ARCHlTECTLRE OF THE HUMAN SOLEUS MUSCLE: THREE-DIMENSIONAL COMPUTER MODEKING OF CADAVERIC MUSCLE AND ULTRASONOGRAPHIC DOCUMENTATION IN VIVO
Anne Maria Reet Agur
A thesis submitted in confonnity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Institute of Medicai Science
University of Toronto
Copyright by Anne Maria Reet Agur 200 1 National Library Bblioth ue nationale of Canada du Cana% uisiions and Acquisitions et 6&graphic Services seniices bibüographigues
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The author =tains ownership of the L'auteur conserve la propriété du copyrighî in this thesis. Neither the &oh d'auteur qui protège cette thèse. thesis nor substantial exbtacts fiom t Ni la thèse ni des exüah substantieIs may be printed or otherwise de celle-ci ne doivent être imprimés reproduced wahout the author's ou autrement reproduits sans son permis sion. autorisation. Architecture of the human soleus muscle: Three-dimensional computer modelhg of cadaveric muscle and uitrasonographic documentation in vivo
Anne Maria Reet Agur Doctor of Philosophy, hstitute of Medicd Science Facuity of Medicine, University of Toronto, 2001
Abstract
The purpose of this study was to visualize and document the architecture of the human soleus muscfe throughout its entire volume. The architecture was visualized by creating a three-dimensional manipulatable computer mode1 of an entire cadavenc soleus, in siru, using B-spline solids to display muscle fiber bundles that had been seridiy dissected, pinned and digitized. A database of uber bundle length and angle of pemation throughout the marginal, postenor and anterior soleus was compiled fiom three sources: the computer model, manuaily measured cadavenc specimens and hmuitrasonographic scans of relaxed and contracted muscle of living subjects. The computer model dlowed documentation of the architectural parameters in the-dimensionai space, with the angle of pennation being measured relative to the tangent plane of the point of amchment of a fiber bunàie. The architecturai panmeters recorded to date have been two-dimensionai, Like those obtained from the scans and manuaiiy measured cadaveric specimens in this study. Thne-dimensionai recoostmction is an exciting innovation since it provides not ody an architectural database but aisc aiiows visualization of each nber bunde in situ 6rom any perspective. It was concluded rhat the architecture is non-dom throughout the volume of soleus, the percentage change of the architectural parameters on contraction varies by muscle part and the soleus of fernales has significantly longer fiber bundles, smalIer angles of pemation and is not as thick as the solens of males. The techniques developed in this thesis provide a novel approach to the study of muscle architecture. Detailed architectural stndies may lead tu the development of muscle models that can more accurately pdict interaction between muscle parts, the effect of pnthoIogic states on muscle fimction and force generation. Acknowledgements
It is with great pleasure that 1express my thanks to ail those that connibuted to this work. 1am particularly indebted to my mentor and research supe~sor,Dr. Nancy
Hunt McKee, for her enthusiasm, interest and guidance throughout the project.
To my fefiow graduate student and coilaborator Victor Ng-Thow-Hing and his supe~sor,Dr. E. Fiume, 1wodd like to express my appreciation for a most memorable and enrichhg expenence. This interdisciplinary work has resulted in two PhD theses with the development of many novel concepts and techniques. To our chical collaborator Dr. R Leekam rnany thanks for his tireless cornmitment and support. It has, dso been a pleasure working with Drs. K. BaU and D. Salonen and Ms. V. Oxorn, and aii of our project and summer students.
My sincerest thadcs to my advisory committee, Drs. C. Rodgers, W. MacKay, K.
Jeejeebhoy, P. Cauwenbergs and K. Bd, for their expert advice and assistance. 1wouid aiso like to recognize the contributions of the examination cornmittee consisting of the advisory committee and Dn. J. Dostrovsky, T. OIson and C. Yip.
A special thank you to my coileagues in the Division of Anatomy, Department of
Surgery, especidy Dr. C. PUicus and Prof. A. Colthurst, and to Dr. C. Whiteside, Graduate Coordinator, Institute of Medicai Science.
Fmdy and most importantly 1am grateful to my husband EMOfor his love and support in helping me make my dream become a reality. A p&cuiar thank you and many hugs to my cMdren Erik and Kristina, and to my mother for her encouragement when it was most needed.
AcknowIedgement is made to the AO/ASIF Fomdatioa, SwitzerIand and the
Department of Surgery, Uoiversity of Toronto for hancial support- Table of Contents
Page
Abstract
Table of Contents
List of Figures
List of Tables
List of Abbreviations
Chapter 1: Lntmduction
1.1 Contents of thesis
Chapter 2: Literahire Survey
2.1 Structure and function of human skeletal muscle
2.1.1 Structure of human skeletai muscie 2.1.2 Enect of fi'bet architecture on skeletal muscie function 2.1.3 Force-length relation 2.1.4 Force-velocity relation 2.1.5 Physiological Cross Sectiond Area 2.1.6 Co~ectivetissue components 2.1 -6.1 Aponeuroses and tendons 2.1.6.2 Bony attachent sites 2.1.7 Why study skele td muscle architecture?
2.2 Architecture of the human soIeus muscle
221 Histoncai perspective 22.2 Methodology of quantitative cadavenc smdies 21.3 Resolts of quantitative cadaverîc shidies 2.2.4 Postmortem muscle tissue 2.3 haging in vivo muscle architecture
23.1 Ultrasonography 23.2 Magnetic resonance irnaging
2.4 Muscle modehg
2.4.1 HiLi's mode1 2.4.2 Use of hman muscie architectural data in muscle models 2.4.3 Modebg of the human soleus muscle
2.5 Fuuctions of the human soleus muscle
Chapter 3: Hypotheses and Objectives
3.1 Hypotheses 3.2 Objectives 3.3 Significance 3.4 Definition of marginal, postenor and antenor soleus
Chapter 4: Methods
4.1 Development of the muscle mode1 based on cadaveric specimens
4.1.1 Caiibration devices 4.1.2 Photognphy 4.1.3 Dissection 4.1.3.1 Specimens 4.1.3.2 Marginal soleus 4.1 3.3 Postenor soleus 4.1.3.4 Anterior soleus 4.1.4 Digitization 4.1.4.1 Digitization of the baseplate 4.1.4.2 Digitization of the volume plate 4.1.4.3 Digitization of the marker clusters 4.1.4.4 Digitization of the serial dissections 4.15 Reconstruction of digitized data nom 2-Dto 3-Dcoordinates 4.1.6 ModeIlhg of the soleus muscle with B-spline solids
4.2 ArcbitecturaI parameters of cadavenc soleus muscle: manuai measurement 77
4.2.1 Specimens 77 4.2.2 Manual meamernent of gros morphological characteristics 77 4.2.3 Manual measurement of nber bundle length and angle of pennation 79 of the marginal, antenor and posterior soleus 423.1 Marginal soleus 79 4.2.3.2 Posterior soleus 4.2.3.3 Anterior soleus 4.2.3.4 Analysis of manual measurements 4.2.4 Cornparison of architectural parameters obtained by manual measurement aud from the computer mode1
4.3 In vivo imaging
4.3.1 Ulmound study 4.3.1.1 Subjects 4.3.1.2 Snidy protocol 4.3.1.3 Measurement of architechual parameters hm ultrasound scans 4.3.1.4 Statisticd anaiysis 4.3.2 Magnetic resonance imaging: Püot study
4.4 Cornparisonlanalysis of data obtained hmcadaver studies and in vivo data obtained by ultrasound
4.5 Comparisonlanaiysis of data obtained by computer modeiling, manual meamrement and by ultrasound
5.1 Soleus architecture: Modelling of cadaveric muscle
5.1.1 Three-dimensional visuaikation of soleus muscle atchitecture 5.1.2 Documentation of soleus muscle architecture 5.1.3 Summary of muscle architectural parameters: Fiber bundle length and angie of pemation 5.1.3.1 MarginaI soleus S.1.3.2 Posterior soleus 5. t -3.3 Anterior soleus
5.2 Soleus architecture: Manuai measurement of cadaveric muscle
5.2.1 Gross morphologicd characteristics 5.22 Smaryof muscle architectural parameters: Fiber bunde length and angie of pemation 5.221 Marginal soleus 5.2.2.2 Posterior soleus 5.223 Anterior solens
5.3 Solens architecture: In vivo uitrasound 5.3.2 Anterior soleus 5.3.3 Statistical analysis of in vivo data 5.3.3.1 Relaxed muscle 5.332 Contracted muscle 5.3.3.3 Gender differences
5.4 Soleus architecture: Cornparison of manual (cadavenc) and in vivo measurements
5.5 Soleus architecture: Cornpuison of computer modeiiing (cadaveric), manuai (cadaveric) and in vivo measurements
Chapter 6: Discussion
6.1 Visualization of muscle architecture using a B-spliae solids mode1
6.2 Measurement of architechiral parameters of human muscle
6.3 Architectural parameters of cadavenc human soleus muscle 6.3.1 Muscle length 6.3.2 Muscle volume 6.3.3 Fiber bundle length 6.3.4 Angle of peunation
6.4 Architectural parameters of in vivo human soleus muscie 6.4.1 Anterior and posterior soleus 6.4.2 Gender differences
6.5 Cadavenc and in vivo rneasurements of the architectural panuneten
6.6 Architectural parameters aad muscle modeliing
6.7 Fmctiond considerations
Chapter 7: Conclusions
Chapter 8: Future Directions
Appendix A: Photogmnmetric 3-D Point Reconstruction
Appendix B: Mathematics of Vectors and Matrices List of Fignres
Chapter 2:
Figure 2.1. The organization of human skeletal muscle. Figure 2.2. Fascicdar architecture of skeletal muscle, Figure 2.3. Schematic iiiustration of a sarcomere. Figure 2.4. Effect of fiber pennatioa angle on force production. Eigure 2.5. Theoreticai force-length relationship. Figure 2.6. Nomalized force-velocity curve. Figure 2.7. Termination of skeletal muscle in tendon, longitudinal section. Figure 2.8. Transverse section through the middle third of the human soleus muscle.
Chapter 3:
Figure 3.1. Marginal soleus, posterolaterai view. Figure 32. Postenor soleus, posterdateral view. Figure 3.3. Anterior soleus, anterior view.
Chapter 4:
Figure 4.1. CaLbration devices. A. Schematic illustration of the baseplate and volume plate, laterd view. B. The baseplate with one specimen support, superolaterai view. C. The volume plate positioned on baseplate, superdateral view.
Figure 4.2. Marker clustea pinned to a specimen, postenor view.
Figure 4.3. Schematic illustration of the position of the three cameras relative to the baseplate and volume plate.
Figure 4.4. Pinned fiber bundles of marginal soleris, postenor view.
Figure 45. Pinned fiber bnndies of postenor soieus, postenor view.
Figure 4.6. Pinned fiber bundes of the anterior soleus, posterior view.
Figare 4.7. Recording sheet showing the nambering of the coorduiates of the baseplate and volume piate.
Recording sheet for each levef of seriai dissection. Ismesand iso-surfaces generated from a B-sphe soüd. Figure 4.10. Generation of fiber bandles using the Sobol sequence.
Figure 4.1 1. A. Schematic illustration of the measurement of angle of pemation using the B-spline muscle model. B. Measurement of fiber bundle length (mm) and angie of pemation (degrees) hmthe B-spline muscle rnodel. Figure 4.12. Nunbe~gscheme and location of Eiber bundles (streadhes) used to record fiber length and angles of pennation. A. Right marginal soleus, posterornedial view B. Right posterior soleus, posterior view. Figure 4.13. Nttmbe~gscheme and location of fiber bundles (streamlines) used to record fiber length and angles of pennation of right anterior soleus, anterior views. A. Most posterior layer. B. Most anterior layer.
Figure 4.14. Measurement of soleus muscle length. Figure 4.15. Manual measurement of fiber length (FL) and angle of pennation ($1 of marginal soleus.
Figure 4.16. Manual measurements of postenor soleus. A. Sites of sagittal incisions (1-3). B. Measurement of fiber length (FL) and angles of pemation (8,and (&).
Figue 4.17. Manual measmement of fiber length (FL) and angles of pemation (bs)on the medial and lateral sides of the rnedian septum. Figure 4.18. Location of the sonographic scnnning sites of posterior soleus, postenor view. Figure 4.19. Location of the sonographic scanning sites of anterior soleus, medid view. Figure 4.20. Measurement of architectural parameters hm~Itrasound scam. A. Schematic illustration. B. Relaxed uitrasormd scan, sagittal plane. C. Contracted uitrasound scan, sagittal plane.
