while the latter choose to forage lower in the canopy (Oates, 1994). In areas where both of these colobine groups co-occur, the red colobus monkeys choose a more diverse diet than the king colobus.
Another difference is the amount of seeds that are consumed. All colobus species ingest seeds, but only the black and white colobus spp. do seeds sometimes dominate the diet (Oates, 1994).
Some researchers argue that African colobines eat a large portion of seeds whenever the quality of the tree foliage is poor via poor soils (Maisels et al., 1994). Evidence supports this statement for some areas in central Africa (formerly Zaire; Maisels et al., 1994), but this does not explain the difference in seed exploitation between sympatric species of colobus monkeys.
Procolobus badius and C. polykomos are sympatric throughout most of their range and are similar in body size and diets except the king colobus exploits a seed from the African oil bean (Pentaclethra macrophylla, Mimosaceae) that has a particularly hard husk at a much larger frequency than the red colobus monkeys. This African oil bean tree is usually 21 m in height with a girth of about 60 cm. The pods are 40-50 cm long and usually 5-10 cm wide. Inside the
76
pods are 6-10 flat glossy brown seeds that are up to 7 cm long. C. polykomos focuses on seeds from this plant and others like it whereas P. badius focuses more on leaves (Davies et al., 1999).
The reason for this difference probably stems from their individual preference in foraging, i.e. upper versus lower canopy. When the king colobus feeds on these seeds, they expend a great amount of effort gnawing through the husks until they break through the encasing (Davies et al.,
1999).
Olive colobus (P. verus) are the most consistently folivorous of the African colobines consuming far less fruit than sympatric C. polykomos and P. badius in West Africa (Fashing,
2007). They dwell in mostly lowland rain forests and move through the dense vegetation in the lower and middle canopy (Fashing, 2007).
Guerezas (C. guereza) are one of the few primate groups that seem to reach higher population densities in logged rather than unlogged forest and they thrive in fragmented and secondary forests in east and central Africa (Fashing, 2007). They are more flexible in their diets compared to olive colobus. Guereza diets consist of large quantities of whole fruits and/or seeds in their annual diet (Fashing, 2007).
Hominoid ecology
The hominoids can be divided into 2 general groups: the lesser apes (Hylobates) and the great apes (Pongo, Pan, and Gorilla). H. lar (lar or white-handed gibbon) and H. syndactylus
(siamang) are mostly frugivorous (Bartlett, 2007). The lesser apes are limited in distribution to
Southeast Asia. Leaves are the second most common item found in their diet with the siamangs relying on this food source more heavily than the sympatric lar gibbon.
The great apes are omnivorous but rely mostly on fruits and leaves. Gorillas (G. gorilla) are mostly folivores (Fleagle, 1999) and frugivores (Caldecott et al., 1996) and are limited in
77
their distribution to the tropical forests of sub-Saharan Africa. Orangutans (P. pygmaeus) are primarily frugivores but also exploit hard seeds (Fleagle, 1999). Geographically orangutans are found in Southeast Asia, P. pygmaeus specifically in Borneo and Sumatra (Fleagle, 1999).
Chimpanzees (P. troglodytes) are the most omnivorous of the great apes relying on termites and small mammals as well as fruits and leaves (Fleagle, 1999). They have a broader distribution ranging throughout much of central Africa, from Senegal in the west to Tanzania in the east
(Fleagle, 1999).
Allometric Scaling
For the allometric scaling analysis, the first step was to conduct one-way ANOVAs on the ratios of the variables of each species to determine whether or not sex differences existed for each of the measured variables. Since each of the species in my study exhibits sexual dimorphism these tests were necessary to determine whether or not the sexes could be pooled for further analysis.
The next step was to conduct one-way ANOVAs on species within a given group.
Groups were defined based on phylogenetic relationships. The groups consisted of: colobines
(genera Colobus and Procolobus), macaques (genus Macaca), baboons (genera Papio,
Theropithecus, Mandrillus), mangabeys (genera Cercocebus and Lophocebus), lesser apes
(genus Hylobates) and great apes (genera Pongo, Pan, and Gorilla).
Based on the results of the phylogenetic one-way ANOVA analyses, the species were arranged into three broad categories, papionins, colobines, and hominoids, for further analysis with the sexes separated (Table 3-1). The phylogenetic one-way ANOVAs yielded mostly nonsignificant differences between the macaques, baboons, and mangabeys so these were combined into the papionin group, while the lesser and greater apes were combined into the
78
hominoid group for the same reason. Reduced major axis (RMA) regressions were conducted on the skull measurements and phylogenetic groups using software developed by Bohonak and van der Linde (2004). RMA2 analysis was also performed in order to test for slope differences among the phylogenetic groups based on ratio measurements (Clark, 1980; Cole 1997).
Sutural Complexity Analysis
One of the most difficult tasks facing morphologists is that of quantifying and measuring size and shape. Traditionally, parameters such as length and volume were used to try to quantitatively describe and compare morphological characteristics. In Euclidean geometry linear measures are considered one dimension, smooth surfaces are two dimensions, and volumes and weights are three dimensions. Objects that occur in nature, however, seldom have edges that are straight or surfaces that are smooth (Long, 1985). Some objects in nature possess certain qualities that can be described by a non-Euclidean fractional dimension, which lies between the values of one and two (Mandelbrot, 1977). These objects are known as fractals. Fractals are geometric objects that are self-similar in nature. Self-similarity means that the fractal object is composed of smaller units that possess the same shape as the whole object. Fractals have complex edges or surfaces that increase linearly as the resolution of the units used to measure them increase (Hartwig, 1991). Fractal analysis is a technique used to interpret the geometric complexities of fractals.
Several researchers believe some cranial sutures are fractal objects (Long, 1985; Hartwig,
1991; Long and Long, 1992; Gibert and Palmqvist, 1995; Montiero and Lessa, 2000; Yu et al.,
2003). Long (1985) explored the idea of whether or not complex sutures exhibit fractal properties such as self-similarity and a dimension between one and two. To address this question, Long (1985) examined the sutures on the shells of extinct ammonites and cranial
79
sutures of white-tailed deer. The sutures in both of these organisms are structurally complex and did exhibit fractal properties. Other cranial sutures that have been examined using fractal analysis are the sagittal suture in humans (Hartwig, 1991; Yu et al., 2003), the sagittal and lambdoid sutures in humans (Long and Long, 1992; Gibert and Palmqvist, 1995), and cranial sutures in the genus Caiman (Montiero and Lessa, 2000). In each of these studies, the structures under examination exhibited the characteristics of fractals.
In my study, fractal analysis was conducted with the use of a software program known as
Benoit 1.3 (St. Petersburg, FL). This program allows the user to choose from several different methods on how the fractal analysis is conducted. The different methods provided in this program are tailored to accommodate different types of data sets. Based on my data set, the method chosen for analysis was the information box dimension, which is a variant of the box dimension.
The box dimension method of fractal analysis is one of the most widely used methods due to the relatively simple mathematics involved (Falconer, 1990). In Benoit 1.3, the box dimension is defined as the exponent Db in the relationship:
1 dN )( (3-4) d Db where N(d) is the number of boxes of linear size d necessary to cover a data set of points distributed in a two-dimensional plane. A number of boxes are used to cover the data set points that are evenly distributed on a plane. This may indicate that point density may influence the results, i.e. the number of data points collected will affect the outcome of the fractal dimension.
This method is often referred to as the grid dimension because the boxes used are usually part of a grid system.
80
To accomplish this method, a series of different box sizes d are laid over the object and the program works by tallying the number of boxes filled during each box size overlay. One of the problems with this method is that the boxes are weighted the same whether the entire box is full or just a tiny portion. The information dimension method addresses this problem by assigning weights to the boxes so boxes containing more points are counted more than the boxes with fewer points (Benoit 1.3). Unfortunately this makes the mathematics involved much more complicated.
In order to collect the data for the fractal analysis, the palate of each specimen was photographed using a Pentax K100D SLR digital camera. Each specimen was oriented with the palate parallel to the lens of the camera. The images were uploaded and imported into
SigmaScan (Systat Software, Inc, Chicago) where the mid-palatal suture of each specimen was digitized. The x-y coordinates were imported into SigmaPlot (Systat Software, Inc, Chicago) and subsequently graphed using a single spline curve. The spline curve option was chosen over the single straight line option because this represented a more accurate depiction of the sutures. The scale of the graphs was changed so equal units were represented on the x and y axes. The image was then inverted from black on white to white on black because Benoit 1.3 software recognizes white points as data points and the black points as the background.
The images were converted to bitmap files and imported into Benoit 1.3 for the fractal analysis. After exploring the different methods available through the software, the information dimension method was chosen. The information dimension was chosen over the box dimension because the boxes are weighted and therefore provide a more accurate fractal dimension than the box dimension.
81
An alternative method of measuring suture complexity is calculating suture length ratio.
This method involves measuring the chord of the suture and dividing by the total length of the suture. Based on this method lower ratio values indicate a more complex suture. The total length and chord length of the sutures were measured in SigmaScan.
Once the fractal dimensions and suture length ratios were obtained, several statistical procedures were conducted using nonparametric tests since the data did not have a normal distribution. First, Kruskal-Wallis tests were performed to determine if there were differences among the phylogenetic groups and between the individual species. Since these tests yielded significant differences, Mann-Whitney U tests were performed to determine which of the groups and species differed from each other. Reduced major axis (RMA) regressions were also conducted with the RMA software by Bohonak and van der Linde (2004) between the fractal dimensions and each size/shape variable as well as the suture length ratio and each size/shape variable to try to determine if there were any predictable relationships. The regressions were conducted with the sexes pooled for each species. All of these procedures were evaluated for significance based on a P-value < 0.05.
82
Table 3-1. Samples sizes for comparative study Species Phylogenetic Group Total Males Total Females Lophocebus albigena papionin 10 10 Cercocebus torquatus papionin 9 9 Cercocebus agilis papionin 9 7 Cercocebus atys papionin 4 4 Mandrillus sphinx papionin 9 3 Theropithecus gelada papionin 5 4 Papio anubis papionin 10 10 Papio hamadryas papionin 4 0 Papio papio papionin 6 0 Papio ursinus papionin 7 4 Macaca sylvanus papionin 6 8 Macaca fuscata papionin 4 2 Macaca mulatta papionin 10 10 Macaca fascicularis papionin 10 10 Colobus guereza colobine 10 10 Colobus polykomos colobine 10 10 Procolobus badius colobine 9 10 Procolobus verus colobine 5 3 Hylobates syndactylus hominoid 9 10 Hylobates lar hominoid 10 10 Pongo pygmaeus hominoid 10 10 Gorilla gorilla hominoid 10 6 Pan troglodytes hominoid 10 10
83
Table 3-2. Definitions of measurements collected Measurement Definition (Craniometric points*) Skull and Facial facial width zygion to zygion upper facial height nasion to alveolare total facial height nasion to gnathion skull length glabella to opisthocranion bipterygoid breadth between anterior junction of medial and lateral pterygoid plates Palatal external palate breadth ectomolare to ectomolare internal palate breadth endomolare to endomolare palate depth endomolare to midpalatal suture palate width edge of alveolar bone at canine to edge of alveolar bone at opposite canine maxillary palate length alveolare to intersection of transverse palatine and midpalatal sutures palatine palate length intersection of transverse palatine and midpalatal sutures to alveolon total palate length maxillary plus palatine palate length *Craniometric points defined in Bass (1995). All measurements in mm.
84
Figure 3-1. Original position of skull in the µCT scanner.
85
Figure 3-2. Strain gage locations on Sus domesticus. The numbered circles represent the rosette strain gages. The vertical boxes represent the single element gages. The horizontal box represents the 5-element strip gage.
86
Figure 3-3. Schematic of torsional pig loading regime. This is an anterior view of the pig cranium. The gray circle represents the commercial polyester resin in which the snout was embedded. The rods were screwed into either side of the resin. The orange arrows represent the torque applied at the ends of the rods.
87
Figure 3-4. Strain gage locations for the Macaca fascicularis specimen. A) This is a view of the four rosette gages and 2 single element gages bonded to the palate. B) This is an anterior view of the cranium showing the rosette gage bonded to the interorbital region. C) This is a lateral view of the right side of the cranium showing the rosette gage bonded to the maxilla and the single element gage bonded to the zygomatic arch.
88
Figure 3-5. Molar loading set-up for the macaque. The white arrow represents the load applied by the force transducer.
Figure 3-6. Incisor loading set-up for the macaque. The white arrow represents the location of the applied load to the incisors.
89
Figure 3-7. Twisting set-up for the macaque experiment. The black dot on the inferior side of the metal grip around the snout represents the point that the load was applied for twisting.
90
CHAPTER 4 RESULTS
Theoretical Modeling and Experimentation
This section encompasses the micro-computed tomography (µCT), microindentation and strain gage experiments of the Macaca fascicularis cranium. Strain gage experiments were also conducted on several pig crania. These 3 methodologies are interrelated. The µCT scans provide density information that was calculated from the grayscale values of the scans as well as providing information on the internal geometry of the macaque skull to allow for the calculation of the moment of inertia. The moment of inertia was used to calculate theoretical predictions of stress and strain based on idealized geometrical models. Stress and strain are related, but in order to calculate strain from stress, the elastic modulus is needed. This was obtained from the microindentation of the macaque palate. The elastic modulus was then used to calculate predicted strain from the predicted stress and these predictions were compared to the observed strain in the strain gage experiments.
Bone Density and Elastic Modulus
To determine the density of the bone, individual µCT scans were analyzed. Grayscale values were sampled from either 4 or 5 bony regions depending on the scan. The four regions sampled from each scan were the sutural area (within 1-2 mm of the mid-palatal suture), hard palate (the roof of the mouth not located near the mid-palatal suture), medial alveolar process
(immediately medial to the tooth), and lateral alveolar process (immediately lateral to the tooth).
On several of the scans an additional region in the zygomatic area was sampled to compare palatal bone density to the bone density of another facial region. Anywhere from 80 to over 100 pixels were sampled in each of the designated areas on the scans. The variance in sample size was due to the area of bone available in each region; edges were avoided to eliminate partial
91
edge effects. A one-way ANOVA was performed to determine if there were any differences in bone density between the regions. For this test, the regions from each of the scans were pooled.
The test yielded a P-value < 0.001 which means there are significant differences. A Hochberg’s
GT2 post hoc test was run to determine which regions differed. This post hoc test was chosen because the sample sizes varied (Gamst et al. 2008). The results were that the medial alveolar process, sutural area, and hard palate did not differ from each other (P-values ranged from 0.342-
0.942) but they did differ from the lateral alveolar process and the zygomatic region (P-value <
0.001). The zygomatic and lateral alveolar regions did not differ from one another (P-value =
0.872).
In addition to testing for regional differences, the right and left sides of the palate were tested for differences as well. No differences were expected; rather this test was conducted to ensure that modulus is comparable on both sides and therefore, that the assumption that the left and right sides would not differ was correct. Based on the one-way ANOVA, this assumption proved to be accurate (P-value = 0.492).
The next question investigated concerning density was whether or not there were any differences among the slices examined and the locations within the slices. In other words, were there any differences within the regions examined between the anterior portion of the palate and the posterior? A univariate generalized linear model, i.e. a 2-way ANOVA, was conducted to address this question. This test yielded significant results for slice and region as well as a significant interaction effect between slice and region (all P-values were less than 0.001).
Hochberg’s GT2 post hoc tests were performed to determine where that variation occurred.
Among the slices only slices 3 and 6 differed from each other significantly (P-value = 0.012).
Among the locations, there were many significant differences observed (most P-values were less
92
than 0.001). The areas that showed no significant differences were the medial alveolar process and hard palate (P-value = 0.904) and the lateral alveolar process and the zygomatic regions (P- value = 0.502). The suture area differed significantly from all of the other regions. Examining the density difference from the mid-palatal suture to the tooth in a single scan shows some indication of a gradient with higher densities being located near the suture and lower density by the tooth (Figure 4-1)
After the cranium was µCT scanned, the palate was sectioned for indentation studies.
One coronal section was prepared for nanoindentation, while the remaining sections were prepared for microindentation as described in the methods. Nanoindentation was originally pursued due to concerns over the limitations of microindentation, specifically the inability to indent too close to a void. This makes microindentation not well suited for particularly porous material. The nanoindentation results produced very low elastic moduli for what was expected from bone (Table 4-1). Some of the moduli values were less than 1 GPa which indicates a void was indented. The lower than expected values could be due to poor specimen preparation (e.g. insufficient polishing of the section). The results from nanoindentation suggest that this method is not particularly helpful for my study, so the remaining sections were microindented.
A total of 7 sections were microindented representing 2 different planes (6 coronal sections and 1 transverse section) (Figures 4-2 through 4-8). A sagittal section was also prepared but proved too porous to indent. The elastic modulus was calculated from the regression formula given in the methods chapter (Tables 4-2 through 4-8).
The next question of interest was whether or not bone density is correlated with elastic modulus. This question was answered by sampling grayscale values from the µCT scans and hardness from the indentation sections in the same locations on the palate and performing a
93
regression to see if these 2 variables are correlated. Density values were derived from the grayscale values while the elastic moduli were derived from the hardness values. This was conducted for several sections yielding nonsignificant results and, therefore, no correlation between these 2 variables regardless of section examined (e.g. r = 0.442, p = 0.201) (Figures 4-9 and 4-10).
Strain Experiment Results
The results of the strain gage experiments are best presented based on the loading scenarios. The loading scenarios discussed are bending (incisor and molar loading), torsion, and individual tooth loading. For bending and torsion, the experiments include the Macaca fascicularis specimen and the Sus domesticus specimens. The individual tooth loading was only conducted on the macaque specimen.
Strain profile in bending
A load was applied to the incisors of three pig crania to determine whether or not the crania respond to the load like a tapered beam. The maximum strain at different gage locations in the pig specimens are reported (Table 4-9). The strain reported for the rosette gages are the maximum principal strains. Using beam formulas, strain predictions were calculated for the gage sites on the pig. Theoretical versus observed strains during bending show that congruence was inconsistent (Figure 4-11). Pigs 1 and 3 show a reasonable fit while observed strains for pig
2 do not follow those predicted with any consistency. In addition to the magnitude of the strains, the strain gradients were also calculated. The observed strain gradients were steeper than the predicted gradients. The maximum principal strain directions during bending for all 3 pig specimens are shown (Figure 4-12). The gage on the mid-palatal suture shows no consistency
94
between the 3 specimens, which cover a 45° range of directions. The other gages show directions that are mostly aligned along the long axis of the palate.
The macaque specimen was also cantilever bent by applying a load to the incisors of the specimen. Since this specimen had undergone µCT scanning, the theoretical strain predictions for this specimen were more accurate than those made for the pig. The reason for this is because the pig internal geometry had to be estimated, while the internal geometry of the macaque was seen via the µCT scans. For the macaque, stress predictions for three idealized geometries were calculated from published formulas (Young and Budynas, 2002). Figure 4-13 shows the idealized geometries (trapezoid, thin annulus, and hollow ellipse) used to make the stress predictions. The stress predictions were then used to make strain predictions. This was necessary since the experiments conducted measured strain and not stress at each gage site.
The generalized formula for calculating stress (σ) in beams is the bending moment (M) times the distance to the outermost fiber (c) divided by the moment of inertia (I).
c (4-1) I
The bending moment and distance from the centroid to the outermost fiber are measured from the macaque specimen. The moment of inertia is calculated based on the idealized geometry that is being tested. Once stress is calculated, then the relationship between stress and elastic modulus can be used to determine strain. As previously discussed, the elastic modulus of this macaque specimen was determined through microindentation.
For this portion of the analysis, the six gages located on the palatal surface were divided into three positions starting anteriorly and moving posteriorly (Figure 4-14). Tables 4-10, 4-11, and 4-12 report the values for the moment of inertia (I), the predicted stress, the predicted microstrain, and the observed strain from the cantilever bending experiment.
95
For position 1, the trapezoid model has a very high moment of inertia because this model assumes a solid structure. As expected, the predicted stress and microstrain values underestimate the amount of observed strain (average 358% error). Percent error was calculated by subtracting the observed value from the predicted value and dividing by the predicted value and then multiplying by 100. Although the predicted values from the trapezoid model were expected to underestimate the magnitude of strain, this model was still used to determine if it could be useful for estimating relative strains in a comparative context. The thin annulus and hollow ellipse moments of inertia are lower because of the more accurate assumption that the face is hollow
(average 44% and 32% error, respectively). These two models more accurately predict the magnitude of strain, in that both predictions fall within the observed range of strain between the gages. The range was determined from the lowest and highest values exhibited on the gages in that position.
For position 2, the moments of inertia increase for each model as does the magnitude of the applied moment. The trapezoid model does not change predicted strain much from position 1 to 2. Even though the moment of inertia increased, the predicted microstrain was the same because the bending moment was relatively larger. The predicted values for the thin annulus and hollow ellipse were less than the values predicted for position 1. However the observed strain increased from position 1 to position 2. All three models predicted values below the observed strain (average percent errors: trapezoid 647%, thin annulus 155%, and hollow ellipse 107%).
The predictions for position 3 were the least accurate. The moments of inertia increased dramatically for all models because this position includes the circumorbital bone. All of the models considerably underestimate the amount of strain (average percent errors: trapezoid
4175%, thin annulus 246%, and hollow ellipse 396%). The trapezoid and hollow ellipse models
96
predict the smallest amount of strain in this position. The thin annulus predicts higher strain than position 2 but lower strains than position 1.
Figure 4-15 shows a summary of the predicted stress gradients for each of these models moving from position 1 (anterior) to position 3 (posterior). The hollow ellipse shows a decline in stress as you move from anterior to posterior. The trapezoid model shows no change from position 1 to 2 and then decreases in position 3. The thin annulus predicts a decrease from position 1 to position 2 and then a slight increase in position 3. The experiment showed an increase in strain from anterior to posterior so none of the models correctly predicted the observed strain gradient.
An alternative to using the formulas from the idealized geometries to determine moment of inertia is to calculate this variable directly from cortical contours. The technique requires a grid to be imposed over the section of interest, and an arbitrary x-y axis is imposed. The boxes containing bone are then counted at each position and a series of calculations are performed, which is based on the parallel axis theorem. In the following equations, ∆Ai represents the area of the boxes that were overlaid on the section of interest. The boxes are identical in size to aid in geometric calculation. The first equation calculates the moments of inertia about the arbitrary axes x and y.
2 2 ,, xyyyxx AyxAxAyIII iiiiiii ,,, (4-2)
The next equation involved calculating the distances from the centroidal axes xc and yc from the arbitrary axes x and y.
Ax ii Ay ii , yx , (4-3) Ai Ai
97
Those values were then used to determine the moment of inertia about the centroidal axes with the following equation.
2 2 yxyyxx ),,( xx , yyi , xyi AyxIAxIAyIIII i (4-4) cccccc
Finally the principal moments of inertia were calculated using the following equation.
2 2 yyxx IIII yyxx yyxx IIII yyxx pppp pppp 2 pppp pppp 2 ,, III yxyyxx I yx , I yx 0, (4-5) pppppp cc cc 2 2 2 2
Since none of the idealized models produced the expected results, this technique was used for five coronal sections of the macaque face (Figure 4-16). The slices are taken from anterior
(rostral) to posterior (caudal). Slice 1 corresponds to position 1, slice 2 corresponds to position
2, and slices 3, 4, and 5 correspond to position 3. Three successive slices were used for position
3 because the exact gage location is only estimated and, as Figure 4-16 illustrates, the geometry changes dramatically with only slight shifts in plane of strain. Table 4-13 shows the results from the actual cortical contours based on the parallel axis theorem. These do not conform to expectations any better than the idealized geometric predictions. The average percent error for each slice is as follows: slice 1 = 2460%; slice 2 = 2513%; slice 3 = 4175%; slice 4 = 5600%; and slice 5 = 4786%.
In addition to strain gradient, maximum principal strain directions were also examined
(Figure 4-17). The reported strain values for the rosette gages were from the B elements which were aligned along the longitudinal axis of the palate; this also corresponded closely to the maximum principal strain direction (approximately an angle difference between 5° to10°). The alveolar process gage shows the maximum principal strain direction moving diagonally through the face indicating the expected orientation in the vicinity of the neutral axis while the direction of the interorbital gage was orthogonal to that of the palate, again conforming to beam behavior.
98
The principal strain ratio compares the maximum principal strain to the minimum principal strain. Considering Poisson’s ratio for bone, beam theory suggests the palate should experience about 3 times more tension than compression. In this experiment, the palate was almost in pure shear (Table 4-14). In the interorbital region, compression should predominate and the strain ratio for the alveolus should be near 1 indicating a condition of shear. In this experiment we see that both the alveolar process and interorbital region are compressed (ε1 < ε2)
(Table 4-14).
Another bending scenario that the macaque specimen was subjected to was unilateral loading of the right molars and unilateral loading of the left molars. The same general trend is seen in both conditions where the strain increases as the load increases (Figures 4-18 and 4-19).
Regardless of which side is loaded, the gages on the transverse palatine suture and zygomatic arch experience more strain (~ 150-300 µε) than any of the palatal gages (~ 40-125 µε) or the alveolar process (~80 µε). Identifying a similar trend among the other gage locations is more difficult. For the left molar loading, the palate gages (excluding the gages on the suture) on the left side experience higher strains (~ 110-125 µε) than those located on the right side (~50-105).
This is not true for the loading on the right molars. When the right molars are loaded, the palate gages show a less obvious trend. Of those four palate gages, the gage located near the right second molar experienced the greatest strain (~ 105 µε), followed by the gages at the left fourth premolar/first molar and left second molar (~ 90 µε and ~ 85 µε, respectively), and finally the gage at the right fourth premolar/first molar location exhibited the least amount of strain (~30
µε). The strain differences between the left fourth premolar/first molar and left second molar are trivial given measurement precision and experimental control.
99
Next the maximum principal strain, minimum principal strain, and shear values are examined on the palate gages. For left molar loading, the right side of the palate was in tension
(ε2 < ε1) while the left side of the palate experienced more compression (ε1 < ε2). For the right molar loading scenario, the left side of the palate experienced tension, while the right side experienced more compression/shear. The alveolar process and interorbital regions both experienced shear regardless of which side the molars were loaded.
Strain Profile in Torsion
The next loading regime was torsion of the snout region. For torsion, the palate was modeled as part of a thin-walled cylinder. The first set of torsion experiments were conducted on the three crania of Sus domesticus (Table 4-15). Shear strains decline along the rostro-caudal axis of the palate and the principal strain ratios deviated from the expected value of -1.0 (i.e. strain ratios ranged from -10.35 to 2.93). Theoretical shear strain was calculated for the pig specimens in torsion and the theoretical predictions indicate lower strain in the caudal portion of the palate when compared to the observed strains (Figure 4-20). Theoretical strains assume shear modulus for human palatal bone (Peterson et al., 2006). The maximum principal strain direction was also obtained from the rosette gages (Figure 4-21). They were oriented approximately 45° from the long axis of the palate which fits with cylindrical model theory.
The Macaca fascicularis specimen was also subjected to twisting. The shear from each of the rosette gages was plotted against the applied load (Fig 4-22). The four rosette gages on the palate experienced more shear than the gage on the alveolar process or on the interorbital region. The gage located near the left fourth premolar/first molar experienced the highest shear
(966 µε) followed by the gage located diagonally, i.e. the gage at the right second molar (936
100
µε). The rosette gage near the right premolar/first molar exhibited a shear of 744 µε, while the remaining palatal rosette gage near the left second molar had a shear of 648 µε.
The four rosette gages on the palate were divided into 2 positions, anterior and posterior, and theoretical shear strains were calculated using the cross sectional geometry of a circle and an ellipse. The shear modulus used in the predictions was from the palatal region of a rhesus macaque (Macaca mulatta) (Wang and Dechow, 2006). Table 4-16 shows the predicted stress and microstrain from both the circle and ellipse formulas and they were compared to the observed shear strain. Table 4-17 reports the same information for position 2 gages. The shear modulus used in the calculations was 2.6 GPa and the load was 33N. As seen in the tables, the observed shear greatly exceeded the predicted shear. This disagreement is not unexpected since the thin tube model assumed uniform thickness. Similar to the pig experiment, the shear strains declined from anterior to posterior along the palate and the strain ratios did not yield the expected value of -1.0 (Table 4-18). Finally the maximum principal strain directions were observed; they were aligned approximately 45° from the long axis of the palate (Figure 4-23).
Strain profile at the sutures
The strain profile at the mid-palatal suture was observed during the experiments with the pig crania, while the strain profile at the transverse palatine sutures was observed for the macaque cranium. On the pig crania, a 5 element strip gage was bonded so that the third element was aligned with the mid-palatal suture and the remaining elements were parallel to the suture.
In addition there was a rosette gage on the mid-palatal suture and single element gages on the transverse palatine suture. For the macaque, no gages were bonded to the mid-palatal suture, but there were 2 single element gages bonded to the transverse palatine suture.
101
During cantilever bending of the pigs, strains varied dramatically between the sutural gage and a control gage (a gage bonded to bone) (Figure 4-24). The sutural gage is clearly exhibiting higher strains compared to the bone. Figure 4-25 illustrates the strain occurring at each of the elements in the 5 element strip gage at 63 Nm during cantilever bending. The element located on the suture is being deformed significantly more than the elements on the adjacent bone. In vitro strain at the sutures during cantilever bending exhibited strain an order of magnitude higher than the surrounding bone in accordance with in vivo inferences (Rafferty et al., 2003).
During cantilever bending in the macaque, the gages located on the transverse palatine suture experienced higher tensile strains when compared to the other palatal gages (as well as the alveolar process and interorbital gages) (Figure 4-26). The gages on the transverse palatine sutures were single element gages which yield the maximum strain. The other palatal gages were rosette gages, so the maximum principal strain, i.e. tensile strain, was used for Figure 4-26.
Strain profile during vertical tooth loading
This load case was performed on the macaque specimen to determine what localized effects occurred in the proximity of the tooth being loaded. Given the limited number of gages on the palate, the results provide some broad generalizations. Figure 4-27 illustrates these general trends by showing the amount of shear strain found at each rosette gage on the palate when each individual tooth was loaded. The graph starts at the left third molar moving sequentially through the teeth until the right third molar is reached. What was observed was that loading the anterior dentition produced higher strains posteriorly than loading the posterior dentition; so localized strain was not higher than strains further away from the loading site. The
102
probable reason is that incisal loads produce bending and local strain concentrations are not large. This is most likely due to the presence of the periodontal ligament.
Theoretical and Experimental Results Summary
The results presented for the density of bone in the palatal region show that there were regional differences between the lateral alveolar process and the remaining palatal areas. There was poor correlation between bone density and elastic modulus. The elastic modulus does vary throughout the palate, but the average range was from approximately 10 GPa to 15 GPa. The strain data from the various load cases show that there was not good agreement between the experimental data and idealized geometries used to formulate predictions. However, the data generated from the sutural gages indicate that the sutures were strained at least an order of magnitude greater than the surrounding bone.
Scaling Analysis
The results that follow are based on the scaling analysis described in the methods chapter.
The results are organized by size dimension measurement, i.e. the facial and skull measurements.
Tables 4-19, 4-20, and 4-21 summarize the results from the reduced major axis (RMA) analysis for each phylogenetic group. Expectations for groups are based on the empirical slope of the
RMA regression line meaning groups that fall either above or below the regression line are deviating from what is expected. Above the line means that the variable is larger/longer/etc. than expected while below the line means that the variable is smaller/shorter/etc. than expected.
Facial Width
Papionins
RMA regressions of palatal dimensions versus facial width yield divided results for the papionins. External palate breadth (Figure 4-28), internal palate breadth (Figure 4-29), palate
103
depth (Figure 4-30), and palatine palate length (Figure 4-31) exhibit isometry while the remaining three variables (palate width (Figure 4-32), maxillary palate length (Figure 4-33), and total palate length (Figure 4-34)) show positive allometry.
One pattern observed for the positively allometric variables is that the majority of the macaques fall below the regression line so those palatal dimensions are smaller than expected based on facial width. This is also true for T. gelada. The other papionin species show more diversity.
For the isometric variables there is no discernible trend to how the species are distributed.
One interesting observation is external palate breadth appears to scale differently based on sex rather than species (Figure 4-28). Nine of the 12 groups below the regression line are males while 8 of the 11 groups above the line are females. Generally speaking, male papionins tend to have relatively narrower external palate breadths while females tend to have larger external palate breadths when compared to facial width. This pattern is also seen for internal palate breadth (Figure 4-29). Eight of 9 groups below the line are males while 11 of 17 groups above the line are females. Palate depth and palatine palate length do not show these sex differences.
Another interesting observation is that regardless of the palatal variable regressed against facial width, both male and female T. gelada always fall below the regression line. This indicates their palates are consistently smaller than would be expected based on their facial width.
Colobines
The predominant allometric trend seen in Model II regressions between palatal dimensions and facial width for colobines is isometry. Two exceptions are palate width (Figure
4-35) and maxillary palate length (Figure 4-36) which both exhibit positive allometry.
104
Regardless of palatal dimension, P. badius always falls below the line indicating their palates are generally shorter and narrower than expected. P. verus exhibits distinct sex differences in all palatal dimensions except palate width. Females exhibit longer and broader palates than expected while males exhibit smaller and narrower palates. For palate width, P. verus males and females exhibit narrower anterior palates than expected.
Colobus guereza exhibit sex differences only for palate width. For this variable, males exhibit narrower palates than expected based on the regression line while females exhibit wider palates. For all of the other palatal dimensions, male and female C. guereza fall above the regression line so their palates are longer and broader than expected.
The final species of colobine monkey, C. polykomos, shows more diversity in their palatal dimensions. Palate width (Figure 4-35), maxillary palate length (Figure 4-36), total palate length (Figure 4-37), and external palate breadth (Figure 4-38) show sex differences; males are below the regression line for these traits while females fall above the regression line.
For the remaining variables including palate depth (Figure 4-39), internal palate breadth (Figure
4-40), and palatine palate length (Figure 4-41), C. polykomos males and females fall above the regression line.
Hominoids
When palatal dimensions were regressed against facial width the predominant allometric trend seen for hominoids is isometry. There were three exceptions to this pattern: palatine palate length (no significant relationship, Figure 4-42), maxillary palate length (positive allometry,
Figure 4-43), and internal palatal breadth (negative allometry, Figure 4-44).
Examining the palatal length dimensions show no discernible pattern concerning sex or species. For maxillary palate length, all but 3 of the 10 groups (male H. syndactylus, male P.
105
troglodytes, and male G. gorilla M) fall above the regression line (Figure 4-43). When palatine palate length is examined, the opposite trend appears (Figure 4-42). All but 4 groups (female H. lar, male G. gorilla, and male and female H. syndactylus) fall below the regression line. For total palate length there is a distinct split in the species (Figure 4-45). The lesser ape species have longer palates than expected based on facial width while the great ape species have a shorter palate than expected.
The palatal dimensions involving width or breadth of the palate show mostly sex differences. For internal palate breadth (Figure 4-44), external palate breadth (Figure 4-46), and palate width (Figure 4-47), generally the females exhibit wider and broader palates than expected while the males have narrower palates than expected. Palate width refers to the anterior palate
(canine level) while internal and external breadth is the posterior palate (second molar level).
Interestingly this is the general trend seen in the colobines and papionins as well. Palate depth for the hominoids also shows sex differences (Figure 4-48). Female palates are deeper while male palates are shallower than expected. Palate width and external palate breadth versus facial width show an isometric relationship while internal palate breadth versus facial width show a negatively allometric relationship.
Facial Width Summary
RMA2 tests were conducted to determine whether or not the slopes of each phylogenetic group were significantly different (Table 4-22). Colobines and papionins are very similar with only palate depth scaling differently between these two groups. Colobines and hominoids and papionins and hominoids showed significant differences in slope for the majority of palatal dimensions. External palate breadth was the only palatal trait that when regressed against facial width showed no significant difference between any of the groups.
106
For the traits that were not significant (and therefore had similar slopes), comparisons can be made to the relative size differences between the groups. This was determined by calculating ratios of the size and palatal dimension and then comparing them to each other (Table 4-23).
The papionins are always relatively larger than the colobines. Only external palate breadth had a similar slope between the colobines and hominoids and the hominoids are relatively broader.
Between papionins and hominoids, the hominoids have broader and deeper palates relatively while the papionins exhibit longer palates.
Upper Facial Height
Papionins
RMA regressions of palatal dimensions versus upper facial height all exhibit negative allometry. The general trend observed for the palatal length dimensions is baboons and macaques tend to fall below the regression line thereby exhibiting shorter palates than expected.
Although for total palate length the macaques are fairly evenly split: male and female M. fascicularis are below the line, male and female M. mulatta are above the line, while the sexes are split for the remaining two macaque species (Figure 4-49). Theropithecus and Lophocebus also show diversity based on the length dimensions examined. For palatine palate length
Theropithecus is above the line while Lophocebus is below (Figure 4-50); for maxillary palate length Theropithecus is below while Lophocebus is above (Figure 4-51); and for total palate length Theropithecus is below while Lophocebus has males above and females slightly below the regression line (Figure 4-49). The Cercocebus groups mostly fall above the line so they exhibit longer palates than expected.
For the palatal width (Figure 4-52), breadth (Figure 4-53, Figure 4-54), and depth (Figure
4-55) dimensions there are few discernible patterns in the papionins. One consistent observation
107
is that male and female T. gelada always fall below the regression line indicating palates that are narrower and shallower than expected based on upper facial height. One trend observed is that male papionins generally scale above the regression line for palate width while females fall below the regression line (Figure 4-52). This indicates that males have palates that are wider than expected based on upper facial height while females have narrower palates than expected based on the regression line. A similar trend is observed for palate depth (Figure 4-55). Males have deeper palates than expected while females have shallower palates. The last trend observed is that most of the Cercocebus species fall above the line for external palate breadth (Figure 4-
53) but the same is not true for internal palate breadth (Figure 4-54).
However, care must be taken in the interpretation of these graphs since all of these dimensions exhibit negative allometry. This means that no inferences relative to the regression line can be made with respect to geometric similarity. Only relative size differences between specific traits can be observed based on the calculated ratios.
Colobines
For the colobines, most of the RMA regressions of palatal dimensions versus upper facial height yield an isometric relationship. Two exceptions include maxillary palate length (Figure 4-
56) and total palate length (Figure 4-57) which yield positive allometry. The positive allometric relationship indicates that the palate lengthens disproportionately to upper facial height.
For palate width, all males exhibit wider palates while the females show palates that are narrower than expected (Figure 4-58). External and internal palate breadth dimensions show species differences instead of sex differences (Figure 4-59, Figure 4-60). For these two variables, P. badius exhibits a narrower palate while the remaining species all fall above the regression line indicating a larger palate than expected. Palate depth also exhibits sex
108
differences for P. verus and C. guereza (Figure 4-61). The females of these species have deeper palates compared to the males which exhibit shallower palates. C. polykomos falls above the regression line for palate depth while P. badius falls below the line.
The palatal length dimensions produce variable results. Male and female C. polykomos, female P. verus, and male C. guereza have longer palatine palate lengths than expected (Figure
4-62). However, this pattern changes for maxillary palate length and total palate length. For both of these variables, C. guereza falls above the line while P. badius falls below. P. verus and C. polykomos separate by sex. For total palate length, the females of both species exhibit longer palates than expected while the males have shorter palates (Figure 4-57). Although the same is true for C. polykomos for maxillary palate length, the results for P. verus reverse so that the males have a longer maxillary palate length while the females have a shorter maxillary palate length (Figure 4-56).
Except for palate width, P. badius always falls below the regression line for upper facial height. This is similar to when palatal dimensions were regressed against facial width. This indicates that P. badius have narrower, shorter, and shallower palates than other colobines.
Hominoids
The predominate trend seen in the RMA regression of palatal dimension versus upper facial height is negative allometry. The only exception is palatine palate length which yields no significant relationship (Figure 4-63). Maxillary and total palate lengths are split relative to the regression line mostly by species. For maxillary palate length H. lar, P. pygmaeus, and G. gorilla have longer palates than expected while H. syndactylus and P. troglodytes have shorter palates than expected (Figure 4-64). When examining total palate length, H. lar shows sex
109
differences (males below the line, females above) (Figure 4-65). G. gorilla and H. syndactylus are above the line and P. troglodytes and P. pygmaeus are below.
Palatal width/breadth dimensions show mostly sex differences except for internal palate breadth which is split by species. For palate width, males exhibit wider anterior palates while females exhibit narrower anterior palates (Figure 4-66). Two exceptions to this are P. troglodytes females which are wider than expected and P. pygmaeus males which are narrower than expected. External palate breadth shows the opposite trend (Figure 4-67). Females have broader posterior palates than males, except for female H. lar and female P. pygmaeus which fall below the regression line. Internal palate breadth is split by species (Figure 4-68). H. lar, P. troglodytes, and P. pygmaeus are above the regression line while H. syndactylus and G. gorilla are below the line.
Gorillas and H. syndactylus show sex differences for palate depth (Figure 4-69). Females have deeper palates than expected and males have shallower palates. H. lar and P. pygmaeus are above the regression line and P. troglodytes are below the regression line. There is no discernible pattern with the hominoids for upper facial height versus palate depth other than the generalizations that were noted.
Upper Facial Height Summary
Colobines and papionins as well as colobines and hominoids vary significantly between all of the palatal dimensions and upper facial height (Table 4-22). Papionins and hominoids only show significant differences between upper facial height and palate depth, external palate breadth, and internal palate breadth. This indicates that papionins and hominoids are similar in palatal lengths, but vary when considering breadth and depth.
110
For the ratio comparison, the colobines versus the papionins and hominoids yielded significant differences in slope for all palatal dimensions so no overall comparisons can be made
(Table 4-23). The papionins and hominoids do share similar slopes for palate width, and all three length measurements. The ratios show that the hominoid palates are wider and longer compared to the papionins.
Total Facial Height
Papionins
All but one palatal dimension shows a negatively allometric relationship to total facial height. Maxillary palate length exhibits isometry (Figure 4-70). For maxillary palate length the macaques fall below the regression line except for M. fascicularis. The Cercocebus species fall above the regression line while the baboons are evenly split. Palatine palate length shows a different pattern (Figure 4-71). For this dimension, most of the macaques are above the regression line while most of the baboons are below. Cercocebus groups are split mostly by species except for C. atys which is split by sex. Total palate length exhibits the same trends as maxillary palate length (Figure 4-72). This indicates that macaques have shorter palates than expected while Cercocebus have longer palates than expected. Mandrills always fall above the line for each of these palatal length variables meaning their palates are longer than expected based on total facial height.
When examining palate depth all of the macaques except M. sylvanus, the majority of the baboons, and L. albigena exhibit deeper palates than expected (Figure 4-73). Cercocebus groups are split by sex: the males have deeper than expected palates while the females have shallower palates. M. sphinx and T. gelada both fall below the regression line.
111
For the width and breadth palatal dimensions, the papionins exhibit diversity. For palate width, baboons are split while most of the macaques are below the regression line and most of the Cercocebus are above the regression line (Figure 4-74). L. albigena and M. sphinx have wider anterior palates than expected while T. gelada have narrower anterior palates than expected based on total facial height. External and internal palate breadth exhibit similar scaling patterns with two noticeable differences. For both variables, the macaques are split, the baboons fall mostly above the regression line, and T. gelada falls below the regression line. The two differences are seen in the Cercocebus groups and in L. albigena. For external palate breadth,
Cercocebus groups mostly fall above the regression line while L. albigena falls below (Figure 4-
75). The opposite pattern is observed for internal palate breadth: L. albigena is above the line while most of the Cercocebus is below (Figure 4-76).
Regardless of palatal dimension regressed against total facial height, T. gelada always fell below the regression line. So compared to other papionins, T. gelada have narrower, shorter, and shallower palates.
Colobines
The results of the RMA regressions in terms of allometric relationships for total facial height are identical to those seen in the colobine results for upper facial height. Palate width
(Figure 4-77), palate depth (Figure 4-78), external palate breadth (Figure 4-79), internal palate breadth (Figure 4-80), and palatine palate length (Figure 4-81) exhibit isometry, while maxillary palate length (Figure 4-82) and total palate length (Figure 4-83) exhibit positive allometry.
The results for palate width versus total facial height are identical to those results observed for upper facial height. Each species separated by sex with the females exhibiting narrower anterior palates and the males exhibiting wider anterior palates (Figure 4-77). The
112
results for palate depth were also the same as those seen for upper facial height (Figure 4-78).
Differences develop however when observing the remaining palatal dimensions.
External palate breadth shows a sex difference for only P. verus: males are broader than females (Figure 4-79). C. guereza and C. polykomos exhibit broader posterior palates than expected while P. badius falls below the regression line indicating narrower posterior palates.
For internal palate breadth, the same pattern is observed for C. polykomos and P. badius, but P. verus shows no sex differences and C. guereza does (Figure 4-80). P. verus have broader internal palate breadths than expected while the same is true for female C. guereza but not males.
Palatal length dimensions yield differing results from each other. Total palate length has the most discernible pattern with all of the females having palates longer than expected while the males have palates that are shorter (Figure 4-83). The results for palatine palate length are similar except male C. polykomos also falls above the regression line while female C. guereza falls below (Figure 4-81). Other than these two groups, the remaining groups above the line are female while the remaining groups below the regression line are male. Maxillary palate length separates more by species than sex (Figure 4-82). Only P. badius show sex differences: males below the regression line and females above the line. P. verus falls below the line while the remaining species fall above the line.
Hominoids
These results were similar to those of upper facial height: negative allometry except for palatine palate length which is not significant. The distribution of the groups around the regression line was also very similar to those seen for upper facial height as well. The only difference was for internal palate breadth which showed sex differences for H. lar (Figure 4-84).
The females were above the regression line while the males fell below.
113
Total Facial Height Summary
The overall group comparisons for total facial height are similar to upper facial height
(Table 4-22). Colobines scale differently in all palatal dimensions than papionins and hominoids. Hominoids and papionins only scale differently in three palatal dimensions: palate depth, maxillary palate length, and total palate length.
Since colobines differ significantly in slope from both groups no relative comparison can be made concerning the overall size of the palate (Table 4-23). For papionins and hominoids, the hominoids exhibit broader palates while the papionins are longer.
Skull Length
Papionins
RMA regressions for all of the palatal dimensions exhibit a positive allometry against skull length for papionins. Palatal length dimensions show varying patterns with maxillary palate length (Figure 4-85) being most similar to total palate length (Figure 4-86). For these two variables macaques exhibit shorter palates than expected while Cercocebus groups exhibit longer palates than expected. The baboons show more diversity in these two variables. For maxillary palate length, the majority of baboons are above the regression line while the baboons are split by sex for total palate length (males above the line and females below). So females have shorter overall palate length compared to the males. Palatine palate length shows opposite results from maxillary palate length: most macaques and Cercocebus are above the regression line while most of the baboons are below (Figure 4-87). T. gelada is always below the line for these variables.
For palate width (Figure 4-88) and depth (Figure 4-89), the macaques fall below the line except for M. fascicularis which is above. Cercocebus groups are split for palate depth, but fall mostly above the regression line for palate width so overall their anterior palates are wider than
114
expected. Baboons also show diversity in these variables. Baboons mostly have deeper palates than expected, but for palate width they are split. L. albigena have deeper and wider anterior palates while T. gelada have shallower and narrower anterior palates. M. sphinx is split based on sex. Males have wider and deeper palates while females have shallower and narrower palates.
External and internal palate breadth exhibit similar patterns: macaques and Cercocebus are split while all the baboons except for P. ursinus are above the line. L. albigena and T. gelada are both below the regression line for both variables while M. sphinx is split based on sex (Figure
4-90, Figure 4-91). Male mandrills have broader palates than expected while female mandrills have narrower palates than expected.
As with total facial height and facial width, T. gelada always fell below the regression line indicating that their palates are shorter, narrower, and shallower compared to other papionins.
Colobines
All RMA regressions of palatal dimensions versus skull length are positively allometric.
One noticeable trend is that P. verus exhibits sex differences in all of the palatal dimensions except for palate width. For palate width both male and female P. verus scale below the regression line (Figure 4-92). For the other dimensions, females scale above the line while males scale below. This means that the female palates are deeper, longer, and broader than expected.
The other species show more diversity.
Breadth/width palatal dimensions show sex differences more than species distinctions.
Palate width shows males have wider anterior palates and female palates are narrower anteriorly except for P. verus and C. polykomos. For external and internal breadth, females have broader posterior palates compared to the males except for C. guereza (Figure 4-93, Figure 4-94). This
115
species scales above the regression line so they have broader posterior palates than the males of the other colobine species. Internal palate breadth also shows both male and female P. badius scaling below the regression line (Figure 4-94).
Palatal length dimensions scale similarly as well. Maxillary and total palate length produce identical results which are mostly sex differences (Figure 4-95, Figure 4-96). Female colobines have longer palates than expected while males have shorter palates. The only exception is C. guereza. Both males and females exhibit longer palates than expected. Palatine palate length shows more diversity (Figure 4-97). C. polykomos scales above the regression line along with male C. guereza, female P. verus and female P. badius. Female C. guereza, male P. verus and male P. badius scale below the line.
Palate depth also shows sex distinctions (Figure 4-98). Females have deeper palates while the males have shallower palates than expected. Two exceptions are C. polykomos, which falls above the regression line, and P. badius, which falls below the regression line.
Hominoids
The predominate trend in these RMA regressions is not clear cut. Three of the seven regressions show positive allometry (palate depth (Figure 4-99), palate width (Figure 4-100), and maxillary palate length (Figure 4-101)), three show isometry (external palatal breadth (Figure 4-
102), internal palatal breadth (Figure 4-103), and total palate length (Figure 4-104)), and palatine palate length (Figure 4-105) shows no significant relationship to skull length.
Palate depth shows species distinctions but no sex differences. H. lar and P. pygmaeus have deeper palates than expected while H. syndactylus, P. troglodytes, and G. gorilla have shallower palates (Figure 4-99).
116
Palatal length measurements show species distinctions as well but no sex differences.
The distribution for maxillary palate length was identical to the distribution for palate depth
(Figure 4-101). The great apes have the same distribution for total palate length, but the lesser apes reversed positions. For total palate length H. syndactylus is longer while H. lar is shorter than expected (Figure 4-104).
Palate width/breadth dimensions show very little consistency among the three measurements. For palate width the great apes sort by species (orangutans and chimpanzees are above the regression line while gorillas are below the line) (Figure 4-100). The lesser apes are separated by sex; the males have wider anterior palates than expected while the females have narrower anterior palates. External and internal palate breadth is separated by sex and species.
Orangutans are above the line for internal palate breadth as well as the female chimpanzees and
H. lar. Male chimpanzees, male H. lar, H. syndactylus, and gorillas are below the regression for internal palate breadth (Figure 4-103). Gorillas, orangutans, male chimpanzees, and male H. syndactylus have narrower external palate breadths than expected while female chimpanzees, female H. syndactylus, and H. lar (males and females) have wider external palate breadths
(Figure 4-102). There is no clear cut pattern that can be observed based on the palate width/breadth measurements.
Skull Length Summary
For skull length, papionins and colobines scale similarly in their palatal dimensions with only two exceptions (Table 4-22). Palate depth and internal palate breadth show significant differences in slopes for colobines and papionins. Colobines and hominoids are significantly different for all palatal dimensions. Papionins and hominoids show significant differences for
117
palatal dimensions except for palate depth and external palate breadth. Overall palatal lengths between papionins and hominoids are similar.
Based on ratio comparisons, papionins exhibit wider, broader, and longer palates than colobines while colobines and hominoids cannot be relatively compared due to significant differences in slopes (Table 4-23). For papionins and hominoids, the hominoids exhibit deeper palates while the papionins possess broader palates.