Cornputer modeMing of right marginal soleus. Streamlines (IO0 fiber bundes): A. Postenor view B. Anterior view C. Posteromedid view D. Posterolated view E. Anterornedial view F. Anterolaterai view G. Posterosupetior view K Superornediai view Streamlines (400 fiber bundes): 1. Posterulated view J. Posterornedial view Template: K, Posterior view L. Posterolateral view
Figure 52. Computer modelling of right posterior soleus. Streamlines (100 fiber bundles): A. Posterior view B. Anterior view C. Supenor view D. Merior view E, Medial view F- Lateral view G. Aaterolaterd view H. Posterornediai view Streamlines (400 fiber bundles): 1. Posterior view J. Posteroiaterai view Template: K. Posterior view L. Lateral view
Figure 5.3. Computer modebg of right anterior soleus. Stremdines (100 fibet bundlu) for each layer, where layer I is most postenor and layer 4 is most anterior: a posterior view is shown of each layer. A. Layer 1 B. Layer 2 C. Layer 3 D. Layer 4 Streamlines (400 fiber bundes): E. Posterior view F. Mediai view Template: G. Posterior view K. Anterior view
Figure 5.4 Numbered fiber bundies of right marginal soleus, posterornedial view . Figure 5.5 Numbered fiber bundles of right posterior soleus, posterior view.
Figure 5.6 Numbered fiber bundles of right anterior soleus, posterior views. A. Layer I B. Layer 2 C. Layer 3 D. Layer4
Appendix A:
Figure A. 1. Two-dheasional representations of grid pattern in image planes (CIk, K), k = 1.2 and 3 of the three-dimensionai object in object space (X,Y, 2). Figure A2 Camera intemal parameters.
Figure A3 Base plate and &%ration plate for DLT parameter estimation. List of Tables
Page
Chapter 2:
Table 2.1 Summary of the type of architecturai data obtaiaed in cadavenc studies of the hman soieus muscle.
Table 2.2 Cornparison of the methodology used by Friedench and Brand (L990) and Wickiewin et al. (1983).
Table 2.3 Summary of mean architectural data of published cadaveric studies of soleus.
Table 2.4 Summary of individual cadaver architecturai data of soleus as rcported in the literature.
Table 25 Summary of mean architectural data of cadaveric studies of soleus by gender.
Table 2.6 Summary of architechual data of published ultrasonographic studies of soleus.
Table 2.7 Overview of source(s) of architectural data used in modelüng studies of human muscle-
Table 4.1 Compater model: Number of tiber bundles in each subdivision of The marginal, posterior and anterior soleus used for data anaiysis.
Chapter 5:
Table 5.1 Cornputer model: 3-Dangles of pennation and fiber length measurements of the fiber bundles of the right marginal soleus.
Table 52 Computer model: 3-D angles of pennation and £iber Iength measurements of the fiber bundes of the rîght posterior soleus.
Table 53 Computer model: 3-D angles of pemation and fiber length measmements of the fiber bmdles of the rîght anterior soleus. A. Layers I and 2. B. Layers 3 and 4.
Table 54 Computer model: Fiber bnnàle length of right margùial soleus. Table 5.5 Computer model: 3-D mgIe of petmation of right marginal soleus 118 rneasured relative to the posterior aponeurosis (Op) and to the artterior aponeurosis (@A).
Table 5.6 Computer model: Average nber bundle length of nght posterior soleus.
Table 5.7 Computer model: 3-D antenor (BA) and posterior (&) mgie of 119 pennation of right postenor soleus.
Table 5.8 Computer model: Fiber bundle length of nght anterior soleus. 120 Table 5.9 Computer model: 3-D angle of pemation of nght anterior soleus 121 relative to the median septum (OMs ) and to the anterior aponemsis (O!
Table 5. 10 Manuai measurements: Average soleus muscle beiîy leogth. 122
Table 5.1 1 Manual measurements: Volume of the anterior, postenor 123 and marginal soleus.
Table 5.12 Manual measurements: Fiber bunde Iength of marginal soleus. 124 Table 5-13 Manuai measurements: Angle of petmation of marginal soleus. 125 Table 5.14 Manuai measurements: Fiber bundle Iength of posterior soleus. 126
Table 5-15 Manual measurements: Anterior (B.)and postenor (Op) angle of penaatioa of postenor soleus-
Table S. f 6 Manual meamments: Fikr bundle length of anterior soleus. 128 Table 5-17 Manuai measurements: Angle of pe~ationof anterior soleus relative to the median septum (@Ms)-
Table 5.18 In vivo ulhasound: Fiber bundle length of posterior soleus. 130 A. Fiber blmdle length of postenor soleus. B. Distriiution of Eber bundle sampling.
Table S. 19. In MVO UItnsound: Muscle thickness of posterior soleus. 131
Table 5.20 In vivo dtrasomd: Antefior (BA) and posterior (6)angle 131 of pennation of posterior soleus.
In vnto ultrasotmck A- Fiber bundle length of anterior soleus. 132 B. Distrr'bution of fiber bundle samphg. TabIe 5-22 In vivo ultrasound: Muscle thickness of anterior soleus, 133
Table 5.23 In vivo ultrasound: Medial (h)and laterai (Bu) angles 133 of pemation of the medial half of the anterior soleus.
Table 5.24. In vivo ultrasound: Percentage changes in fibre bundle length, 135 muscle thickness and angles of pemation of anterior and posterior soleus.
Table 5.25. In vivo ultrasound: Fiber bundle length of the anterior and posterior soieus of males and females.
Table 5.26. In vivo ultrasound: Percentage dinerence between the architectural panuneters of the anterior and posterior soleus of males and femdes.
Table 5.27. In vivo ultrasoand: Angles of peunation of the anterior and postenor soleus of males and females.
Table 5.28. In vivo uitrasound: Muscle thickness of the anterior and posterior soleus of males and fernales.
Table 5.29, Fiber bundle length and angle of peunation in cadaveric and in vivo anterior and posterior soleus.
Table 5.30. Cadaver (computer), cadaver (nimuai measurement) and in vivo ultrasound: Average fiber bundle length of postenor soleus.
Table 5.3 1. Cadaver (computer). cadaver (manual measmment) and in vivo ultrasound: Average nber bunde length of anterior soleus.
Appendix A:
Table A. 1 Initial catiiration data for camera k,
Table A2 Recalt'bration for camera k.
xii List of Abbreviations
8 Angle of pennation
Al Change in length of a sarcomere
AL Change in Iength of the rnyofibril et Fiber with Iarger angle of pennation
0s Fiber with smaü angle of pennation 2-D Two-dimensionai
3-D Tùree-dimensional
A Anterior
%b Constants AP Anterior aponeurwis
C Camera
CSA Cross sectional area
D Marker cluster
DLT Direct Linear transformation f Average force exerted by one myofibril F Femaie F Force
uistantaneous Ioad (pg. 14) Fiber bunde Fiber bundle length Force exerted by muscle nber
Force transmitted to tendon
Merforces Fo Maximal force at zero velocity I Merior
Lat Lated L Le ft
M Male
Med Medial
ML Muscle Iength MS Median septum
MT Muscle thickness
N Number of specimens n Number oE sarcomeres in series (pg. 9)
myofibriis ananged in parailel (pg. 10)
P Posterior P Probabiiity PA Posterior aponeurosis
PCSA Physiological cross sec tional area
Po Maximum tetanic tension R Right
S Superior
SD Standard deviation u Gender unspecified
v Velocity Micrometer
Centime ter
Gram
Hour
Meter
Megahertz
Milliliter
Millimeter
Newton angle of pennation two-dimensional: Angle at the site of attachent of a mer bundle to an aponeurosis, septum or tendon; measured on a sectioned coplanar surface using a protractor. three-dimensional: Angle between the tangent vector of the fiber bundle and the tangent plane of the muscle surface at the point where the mer bundle meets the aponeurosis. aponeurosis, pl. aponeuroses*: A fibrous sheet or ff at, expanded tendon, giving attachment to muscle fibers and sekgas the means of origin or insertion of a muscle. bipennate*: Pertaining to a muscle with a central tendon toward which the obers converge on either side Bethe barbs of a feather.
B-sphe solids: A mathematical primitive that cm be used to represent a muscle as three-dimensional vector functions which cm define an enciosed volume as weU as its boundary surface. digitization: In the present thesis is defined as the process of obtaining x and y coorchates of specific points, marked by pins or bail bearings, on photographs of muscle using the Sigma Scan Image (landel Scientific) Prognm, endomysium*: The fme comective tissue sheath (fine reticuiar and collagen fibers) surroundhg a muscle mer. epirnysium*: The fibrous connective tissue envelope surmunding an entire skeletal muscIe, excursion*: Any movement (e.g. of muscleltendon) from one point to another, usudy with the impiied idea of returning again to the original position. fascia, pl. fasciae*: A sheet of nbms tissue that endoses muscles and groups of muscles- fascicle (nber bundIe)*: A bundle of muscle &ers. nber bundle length: The Iength of a £iber bdemeasored between its two attachment sites (in mm). force*: That which tends to produce motion (or deformaiion) in a body. multipemate*: A muscle with several central tendons toward which the muscle fi'bers converge Like the barbs of bathers. muscle architecture: The anangement of muscle nbers and comective tissue within a muscle, muscle fiber (myofiber): A single skeletal muscle ceil. muscle length: Length measured fiom the most proximal to the most distal attachment of muscle fiber bwidies (in cm). muscIe thickness: Measured at the center of each uitrasound scan, as the perpendicular distance between the two aponewses to which the muscle fiber bundles attach. myofibril*: Component of a skeletal muscle fiber; comprising of many reguiarly overlapped thick and thin myofdaments. myofilament*: The ulttamicroscopic kadsof nlamentous protein (actin and myosin) making up the myofibrils in striated muscle. perimysium*: The fibrous sheath enveloping each of the bundles (faxicles) of skeletai muscle fibers. sarcomere*: The segment of a myofibnl between two adjacent Z lines, representing the functionai unit of striated muscle, septum*: A term appiied to aponeurotic sheets separahg various muscles or parts within a muscle; may nui in the center of the muscie for a longer or shorter distance, receiving the muscular fibea almg its surfaces serial dissection: The fiber bundles of a muscle are exposed sequentiaüy in layen hm superficial to deep throughout the volume of the muscle. skeletd muscle*: A muscle consisting of elongated, muitinucleated, transversely stnated skeletd muscle fibers together with comective tissues, blood vessels, and nerves bundles. streamünes: Fiber bundles that have been generated by the B-splioe solid modeI, based on the origlliai dissection data set (template). template: The original fiber bundle data set obtained hmthe pinned specimen and entered into the B-spline solid. tendon*: A fibrous cord or band of variable Iength that connects a muscle with its bony attachment. 1t consists of fascicles of very densely ananged, aimost pardel coliagenous ers,rows of elongated nbrocytes, and a minimum of gromd substance.
xvii three-dimensionai (3-Il) representation of muscle: The description of the location, in space, of points demarcating fiber bundes within a muscIe in terms of a 3-D coordinate system. In the present thesis, a rectilioear coordinate system is utilized in which the three coordinates (x,y,z) are perpendicular to each other. two-dimensional(2-D) representation of muscle: The description of the location in space of points demarcating fÏber bundles within a muscle in terms of a 2-Dcoordinate system. In the present thesis, a nctilinear coorduiate system is utilized in which the two coordinates (x,y) or (u,v) are perpendicular to each other.
In the compter modehg part of this thesis, 2-Drepresentation is used to describe the projection of a 3-D muscle onto a planar surface, for example as captured with a camera. Here, the spatial orientation of the plane is determined by the angle of the camera relative to the muscle.
In the uitrasonographic and maaual meamment parts of this thesis, 2-D representation is a subset of 3-D representation in which the location in space of points in the muscle along a given plane is described in two dimensions. unipennate (semipemate)': Denoting certain muscles with fibers ninning at an acute angle hmone side of a tendon; resembüng one-haif of a feather. velocity*: Rate and direction of movement; specincaily, distance traveiIed per unit time in a given direction. volume*: Space occupied by matter (e-g. muscle), expressed usuaUy in cubic mülimeters, cubic centimeters, Liters, etc. Chapter 1: Introduction
The human body contains over 600 skeletal muscles (Pierryiiowski, 1995) that for the most part attach to the bony skeleton. These muscies form about hdf the mass of the human body and are able to generate forces that act on the skeleton to produce movement or provide stability. For example, to walk one step about 200 muscles (Sedeen, 1986) are activated in a coordinated fishion. Elftman (1966) stated that:
"... the human body is built around a complex of bone levers whose position and movement are controiled by muscles. For this purpose each individual is provided with a quarter billion striated muscle fibers amully assembled into muscles and attached to the skeletal levers in strategic positions."
The arrangement of the quarter billion muscle fibers in a multitude of assembly patterns provides each muscle with its own unique functional charactenstics. The architecture of a muscle consists of its extemal configuration and dimensions, and the internai arrangement and morphology of the contractile and comective tissue elements.
Two muscles having the same extemal configuration may differ greatly in function due to differences in interna1 arrangement of contractile and connective tissue elements.