Bipterygoid Breadth
Papionins
RMA regressions of palatal dimensions versus bipterygoid breadth are identical to the results of palatal dimensions regressed against facial width. External palate breadth (Figure 4-
106), internal palate breadth (Figure 4-107), palate depth (Figure 4-108), and palatine palate length (Figure 4-109) exhibit isometry while the remaining three variables (palate width (Figure
4-110), maxillary palate length (Figure 4-111), and total palate length (Figure 4-112)) show positive allometry.
For palatal length dimensions, the macaques and the baboons are split above and below the regression line for maxillary and total palate length (Figure 4-111, Figure 4-112).
Cercocebus tends to fall below the regression line for all three length variables indicating that they have shorter palates than expected based on bipterygoid breadth. T. gelada and M. sphinx consistently fall above the regression line for each of these variables indicating that they have longer palates than expected based on bipterygoid breadth. L. albigena exhibit shorter palates than expected based on the regression. For palatine palate length, most of the baboons fall below the regression line while the majority of macaques are above (Figure 4-109).
118
Palate width generally sorts by sex except for Cercocebus (Figure 4-110). All of the
Cercocebus fall below the regression line except for C. agilis which is above the line. Overall
Cercocebus have narrower anterior palates than expected based on bipterygoid breadth. The macaques, baboons, and T. gelada are mostly split so that the males exhibit wider anterior palates than expected while the females exhibit narrower anterior palates than expected.
Exceptions to this are M. fuscata and P. ursinus. Both males and females of these species along with L. albigena exhibit narrower anterior palates than expected based on bipterygoid breadth.
External and internal palate breadths exhibit similar patterns to those observed with palate width.
Palate depth shows diversity in the distribution of groups above and below the regression line (Figure 4-108). The macaques are mostly below the regression line except for female M. fuscata and all of M. fascicularis. The Cercocebus groups are also mostly below the regression line except for male C. atys and male C. agilis indicating deeper palates than expected. Male P. papio and male P. ursinus exhibit deeper palates than expected while the remaining baboon groups fall below the regression line. Mandrillus and Theropithecus exhibit deeper palates while
Lophocebus is split with males above the line and females below.
Colobines
RMA regression results for bipterygoid breadth are identical in terms of allometry to both total and upper facial height. Palate width (Figure 4-113), palate depth (Figure 4-114), external palate breadth (Figure 4-115), internal palate breadth (Figure 4-116), and palatine palate length
(Figure 4-117) exhibit isometry, while maxillary palate length (Figure 4-118) and total palate length (Figure 4-119) exhibit positive allometry.
Palate width exhibits sex differences for each of the colobine species (Figure 4-113). The males have wider anterior palates based on bipterygoid breadth while the females have narrower
119
anterior palates than expected. C. polykomos scales differently based on sex for both internal and external palate breadths: males have broader posterior palates than expected while females have narrower posterior palates than expected. P. badius show sex differences for internal palate breadth but for external palate breadth both males and females are found below the regression line. Both male and female P. verus and C. guereza sit above the regression line indicating broader posterior palates than expected.
Palatal length dimensions show differences between variables. Maxillary and total palate lengths are the most similar (Figure 4-118, Figure 4-119). For both of these measurements, C. guereza and male P. badius have relatively longer palates while C. polykomos and female P. badius have shorter palates. P. verus differs between the two variables. For maxillary palate length the males are longer while the females are shorter, but for total palate length females have longer palates than expected while males are shorter. Palatine palate length P. badius have shorter palatine palates as do the females of C. guereza and C. polykomos. The males of C. guereza and C. polykomos have longer palatine palates (Figure 4-117).
P. badius exhibit shallower palates than expected while C. guereza exhibit deeper palates than expected based on the regression line (Figure 4-114). P. verus and C. polykomos are split by sex but in different directions. Male C. polykomos and female P. verus possess deeper palates while female C. polykomos and male P. verus possess shallower palates than expected.
Hominoids
The results for the RMA regressions for hominoid bipterygoid breadth were identical in terms of allometric relationships to those of skull length. Palate depth (Figure 4-120), palate width (Figure 4-121), and maxillary palate length (Figure 4-122) show positive allometry while external palate breadth (Figure 4-123), internal palate breadth (Figure 4-124), and total palate
120
length (Figure 4-125) show isometry. Palatine palate length shows no significant relationship to bipterygoid breadth (Figure 4-126).
Sex differences are observed for palate depth (Figure 4-120). Females have deeper palates than expected while males have shallower palates. Two exceptions are male H. lar which scales above the regression line and female P. troglodytes which scale below the line.
Palatal width/breadth dimensions show some sex and species distinctions. H. syndactylus have wider anterior palates while H. lar have narrower anterior palates than expected. The great apes show sex differences but not consistently. Male chimpanzees and gorillas scale above the regression line as well as female orangutans. Female chimpanzees and gorillas have narrower anterior palates than expected as do male orangutans. For external and internal palate breadths, gorillas and H. syndactylus scale above the regression line while chimpanzees scale below the line (Figure 4-123, Figure 4-124). Orangutans are split by sex with females having broader posterior palates and males having narrower posterior palates than expected. H. lar differs between the two measurements. For external palate breadth this species have narrower posterior palates. For internal palate breadth, male H. lar has a narrower internal palate breadth while females have a broader internal palate breadth.
The distributions for palatal length measurements mimic those of the external and internal palate breadths. Maxillary palate length (Figure 4-122) has the same distribution as internal palate breadth while total palate length (Figure 4-125) has the same distribution as the external palate breadth.
Bipterygoid Breadth Summary
Comparing the phylogenetic groups using RMA2 analysis shows that there are no significant differences between colobines and papionins or hominoids for palatal dimensions
121
regressed against bipterygoid breadth (Table 4-22). Papionins and hominoids show significant differences for palate width, maxillary palate length, and total palate length. The remaining palatal variables exhibit no significant differences.
Bipterygoid breadth exhibits similar slopes for all of the palatal dimensions for colobines versus papionins and colobines versus hominoids (Table 4-23). For papionins versus hominoids, there are only 3 significant slope differences. Hominoids and papionins possess wider and deeper palates relative to colobines. The hominoids contain deeper palates relative to papionins.
For breadth and length, papionins are broader and longer compared to colobines and hominoids.
When examining the ratios for colobines versus hominoids conflicting results are seen.
Colobines have a broader external palate breadth than hominoids but the opposite is true for internal palate breadth. Hominoids show a longer maxillary palate length while colobines have a longer palatine palate length and total palate length.
Overall Scaling Analysis Summary
The palates of the primates analyzed in this study show inconsistent differences based on their phylogenetic grouping. In other words, who is relatively bigger or smaller, shorter or longer, etc. depends on which skull or facial measurement is used as a size proxy. For example, when examining external palate breadth and facial width, hominoids have relatively broader posterior palates than colobines and papionins but when examining this same palatal dimension against bipterygoid breadth the opposite is true.
Papionins and colobines often scale differently making comparisons of overall size differences difficult but generally speaking papionins exhibit relatively larger palatal dimensions compared to the colobines regardless of size dimension. This means the papionins possess relatively longer, wider, and deeper palates compared to colobines.
122
Colobines and hominoids also scale differently for most of the size dimensions except for facial width and bipterygoid breadth. Facial width is discussed above. For bipterygoid breadth, colobines exhibit a relatively broader external palate breadth but narrower internal palate breadth compared to hominoids. For palatal length, hominoids possess a relatively longer maxillary palate length than colobines but shorter palatine palate length and total palate length. This indicates that overall, colobines have a relatively longer palate compared to hominoids.
Papionins and hominoids scale similarly in most respects so more generalizations can be made based on ratios of palatal variables; however these generalizations vary based on the size dimension examined. When palatal dimensions are regressed against cranial dimensions (skull length and bipterygoid breadth), hominoids exhibit relatively deeper, narrower, and shorter palates compared to the papionins. For the facial dimensions (facial width, upper facial height, and total facial height), the generalizations are not as clear cut. All three facial dimensions show hominoids as possessing relatively broader and deeper palates compared to the papionins.
Conflicting results are seen with length among the facial dimensions. Based on facial width and total facial height, hominoids have relatively shorter palates than papionins. Based on upper facial height, the hominoids have relatively longer palates. Overall the hominoids exhibit relatively shorter and deeper palates than the papionins. Relative breadth differs depending on whether or not the size measurement is based on the skull or the face.
Sutural Complexity Analysis
Sutural complexity was examined in the comparative samples to determine whether or not there were any significant differences between species, among phylogenetic groups or groups based on dietary consistency. The sample sizes differed slightly from the scaling analysis due to several factors, mostly because of suture fusion (Tables 4-24 and 4-25). The most notable
123
difference is that Cercocebus atys was not included in the analysis because all of the specimens for this species had fused sutures. Sex differences were also examined since most of these groups exhibit sexual dimorphism. Mann-Whitney U tests were run on each species and the significance values are located in Table 4-26. Most groups showed no significant differences between the sexes so for all further analyses the sexes are pooled. Seven species were excluded from the statistical analysis due to either no females present (P. papio and P. hamadyas) or because either the male or female specimens were too few to evaluate statistically (P. troglodytes, H. lar, C. guereza, G. gorilla and M. fuscata).
Kruskal-Wallis tests were performed between the suture fractal dimension and species
(P-value = 0.03) and then for the suture length ratio and species (P-value < 0.001). Given these significant results the next question was which species were significantly different from each other. To answer this question, a series of Mann-Whitney U tests were completed (Tables 4-27 and 4-28). The values with asterisks in Tables 4-27 and 4-28 show the significant results at a P- value < 0.05. For the fractal dimension, Colobus polykomos and Lophocebus albigena significantly differ from the majority of other species. For the suture length ratio, the picture was unclear (Table 4-28). More species have significantly different suture length ratios from each other, but there is no discernible pattern. The results for both the fractal dimension and suture length ratio analysis did not conform to expectations. The expectations were that a discernible pattern would arise based on either phylogeny or dietary consistency.
In an effort to discover a pattern between the species sutural differences, Kruskal-Wallis tests were conducted on 2 different groupings. For the first group the species were divided into the following phylogenetic groupings: Cercocebus-Mandrillus group (Cercocebus agilis,
Cercocebus torquatus, Mandrillus sphinx), Lophocebus-Papio group (Lophocebus albigena,
124
Papio anubis, Papio hamadryas, Papio papio, Papio ursinus, Theropithecus gelada), macaque group (Macaca fascicularis, Macaca fuscata, Macaca mulatta, Macaca sylvanus), colobine group (Colobus guereza, Colobus polykomos, Procolobus badius, Procolobus verus), and hominoid group (Hylobates lar, Hylobates syndactylus, Pan troglodytes, Pongo pygmaeus,
Gorilla gorilla). The results of the Kruskal-Wallis tests performed on the phylogenetic groups versus fractal dimension (P-value = .048) and phylogenetic groups versus suture length ratio (P- value < 0.001) showed significant differences. To determine exactly which groups differed,
Mann-Whitney U tests were performed. The results are reported in Table 4-29 with the P-values
< 0.05 denoted by an asterisk.
The results from the fractal dimension and suture length ratio differ in terms of which groups are significant. For the fractal dimensions, the Cercocebus-Mandrillus group only differs significantly from the colobines. When examining the suture length ratio for this same group, it differs significantly from all of the groups except Lophocebus-Papio. The suture length ratio of the Lophocebus-Papio group differs significantly from all of the groups except for the
Cercocebus-Mandrillus group, while the fractal dimension differs significantly from the colobines and macaques. For the macaque group, the fractal dimension results show significant differences when compared to the Lophocebus-Papio group only, while the suture length ratio results show significant differences between the Lophocebus-Papio group and the Cercocebus-
Mandrillus group. The hominoids do not differ from any of the other groups for the fractal dimension; however, their suture length ratio differs significantly from both the Cercocebus-
Mandrillus and Lophocebus-Papio groups. These results did not meet expectations, which were
1) that the results would be the same for both the fractal dimension and suture length ratio and 2) that there would be differences based on phylogenetic groups. Significant differences between
125
the groups differed depending on how suture complexity was measured. There was also no clear pattern based on phylogeny among the significantly different groups.
The second grouping of species was based on phylogeny and dietary consistency. Mann-
Whitney U tests were performed to determine if there were significant differences between groups with a soft diet and groups with a hard diet (Table 4-30). The expectation was that each dietary contrast group would show significantly different suture complexity. The first dietary contrast tested was between the genus Mandrillus (hard diet) and Papio (soft diet). There was not a significant difference in sutural complexity between these groups regardless of how it was measured. The second dietary contrast tested was between Colobus polykomos and the remaining colobines (C. guereza, P. badius, P. verus). C. polykomos has a tougher diet compared to the remaining colobine species. These groups showed significant differences in sutural complexity in terms of fractal dimension and suture length ratio in the expected direction, i.e. hard diet group had more complex sutures. The final groups tested for differences based on dietary consistencies were Pongo pygmaeus versus the hylobatids (H. lar and H. syndactylus).
P. pygmaeus has been observed eating harder objects in their diet compared to the hylobatids.
The results were mixed for this contrast. According to fractal dimension, there was no difference in sutural complexity but suture length ratio detected a difference.
Since the results for the Mandrillus-Papio contrast were unexpected and the Pongo-
Hylobates contrast yielded conflicting results, these species were re-grouped and the Mann-
Whitney U tests were repeated. For this set of tests, the Lophocebus-Papio (soft diet) group was contrasted with the Cercocebus-Mandrillus (hard diet) group. The second contrast was between
Pongo pygmaeus and the remaining hominoids (Hylobates lar, Hylobates syndactylus, Pan troglodytes, Gorilla gorilla). The fractal dimension was not significantly different for either of
126
the contrasts, while the suture length ratio was significantly different for both contrasts (Table 4-
30).
The last set of statistical procedures conducted on the suture complexity measures were reduced major axis (RMA) regressions using the software developed by Bohonak and van der
Linde (2004). The skull measurements of the specimens were regressed against the fractal dimension and the suture length ratio. For these regressions, the species were divided into 3 phylogenetic groups: the colobines, the papionins, and the hominoids. These are the same groupings that were used for the allometric scaling analysis. Expectations were that suture complexity and palatal dimensions would be correlated given the two assumptions that 1) the dimensions of the palate influences the mechanical environment and 2) mechanical environment influences suture complexity.
The results varied based on the groups. For the colobines if the r value was greater than
0.707 then the correlation was significant between the 2 variables. Table 4-31 shows the results for all of the colobine regressions performed. Out of 24 regressions performed, none of the variables were significantly correlated.
For the papionins if the r value was greater than 0.404 then the correlation was significant. Table 4-32 shows the results for all of the papionin regressions performed. None of the regressions against the fractal dimension yielded significant results, while all of the suture length ratio regressions for the papionins showed significant correlations.
The final set of regressions was performed on the hominoids. If the r value for the hominoids was greater than 0.632 then the correlation was significant. Table 4-33 shows the results for all of the hominoid regressions performed. None of the regressions performed yielded significant correlations.
127
Sutural Complexity Analysis Summary
When comparing individual species to each other, no discernible pattern emerges for the species that are significantly different. The species were then grouped according to their phylogenetic relationships. Although some significant differences were detected among the phylogenetic groups, they differed depending on which sutural complexity measure was used.
Once phylogeny was controlled for more precisely, the sutural differences observed for the dietary contrast groups conformed more to expectations. In other words, as long as you take phylogeny into account, harder diets do seem to yield more complex mid-palatal sutures. How suture complexity is measured needs to be considered since different techniques yielded different results.
The RMA regressions yielded varying results. For the colobines and hominoids, none of the facial and palatal measurements regressed against the suture complexity measures yielded significant correlations. The papionin results were mixed. None of the fractal dimension regressions were significantly correlated, while all of the suture length ratio correlations were significant.
128
900
850
800
750
) 3 700
650
Density (mg/cm 600
550
500
450
400
Mid-palatal Suture to Tooth
Figure 4-1. Density gradient from mid-palatal suture to tooth for representative coronal section.
129
Table 4-1. Descriptive statistics for elastic moduli (GPa) values from the nanoindentation section. Number of Indentations Mean (s.d.) Range Minimum Maximum 180 8.45 (5.12) 38.11 0.023 38.14
Figure 4-2. Microindented specimen 1. Numbers correspond to the locations of the indentations.
130
Figure 4-3. Microindented specimen 2. Numbers correspond to the locations of the indentations.
131
Figure 4-4. Microindented specimen 3. Numbers correspond to the locations of the indentations.
132
Figure 4-5. Microindented specimen 4. Numbers correspond to the locations of the indentations.
133
Figure 4-6. Microindented specimen 5. Numbers correspond to the locations of the indentations.
134
Figure 4-7. Microindented specimen 6. Numbers correspond to the locations of the indentations.
135
Figure 4-8. Microindented specimen 7. Numbers correspond to the locations of the indentations.
136
Table 4-2. Elastic moduli values from section 1 calculated from microindentation. Indent # E (GPa) 1 5.715734 2 13.1909 3 11.83721 4 9.500311 5 6.576631 6 8.959069 7 10.81593 9 11.55041 10 10.38628 11 9.448972 12 11.62108 Mean (s.d.) 9.963866 (2.26)
137
Table 4-3. Elastic moduli values from section 2 calculated from microindentation. Posterior End Anterior End Indent # E (GPa) Indent # E (GPa) 1 7.32165 1 11.1403 2 11.3424 2 12.8512 3 6.12119 3 11.5504 4 5.27349 4 11.9848 5 8.6399 5 11.8372 6 9.60434 6 11.6924 7 14.5989 7 9.39807 8 14.8043 8 10.5062 9 9.15004 9 10.3863 10 7.93669 10 11.5504 11 12.9349 11 12.1354 12 13.455 12 11.6924 13 13.7275 13 9.1988 14 11.9848 14 11.0088 15 11.4804 15 12.1354 16 10.6284 16 12.9349 17 13.3661 17 14.3979 18 12.6054 18 12.1354 19 14.5989 19 12.6054 20 13.914 20 11.5504 21 19.4329 21 13.278 22 21.3043 22 9.39807 23 11.6211 23 9.00621 24 10.1528 24 14.3979 25 10.7528 25 12.7685 26 23.4689 27 13.278 27 13.8202 28 12.7685 28 9.76382 Mean (s.d.) 11.7625 (1.44) 29 8.05392 30 9.39807 31 9.24798 32 22.6441 33 13.8202 34 16.6233 Mean (s.d.) 12.4586 (4.36)
138
Table 4-4. Elastic moduli values from section 3 calculated from microindentation. Indent # E (GPa) 1 12.9349 2 17.9432 3 16.3774 4 17.6665 5 12.1354 6 11.4111 7 13.1047 8 13.455 9 15.2289 10 15.0143 11 13.8202 12 13.8202 13 16.6233 14 13.1047 15 18.8148 16 13.455 17 16.3774 18 19.4329 19 14.0087 20 13.6357 21 17.6665 22 12.1354 23 9.29758 24 9.92757 25 12.9349 26 12.289 27 13.1047 Mean (s.d.) 14.2859 (2.59)
139
Table 4-5. Elastic moduli values from section 4 calculated from microindentation. Indent # E (GPa) 1 15.2289 2 16.1371 3 14.8043 4 11.9848 5 9.1988 6 9.29758 7 6.69195 8 14.0087 9 15.4483 10 13.1047 11 16.1371 12 11.9848 13 11.9848 15 11.6924 16 12.289 17 15.2289 18 17.3963 19 9.60434 20 9.29758 21 12.1354 22 14.3979 23 14.3979 24 14.2012 25 17.9432 26 18.8148 27 13.8202 28 11.9848 29 12.289 30 10.3863 31 13.6357 33 8.91232 Mean (s.d.) 13.0464 (2.88)
140
Table 4-6. Elastic moduli values from section 5 calculated from microindentation. Indent # E (GPa) 1 15.2289 2 17.9432 3 13.8202 4 10.7528 5 13.278 6 17.6665 7 18.8148 8 20.4207 9 19.4329 10 15.2289 11 13.8202 12 16.8749 13 11.8372 14 10.0392 16 11.0088 18 18.5171 19 18.2266 20 17.9432 21 17.6665 Mean (s.d.) 15.7116 (3.22)
141
Table 4-7. Elastic moduli values from section 6 calculated from microindentation. Indent # E (GPa) 1 13.8202 2 13.8202 3 12.289 5 13.278 6 13.278 7 15.0143 8 16.6233 9 11.9848 10 14.3979 11 15.4483 12 15.4483 13 12.9349 14 13.455 15 13.455 16 11.5504 18 16.8749 19 12.1354 21 11.4111 22 13.278 23 15.6728 24 13.455 25 11.9848 Mean (s.d.) 13.7095 (1.58)
142
Table 4-8. Elastic moduli values from section 7 calculated from microindentation. Indent # E (GPa) 1 13.1047 2 12.4456 3 12.4456 4 9.60434 6 10.6284 7 13.1047 8 16.1371 9 17.9432 10 13.6357 11 15.4483 12 13.278 13 13.278 14 10.1528 18 14.0087 19 14.5989 20 16.1371 21 13.1047 23 13.6357 Mean (s.d.) 13.4829 (2.12)
143
750
y = -15.646x + 3937.8 700 R2 = 0.1951 p = 0.201
650
)
3
600
550
Bone Density(mg/cm
500
450
400 12 13 14 15 16 17 18 19 20
Elastic Modulus (GPa)
Figure 4-9. Regression of bone density versus elastic modulus from section 5. The r-value shows a poor correlation between these two variables.
144
800
y = -1.5271x + 3813.8
R2 = 0.0025
750 p = 0.890
700
) 3
650
Density (mg/cm 600
550
500 12 13 14 15 16 17 18 19 20 Elastic Modulus (GPa)
Figure 4-10. Regression of bone density versus elastic modulus from section 7. The r-value shows a poor correlation between these two variables.
145
Table 4-9. Maximum strain at different gage locations in the pigs. Gage Maximum Strain (µσ) Specimen 1 Specimen 2 Specimen 3 Element 1 Strip Gage 92 279 72 Element 2 Strip Gage 74 -2485 76 Element 3 Strip Gage 4170 -2490 93 Element 4 Strip Gage 88 -2326 -638 Element 5 Strip Gage 64 -2385 -1105 Single Element 1 10 -2069 NA Single Element 1 180 -2504 133 Single Element 1 57 207 628 Single Element 1 56 95 361 Single Element 1 55 166 550 *Rosette 1 372 -219 617 *Rosette 2 161 -396 552 *Rosette 3 316 -424 972 *Rosette 4 2957 163 572 Load (N) at which strain 352 974 759 was achieved *For rosette gages the maximum principal strain is reported.
146
Figure 4-11. Theoretical versus observed strains in the pig specimens during bending.
147
Specimen 1 Specimen 2 Specimen 3
4 3
2
1
Figure 4-12. Maximum principal strain directions for all pig specimens during bending.
148
Figure 4-13. Idealized geometries used to calculate predicted stress for macaque loading.
F
Figure 4-14. Gage classification by positions. Position 1 is anterior and position 3 is posterior.
149
Table 4-10. Position 1 predictions and observed strain. Observed µε Shape I (mm4) Predicted σ (MPa) Predicted µε Right Gage Left Gage Trapezoid 24359 0.0004 28 Thin Annulus 5018 0.0014 111 80 176 HollowEllipse 2666 0.0020 152
Table 4-11. Position 2 predictions and observed strain. Observed µε Shape I (mm4) Predicted σ (MPa) Predicted µε Right Gage Left Gage Trapezoid 28515 0.0004 28 Thin Annulus 10603 0.0011 82 274 144 HollowEllipse 7391 0.0013 101
Table 4-12. Position 3 predictions and observed strain. Observed µε Shape I (mm4) Predicted σ (MPa) Predicted µε Right Gage Left Gage Trapezoid 231454 0.0001 8 Thin Annulus 17457 0.0012 99 311 373 HollowEllipse 22640 0.0008 69
Figure 4-15. Predicted stress at each gage position in for each idealized geometry.
150
Figure 4-16. Five µCT scans of macaque skull used to estimate moment of inertia. They begin anteriorly at slice 1 and proceed posteriorly to slice 5.
Table 4-13. Predicted stress and strain values from hand calculated moment of inertia Slice I (mm4)Predicted σ (MPa) Predicted µε 1 47828 0.00007 5 2 26094 0.0001 8 3 102924 0.0001 8 4 98830 0.00007 6 5 (with zygomatic bone) 292169 0.00008 7 5 (without zygomatic bone) 273478 0.00009 7.5
151
Figure 4-17. Maximum principal strain directions during incisor loading.
Table 4-14. Expected versus observed strain ratios during macaque bending. Gage Location Expected Strain Ratio Observed Strain Ratio Palate << 1 1 Maxilla (alveolar process) 1 0.55 Interorbital 0.3 0.05
Table 4-15. Shear and principal strain ratios for pig specimens in torsion. Specimen 1 Specimen 2 Specimen 3 Gages Shear Principal Shear Principal Shear Principal Strain Ratio Strain Ratio Strain Ratio Rosette 1 178 2.93 226 -0.69 193 -10.35 Rosette 2 599 -0.73 737 -0.34 271 -1.13 Rosette 3 1059 -0.96 735 -0.55 433 -1.11 Rosette 4 NA* NA* 52 -0.41 163 -1.51 Load (Nm) at 53 11 10 measurement *This gage malfunctioned in an earlier experiment.
152
350
Tension vs Load
300
R1 R2 250 R3 R4 R5 R6 200 SE 1 SE 2 ) ε SE 3
150
(µ strain Tensile 100
50
0 -5.7465 -6.9658 -13.062 -15.5005 -17.939 -20.3775 -26.4738 -27.0834 -35.0085 -37.447
-50 Load (N)
Figure 4-18. Tension versus load for right molar loading.
153
250
Tension vs Load
R1
200 R2
R3 R4 R5 R6 SE 1
) 150 ε SE 2 SE 3
(µ strain Tensile 100
50
0 -10.6235 -19.7679 -24.0353 -28.9123 -30.1315 -32.57 -36.2278 Load (N) Figure 4-19. Tension versus load for left molar loading.
154
Figure 4-20. Theoretical versus observed strain during torsion for the pig specimens.
155
Specimen 1 Specimen 2 Specimen 3
98 -65 228 -205
144 -127
176 -20
Figure 4-21. Maximum principal strain direction during torsion. Arrows indicate direction of maximum principal strain for each specimen. Rosette 4 malfunctioned before strain was recorded for specimen 1.
156
1200
Shear vs Load Clockwise Twist
1000 R1 shear R2 shear R3 shear R4 shear 800 R5 shear R6 shear
600 Shear
400
200
0 -8 -12 -16 -20 -24 -26 -33 Load (N)
Figure 4-22. Shear versus load for the macaque cranium during clockwise twisting.
157
Table 4-16. Position 1 shear predictions for the macaque cranium during twisting. Observed Shear Shape Predicted Shear Right Gage Left Gage Circle 198 744 966 Ellipse 253
Table 4-17. Position 2 shear predictions for the macaque cranium during twisting. Observed Shear Shape Predicted Shear Right Gage Left Gage Circle 224 936 648 Ellipse 86
Table 4-18. Shear strains and principal strain ratios for the macaque during twisting Macaque Gages Shear Principal Strain Ratio Rosette 1 936 -1.637 Rosette 2 648 -0.988 Rosette 3 744 -1.884 Rosette 4 966 -0.668 Rosette 5 465 -1.422 Rosette 6 479 -0.372 Load (Nm) 11.55
Figure 4-23. Maximum principal strain direction from clockwise twisting.
158
Figure 4-24. Strain at the suture versus bone on a pig cranium.
Figure 4-25. Strain at the mid-palatal suture and adjacent bone in the pig cranium.
159
600
Tensile Strain vs Load
500 R1 R2 R3 R4 400 R5 SE1 SE2 )
ε SE3 300 R6
200 (µ Strain Tensile
100
0 -10 -13 -14 -16 -18 -22 -25 -30 -33 -35 -36 -37
-100 Load (N)
Figure 4-26. Tensile strain versus load in the macaque during bending.
160
500 Shear on Teeth During Vertical Loading 450
400 R1 R2 R3 350 R4
300
250
Shear 200
150
100
50
0 LM3 LM2 LM1 LP3 LLI LCI RCI RLI RC RP3 RP4 RM1 RM2 RM3 Tooth Position
Figure 4-27. Shear at each tooth during vertical loading at 20N.
161
Table 4-19. Reduced major axis results for papionins. Size Measurement Palate Dimensions Allometry Intercept Slope Confidence Intervals R2 Palate Width Positive -0.9745 1.294 1.071 1.518 0.832 Palate Depth Isometry -1.1010 1.036 0.845 1.226 0.809 External Palate Breadth Isometry -0.1084 0.8964 0.765 1.028 0.878 Facial Width Internal Palate Breadth Isometry -0.6787 1.037 0.848 1.226 0.813 Maxillary Palate Length Positive -1.6060 1.663 1.445 1.882 0.903 Palatine Palate Length Isometry -0.7542 1.04 0.792 1.288 0.679 Total Palate Length Positive -1.0100 1.439 1.252 1.625 0.905 Palate Width Negative 0.3681 0.6437 0.5507 0.7368 0.882 Palate Depth Negative -0.0272 0.515 0.4398 0.5903 0.880 External Palate Breadth Negative 0.8214 0.4458 0.3914 0.5002 0.916 Upper Facial Height Internal Palate Breadth Negative 0.3970 0.5157 0.4419 0.5896 0.885 Maxillary Palate Length Negative 0.1197 0.8272 0.7659 0.8884 0.969 Palatine Palate Length Negative 0.3243 0.5171 0.4049 0.6292 0.735 Total Palate Length Negative 0.4824 0.7156 0.6657 0.7654 0.973 Palate Width Negative -0.03396 0.811 0.6849 0.9371 0.864 Palate Depth Negative -0.3489 0.6489 0.5521 0.7456 0.875 External Palate Breadth Negative 0.5430 0.5616 0.4867 0.6366 0.900 Total Facial Height Internal Palate Breadth Negative 0.0749 0.6497 0.5427 0.7568 0.847 Maxillary Palate Length Isometry -0.3970 1.042 0.9600 1.124 0.965 Palatine Palate Length Negative 0.0010 0.6514 0.5059 0.7969 0.719 Total Palate Length Negative 0.0354 0.9015 0.8300 0.973 0.965 Palate Width Positive -2.100 1.86 1.4990 2.221 0.788 Palate Depth Positive -2.002 1.488 1.2220 1.755 0.819 External Palate Breadth Positive -0.8879 1.288 1.0980 1.479 0.877 Skull Length Internal Palate Breadth Positive -1.5800 1.49 1.2420 1.739 0.843 Maxillary Palate Length Positive -3.0520 2.39 2.0360 2.745 0.876 Palatine Palate Length Positive -1.6580 1.494 1.1760 1.812 0.744 Total Palate Length Positive -2.261 2.068 1.7900 2.346 0.898
162
Table 4-19. Continued Size Measurement Palate Dimensions Allometry Intercept Slope Confidence Intervals R2 Palate Width Positive -0.3226 1.524 1.051 1.997 0.458 Palate Depth Isometry -0.5798 1.219 0.890 1.549 0.588 External Palate Breadth Isometry 0.3431 1.056 0.767 1.344 0.580 Bipterygoid Breadth Internal Palate Breadth Isometry -0.1564 1.221 0.909 1.533 0.631 Maxillary Palate Length Positive -0.7679 1.958 1.401 2.516 0.544 Palatine Palate Length Isometry -0.2305 1.224 0.797 1.652 0.313 Total Palate Length Positive -0.2855 1.694 1.200 2.189 0.521
163
Table 4-20. Reduced major axis results for colobines. Size Measurement Palate Dimensions Allometry Intercept Slope Confidence Intervals R2 Palate Width Positive -1.581 1.623 1.087 2.158 0.891 Palate Depth Isometry -2.761 1.919 0.576 3.262 0.509 External Palate Breadth Isometry -0.7647 1.219 0.542 1.897 0.690 Facial Width Internal Palate Breadth Isometry -1.504 1.465 0.669 2.262 0.704 Maxillary Palate Length Positive -2.717 2.229 1.174 3.284 0.776 Palatine Palate Length Isometry -1.205 1.261 0.573 1.949 0.702 Total Palate Length Isometry -2.117 2.001 0.916 3.086 0.705 Palate Width Isometry -0.5321 1.253 0.593 1.914 0.722 Palate Depth Isometry -1.521 1.482 0.768 2.196 0.768 External Palate Breadth Isometry 0.02345 0.9417 0.616 1.267 0.880 Upper Facial Height Internal Palate Breadth Isometry -0.5565 1.132 0.682 1.582 0.842 Maxillary Palate Length Positive -1.276 1.722 1.329 2.114 0.948 Palatine Palate Length Isometry -0.3898 0.9739 0.623 1.325 0.870 Total Palate Length Positive -0.8228 1.545 1.164 1.926 0.939 Palate Width Isometry -0.7814 1.253 0.698 1.809 0.803 Palate Depth Isometry -1.815 1.482 0.747 2.218 0.753 External Palate Breadth Isometry -0.1638 0.9417 0.619 1.264 0.883 Total Facial Height Internal Palate Breadth Isometry -0.7815 1.132 0.722 1.542 0.868 Maxillary Palate Length Positive -1.619 1.722 1.258 2.185 0.927 Palatine Palate Length Isometry -0.5835 0.974 0.646 1.302 0.886 Total Palate Length Positive -1.13 1.545 1.100 1.99 0.917 Palate Width Positive -2.296 1.993 1.17 2.815 0.829 Palate Depth Positive -3.607 2.357 1.28 3.434 0.791 External Palate Breadth Positive -1.302 1.497 1.091 1.904 0.926 Skull Length Internal Palate Breadth Positive -2.15 1.8 1.344 2.255 0.936 Maxillary Palate Length Positive -3.7 2.737 1.983 3.492 0.924 Palatine Palate Length Positive -1.761 1.549 1.072 2.025 0.905 Total Palate Length Positive -2.998 2.457 1.683 3.231 0.901
164
Table 4-20. Continued Size Measurement Palate Dimensions Allometry Intercept Slope Confidence Intervals R2 Palate Width Isometry -0.0582 1.295 0.382 2.209 0.501 Palate Depth Isometry -0.96 1.532 0.818 2.246 0.782 External Palate Breadth Isometry 0.3796 0.9732 0.685 1.262 0.912 Bipterygoid Breadth Internal Palate Breadth Isometry -0.1285 1.17 0.626 1.713 0.784 Maxillary Palate Length Positive -0.6251 1.779 1.146 2.413 0.873 Palatine Palate Length Isometry -0.02154 1.006 0.701 1.312 0.908 Total Palate Length Positive -0.2384 1.597 1.127 2.067 0.913
165
Table 4-21. Reduced major axis results for hominoids. Size Measurement Palate Dimensions Allometry Intercept Slope Confidence Intervals R2 Palate Width Isometry -0.4455 1.045 0.961 1.129 0.99 Palate Depth Isometry -1.252 1.15 0.985 1.316 0.969 External Palate Breadth Isometry -0.1108 0.8976 0.795 1.001 0.98 Facial Width Internal Palate Breadth Negative -0.2981 0.86 0.724 0.996 0.962 Maxillary Palate Length Positive -0.7405 1.188 1.063 1.313 0.983 Palatine Palate Length * -0.1684 0.7023 0.227 1.177 0.312 Total Palate Length Isometry -0.1326 0.9627 0.839 1.086 0.975 Palate Width Negative 0.3795 0.7174 0.6807 0.754 0.996 Palate Depth Negative -0.3442 0.7896 0.7074 0.8718 0.984 External Palate Breadth Negative 0.5978 0.6162 0.5828 0.6469 0.996 Upper Facial Height Internal Palate Breadth Negative 0.3808 0.5903 0.5352 0.6454 0.987 Maxillary Palate Length Negative 0.1973 0.8155 0.7478 0.8831 0.99 Palatine Palate Length * 0.3861 0.4821 0.1452 0.819 0.265 Total Palate Length Negative 0.6274 0.6608 0.5579 0.7638 0.964 Palate Width Negative 0.1542 0.7693 0.7202 0.8184 0.994 Palate Depth Negative -0.5921 0.8467 0.763 0.9305 0.985 External Palate Breadth Negative 0.4044 0.6608 0.6225 0.699 0.995 Total Facial Height Internal Palate Breadth Negative 0.1955 0.633 0.5699 0.6962 0.985 Maxillary Palate Length Negative -0.0587 0.8745 0.8117 0.9374 0.992 Palatine Palate Length * 0.2347 0.517 0.1559 0.878 0.266 Total Palate Length Negative 0.4199 0.7087 0.6034 0.814 0.967 Palate Width Positive -0.9827 1.297 1.001 1.593 0.922 Palate Depth Positive -1.844 1.428 1.038 1.817 0.888 External Palate Breadth Isometry -0.5722 1.114 0.864 1.364 0.924 Skull Length Internal Palate Breadth Isometry -0.7401 1.067 0.758 1.377 0.873 Maxillary Palate Length Positive -1.351 1.474 1.089 1.86 0.897 Palatine Palate Length * -0.5294 0.8716 0.328 1.415 0.416 Total Palate Length Isometry -0.6274 1.195 0.923 1.467 0.922
166
Table 4-21. Continued Size Measurement Palate Dimensions Allometry Intercept Slope Confidence Intervals R 2 Palate Width Positive -0.08471 1.282 1.163 1.4 0.987 Palate Depth Positive -0.8551 1.411 1.261 1.56 0.983 External Palate Breadth Isometry 0.1991 1.101 0.988 1.214 0.984 Bipterygoid Breadth Internal Palate Breadth Isometry -0.001 1.055 0.957 1.152 0.987 Maxillary Palate Length Positive -0.3303 1.457 1.308 1.605 0.984 Palatine Palate Length * 0.07411 0.8612 0.242 1.48 0.222 Total Palate Length Isometry 0.1998 1.181 0.951 1.41 0.943 * No significant relationship
167
Table 4-22. Significance (alpha) values for phylogenetic group comparisons from RMA2*. Size Colobines vs Colobines vs Papionins vs Dimension Palatal Dimension Papionins Hominoids Hominoids palate width 0.0695 0.0033* 0.0108* palate depth 0.0215* 0.0390* 0.1577 external palate breadth 0.0891 0.0835 0.4921 facial width internal palate breadth 0.0672 0.0149* 0.0447* maxillary palate length 0.0694 0.0032* 0.0001* palatine palate length 0.2023 0.0497* 0.1193 total palate length 0.0698 0.0031* 0.0000* palate width 0.0000* 0.0103* 0.0696 palate depth 0.0001* 0.0035* 0.0000* external palate breadth 0.0002* 0.0056* 0.0000* upper facial internal palate breadth 0.0003* 0.0010* 0.0443* height maxillary palate length 0.0000* 0.0001* 0.3839 palatine palate length 0.0011* 0.0192* 0.4074 total palate length 0.0000* 0.0000* 0.1334 palate width 0.0164* 0.0090* 0.2489 palate depth 0.0009* 0.0072* 0.0016* external palate breadth 0.0019* 0.0118* 0.0964 total facial internal palate breadth 0.0020* 0.0013* 0.3836 height maxillary palate length 0.0006* 0.0001* 0.0007* palatine palate length 0.0130* 0.0278* 0.2196 total palate length 0.0005* 0.0001* 0.0021* palate width 0.3346 0.0167* 0.0058* palate depth 0.0161* 0.0146* 0.3806 external palate breadth 0.1151 0.0229* 0.1056 skull length internal palate breadth 0.0034* 0.0020* 0.0149* maxillary palate length 0.1393 0.0002* 0.0008* palatine palate length 0.4070 0.0259* 0.0319* total palate length 0.1034 0.0002* 0.0001* palate width 0.2939 0.4845 0.0000* palate depth 0.1474 0.3220 0.1416 external palate breadth 0.3154 0.1517 0.3797 bipterygoid internal palate breadth 0.4188 0.2763 0.1253 breadth maxillary palate length 0.3022 0.0847 0.0218* palatine palate length 0.1629 0.3067 0.1478 total palate length 0.3655 0.0511 0.0152* * These values are significantly different based on alpha level < 0.05.
168
Table 4-23. Ratio averages for palatal dimensions versus size. Size Dimension Palatal Dimension Papionins Colobines Hominoids palate width 0.402333 0.386829 0.443775 palate depth 0.09331 0.093044 0.114332 external palate breadth 0.487805 0.444074 0.480169 facial width internal palate breadth 0.247462 0.235396 0.262095 maxillary palate length 0.497399 0.390276 0.43498 palatine palate length 0.213457 0.19383 0.17485 total palate length 0.710856 0.579767 0.620016 palate width 0.521217 0.745657 0.739706 palate depth 0.121737 0.178741 0.189641 external palate breadth 0.639364 0.854885 0.805432 upper facial internal palate breadth 0.323052 0.45266 0.440437 height maxillary palate length 0.636119 0.747884 0.719919 palatine palate length 0.278358 0.37347 0.302496 total palate length 0.914476 1.112943 1.038186 palate width 0.397103 0.471176 0.498143 palate depth 0.09246 0.113056 0.127729 external palate breadth 0.48492 0.540537 0.541311 total facial internal palate breadth 0.245565 0.286264 0.295965 height maxillary palate length 0.486953 0.473421 0.486223 palatine palate length 0.211635 0.235915 0.202297 total palate length 0.698589 0.704004 0.698363 palate width 0.395498 0.377817 0.429243 palate depth 0.091516 0.090759 0.110998 external palate breadth 0.477752 0.432937 0.462313 skull length internal palate breadth 0.242628 0.229583 0.252561 maxillary palate length 0.490726 0.380834 0.42231 palatine palate length 0.208969 0.188833 0.165329 total palate length 0.699695 0.565176 0.597549 palate width 2.161232 1.957668 2.036057 palate depth 0.498351 0.467757 0.524252 external palate breadth 2.606313 2.237651 2.191302 bipterygoid internal palate breadth 1.322789 1.185495 1.194527 breadth maxillary palate length 2.680968 1.964499 1.999286 palatine palate length 1.143918 0.974885 0.790996 total palate length 3.824886 2.916896 2.840857
169
Figure 4-28. Papionin regression of facial width versus external palate breadth.
170
Figure 4-29. Papionin regression of facial width versus internal palate breadth.
171
Figure 4-30. Papionin regression of facial width versus palate depth.
172
Figure 4-31. Papionin regression of facial width versus palatine palate length.
173
Figure 4-32. Papionin regression of facial width versus palate width.
174
Figure 4-33. Papionin regression of facial width versus internal palate breadth.
175
Figure 4-34. Papionin regression of facial width versus total palatine length.
176
Figure 4-35. Colobine regression of facial width versus palate width.
Figure 4-36. Colobine regression of facial width versus maxillary palate length.
177
Figure 4-37. Colobine regression of facial width versus total palate length.
Figure 4-38. Colobine regression of facial width versus external palate breadth.
178
Figure 4-39. Colobine regression of facial width versus palate depth.
Figure 4-40. Colobine regression of facial width versus internal palate breadth.
179
Figure 4-41. Colobine regression of facial width versus palatine palate length.
Figure 4-42. Hominoid regression of facial width versus palatine palate length.
180
Figure 4-43. Hominoid regression of facial width versus maxillary palate length.
Figure 4-44. Hominoid regression of facial width versus internal palate breadth.
181
Figure 4-45. Hominoid regression of facial width versus total palate length.
Figure 4-46. Hominoid regression of facial width versus external palate breadth.
182
Figure 4-47. Hominoid regression of facial width versus palate width.
Figure 4-48. Hominoid regression of facial width versus palate depth.
183
Figure 4-49. Papionin regression of upper facial height versus total palate length.
184
Figure 4-50. Papionin regression of upper facial height versus palatine palate length.
185
Figure 4-51. Papionin regression of upper facial height versus maxillary palate length.
186
Figure 4-52. Papionin regression of upper facial height versus palate width.
187
Figure 4-53. Papionin regression of upper facial height versus external palate breadth.
188
Figure 4-54. Papionin regression of upper facial height versus internal palate breadth.
189
Figure 4-55. Papionin regression of upper facial height versus palate depth.
190
Figure 4-56. Colobine regression of upper facial height versus maxillary palate length.
Figure 4-57. Colobine regression of upper facial height versus total palate length.
191
Figure 4-58. Colobine regression of upper facial height versus palate width.
. Figure 4-59. Colobine regression of upper facial height versus internal palate breadth.
192
Figure 4-60. Colobine regression of upper facial height versus external palate breadth.
Figure 4-61. Colobine regression of upper facial height versus palate depth.
193
Figure 4-62. Colobine regression of upper facial height versus palatine palate length.
Figure 4-63. Hominoid regression of upper facial height versus palatine palate length.
194
Figure 4-64. Hominoid regression of upper facial height versus maxillary palate length.
Figure 4-65. Hominoid regression of upper facial height versus total palate length.
195
Figure 4-66. Hominoid regression of upper facial height versus palate width.
Figure 4-67. Hominoid regression of upper facial height versus external palate breadth.
196
Figure 4-68. Hominoid regression of upper facial height versus internal palate breadth.
Figure 4-69. Hominoid regression of upper facial height versus palate depth.
197
Figure 4-70. Papionin regression of upper facial height versus maxillary palate length.
198
Figure 4-71. Papionin regression of upper facial height versus palatine palate length.
199
Figure 4-72. Papionin regression of upper facial height versus total palate length.
200
Figure 4-73. Papionin regression of upper facial height versus palate depth.
201
Figure 4-74. Papionin regression of upper facial height versus palate width.
202
Figure 4-75. Papionin regression of upper facial height versus external palate breadth.
203
Figure 4-76. Papionin regression of upper facial height versus internal palate breadth.
204
Figure 4-77. Colobine regression of total facial height versus palate width.
Figure 4-78. Colobine regression of total facial height versus palate depth.
205
Figure 4-79. Colobine regression of total facial height versus external palate breadth.
Figure 4-80. Colobine regression of total facial height versus internal palate breadth.
206
Figure 4-81. Colobine regression of total facial height versus palatine palate length.
Figure 4-82. Colobine regression of total facial height versus maxillary palate length.
207
Figure 4-83. Colobine regression of total facial height versus total palate length.
Figure 4-84. Hominoid regression of total facial height versus internal palate breadth.
208
Figure 4-85. Papionin regression of skull length versus maxillary palate length.
209
Figure 4-86. Papionin regression of skull length versus total palate length.
210
Figure 4-87. Papionin regression of skull length versus palatine palate length.
211
Figure 4-88. Papionin regression of skull length versus palate width.
212
Figure 4-89. Papionin regression of skull length versus palate depth.
213
Figure 4-90. Papionin regression of skull length versus external palate breadth.
214
Figure 4-91. Papionin regression of skull length versus internal palate breadth.
215
Figure 4-92. Colobine regression of skull length versus palate width.
Figure 4-93. Colobine regression of skull length versus external palate breadth.
216
Figure 4-94. Colobine regression of skull length versus internal palate breadth.
Figure 4-95. Colobine regression of skull length versus maxillary palate length.
217
Figure 4-96. Colobine regression of skull length versus total palate length.
Figure 4-97. Colobine regression of skull length versus palatine palate length.
218
Figure 4-98. Colobine regression of skull length versus palate depth.
Figure 4-99. Hominoid regression of skull length versus palate depth.
219
Figure 4-100. Hominoid regression of skull length versus palate width.
Figure 4-101. Hominoid regression of skull length versus maxillary palate length.
220
Figure 4-102. Hominoid regression of skull length versus external palate breadth.
Figure 4-103. Hominoid regression of skull length versus internal palate breadth.
221
Figure 4-104. Hominoid regression of skull length versus total palate length.
Figure 4-105. Hominoid regression of skull length versus palatine palate length.
222
Figure 4-106. Papionin regression of bipterygoid breadth versus external palate breadth.
223
Figure 4-107. Papionin regression of bipterygoid breadth versus internal palate breadth.
224
Figure 4-108. Papionin regression of bipterygoid breadth versus palate depth.
225
Figure 4-109. Papionin regression of bipterygoid breadth versus palatine palate length.
226
Figure 4-110. Papionin regression of bipterygoid breadth versus palate width.
227
Figure 4-111. Papionin regression of bipterygoid breadth versus maxillary palate length.
228
Figure 4-112. Papionin regression of bipterygoid breadth versus total palate length.
229
Figure 4-113. Colobine regression of bipterygoid breadth versus total palate length.
Figure 4-114. Colobine regression of bipterygoid breadth versus palate depth.
230
Figure 4-115. Colobine regression of bipterygoid breadth versus external palate breadth.
Figure 4-116. Colobine regression of bipterygoid breadth versus internal palate breadth.
231
Figure 4-117. Colobine regression of bipterygoid breadth versus palatine palate length.
Figure 4-118. Colobine regression of bipterygoid breadth versus maxillary palate length.
232
Figure 4-119. Colobine regression of bipterygoid breadth versus total palate length.
Figure 4-120. Hominoid regression of bipterygoid breadth versus palate depth.
233
Figure 4-121. Hominoid regression of bipterygoid breadth versus palate width.
Figure 4-122. Hominoid regression of bipterygoid breadth versus maxillary palate length.
234
Figure 4-123. Hominoid regression of bipterygoid breadth versus external palate breadth.
Figure 4-124. Hominoid regression of bipterygoid breadth versus internal palate breadth.
235
Figure 4-125. Hominoid regression of bipterygoid breadth versus total palate length.
Figure 4-126. Hominoid regression of bipterygoid breadth versus palatine palate length.