Historicdiy morphological snidies of muscle have been pureiy descriptive in natm (Otten, L988), but a quantitative analysis of muscle architecture is important because the structurai parameters have a profound effect on muscle hction (Muhi,
1982; Woittkz et al., L983b). Architecturai &ta form an integrai part of mathematical models which have been developed to study skeletal muscle (Huijing and Woittiez, 1984;
Herzog and ter Ketus. 1988; men, 1988). Rowever, human muscle architechual data are incomplete and based on relatively small sample sizes (Pienynowski and Morrison, 1985; Yamaguchi et al., 1990). The architecturai parameters of skeletal muscle have usualIy been dehed by one average value for the entire muscle, regardes of the complexity of pemation (Witkiewicz et al., L982; Friederich and Brand, 1990). To
"advance the state of the aa" more specific documentation of fiber architecture may help in understanding the purpose of multiple fiber arrangements within a single muscle.
The stnicturally complex human soleus muscle was chosen as the focus of this study. In bipeds, soleus muscle is an antigravity muscle that keeps the body upright, but at the same thne in humans it is a plantar flexor of the aakle joint. Questions such as:
"How do these Bers work to enable such a great range of ankle movement, and yet provide stabilization in standing?" and "Why does the soleus muscle generate more force than predicted by moéelling?" (Gregor et al., 1988) nmain unanswered. Before these questions cm be aaswered, an accurate mapping and understanding of the fiber architecture of soleus is necessary. In the present thesis, the fiber architecture of the human soleus has been documented throughout its entire volume using many novel techniques that were possible to develop with the help of modern computer and medical technology. Included are:
the creation of a realistic, manipulatable, three-dimensional computer mode1 of
the fiber architecture of the entire cadaveric hwnan soleus.
a database of nber Iength and angle of pemation measurements documented
thmughout the posterior, anterior and marginal soleus of cadaveric and üvhg
subjects. The in vivo soleus muscles werr investigated ushg dtrasonography.
analysis and discussion of architectural data obtained bmcadaveric and in vivo
stndies. 1. Contents of thesis
The present thesis consists of eight chapters preseuted in the foilowing sequence.
Chapter I provides introductory comments of the importance of skeletal muscle architecture and a summary of the rationale for this thesis.
Chapter 2 is the literature survey which is intended to provide background information on the strucnirt and function of skeletal muscle, muscle modeilhg and imaguig modaüties inctuding dtrasound and magnetic resonance imaging used to study human muscle in vivo. The existing lirerature of the architecture and functions of the cadaveric and in vivo human soleus is reviewed in detail.
Chapter 3 includes the hypotheses, objectives and significance of the study. The anatomy and ierrninology used to descni soleus in the present thesis are also defined.
Chapter 4 outlines the methods that are used to address the hypotheses and objectives of this thesis. Three methods are used to visualize and document the architecture of the human soleus muscle: computer modeliing, manual measurement of cadaveric rnuscIe and in vivo uitrasound. The data obtained fiom the three methods is compared and contrasted.
Chapter 5 is a summary of the results of data obtained from the three methods descrhed above. Visuai representation of the fiber arrangement of the cadaveric soleus. throughout its entire volume, is provided by the computer mode1. Data of the architechual parameters obtained using the three methods are summarized and compared regionally throughout the volume of the musde.
Cbpter 6 is a discussion of the resuits and innovations of this thesis.
Chapters 7 d 8 consist of the conclusions and future directions of this work Chapter 2: Literature Smey
The literature survey is intended to provide background information for this architecniral study of the human soleus muscle. Section 2.1 provides a general ove~ew of the structure and function of skeletal muscle, including a discussion of muscle architechual parameters and their importance to fbction. In the Section 2.2 the architecture of the cadavenc human soleus is discussed. The resuits and methodology of previous studies are included. Section 2.3 provides a summary of imaging modalities used to investigate the structure of human skeletal muscle in vivo. Any in vivo fmidings nlated to the soleus are summarized by individual study. Muscle modelihg is discussed in the Section 2.4. Section 2.5 provides an ove~ewof the functions of the human soleus as docwnented in the literature.
2.1 Structure and function of human sketetai muscle
2.1.1 Structure of human siceletal muscle
The architecture of a muscle consists of its extemal codiguration and dimensions, and the internai arrangement and morphology of the contractile and co~ectivetissue elements.
Human skeletal muscle is made of contractile elements, tbe fascicles or fi'ber bundles, and co~ectivetissue wrappings, the epimysium, peOmysium and endomysium.
An entire skeletal muscle is enclosed by the epimysium. Co~ectivetissue partitions, caiIed perimysium, extend hmthe epimysium to surround the bundies of muscle fibers or faScicIes (see Figure 2.1). It can dso be seen in Figure 2.1 that each fascicle is made up of myofibrils or muscle ceils, mged in parallei. Further co~ectivetissue partitions, the endomysium, extend from the perimysium to sunound each myofîbril in the fascicIe,
8 Myofibnl \ \1
Myofilarnents
// ,Myosin head
My osin
Actin
Figme U. The orgapiptioa of haman skdetal mdc. (Reproduced with permifson bmWiliiams et aï. (1989), Figure SAA) The arrangement of fascïcles in skeletal muscle has been grossly descricbed as parailel, oblique (pennate) or spird (Williams et al., 1989) as shown in Figure 2.2.
Parallel Spiral
Fusiform
Bipennate Md tipennate
Figure 2.2. Faîdeuiar architecture of skeletal muscle. (Repdured with permission fmm Wiams et al. (1989),Figure 5J6)
In Figure 2.2 it can be seen that fascic1es of paralle1 muscle are arranged paraiiel
(e-g. stmp muscIes) or aimost paraUeI (e.g jh@onn muscles) to the long axis of the
muscle and terminate in aponemses or tendons. In oblique (pennaîe) muscle the fascicIes are short and attach to tendons within the muscle md in spiral muscle the fascicIes spiral to th& attachrnent to tendon or bone to apply a rotational force.
Pemate muscles can be descriid as tmipe~ate(semipmate), bipemate
(bipedorm) or multipemate. In unipennate muscles the fascicles resemble one-haif of a feather, that is, fascicles running at an acute ande hm one side of a tendon. The fascies of bipemate muscles amch to both sides of a centrai tendon, and in multipennate muscles the fascicles attach to many tendons within the muscle. Muscles that are paraiiel in arrangement have long muscle fibers arranged parallel to one another, but pennate muscles tend to have shorter, angied muscle fibers closely packed together.
This mangement results in pennate muscles producing more force but having less excursion (range) than fusiform muscles (Williams et al., 1989).
At the ultrastnictnml level each myonbril consists of sarcomeres arranged in series as shown in Eigure 2.1. Each sarcomere consists of two types of myofdarnents.
The thin filaments are composed of actin, dong with tropomyosin and troponin, both of which are proteins that mediate the regdation of contraction by calcium ions. The thick filaments are composed of myosin. Each sarcomere is made of a hexagonal array of interposed actin and myosin filaments.
On contraction of the muscle the sarcomeres shorten by the actin and myosin nlarnents sliding on one another by fomiing mss bridges as shown in Figure 2.3. In the presence of calcium the myosin head undergoes a conformational change when bound to the actin. The myosh head moves to a 45 degree angle with the actin nlament, ihus caushg the myosin head to puil the actin filament. The numbers of cross bridges that fom between the acîh and myosin depend on the amonnt of nIament overlap. The more cross-bridges fomed (Le. the greater the number of attach-detach cycles), the Iarger the potential muscle force (Gordon et al., 1966; Gans, 1982; Gans and de Vree, 1987). See ais0 Figure 2.5.
Contracted
Figure 2.3. Schematic EUustration of a sarcome= A and C show a relaxeci sarcomere. C is an enlargement of the boxed area in A. The myosin filaments are black and the thinner actin filaments are represented by white spheres, C and D show a contiracted ssrcomere. D is an enlargement of the boxed area in C, (Reproduced with permission hmCormack (19&1), Figure 10-6)
The fiber type composition of a skeletai muscle also plays a role in force production. The muscle ceils are distinguished by many factors, including differences in: protein composition, metabolic pathways used for energy, and resistance to fatigue.
There are three main fiber types: white muscle cens (fast, anaerobic contractiodATP generated mdy by glycolysis). red muscle celis (slower, longer duration of contractiodaembic metabolism/high concentration of myoglobin), and intermediate muscle ceus (aerobic and anaerobic metabohm). Muscles have a mixture of fiber types, but usualIy th= is a predominance of one fiber type, that influences the contractile properties of the entire muscle. Red muscle ceiis (Type 1 Bers) are found to predominate in poshiral muscks that are able to maintain repetitive contractions for long periods of time before fatigue occm. White and intermediate muscle ceIls (Type II
Ei'bers) fatigue more easiiy, but can contract about three times as fast as Type 1fibers and are suited for generating high forces for short periods of tirne. Each of the three types of muscle has a different protein composition. Hormonal, neuronal and other factors cm change the pattern of RNA splicing Le. altering the specinc amino acid sequence of muscle proteins. These changes can remit in subtle changes in the regdation of muscle contraction (Schauf et al., 1990; Gregor, 1992; Lieber, 1992, Alberts et al., 1989).
BonineMi and Reggiani (2000) suggested that the expression of merent protein isoforms by skeletal muscle may play a role in detenninuig muscle performance. However, the mechanism by which muscle fiber heterogeneity is used in vivo is still unknown.
The force production of a muscle is not only dependent on the intrinsic properties of myofibrils, but also on the length and placement of muscle fibea within the muscle, that is, the muscle architecture (Enoka, 1988). Muscle fiber architecture can be more precisely documented by rneasuring fascicle (fiber bundle) Iength, angle of pennation
(Yamaguchi et al., 1990). Fiber bundle length is measured as the distance between the attachent sites of a fiber bundle. The angle of pe~ationis measured as the angle at which the muscle fibers are oriented relative to "the fine of force" (Wickiewicz et ai.,
1983) of a muscle. Total muscle Iength, volume and mass rnay also be measured. Total muscle Iength is measured as the distance between the proximal and distai attachments of the muscle kny. Volume is usuaily measared using water displacement techniques
(Fnederich and Brand, 1990) and mass as the wet weight of the muscle (Alexander and
Vernon, 1975; Wickiewicz et al,, 1983). 21Effect of fiber architecture on skeietai muscie function
Fiber length, the number of muscle nbers lying in parallel, and the angle of pemation are all important in determining the amount of force a muscie is capable of producing moka, 1988). Each of these factors affecting force generation will be discussed in turn.
The Iength of a muscle fiber or myofibril is determined by the number of sarcomeres ananged in series. The more sarcomeres ananged in series, the longer the fiber. Within one muscle bundle the sarcomere length remains quite consistent
(Wickiewin et al., 1983; LeVeau, 1992). When a muscle contracts, each sarcomere shortens proportionately (Alberts et al., 1989), resulting in shortenhg of the myofibril by about one third of its length (Enoka, 1988). This means that the greater the aumber of sarcomeres in series, the greater the absolute change of leagth of a myofibril on contraction. This is described as
AL = n(&)
where AL is the change in length of the myofibril
n is the number of sarcomeres in series
61 is the change in length of a sarcomere
Therefore the muscle with more sarcomeres in senes, that is, the muscle with the longer muscle mers, undergoes the greater absolute change in length thereby permitting more excursion,
It has been suggested (Morgan, 1990) that sarcomeres behave merently within a single muscle fiber when it is lengthened beyond the plateau region of the length tension curve (see Figure 25). Morgan (1990). using a Hill-type mode1 (see Section 2-4.1) that dowed %dom variation" in the properties of sarcomeres, found that "... lengthening of active muscle on or beyond the plateau of the Iength tension curve wili take place very nonuniformly, essentidy by rapid uncontroiled elongation of individual sarcomeres, one at a the, in order hmthe weakest toward the stroagest."
The force generated by a muscle is nlated to the number of myofibrils arranged in pdel. This is defined as (Enoka, 1988)
Fwfib,il = nf
where F is force
n is the number of myofibrils ananged in pardel
fis the average force exerted by one myofibril
Therefore a muscle with more myonbrils in paralle1 exerts a greater force.
The angle of pe~ation(the angle at which the muscle fiben are oriented relative to the line of action of a muscle) aiso plays a role in force generation and total possible excursion of a muscle (Enoko, 1988). The relationship is descriied as - Crarrhmmr ,- Fqvfibd cos@
where Fis force
@ is the angle of pennation of a fiber
Therefore as the angIe of pennation of the nber inmases, the force transmitted to the attachent site wül decrease (Figure 2.4). Using this cosine Iaw, if the aagie of pemation is 60 degrees the force transmitted to the attachent site will be about 50 per cent les than the actual force produced by the myonbrils (cos 60" = 05). When pennate muscle contracts there is an increase in angle of pemation which Merdecreases the force transmitted to the tendon (Gans, 1982; Gans and de Vree, 1987; Ouen, 1988). If two muscles have the same volume and equal number of sarcometes in series the muscle with less pennation will exert a lower maximal force, but have greater range of active
Iength than the other muscle with a pater degree of pennation (Huijing and Woittiez,
1984). The functionai implications of pennation (maKimal force and Ieagth of range of motion) are expressed as the force-length relationship, to be discussed in the next section of the present thesis.
sin Os cos 0.5 -.
sin % sin 0
Figure 2.4. Effeft of fiber pematioa Pngle on force production. A Fiber with smaii angle of pemtion (0s) B. Fiber with larger angle of pennation (83 where FMis the force exerteà by the mdefibers, FM cos 8 is the force transmitted to the tendon, FM sin 0 are the other hreos (e.g. laterai).