236
Table 4-24. Descriptive statistics of fractal dimensions for species by sex Species Sex n Mean (s.d.) Minimum-Maximum Cercocebus agilis Female 7 1.21 (0.026) 1.16-1.23 Male 8 1.20 (0.031) 1.15-1.23 Lophocebus agilis Female 10 1.19 (0.35) 1.11-1.23 Male 9 1.20 (0.051) 1.11-1.27 Cercocebus torquatus Female 5 1.17 (0.051) 1.10-1.22 Male 4 1.23 (0.029) 1.20-1.26 Colobus guereza Female 2 1.21 (0.125) 1.12-1.30 Male 6 1.19 (0.027) 1.15-1.23 Colobus polykomos Female 10 1.23 (0.033) 1.19-1.27 Male 9 1.26 (0.038) 1.21-1.32 Gorilla gorilla Female 2 1.18 (0.084) 1.12-1.24 Male 4 1.32 (0.058) 1.25-1.38 Hylobates lar Female 1 1.18 (-) 1.18-1.18 Male 2 1.22 (0.070) 1.17-1.27 Hylobates syndactylus Female 4 1.22 (0.042) 1.18-1.28 Male 4 1.18 (0.037) 1.14-1.21 Macaca fascicularis Female 4 1.21 (0.040) 1.15-1.24 Male 5 1.26 (0.043) 1.21-1.31 Macaca fuscata Female 1 1.21 (-) 1.21-1.21 Male 4 1.22 (0.048) 1.18-1.29 Macaca mulatta Female 10 1.21 (0.054) 1.10-1.28 Male 10 1.22 (0.044) 1.16-1.30 Macaca sylvanus Female 8 1.20 (0.026) 1.17-1.24 Male 5 1.21 (0.036) 1.17-1.25 Mandrillus sphinx Female 3 1.20 (0.051) 1.15-1.26 Male 7 1.19 (0.038) 1.13-1.24 Pan troglodytes Female 1 1.26 (-) 1.26-1.26 Male 3 1.27 (0.078) 1.20-1.35 Papio anubis Female 4 1.20 (0.029) 1.17-1.24 Male 9 1.19 (0.046) 1.11-1.24 Papio ursinus Female 5 1.22 (0.061) 1.15-1.30 Male 10 1.19 (0.064) 1.07-1.28 Pongo pygmaeus Female 3 1.21 (0.047) 1.16-1.25 Male 8 1.21 (0.048) 1.15-1.28 Procolobus badius Female 9 1.20 (0.043) 1.11-1.26 Male 9 1.22 (0.036) 1.15-1.27 Procolobus verus Female 3 1.24 (0.015) 1.22-1.25 Male 5 1.23 (0.039) 1.18-1.28 Theropithecus gelada Female 4 1.17 (0.032) 1.13-1.20 Male 5 1.20 (0.045) 1.15-1.27 Papio hamadryas Male 3 1.23 (0.029) 1.20-1.25 Papio papio Male 6 1.21 (0.062) 1.12-1.28
237
Table 4-25. Descriptive statistics of suture length ratio for species by sex Species Sex n Mean (s.d.) Minimum-Maximum Cercocebus agilis Female 7 0.835 (0.030) 0.79-0.88 Male 8 0.880 (0.056) 0.79-0.93 Lophocebus agilis Female 10 0.880 (0.033) 0.82-0.94 Male 9 0.890 (0.044) 0.81-0.94 Cercocebus torquatus Female 5 0.841 (0.024) 0.81-0.87 Male 4 0.848 (0.039) 0.79-0.88 Colobus guereza Female 2 0.916 (0.017) 0.90-0.93 Male 6 0.860 (0.033) 0.83-0.92 Colobus polykomos Female 10 0.757 (0.048) 0.69-0.84 Male 9 0.749 (0.067) 0.66-0.83 Gorilla gorilla Female 2 0.712 (0.078) 0.66-0.77 Male 4 0.546 (0.105) 0.46-0.69 Hylobates lar Female 1 0.825 (-) 0.83-0.83 Male 2 0.751 (0.023) 0.73-0.77 Hylobates syndactylus Female 4 0.742 (0.109) 0.65-0.90 Male 4 0.788 (0.107) 0.66-0.90 Macaca fascicularis Female 4 0.737 (0.073) 0.67-0.84 Male 5 0.773 (0.053) 0.72-0.85 Macaca fuscata Female 1 0.728 (-) 0.73-0.73 Male 4 0.811 (0.087) 0.69-0.89 Macaca mulatta Female 10 0.811 (0.105) 0.63-0.95 Male 10 0.799 (0.044) 0.72-0.89 Macaca sylvanus Female 8 0.850 (0.032) 0.81-0.91 Male 5 0.844 (0.074) 0.78-0.95 Mandrillus sphinx Female 3 0.835 (0.020) 0.81-0.85 Male 7 0.875 (0.052) 0.80-0.92 Pan troglodytes Female 1 0.770 (-) 0.77-0.77 Male 3 0.665 (0.166) 0.51-0.84 Papio anubis Female 4 0.837 (0.052) 0.80-0.91 Male 9 0.849 (0.047) 0.77-0.92 Papio ursinus Female 5 0.866 (0.083) 0.72-0.92 Male 10 0.896 (0.091) 0.65-0.97 Pongo pygmaeus Female 3 0.902 (0.037) 0.86-0.94 Male 8 0.827 (0.068) 0.71-0.89 Procolobus badius Female 9 0.814 (0.056) 0.69-0.88 Male 9 0.838 (0.044) 0.74-0.88 Procolobus verus Female 3 0.674 (0.054) 0.63-0.74 Male 5 0.786 (0.039) 0.74-0.83 Theropithecus gelada Female 4 0.861 (0.037) 0.81-0.89 Male 5 0.839 (0.024) 0.81-0.87 Papio hamadryas Male 3 0.875 (0.078) 0.78-0.92 Papio papio Male 6 0.896 (0.034) 0.84-0.92
238
Table 4-26. Mann-Whitney U P values for the sexes of each species Species Fractal Dimension Suture Length Ratio Cercocebus agilis 0.247 0.105 Lophocebus albigena 0.327 0.514 Cercocebus torquatus 0.142 0.624 Colobus guereza + + Colobus polykomos 0.050* 0.744 Gorilla gorilla + + Hylobates lar + + Hylobates syndactylus 0.248 0.386 Macaca fascicularis 0.221 0.221 Macaca fuscata + + Macaca mulatta 0.705 0.326 Macaca sylvanus 0.661 0.558 Mandrillus sphinx 0.569 0.210 Pan troglodytes + + Papio anubis 0.440 0.537 Papio hamadryas - - Papio papio - - Papio ursinus 0.624 0.142 Pongo pygmaeus 0.838 0.102 Procolobus badius 0.200 0.402 Procolobus verus 0.881 0.025* Theropithecus gelada 0.462 0.327 +Sample sizes too small for statistical analysis. * Shows significant P values at a significance level of ≤ 0.05 - Only data from male specimens were collected from these species.
239
Table 4-27. Mann-Whitney U tests significance values for species versus fractal dimension (FD) Colobus Procolobus Colobus Procolobus Theropithecus Mandrillus Cercocebus Papio Species vs FD guereza badius polykomos verus gelada sphinx torquatus hamadryas Procolobus badius 0.222 Colobus polykomos 0.015* 0.014* Procolobus verus 0.093 0.201 0.559 Theropithecus gelada 0.923 0.034* 0.002* 0.123 Mandrillus sphinx 0.79 0.314 0.009* 0.076 0.683 Cercocebus torquatus 0.564 0.797 0.037* 0.178 0.31 0.683 Papio hamadryas 0.221 0.615 0.473 0.838 0.079 0.31 0.405 Papio anubis 0.717 0.317 0.003* 0.03* 0.713 0.975 0.526 0.201 Papio papio 0.519 0.641 0.408 0.699 0.346 0.386 0.556 0.796 Papio ursinus 0.439 0.885 0.054 0.22 0.2 0.542 0.976 0.515 Macaca sylvanus 0.218 0.749 0.012* 0.096 0.217 0.42 0.867 0.313 Macaca fuscata 0.306 0.881 0.166 0.38 0.125 0.327 0.841 0.456 Macaca mulatta 0.17 0.397 0.152 0.416 0.048 0.147 0.322 0.927 Macaca fascicularis 0.068 0.1 0.941 0.773 0.019* 0.072 0.145 0.644 Hylobates syndactylus 0.6 0.657 0.034* 0.093 0.501 0.722 0.773 0.307 Hylobates lar 0.838 0.763 0.165 0.414 0.782 0.735 0.926 0.513 Pongo pygmaeus 0.509 0.753 0.027* 0.16 0.271 0.673 0.909 0.392 Gorilla gorilla 0.053 0.046* 0.252 0.302 0.059 0.051 0.077 0.302 Pan troglodytes 0.062 0.148 0.746 0.396 0.031* 0.066 0.165 0.289 Cercocebus agilis 0.245 0.971 0.018* 0.071 0.101 0.542 0.698 0.515 Lophocebus albigena 0.633 0.485 0.002* 0.029* 0.476 0.819 0.825 0.165 * Shows significant P values at a significance level of ≤ 0.05
240
Table 4-27. continued Papio Papio Papio Macaca Macaca Macaca Macaca Hylobates Hylobates Species vs FD anubis papio ursinus sylvanus fuscata mulatta fascicularis syndactylus lar Procolobus badius Colobus polykomos Procolobus verus Theropithecus gelada Mandrillus sphinx Cercocebus torquatus Papio hamadryas Papio anubis Papio papio 0.335 Papio ursinus 0.394 0.586 Macaca sylvanus 0.343 0.539 0.982 Macaca fuscata 0.301 0.855 0.827 0.588 Macaca mulatta 0.113 0.903 0.317 0.377 0.634 Macaca fascicularis 0.057 0.346 0.114 0.089 0.205 0.37 Hylobates syndactylus 0.664 0.519 0.796 0.942 0.558 0.222 0.102 Hylobates lar 0.84 0.606 0.859 0.737 0.456 0.648 0.309 0.838 Pongo pygmaeus 0.543 0.482 0.586 0.706 0.533 0.248 0.102 0.869 0.815 Gorilla gorilla 0.035* 0.15 0.043* 0.054 0.144 0.078 0.157 0.071 0.302 Pan troglodytes 0.024* 0.394 0.162 0.054 0.221 0.215 0.537 0.126 0.289 Cercocebus agilis 0.504 0.876 0.787 0.908 0.896 0.351 0.114 0.366 0.859 Lophocebus albigena 0.833 0.408 0.716 0.020* 0.546 0.16 0.041* 0.915 0.962 * Shows significant P values at a significance level of ≤ 0.05
241
Table 4-27. continued Pongo Gorilla Pan Cercocebus Species vs FD pygmaeus gorilla troglodytes agilis Procolobus badius Colobus polykomos Procolobus verus Theropithecus gelada Mandrillus sphinx Cercocebus torquatus Papio hamadryas Papio anubis Papio papio Papio ursinus Macaca sylvanus Macaca fuscata Macaca mulatta Macaca fascicularis Hylobates syndactylus Hylobates lar Pongo pygmaeus Gorilla gorilla 0.108 Pan troglodytes 0.117 0.831 Cercocebus agilis 0.586 0.020* 0.057 Lophocebus albigena 0.683 0.026* 0.029* 0.499 * Shows significant P values at a significance level of ≤ 0.05
242
Table 4-28. Mann-Whitney U tests significance values for species versus suture length ratio Colobus Procolobus Colobus Procolobus Theropithecus Mandrillus Cercocebus Papio Species vs Ratio guereza badius polykomos verus gelada sphinx torquatus hamadryas Procolobus badius 0.02* Colobus polykomos <0.001* 0.001* Procolobus verus 0.001* 0.005* 0.595 Theropithecus gelada 0.149 0.004* 0.001* 0.328 Mandrillus sphinx 0.594 0.125 <0.001* 0.003* 0.568 Cercocebus torquatus 0.149 0.471 0.001* 0.003* 0.691 0.514 Papio hamadryas 0.683 0.269 0.031* 0.041* 0.405 0.612 0.405 Papio anubis 0.111 0.471 <0.001* 0.004* 0.867 0.239 0.973 0.313 Papio papio 0.366 0.003* <0.001* 0.002* 0.025* 0.278 0.025* 0.796 Papio ursinus 0.121 0.001* <0.001* 0.002* 0.008* 0.086 0.004* 0.767 Macaca sylvanus 0.169 0.423 <0.001* 0.002* 0.664 0.385 0.973 0.459 Macaca fuscata 0.057 0.602 0.337 0.242 0.463 0.111 0.317 0.18 Macaca mulatta 0.013* 0.267 0.025* 0.067 0.099 0.022* 0.099 0.201 Macaca fascicularis 0.003* 0.016* 0.98 0.847 0.004* 0.003* 0.005* 0.052 Hylobates syndactylus 0.046* 0.2671 0.753 0.178 0.041* 0.178 0.066 Hylobates lar 0.014* 0.088 0.738 0.683 0.033* 0.043* 0.052 0.127 Pongo pygmaeus 0.62 0.208 0.002* 0.013* 0.518 0.673 0.382 0.312 Gorilla gorilla 0.002* 0.001* 0.009* 0.053 0.001* 0.001* 0.001* 0.02* Pan troglodytes 0.017* 0.061 0.57 0.734 0.031* 0.016* 0.031* 0.077 Cercocebus agilis 0.519 0.129 <0.001* 0.001* 0.698 0.912 0.612 0.678 Lophocebus albigena 0.49 <0.001* <0.001* <0.001* 0.019* 0.291 0.011* 0.738 * Shows significant P values at a significance level of ≤ 0.05
243
Table 4-28. continued Papio Papio Papio Macaca Macaca Macaca Macaca Hylobates Hylobates Species vs Ratio anubis papio ursinus sylvanus fuscata mulatta fascicularis syndactylus lar Procolobus badius Colobus polykomos Procolobus verus Theropithecus gelada Mandrillus sphinx Cercocebus torquatus Papio hamadryas Papio anubis Papio papio 0.023* Papio ursinus 0.008* 0.392 Macaca sylvanus 0.98 0.028* 0.016* Macaca fuscata 0.349 0.018* 0.032* 0.257 Macaca mulatta 0.09 0.005* 0.003* 0.122 0.839 Macaca fascicularis 0.006* 0.002* 0.002* 0.006* 0.549 0.12 Hylobates syndactylus 0.096 0.014* 0.010* 0.096 0.77 0.387 0.923 Hylobates lar 0.051 0.020* 0.051 0.051 0.655 0.361 0.518 0.683 Pongo pygmaeus 0.75 0.108 0.052 0.706 0.282 0.173 0.009* 0.083 0.102 Gorilla gorilla 0.001* 0.004* 0.001* 0.001* 0.028* 0.001* 0.018* 0.039* 0.071 Pan troglodytes 0.031* 0.019* 0.009* 0.031* 0.327 0.104 0.537 0.308 0.724 Cercocebus agilis 0.369 0.161 0.044* 0.534 0.15 0.026* 0.002* 0.039* 0.038* Lophocebus albigena 0.018* 0.525 0.182 0.578 0.025* 0.001* <0.001* 0.009* 0.011* * Shows significant P values at a significance level of ≤ 0.05
244
Table 4-28. continued Pongo Gorilla Pan Cercocebus Species vs Ratio pygmaeus gorilla troglodytes agilis Procolobus badius Colobus polykomos Procolobus verus Theropithecus gelada Mandrillus sphinx Cercocebus torquatus Papio hamadryas Papio anubis Papio papio Papio ursinus Macaca sylvanus Macaca fuscata Macaca mulatta Macaca fascicularis Hylobates syndactylus Hylobates lar Pongo pygmaeus Gorilla gorilla 0.001* Pan troglodytes 0.037* 0.286 Cercocebus agilis 0.815 <0.001* 0.016* Lophocebus albigena 0.162 <0.001* 0.005* 0.123 * Shows significant P values at a significance level of ≤ 0.05
245
Table 4-29. Mann-Whitney U tests significance values for phylogenetic groups versus suture measurement Phylogenetic groups vs Cercocebus- Lophocebus- Fractal Dimension Mandrillus Papio Macaques Colobines Lophocebus-Papio 0.71 Macaques 0.119 0.03* Colobines 0.045* 0.01* 0.707 Hominoids 0.275 0.119 0.92 0.724
Phylogenetic Groups vs Cercocebus- Lophocebus- Suture Length Ratio Mandrillus Papio Macaques Colobines Lophocebus-Papio 0.058 Macaques 0.001* <0.001* Colobines <0.001* <0.001* 0.501 Hominoids 0.001* <0.001* 0.124 0.314 * Shows significant P values at a significance level of ≤ 0.05
Table 4-30. Mann-Whitney U tests significance values for dietary contrasts Diet Group vs Fractal Dimension Hard Diet Group Soft Diet Group Significance Value Mandrillus Papio 0.507 C. polykomos Remaining Colobines 0.037* Pongo Hylobates 0.974
Diet Group vs Ratio Hard Diet Group Soft Diet Group Significance Value Mandrillus Papio 0.516 C. polykomos Remaining Colobines <0.001* Pongo Hylobates 0.039*
Diet Group vs FD Hard Diet Group Soft Diet Group Significance Value Cercocebus-Mandrillus Lophocebus-Papio 0.957 Pongo Remaining Hominoids 0.258
Diet Group vs Ratio Hard Diet Group Soft Diet Group Significance Value Cercocebus-Mandrillus Lophocebus-Papio 0.027* Pongo Remaining Hominoids 0.001* * Shows significant P values at a significance level of ≤ 0.05
246
Table 4-31. Reduced major axis (RMA) regression results for colobines Palatal Dimension Suture Measurement Intercept Slope St. Error Confidence Intervals R2 R palate depth fractal dimension -0.0105 0.116 0.0472 0.0003 0.2312 0.003 0.0548 external palatal breadth fractal dimension 0.3635 -0.182 0.0736 -0.3622 -0.0022 0.022 0.1483 internal palatal breadth fractal dimension 0.2749 -0.152 0.0618 -0.3028 -0.0003 0.002 0.0447 palate width fractal dimension 0.2864 -0.137 0.0556 -0.2730 -0.0008 0.009 0.0949 maxillary palate length fractal dimension 0.2321 -0.100 0.0388 -0.1947 -0.0005 0.089 0.2983 palatine palate length fractal dimension 0.2905 -0.173 0.0719 -0.3520 -0.0004 0.002 0.0447 total palate length fractal dimension 0.2679 -0.111 0.0440 -0.2188 -0.0033 0.056 0.2366 facial width fractal dimension 0.5028 -0.222 0.0896 -0.4413 -0.0030 0.025 0.1581 upper facial height fractal dimension 0.3592 -0.172 0.0684 -0.3388 -0.0043 0.048 0.2191 total facial height fractal dimension 0.3933 -0.172 0.0690 -0.3404 -0.0028 0.030 0.1732 skull length fractal dimension 0.6007 -0.273 0.1110 -0.5444 -0.0012 0.007 0.0837 bipterygoid breadth fractal dimension 0.2943 -0.177 0.0717 -0.3527 -0.0019 0.019 0.1378 palate depth suture length ratio -0.0368 0.999 0.3925 0.0390 1.9600 0.074 0.2720 external palatal breadth suture length ratio -1.5930 1.573 0.5740 0.1690 2.9770 0.201 0.4483 internal palatal breadth suture length ratio -0.8280 1.309 0.4720 0.1540 2.4630 0.220 0.4690 palate width suture length ratio -0.9273 1.182 0.4290 0.1310 2.2320 0.208 0.4561 maxillary palate length suture length ratio -0.4584 0.860 0.2727 0.1930 1.5270 0.397 0.6301 palatine palate length suture length ratio -0.9633 1.521 0.5920 0.0730 2.9680 0.092 0.3033 total palate length suture length ratio -0.7676 0.958 0.3317 0.1470 1.7700 0.281 0.5301 facial width suture length ratio -2.7960 1.917 0.6600 0.3030 3.5320 0.290 0.5385 upper facial height suture length ratio -1.5560 1.481 0.4960 0.2680 2.6940 0.328 0.5727 total facial height suture length ratio -1.8510 1.481 0.5190 0.2110 2.7520 0.263 0.5128 skull length suture length ratio -3.6410 2.355 0.8430 0.2930 4.4170 0.232 0.4817 bipterygoid breadth suture length ratio -0.9961 1.531 0.5760 0.1220 2.9390 0.152 0.3899
247
Table 4-32. Reduced major axis (RMA) regression results for papionins Palatal Dimension Suture Measurement Intercept Slope St. Error Confidence Intervals R2 R palate depth fractal dimension 0.1719 -0.098 0.0203 -0.1400 -0.0557 0.052 0.2280 external palatal breadth fractal dimension 0.2634 -0.111 0.0229 -0.1583 -0.0632 0.057 0.2387 internal palatal breadth fractal dimension 0.2104 -0.096 0.0199 -0.1368 -0.0544 0.050 0.2236 palate width fractal dimension 0.2007 -0.077 0.0162 -0.1102 -0.0432 0.025 0.1581 maxillary palate length fractal dimension 0.1800 -0.060 0.0124 -0.0855 -0.0343 0.066 0.2569 palatine palate length fractal dimension 0.2028 -0.095 0.0195 -0.1355 -0.0545 0.071 0.2665 total palate length fractal dimension 0.2060 -0.069 0.0142 -0.0986 -0.0396 0.070 0.2646 facial width fractal dimension 0.2777 -0.100 0.0210 -0.1439 -0.0568 0.037 0.1924 upper facial height fractal dimension 0.1739 -0.050 0.0104 -0.0715 -0.0286 0.060 0.2449 total facial height fractal dimension 0.2053 -0.063 0.0130 -0.0900 -0.0363 0.074 0.2720 skull length fractal dimension 0.3630 -0.143 0.0291 -0.2035 -0.0830 0.095 0.3082 bipterygoid breadth fractal dimension 0.2241 -0.116 0.0237 -0.1650 -0.0668 0.082 0.2864 palate depth suture length ratio 0.2481 0.641 0.1154 0.4012 0.8798 0.286 0.5348 external palatal breadth suture length ratio -0.3510 0.725 0.1313 0.4523 0.9968 0.278 0.5273 internal palatal breadth suture length ratio -0.0039 0.626 0.1093 0.3990 0.8525 0.328 0.5727 palate width suture length ratio 0.0593 0.502 0.0866 0.3223 0.6815 0.345 0.5874 maxillary palate length suture length ratio 0.1949 0.392 0.0659 0.2553 0.5287 0.378 0.6148 palatine palate length suture length ratio 0.0456 0.622 0.1176 0.3779 0.8656 0.213 0.4615 total palate length suture length ratio 0.0246 0.452 0.0774 0.2919 0.6128 0.356 0.5967 facial width suture length ratio -0.4447 0.657 0.1199 0.4082 0.9056 0.267 0.5167 upper facial height suture length ratio 0.2350 0.328 0.0590 0.2051 0.4499 0.285 0.5339 total facial height suture length ratio 0.0292 0.413 0.0723 0.2632 0.5632 0.326 0.5710 skull length suture length ratio -1.0020 0.937 0.1510 0.6240 1.2510 0.429 0.6550 bipterygoid breadth suture length ratio -0.0939 0.759 0.1337 0.4810 1.0360 0.316 0.5621
248
Table 4-33. Reduced major axis (RMA) regression results for hominoids Palatal Dimension Suture Measurement Intercept Slope St. Error Confidence Intervals R2 R palate depth fractal dimension -0.0126 0.091 0.0298 0.0225 0.1599 0.146 0.3821 external palatal breadth fractal dimension -0.1139 0.117 0.0374 0.0306 0.2032 0.180 0.4243 internal palatal breadth fractal dimension -0.0905 0.122 0.0392 0.0317 0.2123 0.176 0.4195 palate width fractal dimension -0.0821 0.100 0.0314 0.0280 0.1728 0.218 0.4669 maxillary palate length fractal dimension -0.0615 0.088 0.0288 0.0220 0.1547 0.152 0.3899 palatine palate length fractal dimension -0.1017 0.149 0.0481 0.0384 0.2604 0.170 0.4123 total palate length fractal dimension -0.1124 0.109 0.0351 0.0281 0.1899 0.171 0.4135 facial width fractal dimension -0.1269 0.105 0.0331 0.0286 0.1812 0.205 0.4528 upper facial height fractal dimension -0.0440 0.072 0.0229 0.0192 0.1249 0.190 0.4359 total facial height fractal dimension -0.0666 0.077 0.0247 0.0203 0.1342 0.182 0.4266 skull length fractal dimension -0.1808 0.130 0.0391 0.0401 0.2204 0.279 0.5282 bipterygoid breadth fractal dimension -0.0906 0.129 0.0412 0.0336 0.2237 0.179 0.4231 palate depth suture length ratio 1.3780 -0.570 0.1958 -1.0214 -0.1186 0.056 0.2366 external palatal breadth suture length ratio 2.011 -0.730 0.2476 -1.3013 -0.1595 0.081 0.2846 internal palatal breadth suture length ratio 1.8640 -0.762 0.2634 -1.3697 -0.1550 0.045 0.2121 palate width suture length ratio 1.8120 -0.627 0.2110 -1.1139 -0.1408 0.095 0.3082 maxillary palate length suture length ratio 1.6830 -0.552 0.1890 -0.9876 -0.1161 0.062 0.2490 palatine palate length suture length ratio 1.9350 -0.934 0.2590 -1.5309 -0.3362 0.384 0.6197 total palate length suture length ratio 2.0010 -0.681 0.2274 -1.2054 -0.1566 0.108 0.3286 facial width suture length ratio 2.0920 -0.656 0.2183 -1.1591 -0.1521 0.113 0.3362 upper facial height suture length ratio 1.5740 -0.450 0.1526 -0.8020 -0.0981 0.080 0.2828 total facial height suture length ratio 1.7150 -0.483 0.1642 -0.8613 -0.1039 0.074 0.2720 skull length suture length ratio 2.4290 -0.814 0.2483 -1.3863 -0.2411 0.255 0.5050 bipterygoid breadth suture length ratio 1.8650 -0.804 0.2737 -1.4352 -0.1727 0.073 0.2702
249
CHAPTER 5 DISCUSSION
The analyses reported in the previous chapter are interpreted in light of the questions of feeding behavior and diet and their influence on skull form proposed earlier. The first question proposed was whether the maxillae and mandible are morphologically responsive to their functional environment in a similar manner. The palate is compared to the mandible based on their material properties and how this influences their morphological responses to loads.
Whether or not a beam is an appropriate model for the palate is also addressed since the mechanical environment cannot be accurately discussed without knowledge of the stress/strain distribution throughout the palate. Beam theory has specific predictions in terms of the expected stress distribution. The second question proposed earlier is whether or not sutures influence the biomechanical environment of the palate. The sutural complexity analysis conducted on the comparative samples and the strain gage data from the palatal sutures are examined to address this issue.
The comparative analysis data address the last major question proposed earlier of whether or not the palatal geometry of different species correlate with dietary consistency. The results from the allometric analysis are interpreted to address the issue of body size and palatal dimensions. Facial dimensions were used as a proxy for body size. The implications of this research for understanding the larger context of the functional morphology of the skull is discussed as well as the questions that remain unresolved and approaches to how they could be explored.
Comparing the Material Properties of the Maxillae and Mandible
Clearly the mandible and the maxillae represent two very different structures in terms of morphology, yet they share common functions, e.g. incision and mastication or resistance to the
250
forces produced by these actions and anchoring the teeth. Based on the morphological differences, the question arises as to how they are able to perform the same tasks with such structural differences. These structural differences include not only the overall morphology, but also the presence of sutures in the maxillae. Another major difference is that the mandible is freely movable with respect to the rest of the skull while the maxilla is not. One factor that may allow these structures to function similarly despite their structural differences is the material properties of the bone tissue that comprises each structure. Two material properties that influence their ability to perform mechanical tasks are bone density and elastic modulus.
The bone density reported in my study from the female Macaca fascicularis skull is lower than reported density values from another species of macaque, Macaca mulatta (Wang and
Dechow, 2006). Although it is possible the species vary in this particular property, a more likely explanation for the difference is the small sample size in my study and/or the methodology used.
My density values were based solely on one specimen whereas the density values reported by
Wang and Dechow (2006) were based on a larger sample size (n=6). Wang and Dechow (2006) did not report a range of density values, only an average density value, so it is possible that this
M. fascicularis specimen is on the lower end of the density values observed in the M. mulatta.
The density values I obtained are comparable to other bone density values reported in the literature that have been collected in other mammals using µCT (Lam et al., 1998, 1999; Leong and Morgan 2009).