2.13 Force-iength relation
The relation between the maximal force a muscle is capable of exerting and its
Iength is desrnid as the force-length relationship. The force-length curve of a muscle is recorded under static (Le. isomeaic) conditions. Dependhg on the level of muscie morphology studied, the static (isometric) condition can refer to muscle length. fiber length, or the Iength of a sarcomere. In their classic paper examining isolated fibers of hgskeletal muscle, Gordon et al. (1966) showed that force production is dependent on the amount of overlap between the actin and myosin filaments within a sarcomere.
Mgrelaxation, the mpomyosin molecules block the active sites on the actin molecules, preventing the interaction with the myosin head. Ddgcontraction, in the presence of calcium, the configuration of the troponin cornplex is changed, resulting in the tropomyosia shifting to expose the active sites on the actin molecule. This enables the acth molecule to interact with the myosin head by forming cross bridges. These cross bridges result in the sliding of the actin fiament on the myosin filament.
Since each cross bridge attach-detach cycle is assumed to generate the same amount of force, and the cross bridges form at equd distances dong the myosin fdament, the extent of overlap of the actin and myosin filaments determines the total force the muscle is capable of exerting. The greater the number of cross bridges formed (that is, the greater nomber of attachdetach cycles). the stronger the contraction. Figure 2.5
shows the typicai force length mewhere percentage of force exerted is plotted as a
function of sarcomere Iength. The amount of filament overlap is illustrated below the
graph. It should be noted that in positions 2 and 3 there is the largest number of cross bridges formai, corresponding to the plateau region of the curve. At the plateau region
of the curve the sarcomere continues to shorten, but there is no increase in force
generation because no additionai cross bridges are forming. This is due to the iack of
myosin heads in the central portion of the myosin nlament The series elastic element is ako an important part of the force Iength curve.
Dunng an isometric contraction there is an intemal shortenhg of the sarcomeres and a corresponding Iengthening of the tendon (the in series elastic element). The series elastic element aaosmits forces to the attachent sites of the muscle. The parailel elastic elements inchde aponeuroses, septa, epimysium, perimysium and endomysium. The force Iength relationship of paralle1 elastic elements has ken shown, in frog muscle, to be highly nonlinear (Ritchie and Wilkie, 1958) and in series elastic elements the relûtionship, has been shown to be fairly nonhear (Wilke, 1956).
Striation Spacing (mm)
Figure 2.5. Theoretical force-length relaüooship. The graph is baseci on àata from isolateai hgskdetal muscie fibers. The amount of Rlament overlap at various locations on the cweis shoao beîow the graph. The plateau region of the curve (B-C) represents the portion of the focce-length cmeused in vivo- (Repmduceà with permission €mm McMahon (1984), Figare 3.7) 2J.4 Force-velocity relation
The force-velocity relation cm be defined as the relatiomhip between the marUmal force of a muscle and its correspondhg rate of change in length. Hill (1970) generated the equation for the muscle force-velocity relationship using concenaic contractions of hgmuscle. A bundle of muscle fibers was held at a hed length by clamphg both ends. The muscle was electncalIy stimuiated so that maximum tension developed in the muscle and then the muscle was released at one end. The muscle began to contract and the relationship betweea force and velocity was plotted as show in
Figure 2.6.
Force (normalized)
Figure 2.6, Nonnaüzed force-velocity me,Lengthening = eccenbife contraction, shortening = concencn'c contraction, (Reproduced with permission hmNg-Thow-mg (2001))
The equations are shown below as a function of velocity and as a bction of force. where v is the velocity of shortenhg
Fo is the maximal force at zero velocity
F is the instantaneous Ioad
a, b are constants
Hill's equation demonstrates a hyperbolic relation between force and velocity. The pater the force, the slower the contraction velocity or the higher the velocity the lower the force.
From the preceding discussion it cm be concluded that the amount of force a muscle is capable of generating varies with muscle length (force-Iength relation) and muscle velocity (force-velocity relation). It would be very difncult to determine these properties using human muscle due to the excision techniques involved. These principles apply to force production in human muscle, but as Lieber (1992) stated "... it is not possible to simpiy speak of isometric or isotonic muscle contractions in the real world since muscle activation is never tnily perfomed at a constant length or under constant i~ad.~?
2.15 Physiologid Cross Sectional Area
in order to predict muscle force-velocity characteristics. a meastue of muscie size is necessary to keep the predictions realistic (Brand et al., 1986). Physiologicai Cross
Sectional Area (PCSA) has been typically used for this purpose (Herzog, 1994).
Approximation of the PCSA of a muscle relies on knowledge of the architecniral parameters of the muscle, that is, mas. angle of pennation (fi, fiber length, and density.
PCSA(cm2) = (~uscle~ass (g)xcos e)/(~ensity (&m3) x F'iber kngth (on)) Some investigators do not inciude the effecis of the angle of pemation (Friedench and
Brand, 1990) when cdculating PCSA and use the following equation
PCSA (cd) = volme/meunfiber Iength
where volume = rnasddensity
Fnedench and Brand (1986) measured the architectural parameten of soleus
muscle in two cadavers and used these to calculate the PCSA (voIume/rnean fiber length).
The resufts were compared to the PCSAs reponed by Pierrynowski (1982). Pierrynowski
(1982) calculated PCSA as
ms/(density x anutomicat flber length)x muscle shape factor
where muscle shape factor is
maximum anatomical cross-sectional arealmean anatomical cross-seetioml area
In addition, Fnederich and Brand (1986) used the PCSAs calculated from their
study and those cdculated by Pierrynowski (1982) to predict muscle forces in a Living
subject using nonlinear optimization techniques. It was concluded that it is not possible
to predict which one of the three specimens wouid generate the most force based on
PCSA and suggested that PCSA is only a first approximation of muscle size. It was
stated "... but the fact that there are diffe~gdennitions of PCSA in and of itself miplies
that there are mering (or at least evolving) ideas as to the physioIogic implications of
muscle size" and "... at the present tirne, there are no other reasonably straightforward
concepts which dow estimation of a muscle's force generating capability."
The PCSA theoreticalfy represents the cross sectional area of all the muc1e fibers
withh a muscle (Patel and Lieber, 1997). This formula assumes that aU muscle fibers in
a muscie have the same Iength and same angle of pennation, that is, use one average value for each architechiral parameter. Since it is not possible to separate the comective tissue elements within the muscle, they are not considered separately in the equation and may be a source of enor when cdculating PCSA (Enoka, 1988).
This suggests that use of average muscle architecture data as seen in PCSA rnay not be adequate for the prediction of muscle force. More detaüed study of the architecture of human skeIetal muscle may provide insight into aitemate ways to express muscle size as related to its architectural characteristics.
2.1.6 Comective tissue components
The comective tissue components include the epimysium. perimysium and endomysiwn of the muscle beily (see Section 2.1.1), as well as intemal and extemal tendons and aponeuroses. Muscle fiber bundies and their comective tissue covenngs attach to tendons, aponeuroses andfor to the penostem of bone.
2.1.6.1 Aponeoroses and tendons
The tendons and aponeuroses serve to convey forces between muscle and bone and to store elastic energy (Nigg, 1994). A cornputer mode1 developed by Van der
Linden (1998b) showed that Iess force was generated by a muscle when its' aponeurosis was partially or tomy removed Littie consideration has been given to the specinc properties @of, 1998) and location of these structures throughout the musde volume, dthough their importance has been recognized (Gans and de Vree, 1987). Gans and de
Vree (1987) state thar "...thus, not only the change of angle between origin and insertion of the contmcting muscle nber is important, but dso the potential displacement of the connecave tissnes." The epimysium, perirnysium and endomysium of muscle are continuous with the co~mectivetissue structures on which the fascicles attach, that is, aponeurosis or tendon as shown in Figure 2.7.
Figure 2-7. Temination d skeletal mdein tendon, longitudinal section. (Repmduced witb permission from Ham (1974), Figure 18-13)
Tendons and aponeuroses consist of dense connective tissue and contain maidy coIlagen, water, and a mail amount of eiastin. The collagen fiber bundles are regularly arranged in tendons and imgdarly arrangeci in aponeuroses. As a tendon approaches bone to fom the osteotendinous junction, the tendon changes to a zone of nbrocartilage andlor cdcined nbrocartilage or inserts directly into the periosteurn or bone (Woo et ai.,
1988). The amount of nbmcartilage varies arnong tendons and between zones of the same attachrnent,
It has been found that tendons streich and recoil (Proske and Morgan, 1987). At low Ioads a tendon is les SB.,that is, it elongates or snains a considerable amomt for a given alteration in load, but at higher loads the tendon Ïs stiffer and does not elongate as much (Lieber et al., 1991). Lieber et ai. (1991) found that the connective tissue of frog aponemsis pedts more strain thm that of the tendon and osteotendinous junction, suggesting that the physical properties of the connective tissue elements Vary throughout the muscle. It has been suggested, aithough not experhentally verified, that the same strain is distriiuted throughout the intemal aponeuroses (internai tendons) and extemal tendons (Zajac, 1989).
Changes in the shape of a muscle and its connective tissue componeots may also influence adjacent muscles or other parts of the same muscle (Gms, 1989). As a muscle contracts and alters its shape, other muscles wiU have to adjust accordingly. Aithough this change has been observed in ultrasound stuclies (Fukunaga et al., 1993, the interplay between co~ectivetissue covenngs of adjacent muscles, as they relax and contract, has not been studied*
11.62 Bony attachent sites
The attachment sites of a mude as a whole are commody known as the origin and insertion. Aithough the origin and inseaion are usuaily related to bony areas, some muscles origioate or insert into connective tissue, for example, superficial fascia of the ke. The ongin is coasidered to be the proximal attachent that is &en defimed as remaining ked during contraction of the muscle. The insertion is the distal attachment of the muscle that is mobile. The terms, origin and insertion, are used less often because some muscles act in both directions. Therefore, in the present thesis muscle attachent
(pmximaVcüstal, mediaillateral) will be use& When a muscie contracts, a force is generated and exerted at its attachent sites. If a muscle pcoduces force and remains a constant Iength (attafhment sites are the same distaoce spart as before
contraction) it is contracthg isometrically;
shortens (distance between attachent sites is demased) it is contracting
concentricdly; or
lengthens (distance between attachment sites is decreased it is contracting
eccentricd y.
The attachmeats of muscles are usually indicated on drawings of bones. The attachent sites may be hwnfrom specimens (Agur, 199 1) or indicated schematicafiy
(Green and Silver, 1981). These illustrations provide two-dimensional (2-D)views that
Iack three-dimensionai (3-D)specificity. The true 3-D contour of the bony surface(s) of attachent is not depicted.
Tt is often ody the attachment sites connected by a single heof action that are used to determine the function of a muscle. Pienynowski (1995) compiled existing data on the attachment sites and heof action of 48 lower Limb muscles. The attachment sites of the muscles have been summarized with one 3-D coordinate at the centroid of the proximal attachment and a second 3-Dcoordinate at the centroid of the distd attachment.
The Iine joining the centroids represents the Iine of action for the muscle. AU data were nomahed to a 1.70 m individual. The data wece denved hm skeletai diagrams
(Arvikar, 1971), anatomy atlases (Hardt, 1978; Mikosz et al, 1988), cadavea (Dostaf and
Andrews, 198 1; Brand et al., 1982; Burdett, 1982), skeletons @osta1 and Andrews, 198 1;
Pierrynowski, 1982; White et al., 1984) and computed tomographie scans (Nemeth and
Oko, 1989). Yamaguchi (1990) also summarked attachent data as 3-D coordinates of centroids with a cornechg liw of action, but in this reference the raw data (that is, not nomaüzed) was pcesented Two studies not mentioned above were induded in
Yamaguchi's summary: Freivaids (1985) who used scaled photographs from matornical tex&, and Seireg and Adcar (1989) who used a skeleton, cadavers, and scaied diagrams to obtain attachment coordinates. Kepple et ai. (L998) developed a 3-D musculoskeletai database for the lower extremity using 52 dried skeletai specimens. The 3-D coordinates of landmarks were obtaiaed using a digituer. and cenûoids of oigin and insertion were detennined hmanatornical tex& for 43 muscks. A total of 60 muscle lines of action were represented. This musculoskeletai database is much larger than any previously existing database. The authors state that one Limitation of the study is "the use of centroids to estimate origin and insertion". Furthemore, Van der Heh and Veenbaas
(1991) found that broad areas of anachment an required for muscles with large attachment sites if accurate force vectors are to be detedeci.
In summary, when a muscle contracts it is not only the change in length of the origin relative to the insertion, but aiso a deformation and displacement of the comective tissues that are functionally important. The total force exerted by a muscle is a summation of the active component generated by the contraction of the contractile eIements, and the passive component generated b y the connecrive tissue elements.
21.7 Wày stady ske1eta.i mude architecture?
h a letter to the editor of the Journal of Biomechanics, Panjabi (1979) commeoted on the state of biomechanical modehg of muscle that Y.. generdy much effort is spent in fomulating the governing equations of a model. In contrast, the physical pmperties data is screened hm the avdabte literature, which is often meager, inaccurate, incomplete and outdated." Pierrpowski (1995) stated that "... Little has changed in this regard since 1975."
Qwmtitative anatysis of muscle architecture is important because the architectural parameters have a profound effect on muscle fuoction (Haines, 1934; Mm, 1982;
Woittiez et al., 1983a). Lieber (1992) summarized the functional implications of architecturai parameters, that is, fiber Iength is related to velocity and excursion, fiber area to fiber force and fiber type distribution to muscle speed and endurance. In a review article Lieber (2000) emphasized that "... skeletd muscle architecture is the structurai property of whole muscles that dominates their hction."
Despite the importance of muscle architecture to muscle function the available resources for human muscle architectural data are scarce and incomplete. The foIiowing
List summarizes LUnitations of existing architecturai data (see dso page 29).
Muscle mass measurements have been determined by weighing fixed tissue
(Alexander and Vernon, 1975; Wickiewin et al., 1983). The amount of
embalming fixative within the muscle and the addition of variable amounts of
rnoistening fluid have not been considered Muscle volume has been measured
using the water displacement technique (Friederich and Brand, 1990). The use of
a large calibrated beaker for measurements is prone to error and again the amount
of fluid that has been added to the muscle may be considerabie and Vary hm
specimen to specirnen. For mu; and volume measurements it is dso not clear
how much aponeurosis and tendon were included with the muscle (Wickîewicz et
al., 1983). One average fiber length and one average angle of pemation is used to represent
the whole muscle, making the generalization that muscle architecture is
homogenous throughout every muscle. Little attention has been paid to
architecturally different regioos within a muscle (Yamaguchi et al., 1990).
Furtherm~re~available architechuai data is based on studies with srnail sample
&es, n = 1-5 (Alexander and Vernon, 1975; Witkiewicz et al., 1983; Frîederich
and Brand, 1990; Spoor et al., 199 1).
The density of fiesh skeletal muscle of dogs and rabbits was found to be 1.05
gm/cm3 (Mendez and Keys, 1960). This value for muscle density is used for
human muscle as well (Yamaguchi et ai., 1990) and is often rounded to 1.0
gm/cm3 (Faulkner et al., 1982).
The lack of consistency in standardization of data rnakes cornparison of studies
difficnlt. For example, Nishio et al. (1992) found that force nomalization
utilizing various methods cm lead to different conclusions, depending on the
rnethod used. Review articles (Yamaguchi et al., 1990) present data in non-
standardized format and suggest that future studies shodd fms on how
measurements couid be standardued in a meaningfbï way.
To "advance the state of the art", more complex purposes for multiple fiber arrangements within a single muscle need to be considered (Otten, 1988).
The detailed measurement and modehg of the architectural characteristics of the haman soleus muscle were chosen as the focus of the present study, since this complex, muiti-part muscle is a major contriintor to human stabiüty and ambulatory power
(Wmter, 1984). More detailed understanding of the architecture of the human soleus muscle may support the development of more realistic static and dynamic models of this muscle,
2.2 Architecture of the hnman solens muscie
2.21 Historieal perspective
Publications of the late 1800's and early 1900's provide detailed descriptive accounts of the stmcnirr of the soleus muscle. The arrangement of the fibers within the muscle beDy and placement and extent of aponeuroses, septa and tendons were described
(Gniber, 1878; Cleland and Mackay, 1896; Bardeen. 1906; Reid. 19 18; Frazer, 1937:
Anson, 1942). These references include older textbooks, pub lished dissection observations. and articles. Udortunately, this information has been iargely ignored due to its qualitative nature. More recently published anatomy textbooks, due to the brevity of gros anatomy courses, usually mention ody attachrnent sites and make a few bnef cornments, if any, on muscle architecture.
The foliowing description of the soteus muscle is summarized fiom the historical references. The soleus is desrnid as consisting of short, obiique fiers divided into anterior and posterior parts. The fiber bundles attach to three comective tissue sheets: an anterior aponemis (tendon), a postenor aponeurosis (tendon), and a median septum
(raphe). The antenor soleus (1), postenor soleus (Z), anterior aponeurosis (4, postenor apeurosis (3,and the median septum (3) are iilustrated in Figun 2.8. Figure 2.8. Transverse section througb the mïddle third OP the human soleus muscle. I. Anterior soleus 2. Posterior soleus 3. Median septum 4. Anterior aponearosis 5. Posterior aponeuroals MPrginal deas not defined in previous studies.
The posterior aponeurosis (5) lies deep to the gastrocnemius muscle and
has the fiber bundles of the postenor soleus attached to its medial, lateral and
superior margins and to its anterior surface;
is continuous with the calcawal tendon distdy; and
The anterior aponeurosis (4)
attaches proximdy to the fibula, the tibia and to a fibrous arch uniting the tibid
and fibular attachments;
is continuous with the caicaneai tendon distdy;
has the nber bundIes of the posterior soleus attached to its mediai, laterai, and
superior matgins, and to its posterior surface; and
has the fiber bundies of the anterior soIeus attached to its anterior surface (the area
of attachent depends on the length and extent of the anterior soleus). The median septum Lies in the sagittal plane and is visible on the anterior surface of the muscle. The median septum (3) is
continuous with the calcaneal tendon distally;
incornplete proximally; and
has the tiber bundles of the anterior part of soleus attaching to its medial and
lateral surfaces, leavùig only its anterior margin exposed on the antenor sucface of
the soteus.
The larger postenor part of soleus consists of muscle fiber bundies Lying between and joiniag the edges of the antenor and postenor aponeuroses. The fiber bundles are obliquely onented bbslopingdownwards hmthe antenor to the postenor lameIla" (Last,
1959).
The bipemate anterior part of soleus consists of fiber bundles courshg anteroinferiorly hm the antefior aponeurosis to the median sepnim. Therefore, the median septum Lies mainly within the anterior soleus.
As topic of this thesis was developed, it became apparent that there were many discrepancies in the iIlrisaation of soleus muscle. Oxom (1997) studied illustrations of the soleus muscle drawn from the sixteenth to the twentieth century (Vesaüus, 1543;
Spiegel, 1632; Cowper, 1698; Albinos, 1777-78; Bell, 1794; Bourgery, 183 1-54; Ellis,
1867; PIatzer, 1989; Staubesand, 1990) and fomd incousistencies in the accuracy of the muscle architecture when compared to laboratory specimens. The problems most hquently encountered inchded inaccuracies in fiber bundIe length and orientation and the extent of aponeuroses and tendons (Oxom et al, 1998). Oxom et ai. (1998) suggested that ".. . when published resources provide inconsistent information, a return to direct observation of the matornical structure is the most efficient way for an illustrator to verQ and accurately represent the subject."
Larger muscles are fiequentiy presented as a long mass of tissue without differentiation into distinct architecturai regions (Oxom, 1997). This is evident in some textbook iIlustrations of soleus that show the muscle consisting of longitudùial tiber bundles (Green and Silver, 1981; Snell, 1995). In these illustrations of the posterior aspect of soleus the marginal fiber bunàies are not shown.
Histoncaüy much has been learned about the structure of the soleus. It is evident that direct laboratory observation is most important in preventing the dissemination of inaccurate information. Gans and Gaunt (1992) stated that "... conceptuai emrs are dangerous; not only may they Iead to bias, but they may encourage the rejection of correct anatornical observation."
Descriptive studies are not the only source of information about the soleus, more cecent quantitative studies will be discussed in the foilowing sections.
223 Methodology of quantitative cadaveric studies
~ittIework has ken done in quantmg the architecturai characteristics of human muscle and often any tofonnation gaps have been tilled by estirnating the parameter using anatomy atiases (Pieçrynowski, 1982; Yamaguchi et ai., 1990). Spoor et al. (i991), Friederich and Brand (1990), Cutts (1988), Wickiewia et al. (1983),
Alexander and Vernon (1979, Trzemchik and Lnetzke (1969) and Haines (1932) have studied and recorded quantitatively the mer architecture of soleus. AU of the above authoa except Tnenschüc and Loeake (1969) attempted to study numerous (up to 26) muscles OC the Iower hbat one the. The architectural parameters obtained bm cadaveric studies of the human soieus mnscie are sumxnarized in Table 2.1. The &ta obtained hmthese studies are used mutinely in caiculations of muscle force, but are severely kteddue to
smaU sampIe size (n = 1-5);
lack of documentation of site of &ta collection within muscle belly;
lack of consideration of architectural variability in various parts of the muscle;
incomplete data sets, making meaningful cornparison of resuits difficdt; and
lack of documentation of the location of the site(s) measund.
The specific methodology used varieci significantly from study to study. A cornparison of the methodoIogies used in the frequently cited studies by Friederich and
Brand (1990) and Witkiewicz et al. (1983) are outihed in Table 2.2.
In Table 2.2, the marked ciifferences in the preparation of the specimens, rneasurernent techniques used, normalization of resuits, and calculation of PCSA are evident. Most importantiy it cm be seen that soleus was considered as a whole, even though nber bundles hmdifferent regions of the muscle were dissected.
Alexander and Vernon (1975), Cutts (1988), Spoor et al. (1991) and Trenschik and Loetzke (1969) did not macerate the muscle. Alexander and Vemon (1975) removed the muscles to be studied from the nght leg of one male embaimed cadaver. Each muscle was incised dong the plane of the fiber bnndles and photographe& The angle of pemation and muscle thickness was measured from the photographs. Cutts (1988) studied the muscles of rbree embaimed cadavers. AU measurements were taken hmthe deep aspect of the soIeus muscle. Angle of pemation was measured in situ, but the method was not descri'bed. Fiber length and average sarcomere length was rneasured from excised fiber bundies
Part of Fiber Angie of Muscle Volume MmcIe soleus length pemtion thickness length Uexander and X Vmon (1975)
3tts (1988) X
?riederich and X Brand (1990) X
Haines ( 1932) X
Spoor et al. Posterior :t991) (site within x)
An te rior (site within x)
Tnenschik Posterior and Loetzke (site within x) [ 1969) Anterior (site within x)
Posterior (site witbin x)
Anterior (site within x)
Wtckiewin et X ai, (1983)
Table 2.î. Suminnry of the type of cuchitectclrsl data obtained in cadavenc studies of the hmnan soleas mde, M = male, F = hale,U = sex tmpedîed, * = data coiiected, X = site of data coiiection not specioed, and NC = data not coiiected, r 1Frieden'ch and Bd(I990) Witkiewicz et al. (1983) '~ Cadaver 1Embalmed in anatomical position Embalmed with hip and knee in maximai extension, dein maximal planta flexion Muscle Iength 1Measured with derin situ hm Measured with der, muscle removed (-1 4rentroid of ongin to centroid of from body, as distance between the 1insertion, tendons excluded rnost proximal and distal muscle fibers Angle of 1Measured in situ ushg a Measured using a protractor after IGoniorneter Merdetails maceration, measued angle fonned by pemation (no 1provided) individual muscle fibers with the line of force of the muscle (no fuaher detaiis provided) Volume Measured after excision using Not measured water displacement in ml Mass Not measured Wet weight of fixed muscle (g) Processing Muscle soaked in nomal saline Muscles put in 10% formalin bath of muscle for 1-5 days to remove for 2-3 days and cleared in a for subsequent embalming chemicais sodium phosphate buffer measurements 2-5 muscle fiber bundles (5-20 Then were placed in 15% sulfunc mm diameter) were randomly acid to soften and digest the removed hmdifferent parts of comective tissue the muscle, measured and placed Muscles were then cleared in a in 20%nitric acid for 24-48 hrs phosphate buffer and stored in 50% After sacient maceration fiber glycerol solution bundles were retumed to saiine . Fiber length 2-5 fibers bundles were removed bundles of 10-20 muscle fibers randody hmdifferent parts of were dissected fiom sevenl regions the muscle of each muscle Iength of 10-20 mers hmeach Iength of each bundle was bundle were measured using a measured (mm) der(mm) while holding ends average fiber Iength was taut bat withoat stretch detemiined for each muscle average nber Iength and average fiber Iength was standard deviatioa was nomalwd using a sarcomere caIcuIated for the muscle Length 2.2 pm a ratio of average liber length to muscle Iength was caidated
Table 22. Conîinued on next page, Sarcomere Not measured Single fi'bers were dissected length selected bundes and mounted on glass slides in glycerine jeiiy Sarcomere lengths were meastmd for each fiber using a calibrated eyepiece micrometer under a dissecting mimscope (Xm) Average sarcomere length for the muscle was calculated 1 PCSA Volume Muscle mass x cos@ Fiber length Fiber length x density PCSA of each muscie was Used nomalized fiber length for normalized by dividing with the calcuiation average PCSA for ail 38 muscles studied
Table 22. Cornparison of the methoddogy used by Friederich and Brand (WO) and Wickiewkz et al. (1983).