Another possible explanation is that the differences observed are due to the different techniques used to obtain bone density. The technique employed in my study (µCT) and the technique employed by Wang and Dechow (2006) (calculations based on Archimedes’ principal of buoyancy) to determine bone density are both reliable methods. There is arguably a higher
251
margin of error with µCT due to the indirect measurement of density. Grayscale values were collected from the scans and then density was calculated from these values using a regression formula (r2 = 0.9995). Determining density using Archimedes’principle has been shown to yield absolutely higher values than other techniques for measuring density, which could explain why the values obtained by Wang and Dechow were higher than my reported density values (Keenan et al., 1997). Since the methods yield varying magnitudes they cannot be directly compared to each other, so I calculated the coeffiecient of variation for my data as well as Wang and Dechow
(2006) for the hard palate. The coeffiecient of variation for Wang and Dechow (based on 12 samples) was 7.5%, while my coefficient of variation (based on 32 samples) was 8.2%, indicating the amount of variation observed in the palate was approximately the same.
Density data for the mandible of the M. fascicularis used in my study was not determined so no direct comparison of mandibular and maxillary densities can be made. Other studies have addressed the issue of density differences between the upper and lower jaw. There seems to be general agreement that mandibular bone is denser than maxillary bone (Devlin et al. 1998; Drage et al., 2007), which supports the idea that the material property differences between these structures is one way they are able to function similarly, i.e. to resist the mechanical forces of masticatory activities, yet have drastically different morphologies.
How does the density of the palate relate to other areas of the skeleton? Wang and
Dechow’s (2006) results showed that the average density values from the palate were higher than other areas of the face and cranial vault, although not by much. My results showed a different pattern. The palate was less dense than other facial regions, specifically the lateral alveolar process and the zygomatic regions. My data for M. fascicularis agree with other published studies that have compared the density of the maxillae to other regions of the body. These
252
studies showed that maxillary density was less than mandibular, vertebral, and coxal densities
(Lindh et al., 2004; Drage et al., 2007).
Elastic modulus was the next material property that was obtained from the macaque specimen. Elastic modulus is a measure of axial stiffness or the amount of deformation relative to applied load. Mandibular data from humans, baboons, and macaques have shown that there is a similar amount of anisotropy among these different species (Dechow and Hylander, 2000).
This pattern of anisotropy in the mandible shows that the bone is most stiff along the long axis, less stiff in the superior-inferior direction, and least stiff in the direction normal to the bone surface. The M. fascicularis palate was sectioned in three different planes to obtain the elastic moduli from each of these directions to determine the nature of anisotropy in the palate. The
Vickers indenter tip used in the microindentation performed in my study assumes transverse isotropy of the material. Sections in the transverse and coronal planes were successfully indented. The sagittal specimen that was prepared, however, did not fare so well. One of the criteria to obtaining reliable hardness values from indentation is that the indentation cannot be placed too near a void (Johnson and Rapoff, 2007). Once the sagittal section was examined microscopically, the bone proved to be too porous to obtain any reliable hardness data. The porosity implies a low elastic modulus at the structural level in this particular direction for the M. fascicularis compared to the other directions, i.e. coronal and transverse. However, the material may be quite stiff in this direction. There is no way to ascertain this since I was unable to procure any data from the sagittal section. The average elastic moduli in the coronal sections were higher than the transverse section. This means that the bone is stiffest along a superior- inferior or medio-lateral direction, which differs from the mandible.
253
A major advantage to collecting elastic moduli data through the use of microindentation is that it allows the opportunity to evaluate the spatial relationships of elastic moduli within the structure. One relationship examined was whether or not there was a difference in elastic moduli from the anterior palate to the posterior palate. The elastic moduli from the data points on the transverse section were plotted moving from the anterior to the posterior palate. There does not appear to be any discernible differences (Figure 5-1).
In a previous study conducted by Rapoff et al. (2008), the mandible of the same macaque specimen used in my study was also microindented to determine the elastic moduli. This allows a direct comparison of the bone stiffness between the maxillae and mandible of the same specimen. The results show that the mandibular bone is stiffer than the maxillary bone in both coronal and transverse sections. This finding has implications on many levels in terms of modeling, bone biology, and adaptation.
One of the largest implications in terms of modeling these structures is that the elastic moduli from the mandible should not be extrapolated and used for the maxillae and vice versa.
Using incorrect material properties to model the structures will yield inaccurate results. Strait et al. (2005) illustrated the importance of using precise elastic material properties in finite element modeling. They constructed a finite element model of a M. fascicularis skull and ran several simulations varying the elastic material properties. The results showed that when the material properties are modeled imprecisely the model is adversely affected. The elastic modulus is also used to calculate predicted strains so if the elastic moduli used in the formula are inaccurate then the predictions will be inaccurate as well.
The difference in elastic moduli observed between the mandible and maxillae imply that there are compositional differences at the microstructural level. The cortical bone of the
254
macaque contains the same basic structural elements, e.g. Haversian canals, lacunae, lamella, etc., but the proportion of these elements will influence the structural stiffness. On average, maxillary bone has a lower elastic modulus meaning the bone is less stiff than the mandible. A biological explanation for this difference may be found by examining the overall porosity of the bone. Bone porosity is caused by voids such as the Haversian canals and lacunae. Maxillary bone may be more porous in general which would contribute to its lower elastic moduli values; however, the microindentation data is independent of porosity since the pores are avoided. Other microstructural differences that may be responsible for the difference in elastic moduli observed between the mandible and maxilla is the orientation of the collagen fibers of these structures and the degree of mineralization. Collagen fiber orientation has been shown to be a strong determinant of both the bending strength and stiffness of cortical bone (Martin and Boardman,
1993).
In terms of adaptation, if stiffness is proportional to strength, then stiffer structures are able to resist greater mechanical stresses. Stiffer structures are also better at resisting deformation. Comparing the stiffness of the mandible and maxillae, this suggests that the mandible is exposed to higher stresses. Viewing this from an overall structural standpoint, this makes sense. The mandible is a freely movable structure that has only 2 points of articulation to the remainder of the skull, i.e. the temporomandibular joints. On the other hand, the maxillae are part of the entire facial structure and articulate through sutures to various other bones of the face.
This provides a larger distribution area for masticatory loads. In other words, the forces that the maxillae experience can be transmitted to several other structures while the mandible only has the temporomandibular joint as an additional area to potentially distribute the forces to which it
255
is exposed. The overall size of the face is also larger than the mandible which makes the mandible stiffer considering the much larger moment of inertia of the face.
Overall the mandible was stiffer, but the question remains as to whether or not palatal bone is responsive in the same way as the mandible. As previously mentioned, mandibular bone is stiffest along its long axis. The maxillae seem to differ from the mandible in the direction of greatest stiffness. Indentations performed on the coronal sections measure the modulus along a superior-inferior axis and these indentations yielded higher elastic moduli than the transverse section, which measures moduli on a anterio-posterior , i.e. the long, axis. This suggests that palatal and mandibular bone is not responsive to mechanical loads in a similar manner since the plane in which they are stiffest differs. Another difference between the maxillae and mandible is that there seems to be more regional variation within the mandible in terms of stiffness while the palate lacked the same degree of spatial variation. Alveolar bone in the mandible seems to be relatively more compliant than the midcorpus or basal portions of the mandible (Rapoff et al.,
2008). The palatal bone did not exhibit these relative differences.
What does it mean on a basic biological level that the bone in the palate is more compliant (i.e. lower elastic modulus) than mandibular bone? There are 2 possible explanations.
First, this could be an indication that the palate is not strained during mastication. The in vitro strain experiments showed that the palate did experience strain during the loading scenarios tested but the possibility remains that in vivo conditions would yield different results. No in vivo data exists for this area since an animal is highly unlikly to masticate, at least not normally, if strain gages are affixed to their hard palate. Based on the free body analysis conducted in
Chapter 2, it is difficult to imagine that the palate is not loaded at all during mastication. The question is how much strain does the palate exhibit during mastication in vivo. The relative
256
thinness of the palatal bones would suggest that the palate is not highly strained during mastication. A moderate amount of strain is most likely. If there was only minimal strain present then the palate could be made of a material that is less dense (and less metabolically expensive) than bone.
The second explanation is that the palate deals with strain in a fundamentally different way than the mandible. In other words, the palate accommodates the strain to which it is exposed by a means other than structural stiffness. The palate may be tough but not strong.
Toughness refers to the work or energy required to yield or fracture a structure, while strength refers to the load at which a structure fails (Martin et al., 1998). In a load-deformation graph, the toughness would be determined by measuring the area under the curve to the point of yield or failure, the strength would be the load at which the structure fails, and the elastic modulus would be the slope of the line. The low elastic moduli and relatively low stress that the palate experiences could be an indicator of palatal toughness. The compliant nature of the palate is good for energy absorption which is a benefit to a structure that needs to resist fatigue. The palate may be adapted for fatigue resistance, i.e. toughness, rather than to resist high strains, i.e. strength.
According to Wang and Dechow (2006), bone density is correlated to elastic modulus.
The results of my study showed a poor correlation between these variables. Since local areas did not yield a significant correlation, larger regional areas were sampled to see if the problem was a scaling issue. Local areas consisted of a four pixel area compared to one indentation. A regional area compared an average of 100 pixels to 3 or 4 indentations depending on how many indents were present. Each regional area encompasses approximately 1-2 mm areas. However, regional areas also showed a poor correlation (r2 = 0.232, P-value = 0.334) (Figure 5-2). One possible,
257
albeit unlikely, explanation for the discrepancy between these 2 studies is that Wang and
Dechow (2006) use the bone density values (along with ultrasonic velocities) to calculate the elastic moduli. Since the bone density value is used in the calculation, then the fact that these 2 variables are correlated in their study is not surprising.
Leong and Morgan (2009) conducted a similar experiment that examined the relationship between indentation modulus and density on bone fracture calluses. They examined several regions of interest and the median grayscale values (measured to calculate density) were not correlated to average modulus in any of the areas. However when they examined the average grayscale values in a given area of interest to an average indentation modulus they were positively correlated. One reason they found a correlation while I did not may be methodological. Leong and Morgan used nanoindentation, not microindentation, to collect their modulus data. Nanoindentation includes the voids that are present in the bone; there is no way to avoid them. Density measures also include the voids that are present in the bone tissue. In microindentation the voids are intentionally ignored. This could explain why the density and elastic modulus in my study were poorly correlated.
The lack of correlation between elastic moduli and density is not necessarily a methodological problem. These factors are measured indirectly in my study, i.e. elastic moduli were derived from hardness values and density was calculated from grayscale values. So in actuality, it was grayscale and hardness values that were poorly correlated. Another issue that most likely contributed to the poor correlation was invariance among the data. This means that the palatal bone exhibited a narrow range of elastic moduli and grayscale values which makes detecting a significant correlation difficult.
258
Modeling the Palate
Due to the structural complexity of the maxillae, theoretical modeling of the upper jaw is challenging. Beam theory is often utilized as a means of modeling the rostrum. One example is a study by Thomason and Russell (1986) in which they modeled the rostrum of the American opossum as a cantilever beam. Their study supported the idea that the secondary palate in mammals has a mechanical function related to feeding, i.e. without the presence of the palate, the rostrum is severely impaired. Although not explicitly stated by Thomason and Russell (1986), the results of their study imply that morphological variation of the palate can be functionally related to mastication. This is based on their discussion of how the mammalian secondary palate evolved.
The strain experimentation data analysis in my study explores the possibility of beam theory being used for interspecific studies of the mechanics of the rostrum by exploring alternative beam cross sections using several pig crania as well as the macaque specimen that underwent µCT scanning and microindentation. The crania were exposed to several loading scenarios and the strain profiles of each are discussed separately. Although no idealized geometrical model will perfectly predict the behavior of complex structures such as the palate, they may be able to approximate relative strength in a comparative context.
Strain in Bending
In a cantilever beam of uniform geometry that is end-loaded on the free end (incisor loading), strains are expected to increase with proportion to the magnitude of the bending moment arm. In the skull, however, structural stiffness increases progressively along a rostro- caudal axis. In the pig specimens, calculated stresses along the palate suggest 1) a negligible strain gradient or 2) a gradient in which strains decrease posteriorly despite progressively larger bending moments.
259
For the macaque skull, Figure 5-3 illustrates one major obstacle faced when attempting to characterize the stress gradient of the palate during cantilever bending. Based on the change in the moment of inertia, larger stresses are expected in the anterior region where the moment of inertia is smaller. However, the change in the bending moment must also be considered. Based on the moment, larger strains are expected posteriorly where the moment arm is largest.
Therefore, the stress gradient depends on the rate of change in moment of inertia and rate of change in the moment from section to section. The calculated predictions followed the trend hypothesized by the moment of inertia, i.e. strains will decrease caudally, while the observed strain followed the bending moment expectations, i.e. strains will increase caudally.
As illustrated in the results of these experiments, none of the models tested performed well. Poor performance of models can be ascribed to multiple factors. The first was the presence of sutures. The high strains observed in the most posterior portion of the palate can be explained, at least partially, by the presence of the transverse palatine suture. If sutures function to reduce strains transmitted throughout the facial skeleton, then the suture should show greater strains than the surrounding bone (Rafferty et al., 2003). The results of my experiment were consistent with this idea and provide one explanation for why the observed strain gradients do not conform to expectations.
The other factors were problems with idealizing the geometry of the macaque face. The first was the effects of variable cross sections. According to Young and Budynas (2002), as long as the taper in a beam is gradual then the formulas used in beam theory should apply without modification. So the question becomes does the macaque face constitute a gradual taper?
The second geometric issue was that the macaque snout may represent a short beam which violates the proportion assumption of beam theory. Short beams are defined by a
260
span/depth ratio less than 3. In the macaque, the span equates to the length of the palate while the depth equates to the height of the face (Figure 5-4). In beams with a small span/depth ratio, the transverse shear stresses are likely to be high. For extremely short beams, the assumption of linear stress distribution is no longer valid. If a beam has a span/depth ratio between 1.5 and 1, the stress distribution changes radically and the ratio of maximum stress to the equation for calculating stress (Eq. 4-1) becomes greater than 1. The span/depth ratio of this macaque is 1.05 which falls into the category of a short beam; therefore, the predicted stress using the standard equation (Eq. 4-1) underestimates the true stress.
To help determine the significance of these 2 geometric problems, a block of wood was fashioned to approximate the macaque face dimensions including the wedge angle which was about 50 degrees (Figure 5-5). Rosette gages were placed on the wood that corresponded to the locations on the macaque face: 3 on the “palate”, 1 on the “alveolar process”, and 1 on the
“interorbital region.” For the cellulose “palatal” gages the moments of inertia and bending moments increase as you move posteriorly as in the original experiment. The magnitudes and gradients were approximately the same between the predictions and observations (Table 5-1).
This suggests the taper is gradual and therefore the beam theory formulas apply. Thus the general geometry of the macaque face is not problematic per se.
The expected versus observed strain ratios for the wood block indicate that the “palate” was in shear while the “alveolar process” and “interorbital” regions were compressed (Table 5-
2). Strain ratios were expected to indicate that the “palate” would experience about 3 times more tension than compression. In the “interorbital” region, compression should predominate and the strain ratio for the “alveolus” should be near 1 indicating a condition of shear. The strain ratios as well as the maximum principal strain directions were similar to what was observed in the
261
macaque experiment. This supports the idea that the face is behaving like a short beam, and that standard expectations of principal strain ratios do not apply.
Strain in Torsion
Treating the face as a tapered cylinder under axial torsion, the twisting moment is constant from section to section, but the torsional stiffness increases along a rostro-caudal axis.
Consequently, shear strains arising from this load are expected to decrease from anterior to posterior along the palate. The direction of maximum principal strains is expected to be oriented
45° to the long axis of the skull. For the pig crania, shear strains in torsion did decline on a rostro-caudal axis along the palate and maximum principal strain directions were oriented approximately 45° from the palate long axis. Both of these observations are consistent with modeling the rostrum as a thin-walled cylinder; however, in a twisted cylinder the strains should be equal at all sites in a given section and that was not the case for the pig experiments.
Another deviation from the expectations of the tapered cylinder model was seen in the principal strain ratios. The expectation was a value of -1.0 for the principal strain ratios while the observed ratios ranged from -10.35 to 2.93. Although these are inconsistent with the theory, the values are congruent with other experimental observations made from twisted skeletal elements of noncylindrical geometry (Daegling and Hylander, 1998).
The macaque crania behaved in the manner of a tapered cylinder in some respects as well. As stated above, the maximum principal strain direction is expected to be approximately
45° from the palate long axis. This was observed in the macaque skull based on the palatal rosette gages. The shear strain gradients expected for a twisted cylinder were also observed in the macaque palate. The gage exhibiting the highest shear strain was located at an anterior position on the left side with the second greatest degree of shear strain magnitude experienced by the posterior gage on the right side. The remaining rosette gages on the palate exhibited the
262
lowest magnitudes of shear strain. Of these remaining 2 gages, the anterior gage on the right side had the largest magnitude followed by the posterior gage on the left side of the palate. The fact that the palate experiences high shear strains suggests 1) that a thin tube with variable thickness model might yield better results since thin palatal bone would be expected to exhibit the highest shear strains under this model, and 2) this region experiences nominally high strain, which means it might really predispose the face toward even higher strains in the absence of the palate.
Given the shear modulus (Wang and Dechow, 2006), predicted shear strains using a uniform thickness thin wall cylinder model were calculated using a circle and ellipse geometry.
The predictions from neither model fared well when compared to observed shear strains (Tables
4-16 and 4-17). For the more anterior position, the ellipse exhibited the least average percent error (238% ellipse, 332% circle), while the circle fared better for the more posterior position
(254% circle, 653% ellipse). Similar to the pig crania, there was essentially no congruence between the theoretical and observed shear strains; however, the predictions made for the pig crania showed slightly more congruence at some of the gage sites in 2 of the specimens.
As noted above, a more appropriate model may be a thin tube with variable thickness as opposed to uniform thickness, since the cortical bone distribution is not going to be the same throughout the face. Bredt's formula is used to consider the thickness of the walls of a thin tube and the cross sectional area encompassed by the tube (Daegling and Hylander, 1998). Bredt's formula is K = 2Atmin where A is the area enclosed by the median axis of the tube and tmin is the minimum thickness of the tube wall, in this case the palatal thickness. Using this formula, the anterior position yields a value of 222 mm3 and the more posterior position yields a value of 796 mm3.
263
Given the shear modulus (Wang and Dechow, 2006), predicted shear strains were calculated for two positions on the palate. For the anterior position, the predicted shear was 2001
µε, while the observed values were 744 µε from one of the gages in this position and 966 µε from the other gage. So for this position the variable thickness model overestimated the shear strain by 63% and 52%, respectively. For the more posterior position, the predicted shear was
558 µε, while the two gages in this location yielded values of 648 µε and 936 µε. The variable thickness model underestimated the shear strain by 16% and 68%, respectively.
Neither the uniform nor the variable thickness thin wall cylinder models worked particularly well for estimating the strain magnitude; however, for position 2, the variable thickness model came fairly close to the magnitude of shear strain that the palate experienced during torsion. With a variable thickness model, the area that would experience the highest strains is the thinnest area. In this respect, the data does support the variable thickness model, since the palate experienced higher shear strains than either the right maxilla or the interorbital regions.
The strain experimentation data illustrates the fact that the palate is highly strained during facial torsion. As long as the face is torqued during masticatory activities (and there is evidence that implies that it is twisted (Rafferty and Herring, 1999; Ross, 2008)), then the palate seems to serve an important role by acting as a strut. Thomason and Russell (1986) performed a theoretical analysis to test the mechanical role of the hard palate and they found that removing material from the hard palate reduced strength by up to 80%. When the maximum strains are examined at a common load (e.g., Nm), the gages during twisting all exhibit more strain, up to twice as much in most locations, when compared to the maximum strains examined for incisor and molar biting, i.e. bending (Table 5-3). The gages on the palate exhibit more strain than than
264
the gage on the right maxilla and interorbital region regardless of the loading regime. This provides evidence that the palate may be more important for resisting loads during torsion than in bending.
To summarize, this study of material properties contributed to improving our ability to test different geometrical models, particularly in formulating predictions of expected strain patterns during loading in this specimen. The mandible and maxilla are not stiffest along the same plane suggesting a difference in response to their shared mechanical functions. The results from the bending experiments illustrated that beam theory is far from an ideal method to use for modeling the palate since there was no cross sectional geometry that was able to predict the magnitude of strains that were observed or the gradient of strains observed. For the torsion experiments, the strain ratios do not conform to expectations based on a cylindrical structure, except for the maximum principal strain directions.
The methodologies employed to obtain the data to address the issues just discussed all yielded useful information. In order to make these results more comparable to other studies, however, more work needs to be conducted on determining the differences that various techniques yield. For example, are the differences in density values as determined by
Archimedes’ principle versus µCT consistent? Is there a way to correct for the absolute value differences that these different techniques yield for density? Also, is microindentation comparable to determining elastic moduli through ultrasound techniques? Are the elastic moduli values approximately the same regardless of the technique used? The assumption is that for all these questions the answer is yes, but thorough investigations should be conducted to determine if this is true. Alternative methods beyond beam theory need to be explored in order to model
265
the palate. Clearly beam theory is not going to yield the most accurate results and therefore other means of modeling the palate need to be explored.
In Chapter 1, I also proposed the possibility that a plate or shell model may be more appropriate for the palate. The issue with the plate and shell models is that they assume the palate is loaded relatively independent from the remainder of the skull which the strain data has shown is not the case. Both the lateral alveolar process and the interorbital regions were loaded when the palate was bent, from the incisor and molar loads, and twisted.
Sutural Complexity and Loading
With increased loading environments, the morphological complexity of the suture is expected to increase. Rafferty et al. (2003) have proposed the idea of the facial sutures functioning as “strain sinks” in order to prevent the adjacent bone from experiencing large dynamic strains thus allowing the facial bones to stay light and thin. The in vitro strain gage experiments conducted on the pig crania and the macaque examined the strains at the mid-palatal and transverse palatine sutures respectively. In the pig crania, the strain at the sutures during cantilever bending exhibited strain an order of magnitude higher than the surrounding bone which is in accordance with in vivo inferences (Rafferty et al., 2003). The macaque palate only had single element gages bonded across the transverse palatine suture. These gages exhibited the highest amount of strain compared to the other gage sites on the bony palate, which fits the theoretical expectation of the suture experiencing more strain than the bone.
Sutural complexity was measured using 2 different methods in the comparative analysis, fractal dimension and suture length ratio. If both of these methods are measuring complexity in the same way, then these 2 methods should be highly correlated. A simple regression of fractal dimension versus suture length ratio was performed to determine if this was the case (Figure 5-
6). As the regression line illustrates, these two measures are poorly correlated (r2 = 0.095).
266
Since this is the case, the next question was which one provides a more accurate measure of sutural complexity.
Fractal analysis has become a popular method for quantifying the complexity of intricate cranial sutures. Long (1985) published one of the earliest works on fractals in biology when he examined the sutures present on the shells of ammonites and the cranial sutures of antlered deer.
This study was also the first to describe how fractal elaboration is important in the evolutionary process. Long and Long (1992), however, criticize the use of fractal analysis on human cranial sutures because they feel that these particular sutures are not self-similar and therefore are not fractals, even though they yield a dimension between 1 and 2. They state that some waveform curves may yield a dimension up to 1.2, but this is not sufficient to classify them as fractals.
Using this reasoning the sutures presented in my study are not fractals.
The problem with the above supposition is that these sutures do fit the definition of a fractal, i.e. they are self-similar and have a dimension between 1 and 2. The main critique of
Long and Long (1992) is that the waveforms that possess a dimension above 1 are not self- similar. Studies conducted on human cranial sutures have shown that these sutures are self- similar through the use of logarithmic plots. These graphs show the relationship of the logarithms of the number of squares with length r occupied by the suture against the logarithm of
1/r. Benoit 1.3 (St. Petersburg, FL) provided the logarithmic graphs for each suture analyzed and all of them clearly showed a linear relationship. This suggests that these sutures are self-similar and therefore, by definition, are fractal.
The second method chosen for measuring sutural complexity was suture length ratio, which measured the chord of the suture and then divided that by the true length of the suture.
This method has been employed in several sutural complexity studies (Nicolay and Vaders,
267
2006; Markey and Marshall, 2007). This method is more straightforward and lacks any specific criteria that the sutures must meet in order to utilize this method. Therefore, since there is ambiguity surrounding whether or not the palatal sutures are fractal objects, the suture length ratio provides a less controversial (and more straightforward) measure of sutural complexity.
Regardless of which measure of suture complexity was used, no discernible patterns were seen based on phylogeny. When the suture length ratio measurement was used, there were significant differences that emerge between the groups based on dietary contrast. C. polykomos differed from the remaining colobine species, Lophocebus-Papio group differed from the
Cercocebus-Mandrillus group, and P. pygmaeus differed from the remaining hominoid species, all in the expected direction meaning the hard object feeders exhibited more complex sutures.
These observations all support the idea that a diet consisting of harder food objects will yield mid-palatal sutures that are more structurally complex.
Another question addressed was whether or not sutural complexity was correlated to palatal and facial dimensions. The results of the reduced major axis regressions performed indicate that for most dimensions there was not a significant correlation. None of the correlations were significant for the colobines and hominoids. The papionins yielded significant correlations between the facial and palatal measurements and the suture length ratio, but none of the fractal dimension regressions were significantly correlated. The papionin results provide additional support for the notion that the suture complexity measures are not comparable.
What does it mean that the palatal and facial dimensions are not correlated to suture complexity? The answer to this question is unclear. Obviously the facial and palatal dimensions influence how the palate is loaded. The morphological differences observed within each phylogenetic group must impact how the forces are distributed throughout the palate, yet, except
268
for the papionins, there does not appear to be a significant correlation among any of the measured variables and suture complexity.