Spoor et al. (1991) divided the soleus into antenor and posterior parts, and studied each part separately. The muscles were removed fiom the cadavers and 5 to 10 fiber bundes were excised fiom each muscle, without stretching the fibers. The length of the fiber bundle and the angle of pennation (angle between the fïber and the estimated direction of muscle pull) were recorded Trenschik and Loetzke (1969) ais0 reported dtsfor the anterior and posterior soleus. In this study, the muscles were removed bm the cadavers, sectioned, and the angle of pemation and fiber length measured.
Rdtswere nonmhed to tiibial Iength.
The experimentai protocol for each shidy varies, making the cornparison of resuits diffidt. Finthemore, the data collection is designed to establish one average vaine of each of the architecniral parameters for the soleus as a whole or for the anterior and posterior parts separately. Focus has not ken placed on documenting the fiber
architecture throughout the volume of the muscle. An experimentai design utilizing new
technologies may provide more detailed and region-specific resuits.
22.3 Resuits of quantitative cadaveric stuclies
The soleus architectural data coiiected by Spoor et ai. (1991), Friedench and
Brand (1990), Cutts (1988), Wickiewicz et ai. (1983), Alexander and Vernon (1975) and
Trenschik and Loetzke (1969) are summarized as average values in Table 2.3 and as
individual specimen data in Table 2.4. These tables provide an overview of the publlshed
architecturai data on the cadavenc soleus muscle, but aiso dow for quick visuaüzation of
A uthor (year) Part of 8 Volume soleus (degrees)
Alexander and - Vernon (1975)
Cutts (1988) -
Friederich and - Brand (1990) Haines (1932) -
Spoor et al. posterior (199 1) anterior Tnenschik and posterior Loeîzke (1969) anterior
Wickiewicz et al. - (1983)
Table 2.3. Siunmary of mean architecturai data of pubtished cadaveric studies of soh Ft = fiber Iength, O= angie of pennatiou, MT = made thickness, and ML = muscIe Iength. Part of 8 Volume soleus (degrees) Aiexander and - 20 Vernon ( 1975)
Cutts (1988) - 20 - 18 - 20
Friederich and - - Bmd (1990) - 32
Haines (1932) - -
Spoor et al. postenor 41 (2r 13) :WL) 22 (4: 1 1) 39 (& 18) anterior 35 (k 15) 23 (& 12) 34 (k 4)
rrzenschik and posterior 20 Laetzke (1969) (average)
anterior 25 (average)
- 30 20
Tabte 2.4. Summary of individual cadrver architecturai data of sokus as ceporteci in the iïteratare, PL = fiber Iengtb, O= angle of penmtion, MT = muscie Lhicknesq ML = made Iengtb, M = male, F = fernale, U = sex LIllspeciEied, Spoor et ai. (1Wl)incioded the standard deviation (k) and Trzenschik and ktzke(1969) ranges (iow-hi&) for some of the data what information is rnissing. A generai lack of topogaphical specincity (that is, the precise location where the data were obtaùied) is evident. Table 2.5 provides a summary of the published architectural data by sex.
The data reported in Tables 2.3 and 2.4 do not provide insight into the detailed architecture of the soleus muscle descnid by the early anatomists and as observed in the dissection laboratory (Agur and McKee, 1997). In Table 2A Trrenschik and Loetzke
(1969) report a range of fiber length of 18 to 36 mm in both the antenor and posterior soleus. Similady, Spoor et al. (1991) report large standard deviations of the angle of pemation in some cadavers. This large variance between specimens is not accounted for in the studies reporthg only the average fiber length or a single fiber Iength hmone cadaver.
When cornparhg male to female data in Table 2.5 it seems that males tend to have a soleus with larger volume andor mass and longer total muscle length (Spret ai., 1991). Frorn the scant data it dso appears that femaies rnay bave longer Fiber Iength
(Trzenschik and Loetzke. 1969), but this is not the case in Fnederich and Brand's study
(1990), where the male cadaver has an average fiber length of 1 mm more than the female. Again it is difficult to draw conclusions based on the available data. The large nurnber of ernpty spaces on each of the tables show how few data there are quantmg the architecturai parameters of the human soleus muscle. If the architectural data are scarce and do not reffect the mai structure of the component parts of a muscIe, predictions based on these data may not represent reaiity. 2.2.4 Postmortern muscle üssue
The results of cadavenc studies have been used extensiveiy in solving biomechanical problems and in muscle modebg, but it has been suggested that the architectural parameters of cadavenc muscle differ hm those of Living tissue
(Rutherford and Jones. 1992; Fukunaga et ai., 1997).
Author (year) Part of Volume soleus Alexander and - Vernon (1975)
Friederich and - Brand (1990) -
Spoor et al. posterior (1991) anterior Trzenschik and pos terior Loetzke (1969) anterior pos terior anterior
Table 2.5. Simunary of mean architectural data of cadaveric studies of deus by gender. FL = fiber length, O= angle OC pennstioo, MT = muscle thickness, and ML = muscle length.
There is iittle infornation in the Merature that documents the relationship
between living and cadavenc skeletai muscle architecturai parameters. Cadavenc tissue
is subject to a standard embalming procedure. Cutts (1988) has shown that this
procedure wiii not shorten the "contractile portion" of skeletal muscle if muscle is fixed
while intact upon the skeleton. Friederich and Brand (1990) reported Ioss of muscle
Iength when muscle removed hmthe skeleton was macerated However, the effea of
fixation on the mternat fiber architecture of human skeietal muscIe is not known. Cadaveric tissue also undergoes postmortern changes, one of which is rigor mortis. It has beea shown that this change cm produce a slow contraction in skeletai muscle (Bendail, 1951; Davies, 1963). As a dt,this process may not ody change the shape, but also the fiber length and angle of pemation. Although it has ken shown that rigor rnay be resolved when a stretch stress is appiied to the muscle (Bendail, 1973). the degne to which the muscle retums to its pre-rigor shape has yet to be determined. Other possible factors such as muscle degradation or the tempenitme and position at which the body is stored may dso cause architectural changes.
There is uncertauity as to whether cadaveric muscle is representative of in vivo muscle. Cadaveric studies are useful because structurai features of an entire muscle can be directly observed and measured, but recently it has also become possible to shidy in vnto muscle architectm using ultrasonography (see Section 2.3.1) and magnetic resonance imaging (see Section 2.3.2). A combination of cadaver and in vivo shidies may provide the best possible solution.
2.3 Imaging Ut vivo muscle architecture
M~~cuioskeIetaIdtrasound and magnetic resonance imaging have been typicdy used to diagnose pathology (Lammllien et ai., 1988; Schedel et al., 1992; Reimers et al.,
1996). More receotly, it has become possible to study in vivo muscle architecture using these non-invasive techniques. Ultrasonographicaliy it is possible to visuaiîze and document the architecturai parameters of relaxed and contracted muscle (Fukunaga et al.,
1997). For this thesis, ultrasound was chosen as the technique to study soleus muscle architecture bt vivo, although MRL was ais0 attempted- 2.3.1 Ultrasonography
A number of investigators have used ultrasound to study human muscle architecture (Henkssoort-Larsen et al., 1992; Rutherford and Jones, 1992; Kawakarni et al., 1993; Herbert and Gandevia, 1995; Kuno and Fukunaga, 1995; Narici et al., 1996;
Fukunaga et al., 1997; Ichinose et al., 1997; Ichinose et al., 1998; Kawakami et d., 1998).
Ultnisound waves are Mected from coiiagen nch sttuchites, and resuit in a striped pattern in muscle. The echoes are from the fascia1 septa between the fascicles of the muscle. This striped pattern enables measurement of fiber bunde length and angie of pemation. Fiber bundle length is measured as the Ieagth of the fiber bundle between attachment sites. The angle nt which the fiber bundle attaches to the sepnim, aponeurosis or tendon is the angie of pennation. Rutherford and Jones (1992) found that the measures of angle of pennation in vivo give sirnilar values to those measured on cadavers
(Witkiewicz et ai., L983; Alexander and Ker, 1990). Hentiksson-Larsen et ai. (1992) reported the coefficient of variation for repeat measurements to be less than 10 per cent and Rutherford and Jones (1992) reported a coefficient of variation of 13.5 per cent.
Fikr iength and angle of pemation measurements have been documented in daxed and contncted human muscle including quadriceps (Rutherford and Jones, 1992), brachialis (Herbert and Gandevia, 1995), vastus lateraüs (Ichinose et ai., 1997), tibiiilis antenor (Kuno and Fnkwiaga, 1995; Fukunaga et al., 1997), mediai gastrocnemius
(Narici et ai., 1996; Abe et al., 1998, 2000; Kumagai et al., 2000)) and triceps brachü
(Kawakami et aI., 1993).
Two ultrasoand studies of soleus muscle (Kawakami et al., 1998; Magmaris et al, 1998) documented fiber Iength and angle of pemation in reIaxed and contracted muscle. Rawakami (1998) studied one site in the laterai aspect of the iderior part of postenor soleus. Mages (1998) dso studied the posterior sofeus, but investigated three sites: mediai, median and lateral. in the centrai part of the muscle. The results of the studies of soleus are summarized in Table 2.6.
Narici et al. (1996) found that ultrasound measures taken hmcadaveric muscle correspond to manual measurements taken directly from the muscle, supporting the accuracy of this technique.
Part of FL(mm) soletis ReIaxed Contracted Relaxed Contracted Contracted Kawakami Posterior - et al. (idem- ( 1998) laterai)
Maganank Posterioc et ai. Medial 20.9 I2.0 ( 1998) Median 21.0 * 2.7 Laterai 21.8 12.9
Table 2.6. Summary of architecturai data of pubüshed uitrasonographicstudies of soleus. FL = fiber le*, O= angle of penoatioo, and MT = mdethickwss.
No pubiished in vivo data of the muscle architechnal parameters of the proximd part of the postenor soleus and the anterior soleus were found. Insight into the in vivo architecture of the entire vo1me of the soleus muscle may help to mode1 this complex muscie more accurate1y.
Three-dimensional uitrasound has been used to calculate muscle volume in vivo
(Delcker et ai., 1999), but ihis promishg technique has not been adapted for the smdy of Magnetic Resonance Imaging (MRI) can be used to determine architectural characteristics of nomal human muscle. Advancages of this technique include excellent resolution of fat, muscle, bone and comective tissue, dong with the possibility of obtaining scans bmmultiple scdgplanes without baving to move the subject.
Fulcunaga et al. (1992) calculated the volumes of some individual leg muscles and some muscle groups in the right lower Ieg of 12 subjects. The muscles of the posterior cornpartment of the leg were considered individudy, but the muscles of the anterior and laterai compartmeuts were combined into one group. The volumes were calculated by summation of the anatomicai cross sectionai area of each muscle on each scan and the distance between each scan. Muscle length was calculated as the distance between the most proximal and distai images where the muscle was visible. To calculate PCSA the architectural panuneters reported by Wickiewkz et ai. (1983). were used as well as fiber
Iength measurements hmtwo additional cadavers. Fukunaga et al. (1992) reported the foilowhg mean values of the architechiral parameters of soleus muscle: muscle length
32.4 cm, fiber Length 2.0 cm, muscle volume 489.1 cd,percentage of volume of the leg
33.4 per cent, anatomicai cross sectionai area 15.23 cm' and PCSA 230.02 cm2. For cornparison (Berry et al., 1993) in an in vivo MRI study found the mean anatomical cross sectional area of soleus to be 24.6 I1.9 cm' (n = 6 subjects).
Narici et ai. (1992) determined in vivo PCSA of quadnceps muscles by measuring muscle volume. angle of pemation and Iength at rat. The acnrracy of the measmment of the angle of pemation was determined using bovine moscle, The accuracy was fond to be f 0.035 radians, when triking into consideration measurements taken from MRI scans and hmdissected muscle. In the vastus mediah it was found, ushg MRI (Scott et al., 1993), that the pemation a@e ranged hm 5 to 50 degrees, increasing in proximodistal direction. In addition, cross sectional area of most Mgh muscles, measured hmMRIs, were within + 75 per cent of measurements made from the specimem (Engstrom et al., 199 1).
A new technique, the diffusion tensor imaging technique, has been reported for determinhg skeletal muscle fiber direction (van Doom et al., f 996; van Donkelaar et al.,
1999). This technique is based on the imaging of the flow of blood and diffusion of tluid into the tissue. The accuracy of the diffusion tensor imaging technique was compared to high resolution MRI and acnial longitudinal sections, using the rat tibiaüs antenor muscle. It was concluded that this tool could be used to visuahe muscle fiber direction, although correlation with the actual anatomical specimens was not good. In addition. fiber Iength could not be measured.
2.4 Muscle modelling
Muscle rnodels are designed to mathematicaiiy describe nahirally occurring muscle phenomena such as contraction and force generation. There are two main types of muscle models: phenomenological and structural (mechanistic) (Otten, 199 1; van den
Bogert, L998). Phenomenological models attempt to explain phenomena mathematicaiiy, but do not necessarily reflect the stnictd birsis of the properties. Structural models use mathematical formulations that take Înto consideration the structurai characteristics of the muscle. For example, to predict force-length relatiomhips a phenomenological model may include data a database of measmments of force-length relations, but a structurai model would incorporate achial muscle arcbitecm data Otten (1988, 1991) stated that ". .. the phenomenological type cm, up to a certain degree of accuracy, make use of engineering mathematics" and "... the structural type has to corne up with numerical simulations of spatial events and is therefore a melange of existiag numerical techniques and home made algorithms." Van den Bogert (1998) concluded that a hybrid of both muscle models wouId be most accurate.
2.4.1 EIWs mdel
Hill's model has ken used in muscle modeliing since 1938 (HU, 1938). Over rime the model has been adjusted to account for shortcomings (Meijer et al., 1998) and to accommodate new ideas, but that 'Lthis model has been (and remains) the model of choice for rnost modelling shidies of multiple muscle movement systems" (Winters,
1990). The three elernent Hill's model is a phenomenological model that is based on the force-length and force-velocity relationships of hg skeletal muscle (concenaicaily contmcting). The three elements are:
a contractile element consisting of actin and myosin fdaments:
a series elastic element consisting of tendon and other elastic comective tissues in
series with the fi'bers; and
a parailel elastic element consisting of comective tissue around the muscle filibers
and the passive properties of the comective tissue and muscle ceiis.
Fung (1981) stated that "... the basic difncdty with Hill's model and aU its modifications is tbat the division of forres between the paralle1 and contractile elements and the division of extensions between the contractile and the series elements are arbitraryLn Further research into the identincation of the anangement of the muscle fibers, aponemses and tendons within muscle may dow for some distinctioa of these eIements in muscle models,
2.4.2 Use of hnman muscle architecturai data in muscle modeis
The importance of angles of pe~ationand other muscle mer architectural parameters with respect to function andlor modelling has been well documented (Spector et al., 1980; Sacks and Roy, 1982; Woittiez et ai., L983a; Huijing, 1985; Huijing et al.,
1989; Legreneur et al., 1996; Roy and Ishihara, L997, van der Linden, 1998a). To date, structural muscle models have been based on a wide variety of architechiral parameters.
The source and type of architectural data used in the modeKing process varies nom study to snidy. In Table 2.7 the source(s) of architechual data used in a variety of modelling studies of human muscle are summarized.
Muscle models using results hmanimal studies are more easily implemented and verified, For exampie, Woittiez et al. (1983a), Huijing and Woittiez (1984) and
Woittiez et al. (1984) used length-force data obtained hmWistar rats, and Van Leeuwen and Spoor (1992) used architectural data fiom cat mediai gastrocnemius muscle for verifkation of their mathematical models. More recentiy, Meijer et al. (1998) designed a
Hü1-type mode1 of the rat mediai gastrocnemius bat attempts to encompass the effects of shortenhg history.
A simpiifïed line drawing is often used to show a muscle exerting a force vector.
The geometry of a muscle determines the heof action (direction) of the force vector.
There are tsvo methods commonly used for representing the iine of action. Fmtly, the he of action may be dehed using a straight heor hesegments pieced together. Piece-wise iine segments aid in the constraint of the heof action when the mascfe changes direction Source of muscle data Bm4 A mode1 of lower extremity masmlar 6 unembalmed cadaveric Iower Crowninsbeild anatomy limbs et al. (1982) using radiographie images coordinates of bony landrnarks and centroids of ongin and insertion of 47 muscles were digitized Forces predicted at the ankle dunng 5 cadavers, hmphotographs of ankle region x, y and z coordinates were obtained at insertion of tendon into foot and the tendon at the margin of the appropriate retinaculum as it exists hmthe Ieg Resting length of the human soleus 30 embalmed lower limbs muscle muscle length before and after cutting the caicaned tendon, length of fibula, ankle angle Preserving plantar flexion strength anatomical data from: after surgical treatment for Witkiewicz, Roy et al*(1983); contracture of triceps surae, computer Fiedeich and Brand ( 1990) simulation smdy -- -- - Dostd and Three-dimensional biornechanicd 1 bony pelvis and femur Andrews ( 198 1) model of hip musculature coordinates for ongin and insertion of 22 hip muscIes . Godez, Mode1 to estimate moment anns, 1 male skeleton: digitized muscle Buchanan et ai, ~mumisometric forces and attachment sites and some ( 1997) fiexionextension moments generated intemediate points by 15 wrist muscles architecturai data hm:facobson, Raab et al, (1992); Lieber et ai. ( 1992)
------Herzog and ter Method for the determination of mathematicai model Keurs (1988); the force-lengtb relation 4 fresh cadavers Herzog (1990) Theoreticai determination of fiber length, sarcomere length force-length dations (human measnred quadriceps) Legreneur et ai. Effects of pemation angle and data hmFriederich and Brand (1996,199'7) tendon compliance on fiber length ( 1990) in Ïsometrïc contraction
Table 2.7. Continued next page, Author (year) Source of rndedata Prediction of muscle fecNitment and compnted tomographic and its effect on joint mction forces rnagnetic resonance images of one during knee exercises male snbject muscles were represented as vectors dong the sûaight line connecting the origin and insertion points Loren et al. Mode1 of wrist toque-joint angle &ta hm: Loren and Lieber ( 1996) relation (1995) (5 cadavers)
- - Spoor et al. Active force-length relationship of 3 embaimed lower-legs (1991) human tower-leg muscles, musde length, volume, mass, comparison of geomettic muscle fiber Iength, pennation angie and models sarcomere Iength memd Pierrynowski Physiological mode1 for evaluation of coordinates of skeletal reference and Momson muscular forces in human Iocomotion systern and line of action of each (1985) muscle hmone disarticulated male skeleton muscle length, fibex length, anatomicai cross sectional area, muscle mas, angle of pennation, tendon length and cross sectional area hm: Voss ( I956); Schurnacher and Wolff (1966a, 1966b); Eycleshymer and Schoeniaker (1970); Alexander and Vernon (1975); Pedotti et al. ( t 978) Wickiewicz et Muscle architecture and force- Data hm: Wickiewicz et ai, ai. (1984) velocîty relationships in humans ( 1983); Wickiewicz et al, ( 1982) Van der Heim ModeIling the mechanicd effect of 14 shouiders of 7 cadavers and Veenbaas muscles with large attachment sites 3D coordinates of a nurnber of (199 1) pomts at the ongin and insertion digitued relative to fiber bundie attachment White et ai, 3D mnscnioskeletai mode1 for gait coordinates of origin and ( 1984) anaiysis insertion from bones: 6 pelves, 9 femurs, 9 tibia-fibula complexes, 1 foot and I cadaver foot (Dosta1 and Andrews, 1981)
Table 2.7. Overview of saruce(s) of architecturai data ased in modelh'ng studies of human mde as it passes over a joint or when it wraps around a bone. Secondy, centroid mesare interpolated by estimating the centroids hm many axial (cross) sections through a muscle. These single heapproaches use coordinates of muscle attachment sites alone or in conjunction with coonlinates of intemediate points dong the course of the muscle. In
Table 2.7 it can be seen that numerous studies used this approach. Van der Helm and
Veenbaas (1991) expressed concem about the use of single Line of action in the representation of the mechanical effect of a muscle that is transmitted via large anachment sites. One line becomes hadequate to represent the possible forces on a large tendon of insertion. Van der Helm and Veenbaas (1991) created a mode1 with up to 200 ihes of action per muscle and Lengsfeld et ai. (L994)characterised attachment sites with up to 144 points. Even with the increased number of attachent pohts/lines of action, these modeis do not take into account complex muscle architecture, such as that of the soieus, nor do they address the effects of neighbouring muscles (extemai forces). The inter-reiationships of muscle function and specifîc muscle architecture are lacking.
Modehg aiso needs to take into consideration that volume or mas of a muscle remains constant during the contraction process (Baskin and Paolini. 1966; Otten, 1988; van der Linden et al., 1998a). Otten (1988) descnies two ways in which this has ken done in anipennate and bipemate models, fim by keeping the distance between the attachment daces(e.g. aponeuroses) of the nber constant (Benninghoff and Roihauser,
1952; Gans and Bock, 1965; Alexander. 1968; Na& et al., 1996) and by using least square parameter estimation on a nomber of muscle segments together (Woittiez et ai.,
1984)- Van Leeuwen and Spoor (1992) developed a mode1 for unipe~ateand bipennate muscle that enabled the prediction of the shape of the muscle fibers and aponeuroses and the intemal pressure distribution during contraction. Ushg this model, the balance between the extemal forces and internai pressure caused the aponeurosis and fiben to curve. This prediction was also made by Otten (1988) and Zuurbier and Huijing (1992).
Compter modelIing has ken effectively utilized to improve the understanding of physical phenomena and cluucal treatment techniques such as:
gait (Gemtsen et ai, 1995)
joint movement including knee (Piazza and Delp, 1996, Baii & Pierrynowski.
1995; Marshall et ai. 1990). shoulder (Sharkey and Marder, 1995), elbow
(Raikova, 1996). wrist (Delp et ai.1996, Loren et ai, 1996 and Goozalez et ai,
1997) and spine (Gracovetsky, 1986)
the design and process of knee nplacement (De@ et al, 1995), tendon transfers
(Loren et al., 1996) and tendon releases (De@et ai, 1994).
These models are generaily helpful in visualizing joint movement, expressing moment arms and caiculatirîg the forces, but are not designed to accommodate multi-part muscles with complu< nber architecture (Van der Linden, 1998b). Van der Linden et ai.
(1998a) suggested that finite element modebg may enable the "study of muscle morphology and its fonctional effects in more detail" and ''ailow identification of important factors that need to be incorporated in simpler modeIs of muscles of dinerent architecture."
Patel and Lieber (199'7) have expressed optimism that friture studies will elucidate the complexities of force transmission hm muscle fibers in different arrangements converging "on the comective tissue matrix". A model that includes the complete fiber architecture of an entire muscle is not currently available.
2.4.3 MoàeIiing O€ the human soleus muscle
Pierrynowski (1982) and White et al. (1984) both designed models for gait analysis. Pierrynowski's mode[, based on architectural data from a wide variety of sources (set Table 2.7). predicted individual muscle forces during normal human walking. He concluded that "... the results partially demonstrate that it is feasible to constnict a hierarchical physiological model to evaluate muscle forces. This statement must be tempered somewhat knowing that better anatomicd and neurophysiological data must be made available .. ."
White et al. (1984) modeiled 40 lower Limb muscles by obtaining 3-Dcoordinates of the muscle attachent sites from boues (n = 6). In this model, single or multiple he(s) of action spaaning hmthe centroid(s) of the attachment sites were used. Soleus was modelled using a single Line of action. White (1984) attempted to map the scaied 3-
D coordinates on to live subjects but found "iinatomicd clifferences between specimens are one source of error in detining a rnusculoskeletal model but Iarger errors are introduced when such models are mapped to living subjects."
Legreneur et al. (1996) designed a model to simulate in situ soleus isometric force output as a function of neural excitation, using the muscle architectural data of Frîederich and Brand (1990) and the geomemcd data of White et al. (1984). The authors stated that
''...the effect of rnuscplar architecture shoold be takeri into account to analyze the effect of neural excitation level on isometric force output." Legrenem et al. (1997) used the same model to simulate the joined effects of pe~ationangle and tendon cornpliance on nber Iength in isometric contractions. They found that the main effect of tendon elasticity and variation of pemation angle was to reduce variation in nber length by absorption of musculotendon lengthening. In both studies this mode1 was based on the assumption that soleus has a constant pe~ationangle. The authors commented on this assumption that "... however, it is not really the case in vivo. Indeed, the human soleus is a very cornplex muscle, at Ieast bipennate.. ." and ". .. thus, the model codd not pretend to simufate the real behaviour of the human soleus in in vivo conditions,"
Presently there is no mathematical or contractile muscle model that can relate the complex architecture of the human soleus to its many functions. It is the aim of the present study to create a 3-D mode1 of hum= soleus architecture that is representative of all parts and portions of the muscle, using both cadaveric and in vivo data This type of documentation of the soleus muscle could Lead to more realistic modelling of the soleus and to better understanding of its hction.