The next question is why the papionins show a scaling effect while the remaining two groups do not. This difference could indicate a qualitatively different stress environment among the groups. The stresses in the papionins from masticatory activities may be distributed in such a way as to have a more direct impact on sutural variation. This could be related to dietary consistency but a more likely explanation is a wider range of palatal shape and variation present in the papionins. The papionin group had a larger number of species represented in the analysis
(n = 14) compared to the hominoids (n = 5) and the colobines (n = 4). The small sample sizes may have contributed to the lack of significance. The suture length ratio versus palatal and facial dimension regressions for the hominoids and colobines show a trend toward significance; if the sample sizes were larger, then a significant correlation between these variables may have been detected.
What if the palate were considered to be an arch? Arches that are bent do not have a linear distribution of stress (or strain) due to the different lengths of fibers on the inner and outer portion of the beam (Young and Budynas, 2002). The degree of curvature also impacts how the structure is loaded. In the strain experiment where the left molar was loaded, the right side of the macaque palate was tensed while the left side was compressed. The palate was sheared as well.
Arching of the palate would presumably move the bony material closer to the neutral axis which would most likely increase the amount of stress on the palatal bone, although this would be true for either a straight beam or an arch. Since increasing the palatal depth would most likely increase the magnitude of stress, other factors such as palate width are most likely changed instead.
269
One aspect of the sutures that was not represented in the analysis conducted was the presence of fused sutures. Out of 23 species examined only 5 had specimens consisting of all patent sutures (P. verus, T. gelada, P. papio, M. sylvanus, and M. mulatta). All 8 of the
Cercocebus atys specimens had sutures that were fused. These mangabeys eat hard items in their diets and they use their premolar more in intial processing of food in contrast to Lophocebus.
Other mangabeys and baboons also had individuals with fused sutures although none exhibited as high a rate of sutural fusion as the C. atys. For example, Lophocebus albigena also has hard objects in their diets but only 1 out 20 specimens examined possessed a fused suture. The other species that exhibited a high rate of sutural fusion were mostly the hominoids (Table 5-4). Over half of both species of hylobatids possessed fused sutures as well as over half of the chimpanzees and gorillas. The number of fused sutures was difficult to determine for the orangutans because
4 of the specimens had taphonomy (e.g. root etching) on the palate that made it difficult to see.
Other than the high rate of fusion observed in most of the hominoids, suture fusion does not seem to be clade-specific.
What causes suture fusion? Is it related to the mechanical environment and if so, how?
The fusion exhibited by the C. atys circumstantially argues for the assumption that the mechanical environment is a factor, while the hylobatid data argue against it. Mechanical factors have been suggested as one factor involved in suture closure (Sun et al., 2004). In this study on the interparietal suture of macaques, the sutural strain on the ectocranial surface increased with the age of the macaque. The fusion of the suture may be a result of rapid ectocranial bone apposition which essentially closes the suture.
Structurally, sutures are not two-dimensional although the methods in my study treat them as such. Fractal analysis and suture length ratio only take into account the external surface
270
complexity of the suture and these methods are unable to treat the sutures as the three- dimensional structures that they truly are. The statements made about suture complexity drawn from my study can only address the external surface of the suture and not its internal structure or the internal surface. Caution must be used when making generalizations about suture complexity since only a partial representation of the situation is presented due to this limitation of the methods employed.
Allometry of the Palate
The dimensions of the palate influence the mechanical environment since they affect how loads are distributed throughout the structure. The main question of interest is: do these palatal dimensions vary in such a way that can be explained mostly due to the mechanical environment?
The scaling of structures is certainly going to affect the mechanical environment, but what is the general effect of body size on how the palate is loaded? The answer to this question remains unclear even after the allometric analysis conducted.
Only generalized patterns were discovered within the palatal morphologies of the phylogenetic groups studied. Depending on the facial dimension used for a size proxy, the results changed. This illustrates that care must be taken when choosing a variable as an overall size indicator since the results may change depending upon the variable selected (Smith, 1984).
If this is the case, then why not just use body mass as an indicator? One reason is in paleoanthropology and most museum collections, fossils are the material that is available for analysis and there is no reliable way to infer body mass from skeletal material alone. Also most museum collections do not have associated body weights for their specimens. In addition, it is rare to find a whole skeleton of an organism so relying on a size proxy such as a facial measurement may be necessary if only the skull is available for analysis.
271
For the papionins, the type of allometry observed varied depending on which facial dimension was used as the size proxy. For facial width and bipterygoid breadth, the results were fairly evenly split between positive allometry and isometry. Skull lengths versus the palatal dimensions were all positively allometric, while total and upper facial heights versus palatal dimensions were almost exclusively negatively allometric. Skull lengths versus the palatal dimensions for the colobines were also positively allometric. The remaining variables for the colobines exhibited mostly isometry. The hominoids were more diverse in the allometric patterns observed. For facial width, skull length, and bipterygoid breadth, the patterns were split between positive allometry and isometry. Total and upper facial heights resembled the trend seen in the papionins showing almost exclusively a negatively allometric relationship.
One interesting finding in the allometry results was that the two palatal breadth measurements, internal and external, did not always scale similarly. The most likely explanation for this discrepancy is tooth size, specifically molar tooth size, since this was where the measurements were taken.
From the results of the allometric analysis the generalizations that can be made between the phylogenetic groups based on the ratio averages for palatal dimensions versus size (Table 4-
23) are as follows: papionins possess relatively longer, wider, and deeper palates compared to colobines and longer and shallower palates compared to hominoids; and colobines have a relatively longer palate compared to hominoids.
What are the biomechanical consequences of these morphological differences? Longer palates increase the moment arm during cantilever bending which most likely occurs during incisal biting. Larger bending moment arms increases the amount of strain experienced when moving from the anterior to the posterior portion of the palate, unless the moment of inertia
272
compensates for the changing moment arm. The vertical tooth loading strain experiments conducted in my study on the macaque illustrated that loading anterior dentition produced higher loads posteriorly than when loading the posterior dentition. This suggests that strains closer to the loading site are not higher than strains further away from the loading site so this supports the presence of the strain gradient in the macaque palate during incisal loading, i.e. strains increase from anterior to posterior. For incisal loading only the length of palate should theoretically influence loading assuming only mid-sagittal bending occurs; therefore palatal width would be inconsequential in this loading scenario.
During unilateral molar biting, not only is bending likely occurring, but the face is twisted as well (Greaves, 1985; Ross, 2008). For parasagittal bending and torsion, palate depth and width will influence how forces are transmitted throughout this structure while palate length would have relatively little impact; however, longer palates do increase bending moments even in molar biting. A narrower palate brings the tooth rows closer together therefore maximizing bite force although presumably at a cost of higher palatal strain (Hylander, 1975). So for molar biting, a narrower palate would be more beneficial for hard object feeders, while for incision, a longer palate would be more beneficial in order to increase gape. A wider palate may be beneficial in torsion but from a bite force perspective, it would be more beneficial to have a narrow palate to increase occlusal force. Based on the comparative analysis data, there is no discernibe pattern between diet and palate width. However, based on the studies discussed in
Chapter 2, a narrow palate is often associated with soft food diets, although my data did not find this correlation.
Allometric studies have also been conducted on the mandible of Old World monkeys and apes (Ravosa, 1996, 2000). Ravosa (2000) showed that larger bodied hominoid taxa typically
273
exhibited more robust mandibles which are likely due to greater balancing-side jaw muscle recruitment during powerful and frequent mastication. This is thought to be associated with a tougher and/or harder diet. In apes, there was also negative allometry observed between jaw breadth and jaw length suggesting that larger apes experience elevated wishboning stress concentrations at the end of the power stroke (Ravosa, 2000). For the Old World monkeys,
Ravosa (1996) compared the cercopithecines and the colobines and suggested that the differences observed in mandibular morphology is likely due to greater sagittal bending of the balancing side corpus of the colobines during mastication of a tougher diet.
As previously discussed, to interpret the patterns of palatal allometry, the results depend upon the facial dimension used for size proxy. If skull length is used as the size proxy then both papionins and colobines have palatal dimensions that are disproportionate at larger body sizes given the results of positive allometry. This indicates that their palates increase in size disproportionately to their skull size. Some of the palatal dimensions of the hominoids also increased disproportionately compared to the facial or skull size while others were proportionate, i.e. isometric. Does this indicate that these Old World monkeys and apes have palates that are optimized for biomechanical efficiency in terms of hard object feeding? Based on the assumptions made previously, the answer is no, at least for molar biting where a narrower palate would produce a larger bite force. However, a longer palate may be necessary during incisal biting in order to maximize gape, but it would also increase the load moment arm which would not be necessarily good for the organism, unless the organism needed to produce more bite force.
Not all of the species examined have diets containing hard items; however, species such as
Colobus polykomos have been known to gnaw open hard seed pods which means a longer palate
274
might be helpful, but if the seed itself is not particularly hard then the narrower palate may not be necessary to generate more molar bite force.
The palatal allometric data are difficult to interpret. One variable that I was unable to collect in my comparative study was palate thickness. This could be potentially informative although given the cross section of the rostrum, a 1mm versus a 2mm thick palate is probably not going to have a dramatic effect on the mechanics of the palate. The mandibular allometric data are interpreted using the tenets of beam theory as a framework. Although the same is done here for the palatal data, it is important to remember that the theoretical modeling discussed earlier showed that the palate does not behave like a beam even though its geometry might be interpretable as a short beam (sensu Young and Budynas (2002)). This does not invalidate the interpretations of the palatal data above but does warrant that the interpretations be viewed with the understanding of this limitation.
Implications of Research for Understanding the Functional Morphology of the Skull
My research project contributes towards an improved understanding of the functional morphology of the vertebrate, specifically the primate, skull. This knowledge is fundamental for an understanding of how biomechanical factors influence metabolic activity in bone tissue.
Loads have long been recognized as having a significant influence on modeling and remodeling of bone. In the context of paleoanthropology, this research will contribute to the question of which mechanical variables are important in regulating bone mass. This is vital if credible functional linkages are to be made between masticatory activities and palatal morphology. This research will aid the longer term goals of determining the functional significance of skeletal elements found in the fossil record and providing an increased understanding of how the stress/strain field in the palate relates to masticatory activities. Another long term goal of this research is to contribute to the field of mechanobiology and add to the current understanding of
275
craniofacial disorders such as cleft lip and palate. Mechanobiology is a growing area of research that studies the interaction between mechanical signals and biological processes in cells and tissues. In order to effectively understand craniofacial anomalies, an understanding of the relationship between mechanics and craniofacial growth is necessary (Mao and Nah, 2004).
One issue related to the palate that has been discussed in the literature concerns the palate thickness of the fossil genus Paranthropus. The heavily built facial features of this robust australopithecine have been linked to a hard diet that required powerful mastication (Rak, 1983).
The thicker palate has traditionally been viewed as a structural adaptation whose purpose is to counter high magnitude masticatory stresses. However, alternative models have been proposed to explain the thickened palate in Paranthropus that are related to developmental aspects of the facial skeleton (McCollum, 1994, 1997)
McCollum (1997) proposed two alternative non-mechanical models based on the structural relationships between 1) the hard palate and the premaxilla and 2) the hard palate and posterior facial skeleton. The first developmental model proposed, referred to as the “subnasal morphology” model, states that there is a positive correlation between palate thickness and the degree of overlap of the subnasal elements (premaxilla). This hypothesis is based on the knowledge that these subnasal elements are linked to the respiratory mucosa found in this area and that the thickened hard palate is simply a method of maintaining the necessary spatial relations of the nasal capsule with the remainder of the facial skeleton (McCollum, 1997). The second developmental model is known as the “posterior facial hyperplasia” model. Posterior facial hyperplasia refers to a growth process where the vertical growth of the posterior maxilla exceeds that of the anterior portion. This second model states that the thickened palate is simply a byproduct of this growth process.
276
Recent studies have provided more support for the structural adaptation of the thickened
Paranthropus palate as a means of countering high stresses due to masticatory demands (Strait et al., 2007; Menegaz et al., 2009). Strait et al. (2007) constructed a finite element model of a macaque skull with a normal palate and a thickened palate. The results of the analysis support the idea that the palate acts to withstand torsional loads associated with mastication by stiffening and strengthening the rostrum (Thomason and Russell, 1986). However, they do also point out that the interpretation of a thickened palate is not straightforward since it also increases stress in other parts of the face. Essentially this implies that a thickened palate had to evolve as a suite of facial characteristics and not independently (Strait et al., 2007).
The results of my study contribute to our overall knowledge of the functional morphology of the skull by providing experimental data on the strain profile of the hard palate of the macaque during bending and torsion. Material property data, i.e. elastic moduli and density, also provided more information on the structural composition of the bony palate. The relatively low elastic moduli of palatal bone imply that stiffness is not as large a concern in this structure as other skeletal elements. Density is also relatively low in the palate suggesting that strength may not be of primary importance, but rather increasing toughness may be more important. The data suggests that the palate likely functions as a strut to help the face resist twisting during biting.
The comparative analysis provided a broad overview of the sutural complexity present in representative species of Old World monkeys and apes as well as the diversity seen in the dimensions of the palate among these species. The sutural complexity data supports the idea that the morphology of the suture will become more complex when it is exposed to higher loads.
Unresolved Questions
There are still many unresolved questions that need to be addressed in order to obtain a more complete understanding of the mechanical environment of the hard palate in primates. One
277
of the first unresolved questions is how to best model the rostrum. My study showed that modeling the palate as a beam does not provide accurate predictions for the strains that occur in this area although the problem seems to be a material and inhomogeneity issue rather than geometrical. In addition, my comparative analysis reinforced the fact that there is much structural diversity among the primates in terms of rostrum geometry which means that multiple geometrical models are more than likely needed in order to make accurate predictions of the strain profile. A systematic approach to testing different geometrical models needs to be developed in order to determine which would be the most appropriate for various primate groups. The only way a beam model might work is if the sutures and the voids, i.e. sinuses, could be included in the model.
In the future, a heterogeneous moment of inertia model should be conducted for the palate and maxillary region (Bhatavadekar et al., 2006). In my study, when the moment of inertia for a section was calculated, all of the areas within that section were assumed to have the same material properties, i.e. elastic modulus. This is a simplification; the elastic modulus is not uniform over the entire section. A heterogeneous moment of inertia model would take into account the different elastic moduli values present throughout an entire section. This would yield a more accurate representation of the stiffness throughout the section and should yield a more accurate moment of inertia. Theoretically, using a more accurate moment of inertia value would increase the accuracy of the strain predictions for that section.
A second area that requires further research is the link between dietary consistency and sutural complexity. There are several questions in this area that still need to be addressed. The first unresolved question is whether or not dietary differences between primate groups are sufficiently large enough to elicit differing morphological responses from the bone. Reliable
278
dietary data for the primates involved in the comparison are critical in order to answer this question. For many of the mandibular studies (and maxillary studies), the dietary data are often from a different population than the study samples and only broad dietary categories are used.
Collecting dietary data in the field is difficult, but necessary, if this question is going to be resolved. Mechanical property data on the objects involved in the diets of the primates is also necessary for making accurate judgments as to differences in dietary consistency. Without accurate information concerning the diet and the material properties of the objects that make up the diet, resolving this question is difficult, if not impossible.
Another difficulty with addressing issues surrounding suture complexity is the methodology involved in measuring this variable. The difficulties with using fractal analysis have already been discussed. Suture length ratio fares better than fractal dimension due to the ease of the method and lack of assumptions needed to use the method. However suture length ratio also has a major limitation. This method can only measure the complexity of one surface of the suture. Sutures are three-dimensional structures and a method needs to be developed that can measure the complexity of the entire suture. The internal anatomy of the suture can vary dramatically from the external anatomy. For that matter, the two surfaces of the suture can also vary in complexity. In order to address this issue, a method needs to be developed that can capture (and measure) the complexity of the entire suture.
One phenomenon observed when collecting the sutural complexity data was the fusion of some of the sutures. However the mechanism involved that causes sutures to fuse is still unknown. Increased loads do seem to have an impact on suture fusion. The closure of the mid- palatal sutures of all of the mangabey (C. atys) specimens provides some anecdotal support for this idea, but more data needs to be gathered to truly address this question particularly since
279
other hard object feeders (Lophocebus albigena) showed very little suture fusion. Since suture closure is known to occur in most individuals as they age, developmental studies need to be conducted to address this question. The ages of the specimens used in my study were unknown so it possible the differences in sutural fusion observed were related to age rather than diet.
Documenting the life histories of the organisms involved as well as looking at the genetic factors involved are all areas that need to be addressed to answer these questions related to the fusion of sutures.
280
25
20
15
10 Elastic Modulus (GPa) Modulus Elastic
5
0 Anterior to Posterior Palate
Figure 5-1. Elastic moduli values from the anterior to posterior palate in the transverse section.
281
800
y = -25.07x + 1045.2 R2 = 0.2316
p = 0.334
750
) 3 700
Density (mg/cm 650
600
550
11 12 13 14 15 16 17 Elastic Modulus (GPa)
Figure 5-2. Elastic moduli versus density regression at a regional level of comparison.
282
Figure 5-3. Expectations of stress (σ) prediction based on the change in moment of inertia and bending moment.
Figure 5-4. Span and depth of the macaque skull.
283
Figure 5-5. Wood block set-up to simulate the macaque skull.
Table 5-1. Predicted versus observed strains during cantilever bending of wood block Gage Position I (mm4) Predicted σ (MPa) Predicted µε Observed µε Anterior "Palate" 96775 0.0004 332 498 Middle "Palate" 269787 0.0003 287 219 Posterior "Palate" 959301 0.0002 190 146
Table 5-2. Expected versus observed strain ratios at gage locations in the wood block experiment Gage Location Expected Strain Ratio Observed Strain Ratio “Palate” << 1 1 “Maxilla (alveolar process)” 1 0.39 “Interorbital” 0.3 0.68
284
Table 5-3. Maximum strain at common loads (32-33N) during bending and twisting of the macaque Gage Twisting Incisor Loading Left Molar Loading Rosette 1 581 239 102 Rosette 2 322 171 110 Rosette 3 486 121 38 Rosette 4 387 227 121 Rosette 5 273 141 67 Rosette 6 130 8 32 Single element 1 306 362 142 Single element 2 -26 432 200 Single Element 3 * 292 188 *No strain recorded for this gage during twisting.
Figure 5-6. Regression of fractal dimension and suture length ratio.
285
Table 5-4. Number of specimens whose mid-palatal suture is fused for each species. Total Number Total Number Percentage of Sample Species Examined Fused with Fused Suture Cercocebus torquatus 18 9 50 Lophocebus albigena 20 1 5 Cercocebus agilis 16 1 6 Papio anubis 20 6 30 Mandrillus sphinx 12 2 17 Colobus guereza 20 12 60 Procolobus badius 19 1 5 Colobus polykomos 20 1 5 Procolobus verus 8 0 0 Theropithecus gelada 9 0 0 Papio papio 6 0 0 Papio ursinus 11 4 36 Macaca sylvanus 14 0 0 Macaca fuscata 6 1 17 Macaca mulatta 20 0 0 Macaca fascicularis 20 9 45 Hylobates syndactylus 19 11 58 Hylobates lar 20 17 85 Pongo pygmaeus 20 4 20 Gorilla gorilla 16 9 56 Pan troglodytes 20 16 80 Papio hamadryas 4 1 25 Cercocebus atys 8 8 100
286
CHAPTER 6 CONCLUSIONS
My study provided additional insight into how the macaque palate functions mechanically during incision and mastication through the use of several methodologies.
Material property data were collected through microindentation and micro-computed tomography while strain data was collected by strain gage experimentation. Comparative data on the dimensions of the palate and face were collected for representative species of Old World monkeys and apes as well as their external mid-palatal sutural morphology. Each of these pieces of data has contributed to a better understanding of the loading environment of the hard palate.
Based on the elastic moduli data generated from the microindentation study, the palate and mandible do not seem to be morphologically responsive to the functional environment in a similar manner. The plane that experienced the greatest amount of stiffness was different between the mandible (stiffest along its long axis) and maxillae (stiffest along superior-inferior axis). Overall the mandible had average elastic moduli values that were larger than the palate indicating that the mandible is stiffer and is perhaps subjected to greater stresses than the palate.
A reasonable explanation for this difference is that the mandible has only two points of articulation to the remainder of the skull while the maxillae are in more contact with the rest of the facial skeleton. This provides more area for the loads to be transmitted so the maxillae, specifically the palate, do not have to bear all of the force. Plus the moment of inertia is larger for the face compared to the mandible. The mandible lacks this option so the material properties reflect this difference and the mandible has adapted stiffer bone to withstand the loads. This also ties into the presence of sutures in the maxillae, which are thought to help transmit forces throughout a structure. The mandible lacks sutures and therefore the bone tissue must compensate by producing stiffer and denser bone material.
287
Geometrically the palate has proven to be difficult to model. Beam theory has traditionally been used to model the rostrum so in my study alternative cross sectional geometries were explored to see if any could accurately predict the strains that the structure experiences during loading. None of the geometrical models fared well. As an alternative to beam theory, plate and shell models were also considered; however, these models really are only applicable if the palate functions relatively independent form the rest of the skull which the strain data illustrated is not the case. Therefore, neither the plate nor the shell models provide good alternatives to beam theory. One suggestion for modifying beam theory so it works better is to apply the corrections needed to accommodate short beams at least for modeling the macaque face. If beam theory is going to be applied to the rostrum, then the model needs to develop a way to accommodate the presence of sutures.
There were certain aspects of the models that worked well. For example, the geometry of the snout region was not really an issue once short beam corrections are taken into account. The strain experiments with the wood block suggested the problem was with the material property and inhomogeneity of the structure. These variables need to be scrutinized better in the palate in order to create models that might work. Since the main rationale for developing a way to model the palate is for comparative purposes, more species need to be examined experimentally.
Ideally strain data and material property data need to be collected on each of the species used in the comparative analysis. Then the models evaluated in my study with the macaque could be tested against other primate species.
Although the strain experiments illustrated that the palate experiences strains in both bending and torsion, the strains were overall higher in torsion. This lends support to the idea that the main mechanical function of the palate is to act as a strut when the face is twisted, which
288
occurs during masticatory activities (Ross, 2008). Without the hard palate present, the strain on the face during torsion would increase and most likely these bones would need to be thicker and denser than they currently are in order to prevent fracture. Two thin tube models were used to predict the shear strain, a uniform thickness model and a variable thickness model. Although neither was able to accurately predict the magnitudes of the strains, the variable thickness model was able to account for the high strains that the palate experienced during twisting. In the variable thickness model, the thinnest area will experience the greatest amount of strain.
Examining the coronal section of the face, the palate is the thinnest region of cortical bone and it did experience higher strains compared to the right maxilla and interorbital regions.
The comparative data were used to address issues of allometry of the palate and sutural complexity based on dietary differences. The allometric study showed that the groups scaled idiosyncratically, thus there does not seem to be a general "anthropoid" scaling pattern. Many of the species showed positive allometry for several of the palatal dimensions indicating the palates are increasing disproportionately to skull and facial size. However this statement must be made with caution since the facial dimension used as a size proxy affected the outcome of the results.
Mid-palatal sutures also seem to have a relationship to dietary consistency. The species that had harder food items in their diets showed more suture complexity than those with softer diets. This supports the idea that sutures respond to increased mechanical loads by becoming more interdigitated, i.e. complex. This method did not account for the three-dimensional nature of the suture. Only the complexity of the external suture is accounted for using this method which means the internal anatomy and the internal surface are not included in the complexity measure. Sutures can vary in terms of complexity among these different areas.
289
One of the next steps that should be taken is to develop a method than can accurately measure the three-dimensional complexity of the suture. This could possibly be achieved by combining 3-D imaging of the suture and a modification of the suture length ratio method.
Ontogenetic studies would also be helpful to see how the morphology of specific sutures changes throughout development in individuals with known diets. The material properties of the food items should also be tested to get a better understanding of how hard the food actually is.
One variable that was not examined for the palate was its thickness. Possibly this variable should be taken into account when the palate is mechanically modeled. If the palate were being modeled completely isolated from the remainder of the facial skeleton then it very well could impact loading. However, as the strain experiments showed the palate does not work in isolation from the rest of the face and therefore the palate thickness is not likely to dramatically impact the amount of stress the palate experiences. In other words, a 1mm thick palate versus a 2mm thick palate will have a minimal effect on the moment of inertia when the entire rostrum is considered. However, the thin tube model suggests that palatal thickness would become extremely important for resisting torsion. It would be interesting to examine the palate thickness from comparative samples to determine whether or not this trait could be linked to dietary consistency.
In conclusion, my study has contributed to a better understanding of the mechanical characterization of the hard palate in terms of modeling and overall morphological differences among Old World monkeys and apes. The elastic moduli of palatal bone showed it to be relatively compliant compared to the mandible. The density obtained from the µCT scans suggested that the palate is less dense than the mandible. Both of these material properties suggest that the mandible is subjected to greater stresses than the palate. The sutures present in
290
the palate also have a major impact on how the structure responds to loads. This is one of the major structural differences between the mandible and the maxilla. Another difference is that while the mandible can function relatively independent from the remainder of the skull, the maxillae cannot. To some extent, the whole skull must be modeled rather than just the hard palate or even just the maxilla. However, these structural constraints of the hard palate do not mean that it cannot be examined from a functional or ecomorphological perspective. It simply means that other variables such as the morphology of the suture and the material properties of the sutures and the bone need to be considered as well as the overall morphology of the maxillae.
291
LIST OF REFERENCES
Atmaram GH, and Mohammed H. 1981. Estimation of physiologic stresses with a natural tooth considering fibrous PDL structure. J Dent Res 60(5):873-877.
Bartlett TQ. 2007. The hylobatidae: small apes of Asia. In: Campbell CJ, Fuentes A, Mackinnon KC, Panger M, Bearder SK, editors. Primates in Perspective. New York: Oxford University Press. p 274-289.
Bass WM. 1995. Human osteology: a laboratory and field manual, 4th ed. Missouri: Missouri Archaeological Society, Inc.
Beecher RM, Corruccini RS. 1981. Effects of dietary consistency on craniofacial and occlusal development in the rat. Angle Orthod 51:61-69.
Beecher RM, Corruccini RS, Freeman M. 1983. Craniofacial correlates of dietary consistency in a nonhuman primate. J Craniofac Genet Dev Biol 3:193-202.
Beertsen W, McCulloch CAG, and Sodek J. 1997. The periodontal ligament: a unique, multifunctional connective tissue. Periodontol 2000 13(1):20-40.
Bender PL. 2000. Genetics of cleft lip and palate. J Pediatric Nursing 15:242-249.
Berkovitz BKB. 1990. The structure of the periodontal ligament: an update. Eur J Orthod 12:51- 76.
Bhatavadekar NB, Daegling DJ, and Rapoff AJ. 2006. Application of an image-based weighted measure of skeletal bending stiffness to great ape mandibles. Am J Phys Anthropol 131(2):243-251.
Bohonak AJ, van der Linde K. 2004. RMA: software for reduced major axis regression for Java. http://www.bio.sdsu.edu/pub/andy/rma.html.
Bollert JA, Hendrickx AG. 1971. Morphogenesis of the palate in the baboon (Papio cynocephalus). Teratology 4:343-354.
Booth AH. 1956. The distribution of primates in the Gold Coast. J W Afr Sci Ass 2:122-133.
Bouvier M. 1986. Biomechanical scaling of mandibular dimensions in New World monkeys. Int J Primatol 7(6):551-567.
Bouvier M, Hylander WL. 1984. The effect of dietary consistency on gross and histologic morphology in the craniofacial region of young rats. Am J Anat 170:117-126.
Brinkley LL, Morris-Wiman J. 1984. The role of extracellular matrices in palatal shelf closure. Curr Top Dev Biol 19:17-36.
Burr DB, Martin RB, Schaffler MB, Radin EL. 1985. Bone remodeling in response to in vivo fatigue microdamage. J Biomech 18:189-200.
292
Caldecott JO, Feistner ATC, Gadsby EL. 1996. A comparison of ecological strategies of pig- tailed macaques, mandrills and drills. In: Fa JE, Lindburg DG, editors. Evolution and ecology of macaque societies. New York: Cambridge University Press. P 73-94.
Campbell BG, Loy JD. 2000. Humankind emerging, 8th ed. Boston: Allyn and Bacon.
Carter DR. 1984. Mechanical loading histories and cortical bone remodeling. Calcified Tissue Int 36:S19-S24.
Carter DR, Beaupre GS. 2001. Skeletal function and form: mechanobiology of skeletal development, aging, and regeneration. New York: Cambridge University Press.
Carter D, van der Meulen M, Beaupre G. 1998. Mechanobiologic regulation of osteogenesis and arthrogenesis. In:J Buckwalter, M Ehrlich, L Sandell, S Trippel, editors. Skeletal growth and development: clinical issues and basic science advances. Illinois: American Academy of Orthopaedic Surgeons. p 99-130.
Ciochon RL, Nisbett RA, Corruccini RS. 1997. Dietary consistency and craniofacial development related to masticatory function in minipigs. J Craniofac Genet Dev Biol 17:96-102.
Clark MRB. 1980. The reduced major axis of a bivariate sample. Biometrika 67:441-446.
Clutton-Brock TH. 1975. Feeding behaviour of red colobus and black and white colobus in East Africa. Folia Primatol 23:165-207.
Cohen MM. 2000. Sutural Biology. In: M. Michael Cohen, and MacLean RE, editors. Craniosynostosis: Diagnosis, Evaluation, and Management. New York: Oxford University Press. p 11-23.
Cole TM. 1992. Postnatal heterochrony of the masticatory apparatus in Cebus apella and Cebus albifrons. J Hum Evol 23:253-282.
Cole TM. 1997. RMA: software for reduced major axis regression. Baltimore: The Johns Hopkins University, Department of Cell Biology and Anatomy.
Copray JCVM, Jansen HWB, Duterloo HS. 1985. An in vitro system for studying the effect of variable compressive forces on the mandibular condylar cartilage of the rat. Archs Oral Biol 30:305-311.
Daegling DJ. 1990. Geometry and biomechanics of hominoid mandibles. UMI Dissertation Services. PhD Dissertation.
Daegling DJ. 1992. Mandibular morphology and diet in the genus Cebus. Int J Primatol 13(5):545-570.
Daegling DJ, Hylander WL. 1997. Occlusal forces and mandibular bone strain: is the primate jaw overdesigned? J Hum Evol 33:705-717.
293
Daegling DJ, and Hylander WL. 1998. Biomechanics of torsion in the human mandible. Am J Phys Anthropol 105(1):73-87.
Daegling DJ, McGraw WS. 2001. Feeding, diet, and jaw form in West African Colobus and Procolobus. Int J Primatol 22:1033-1055.
Dasilva GL. 1994. Diet of Colobus polykomos on Tiwai Island: selection of food in relation to its seasonal abundance and nutritional quality. Int J Primatol 15: 655-680.
Davies AG, Oates JF, Dasilva GL. 1999. Patterns of frugivory in three West African colobine monkeys. Int J Primatol 20:327-357.
Dechow PC, and Hylander WL. 2000. Elastic properties and masticatory bone stress in the macaque mandible. Am J Phys Anthropol 112(4):553-574.
Del Santo M, Minarelli AM, Liberti EA. 1998. Morphological aspects of the mid- palatal suture in the human foetus: a light and scanning electron microscopy study. Eur J Orthod 20:93- 99.
Devlin H, Horner K, and Ledgerton D. 1998. A comparison of maxillary and mandibular bone mineral densities. J Prosthet Dent 79(3):323-327.
Dibbets JMH. 1992. One century of Wolff’s law. In: DS Carlson, SA Goldstein, editors. Bone biodynamics in orthodontic and orthopedic treatment. Michigan: Center for Human Growth and Development. p 1-13.
Drage NA, Palmer RM, Blake G, Wilson R, Crane F, and Fogelman I. 2007. A comparison of bone mineral density in the spine, hip and jaws of edentulous subjects. Clin Oral Impl Res 18:496-500.
Engstrom C, Kiliardis S, Thilander B. 1986. The relationship between masticatory function and craniofacial morphology. II. A histological study in the growing rat fed a soft diet. Eur J Orthodont 8:271-279.
Enlow DH, Hans MG. 1996. Essentials of facial growth. New York: W.B. Saunders Company.
Falconer K. 1990. Fractal geometry: mathematical foundations and applications. New York: John Wiley and Sons.
Fashing PJ. 2007. African colobine monkeys: patterns of between-group interaction. In: Campbell CJ, Fuentes A, Mackinnon KC, Panger M, Bearder SK, editors. Primates in perspective. New York: Oxford University Press. p 201-224.
Fleagle JG. 1999. Primate adaptation and evolution, 2nd ed. New York: Academic Press.
Friede H. 1998. Growth sites and growth mechanisms at risk in cleft lip and palate. Acta Odontol Scand 56:346-351.
294
Gamst G, Meyers LS, Guarino. 2008. Analysis of Variance designs. New York: Cambridge University Press.
German RZ, Crompton AW, Levitch LC, Thexton AJ. 1992. The mechanism of suckling in two species of infant mammal: miniature pigs and long-tailed macaques. J Exp Zool 261:322- 330.
Gibert J, Palmqvist P. 1995. Fractal analysis of the Orce skull sutures. J Hum Evol 28: 561-575.
Gingerich PD. 1971. Functional significance of mandibular translation in vertebrate jaw mechanics. Postilla 152:1-10.
Greaves WS. 1985. The mammalian postorbital bar as a torsion-resisting helical strut. J Zool, Lond (A) 207:125-136.
Hall BK. 1984. Developmental processes underlying the evolution of cartilage and bone. Sym Zool S 52:155-176.
Hartwig WC. 1991. Fractal analysis of sagittal suture morphology. J Morphol 210:289-298.
Henderson JH, Longaker MT, and Carter DR. 2004. Sutural bone deposition rate and strain magnitude during cranial development. Bone 34(2):271-280.
Hendrickx AG, Peterson PE. 1997. Perspectives on the use of the baboon in embryology and teratology research. Hum Reprod Update 3:575-592.
Herring SW. 1972. Sutures- a tool in functional cranial analysis. Acta Anat 83:222-247.
Herring SW. 1993. Epigenetic and functional influences on skull growth. In: J Hanken and BK Hall, editors. The skull: volume 1. Chicago: University of Chicago Press. p 153-206.
Herring SW. 2000. Sutures and craniosynostosis: a comparative, functional, and evolutionary perspective. In: MM Cohen, RE MacLean editors. Craniosynostosis: diagnosis, evaluation, and management, 2nd ed. New York: Oxford University Press. p 3-10.
Herring SW. 2007. Masticatory muscles and the skull: a comparative perspective. Arch Oral Biol 52(4):296-299.
Herring SW, Teng S. 2000. Strain in the braincase and its sutures during function. Am J Phys Anthropol 112:575-593.
Hinton RJ. 1988. Response of the intermaxillary suture cartilage to alterations in masticatory function. Anat Rec 220:376-387.
Hylander WL. 1975. The human mandible: lever or link? Am J Phys Anthopol 43: 227-242.
Hylander WL. 1979a. Mandibular function of Galago crassicaudatus and Macaca fascicularis: an in vivo approach to stress analysis of the mandible. J Morphol 159:253-296.
295
Hylander WL. 1979b. An experimental analysis of temporomandibular joint reaction force in macaques. Am J Phys Anthropol 51(3):433-456.
Hylander WL. 1979c. The functional significance of primate mandibular form. J Morphol 160:223-239.
Hylander WL. 1984. Stress and strain in the mandibular symphysis of primates: a test of competing hypotheses. Am J Phys Anthropol 64(1):1-46.
Hylander WL. 1985. Mandibular function and biomechanical stress and scaling. Am Zool 25(2):315-330.
Hylander WL. 1992. Functional anatomy. In: Sarnat BG, and Laskin DM, editors. The Temporomandibular Joint: A Biological Basis for Clinical Practice. Philadelphia: W.B. Saunders Co. p 60-92.
Hylander WL, Johnson KR. 1997. In vivo bone strain patterns in the zygomatic arch of macaques and the significance of these patterns for functional interpretations of craniofacial form. Am J Phys Anthropol 102: 203-232.
Hylander WL, Picq PG, Johnson KR. 1991. Masticatory stress hypotheses and the supraorbital region of primates. Am J Phys Anthropol 86:1-36.
Jablonski N. 1998. The evolution of the doucs and snub-nosed monkeys and the question of the phyletic unity of the odd-nosed colobines. In: Jablonski NG, editor. The natural history of the doucs and snub-nosed monkeys. Singapore: World Scientific Publishing. P 13-52.
Jaslow CR. 1990. Mechanical properties of cranial sutures. J Biomech 23:313-321.
Johnson WM, and Rapoff AJ. 2007. Microindentation in bone: hardness variation with five independent variables. J Mater Sci-Mater M 18(4):591-597.
Jolly CJ. 2007. Baboons, mandrills, and mangabeys: Afro-papionin socioecology in a phylogenetic perspective. In: Campbell CJ, Fuentes A, Mackinnon KC, Panger M, Bearder SK, editors. Primates in Perspective. New York: Oxford University Press. p 240- 251.
Keenan MJ, Hegsted M, Jones KL, Delany JP, Kime JC, Melancon LE, Tulley RT, and Hong KD. 1997. Comparison of bone density measurement techniques: DXA and Archimedes' principle. J Bone Miner Res 12(11):1903-1907.
Kiliaridis S, Engstrom C, Thilander B. 1985. The relationship between the masticatory function and craniofacial morphology. I. A cephalometric longitudinal analysis in the growing rat fed a soft diet. Eur J Orthod 7:273-283.
King AH, Schneiderman ED. 1993. Differential growth among components of the palate in rhesus monkeys. Cleft Palate-Craniofac J 30:302-308.
296
Kirschner RE, LaRossa D. 2000. Cleft lip and palate. Otolaryng Clin N Am 33:1191-1215.
Koolstra JH. 2002. Dynamics of the human masticatory system. Crit Rev Oral Biol M 13(4):366- 376.
Kopher RA, Mao JJ. 2003. Suture growth modulated by the oscillatory component of micromechanical strain. J Bone Miner Res 18:521-528.
Lam YM, Marean CW, and Frey CJ. 1998. Bone density and long bone representation in archaeological faunas: comparing results from CT and photon densitometry. J Archaeol Sci 25:559-570.
Lam YM, Chen X, and Pearson OM. 1999. Intertaxonomic variability in patterns of bone density and the differential representation of bovid, cervid, and equid elements in the archaeological record. Am Antiquity 64(2):343-362.
Lamaye A. Drishti - Volume exploration and presentation tool. Poster presentation, Vis 2006, Baltimore.
Lanyon LE. 1973. Analysis of surface bone strain in the calcaneus of sheep during normal locomotion. J Biomech 6:41-49.
Lanyon LE. 1974. Experimental support for the trajectorial theory of bone structure. J Bone Joint Surg 56B:160-166.
Lanyon LE. 1984. Functional strain as a determinant for bone remodeling. Calcified Tissue Int 36:S56-S61.
Lanyon LE, Goodship AE, Pye CJ, MacFie JH. 1982. Mechanically adaptive bone remodeling. J Biomech 15:141-154.
Lanyon LE, Rubin CT. 1984. Static vs dynamic loads as an influence on bone remodeling. J Biomech 17:897-905.
Leong PL, and Morgan EF. 2009. Correlations between indentation modulus and mineral density in bone-fracture calluses. Integr Comp Biol 49(1):59-68.
Lindh C, Obrant K, and Petersson A. 2004. Maxillary bone mineral density and its relationship to the bone mineral density of the lumbar spine and hip. Oral Surg Oral Med Oral Pathol Oral Radiol Endod 98:102-109.
Linge L. 1970. A technique for the study of morphology in facial sutures under mechanical influence. Rep Congr Eur Orthod Soc 553-567.
Long CA. 1985. Intricate sutures as fractal curves. J Morphol 185:285-295.
Long CA, Long JE. 1992. Fractal dimensions of cranial sutures and waveforms. Acta Anat 145:201-206.
297
Maisels F, Gautier-Hion A, Gautier JP. 1994. Diets of two sympatric colobines in Zaire: more evidence on seed-eating in forests on poor soils. Int J Primatol 15:681-701.
Mandelbrot BB. 1977. Fractal geometry of nature. New York: W.H. Freeman and Company.
Mann RW, Symes SA, Bass WM. 1987. Maxillary suture obliteration: aging the human skeleton based on intact or fragmentary maxilla. J Forensic Sci 32:148-157.
Mao JJ. 2002. Mechanobiology of craniofacial sutures. J Dent Res 81:810-816.
Markey MJ, and Marshall CR. 2007. Linking form and function of the fibrous joints in the skull: a new quantification scheme for cranial sutures using the extant fish Polypterus endlicherii. J Morphol 268:89-102.
Marshall C. 1982. The physical basis of computed tomography. Missouri: Warren H. Green, Inc.
Martin RB, and Boardman DL. 1993. The effects of collagen fiber orientation, porosity, density, and mineralization on bovine cortical bone bending properties. J Biomech 26(9):1047- 1054.
Martin RB, Burr DB, Sharkey NA. 1998. Skeletal tissue mechanics. New York: Springer- Verlag, Inc.
McCollum MA. 1994. Mechanical and spatial determinants of Paranthropus facial form. Am J Phys Anthropol 93(2):259-273.
McCollum MA. 1997. Palatal thickening and facial form in Paranthropus: examination of alternative developmental models. Am J Phys Anthropol 103(3):375-392.
McCulloch CAG, Lekic P, McKee MD. 2000. Role of physical forces in regulating the form and function of the periodontal ligament. Periodont 2000 24:56-72.
Meade JB, Cowin SC, Klawitter JJ, Van Buskirk WC, Skinner HB. 1984. Bone remodeling due to continuously applied loads. Calcified Tissue Int 36:S25-S30.
Melsen B. 1975. Palatal growth studied on human autopsy material. Am J Orthod 68:42-54.
Menard N. 2004. Do ecological factors explain variation in social organization? In: Thierry B, Singh M, Kaumanns W, editors. Macaque societies: a model for the study of social organization. New York: Cambridge University Press. p 237-262.
Menegaz RA, Sublett SV, Figueroa SD, Hoffman TJ, Ravosa MJ. 2009. Phenotypic plasticity and function of the hard palate in growing rabbits. Anat Rec 292:277-284.
Montiero LR, Lessa LG. 2000. Comparative analysis of cranial suture complexity in the genus Caiman (Crocodylia, Alligatoridae). Rev Brasil Biol 60:689-694.
298
Moore KL, Persaud TVN. 2003. The developing human: clinically oriented embryology, 7th ed. Philadelphia: Saunders Publishing. p 221-234.
Moss M. 1969. A theoretical analysis of the functional matrix. Acta Biotheor 18: 195-202.
Muller R, Van Campenhout H, Van Damme B, Van Der Perre G, Dequeker J, Hildebrand T, Ruegsegger P. 1998. Morphometric analysis of human bone biopsies: a quantitative structural comparison of histological sections and micro-computed tomography. Bone 23(1):59-66.
Nicolay CW, Vaders MJ. 2006. Cranial suture complexity in white-tailed deer (Odocoileus virginianus). J Morphol 267(7):841-849.
Oates JF. 1994. The natural history of African colobines. In: AG Davies, JF Oates, editors. Colobine monkeys: their ecology, behaviour and evolution. Cambridge: Cambridge University Press. p 75-128.
O’Connor JA, Lanyon LE, MacFie H. 1982. The influence of strain rate on adaptive bone remodeling. J Biomech 15:767-781.
Oudhof HAJ. 1982. Sutural growth. Acta Anat 112:58-68.
Persson M. 1970. Postnatal growth of facial sutures. Rep Congr Eur Orthod Soc 543- 552.
Persson M. 1995. The role of sutures in normal and abnormal craniofacial growth. Acta Odontol Scand 53:152-161.
Pirelli P, Botti F, Ragazzoni E, Arcuri C, Cocchia D. 1999. A light microscopic investigation of the human midpalatal suture. It J Anat Embryol 104:11-18.
Preuschoft H. 1989. Biomechanical approach to the evolution of the facial skeleton of hominoid primates. Forts Zool 35:421-431.
Pritchard JJ, Scott JH, Girgis FG. 1956. The structure and development of cranial and facial sutures. J Anat 90:73-86.
Rafferty KL, Herring SW. 1999. Craniofacial sutures: morphology, growth, and in vivo masticatory strains. J Morphol 242:167-179. Rubin CT, Lanyon LE. 1985. Regulation of bone mass by mechanical strain magnitude. Calcified Tissue Int 37:411-417.
Rafferty KL, Herring SW, and Marshall CD. 2003. Biomechanics of the rostrum and the role of facial sutures. J Morphol 257(1):33-44.
Rak Y. 1983. The australopithecine face. New York: Academic Press.
Ramrakhiani M, Pal D, Murty T. 1979. Micro-indentation hardness studies on human bones. Acta Anat 103:358-362.
299
Rapoff AJ, Rinaldi RG, Hotzman JL, and Daegling DJ. 2008. Elastic modulus variation in mandibular bone: a microindentation study of Macaca fascicularis. Am J Phys Anthropol 135(1).
Rasband, W.S., ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/, 1997-2009.
Ravosa MJ. 1996. Jaw morphology and function in living and fossil Old World monkeys. Int J Primatol 17(6):909-932.
Ravosa MJ. 2000. Size and scaling in the mandible of living and extinct apes. Folia Primatol 71:305-322.
Rees JS, and Jacobsen PH. 1997. Elastic modulus of the periodontal ligament. Biomaterials 18(14):995-999.
Rho JY, Pharr GM. 1999. Effects of drying on the mechanical properties of bovine femur measured by nanoindentation. J Mater Sci-Mater M 10(8):485-488.
Robinson M. 1946. The temporomandibular joint: theory of reflex controlled non-lever action of the mandible. J Am Dent Assoc 33:1260-1271.
Ross CF. 2008. Does the primate face torque? In: Vinyard CJ, Ravosa MJ, Wall CE, editors. Primate craniofacial function and biology. Chicago: Springer. p 63-82.
Rubin CT, and Lanyon LE. 1984. Dynamic strain similarity in vertebrates: an alternative to allometric limb bone scaling. J Theor Biol 107(2):321-327.
Rubin CT, and Lanyon LE. 1985. Regulation of bone mass by mechanical strain magnitude. Calcified Tissue Int 37:411-417.
Ruegsegger P, Koller B, and Muller R. 1996. A microtomographic system for the nondestructive evaluation of bone architecture. Calcified Tissue Int 58:24-29.
Ruff CB, and Leo FP. 1986. Use of computed tomography in skeletal structure research. Yearb Phys Anthropol 29:181-196.
Russell AP, Thomason JJ. 1993. Mechanical analysis of the mammalian head skeleton. In: BK Hall, J Hanken, editors. The skull: volume 3. Chicago: University of Chicago Press. p 345- 383.
Sarnat BG. 2003. Gross growth and regrowth of sutures: reflections on some personal research. J Craniofac Surg 14:438-444.
Scheuer L, Black S. 2000. Developmental juvenile osteology. Academic Press: New York.
Sejrsen B, Kjaer I, Jakobsen J. 1996. Human palatal growth evaluated on medieval crania using nerve canal openings as references. Amer J Phys Anthropol 99:603-611.
300
Silau AM, Njio B, Solow B, Kjaer I. 1994. Prenatal sagittal growth of the osseous components of the human palate. J Craniofac Genet Dev Biol 14:252-256.
Simon MR. 1977. The role of compressive forces in the normal maturation of the condylar cartilage in the rat. Acta anat 97:351-360.
Smith RJ. 1978. Mandibular biomechanics and temporomandibular joint function in primates. Am J Phys Anthropol 49(3):341-350.
Smith RJ. 1984. Allometric scaling in comparative biology: problems of concept and method. Am J Physiol 246:R152-R160.
Sokal RR, Rohlf FJ. 1981. Biometry, 2nd ed. New York: WH Freeman and Company.
Strait DS, Wang Q, Dechow PC, Ross CF, Spencer MA, Patel BA. 2005. Modeling elastic properties in finite element analysis: how much precision is needed to produce an accurate model. Anat Rec 283A(2):275-287.
Strait DS, Richmond BG, Spencer MA, Ross CF, Dechow PC, and Wood BA. 2007. Masticatory biomechanics and its relevance to early hominid phylogeny: an examination of palatal thickness using finite-element analysis. J Hum Evol 52(5):585-599.
Sun Z, Lee E, and Herring SW. 2004. Cranial sutures and bones: growth and fusion in relation to masticatory strain. Anat Rec 276A(2):150-161.
Swindler DR, Sirianni JE. 1973. Palatal growth rates in Macaca nemestrina and Papio Cynocephalus. Am J Phys Anthropol 38:83-92.
Takahashi S. 1981. Illustrated computer tomography: a practical guide to CT interpretations. New York: Springer-Verlag.
Thexton AJ, Crompton AW, German RZ. 1998. Transition from suckling to drinking at weaning: a kinematic and electromyographic study in miniature pigs. J Exp Zool 280:327-343.
Thierry B. 2007. The macaques: a double layered social organization. In: Campbell CJ, Fuentes A, Mackinnon KC, Panger M, Bearder SK, editors. Primates in Perspective. New York: Oxford University Press. p 224-239.
Thomason JJ, and Russell AP. 1986. Mechanical factors in the evolution of the mammalian secondary palate: a theoretical analysis. J Morphol 189:199-213.
Throckmorton GS, Dechow PC. 1994. In vitro strain measurements in the condylar process of the human mandible. Archs Oral Biol 39:853-867.
Vander Voort GF, and Lucas GM. 1998. Microindentation hardness testing. Mater Sci Forum 154(3):21-25.
301
Vinyard CJ, and Ravosa MJ. 1998. Ontogeny, function, and scaling of the mandibular symphysis in papionin primates. J Morphol 235(2):157-175.
Wagemans PAHM, van de Velde JP, Kuijpers-Jagtman AM. 1988. Sutures and forces: a review. Am J Orthod Dentofacial Orthop 94:129-141.
Wang Q, and Dechow PC. 2006. Elastic properties of external cortical bone in the craniofacial skeleton of the rhesus monkey. Am J Phys Anthropol 131(1):402-415.
Wainwright SA. 1988. Form and function in organisms. Amer Zool 28:671-680.
Walker A. 1978. Functional anatomy of oral tissues: mastication and deglutition. In: Shaw JH, Sweeney EA, Cappuccino CC, and Meller SM, editors. Textbook of Oral Biology. Philadelphia: W.B. Saunders Co. p 277-296.
Whiten A, Byrne RW, Barton RA, Waterman PG, Henzi SP. 1991. Dietary and foraging strategies of baboons. Phil Trans R Soc Lond B 334:187-197.
Yamamoto S. 1996. The effects of food consistency on maxillary growth in rats. Eur J Orthod 18:601-615.
Young WC, Budynas RG. 2002. Roark’s formulas for stress and strain, 7th ed. New York: McGraw-Hill.
Yu JC, Wright R, Williamson MA, Braselton JP, Abell ML. 2003. A fractal analysis of human cranial sutures. Cleft Pal-Craniofac J 40:409-415.
302
BIOGRAPHICAL SKETCH
Jennifer Hotzman is one of four children and was born in Meridian, Mississippi. She received her Bachelor of Arts degree in Anthropology from the University of Southern
Mississippi in 2000 and her Master of Arts degree from the University of Florida in 2004. While completing her graduate studies, Ms. Hotzman also worked full-time for 2 years for
Regeneration Technologies, a company that manufactures allografts for surgical procedures.
After obtaining her Master of Arts degree, she taught anatomy and physiology at Santa Fe
College and St. Petersburg College. She has accepted a position as a project manager for a company specializing in anthropometry, Anthrotech, where she will contribute her knowledge and skills to a large scale anthropometric survey of the United States Marines and Army.
303