2.5 Functions of the human solens muscie
Gross anatorny textbooks state the action of soleus as being planta flexion of the ankle (Rosse and Rosse, 1997; Olson, 1996), but often also comment on soleus as stabiïizing the leg on the fwt or acting as an anti-gravity muscle (Williams et al., 1989;
Moore and Ddey, 1999; Sinnatamby, 1999). Electromyoppbic studies have shown that soleus is an important postural mde invohred with maintenance of standing
(Joseph and Nightingale. 1952; Campbell et al., 1973; Heman, 1967). O'ComeH (1958) found that solens maiaiains a tonic contraction to prevent the body hmfWg forward.
In standing the soleus contracts altemately with the Ieg extensor muscIes to maintain balance (Shatamby, 1999). Unilateral soleus activity has also been reported, during inversion and eversion
(O'ComeIl, 1958). Basmajian (1967) suggested that the laterai part of soleus is activated during eversion of the foot and the medial part duting inversion. Campbell et al. (1973) also suggested that the medial and lateral half of soleus have Werent fiinctions and that
"... the medial soleus is a strong mover of the foot on the leg and stabilizer of the leg on the foot. The lateral soleus, while not Unparhg as much power to foot movement ..." and "... is a continuously acting stabilwr of the Ieg on the foot."
The humsoleus muscle has also been reported to be more resistant to fatigue
(Ochs et al., 1977), has longer mean contraction the and has significaatly slower twitches than gastrocnemius (Vandervoort and McComas, 1983). These results are in keeping with fiber type distribution found within each muscle (Johnson et al., 1973;
Golùtick et al., 1974; Edgerton et al., 1975; Green et al., 1981; Elder et al., 1982). Soleus conskts of mainly type 1 fibers, while the gastrocnemius has similx proportions of type 1 and type II mers.
Sekiya (1991) studied the intramuscular distribution of the anterior and posterior branches of the tibial newe in the soleus muscle. Both Sekiya (1991)and Schultz et al.
(1973), found that anterior soleus was innervated by the anterior branch and posterior soleus by the posterior branch of the tibial nerve. Sekiya (1991) traced the nerves thmughont the muscle using a stereoscopic microscope. It was found that the anterior branch had several anastomotic twigs that commtmicated with the postenor branch in the infemmedial and midlateral regions of postenor soleos. The cross sectional maof the anterior branch was 38.6 359 per cent of the total nedarea before division into anterior and posterior branches. It is evident that auterior soleus bas separate innervation, and is partitioned fkom the rest of soleus, but fimctional si@caace of this part of the muscle has not ken determined. A better understanding of the muscle architecture of anterior soleus relative to the rest of the muscle, in conjunction with muscle modelling, may provide insight into its bction. Chapter 3: Hypotheses and Objectives
3. Hypotheses
The hypotheses of this thesis are:
I. It is possible to geaerate a realistic three-dimensional (3-D) computer model and
database of human soleus architecture throughout its entire volume (marginal,
anterior and postenor parts) using embalmed cadavenc specimens.
2. The 3-D model and database are a reaiistic representation of soleus muscle
architecture as compared to rnanually measured architectural parameters of the
cadaveric soleus muscle.
3. In vivo architectural data of relaxed and contmcted human soleus muscle differs
from the cadaveric data,
3.2 Objectives
The objectives of this thesis are:
1. To develop, using photogrammevic techniques, a detaiied anatomical 3-D
computer mode1 and database to document aod visualize the cornplex architecture
of the marginal, anterior and postenor parts of the human soieus muscle.
2. To coIlect arcbitectmii data manually hm embaimed soleus muscles and
compare them to resolts obtained photogrammetrically.
3. To coiIect data, m vivo, on the architectural parameters of the soleus muscle in
relaxed and contracted states using ultrasonography and to compare these findings
to the cadaveric model. 4. To determiue if there is a signincant ciifference between architectural data
obtained hmcadaver studies and in vivo data obiained by ultrasound.
3.3 Signiscance
This study provides a "one of a kind" database of the architecture of the soleus muscle in embalmed cadavea and living subjects. A 3-D computet mode1 of the entire cadaverïc human soleus muscle in situ is developed. Documentation of the architectural characteristics of Live muscle in relaxed and contracted states may aid in understanding how a muscle is engineered for specific hinctional requirements. Architecturally distinct regions in a muscle need to be documented in such a way that their influence in producing the fiai output may be understood.
3.4 Definition of marginal, postenor and anterior soleus
In the present thesis, the anatomy and terminology of the soIeus are dehed as follows:
Marginal soleus: Fiber bundies span hm the medial, laterd and superior margins of the postecior aponeurosis to the antenor aponeurosis mediaiiy and lateraiiy, and the tibia and fibula superiorly as shown in Fig. 3.1. The medial and lateral fiber blmdles are med. Supenorly the fiber bundies are oriented more verticaliy.
Posterior suleur: Fiber bundles attach to the posterior surface of the anterior aponemsis and the anterior surface of the posterior aponeurosis. The fiber bundes are directed from antemsuperior to posteroInferîor as shown in Fig. 32
Anferior soleux The antenor soleus is bipemate and is best visuaüzed on the anterior sdace of the muscle as shown in Fig- 33. The mer bundles join the median septum and the anterior aponeurosis. The median septum is a vertical sheet of aponeinosis, Fiber bundles of antenor soleus attach to its medial and laterd surfaces.
Figure 3.1. Marginal soleus, postemlateral view. (Reproduced with permission lrom Oxorn (1997)) Figure 3.2. Posterior soleus, posterolaterai view. (Repduced with permission hmOxorn (1997))
Figure 3.3. Anterior soleas, antecior vîew. Note that the anterior soleas has been dectedfrom its tibia1 and fibdar attacbments. (Repduced with permission hmOxom (1997)) Chapter 4: Methods
4.1 Development of muscle mode1 based on cadaveric specimens
41Calibdoa devices
In order to be able to mck the location of the specimen in three dimensional (3-
D) space a calibrated baseplate, a plate for volumetrïc calculations and two marker clusters for the specimen were needed. These items were manufactured at the Technicd
Shop, University of Toronto, to a dimensional precision of I0.5 mm with respect to location of the bali bea~gson the two plates.
The baseplate, made from acrylic sheet, was 50 cm x LOO cm and contained 50 baH bearings arranged equidistantly as shown in Figure 4. IA and B. There were 10 rows of embedded bail bearings placed 10 cm apart. Each mw consisted of 5 baIi bearings spaced at 10 cm intervals. The baseplate was placed on a table with a black surface so rhat the bdi bearings couid easily be seen.
The p[ate for volumetric calculatiom consisted of an acrylic sheet 30 cm x 50 cm, containing 30 bail bearings arranged equidistantly (see Figure 4.1 A and C). There were 5 rows of ball bearings placed 10 cm apart. Each row had 3 baU bearings spaced at IO cm intervals. The plate was motmted on four metai posts. Each pst had four markings at IO cm intervals starting at the bottom of the post. This plate couid be moved up or dom dong the posts to any one of the four markings. Figare 4.î. Calibraiion devices. A, Schematic inusbation of the baseplate and volume plate, latdview. Superimposed are the planes O€the x, y and z eoo~ates. B. The baseplate with one speûmen support, saproCaterai vÏew. C. The votmae phte positi~nedon baseplate, superohterd vkw. Note that the votume plPte is attached to four mobile pots& The marker ciusters were circular acryiic discs with 6 baU bearings embedded at eqnal intervais mund the circumference of the circle with a diameter of 10 cm. One market: cluster was screwed to an Itizmv Halt Pin drilled nrmly into the medial epicondyle of the femur. The second marker cluster was also screwed to an nizarov Hait
Pin pIaced in the medial malleolus of the tibia as show in Figure 4.2. Rizarov stainless steel Halt Pins, 4 mm in diameter and 150 mm long, were used.
Figure 4.2. Marker dusters phed to a spedmen, posterior view. The marker ciuster tabeied Dl is pinwd to the mediaï maiieolus of the tibia and the marker ciuster IabeIed D2 is pinned to the mediat epicoudyle of the tibia, S = superior, 1= iderior.
4.12 Photography
Photographs were taken using three spatiaiiy calibrated 35 mm cameras mounted on hipods. The cameras were piaced on the right and left sides and at one end of the baseplate as shown in Figure 4.3. The height of each tnpod and the position of each camera were adjusted to maximize visnakation of the baseplate and the volume plate. Figure 4.3. Schematic illustration O€ the position of the three cameras relative to the baseplate and'votume plate. Cameras are labeled CI, C2 and C3.
Every effort was made to keep the table, tripods md cameras stationary.
However, minute movements of the cameras (that is, from shutter movement, fh advancement, gravitational sag, etc.) couid be detected and adjusted in the computation phase. Lighting was provided by four ningstett Lights placed at each corner of the table.
Kodak Ektachrome 160T siide ftlm was used.
At the beginning of each photography session, a set of photographs (one with
each camera) wûs taken oE
the baseplate alone;
the baseplate with the plate for voIumetric calculations at the LO cm mark; and
the baseplate with the plate for volumetric cdculations at the 20 cm mark.
Next, the Ieg with the attached marker clusters and pinned mer bundles was
placed centered on the baseplate as shown in Figure 42 with its supexior (proximal) end
directed towards the camera at the end of the table. The specimen was positioned and
stabilized with piasticine props so that the posterior aspect of the Ieg was superficiai (facing the cameras). Photographs were then simultaneously taken with ail three cameras. In order to view aLl the pinned fiber bundles throughout the volume of the marginal and posterior soleus two sets of photographs were taken. One set of photographs was taken of the posterior aspect of the spechen. Next, the specimen was rotated so that another set of photographs could be taken of the posterornediai aspect of the specimen. The anterior soleus couid be visualied in its entkty hmpostenor and therefore, each level of dissection ~quiredody one set of photographs.
4.13 Dissection
4.1.3.1 Specimeos
A total of five embalrned cadaveric soleus muscles were seriaüy dissected Ni situ.
On inspection, the cadavenc legs had had no evidence of rnusculoskeletal deformity and the ankle joints were fixed in the matornical position (the fwt at 90 degnes to the leg).
Developrnent of the dissection protocol continued to evolve From the first to the fifth specimen, enabhg the collection of increasingly more detailed data Dissection of the fifth specimen which was the soleus muscle of the right leg was the most comprehensive and wÏU be desmLed below. The method of measmement of the architectural parameters was not altered hmthe htto the fifth specimen. Only the dissection techaique, to expose and pin increasmgly more fiber bundles, evolved hm the Fit to the fifth specimen.
The dissection pmgressed hmposterior to anterior, sequenùdy exposing the marginal, postenor and anterior parts of the soleus muscle. Fiber bundles were dissected
and phed wÏth colorrd beads. One hdf inch sequin pins (number 8) were used ta anchor the beads to the £Ïber bandes. Each fiber bundie was pinned with one color of bead. The colored beads assisted in tracking fiber bundles, but the spefic location of the center of the pin head was the point that was digitized A detded color drawing of each ievel of senal dissection was made pnor to photographiag the specimen with the three statioaary calibrated 35 mm cameras.
4.1.3.2 Marginal Soleus
InitiaDy, the entire postenor aspect of the soleus muscle was exposed and cleaned as shown in Figure 4*4* Next, the margins of the posterior aponeurosis were identified.
Sixty-two marginal fiber bundles were then meticulously cleaned md exposed nom their posterior attachment on the posterior aponeurosis to their anterior attachment on the anterior aponeurosis dong the medial, supenor and lated aspects of the soleus muscle.
To indicate curvature and direction of fiber bundles, each ideniified fiber bunde was pinned at its anterior and postenor attachments and at two to three intervening sites.
Figure 4.4. hedaber bundles of marginal soleus, posterior view. S = superior, 1= infecior, Lat = Iateral.
Each fiber blmdle was pinned with the same color beads, either red, blue, black, or yeiiow as shown in Figure. 4.4. A drawiag was made of the phed specimen and photographs (as descriid in Section 4-12) were taken of the postenor and posterornedial aspects of the specimen. 4.133 Posterior Soleus
The posterior soleus, the largest of the three parts, consists of nber bunciies ninning between the anterior and posterior aponeuroses from anterosuperiorly to posteroinferiorly. A total of one hundred and thkty fiber bundles were pinned in the posterior soleus. Two Ievels of dissection. superficial and deep, were needed to trace entire fiber bundles hm postenor to antenor. To expose the posterior (superficiai) aspect of the posterior soleus, the marginal soleus and postenor aponeurosis must be removed. To remove the posterior aponeurosis, the nber bundies of the postenor soleus attaching to its anterior aspect were released careNly ushg a scalpel. Clean release of these fiber bundies hmthe aponeurosis was essential to preserve full fiber length. The marginal fibers were then released bm the posterior aponeurosis, separated €rom the postenor soleus along a fascia1 cleavage plane, traced anteriorly to the antenor aponeurosis and subsequently removed. The superficial (posterior) aspect of the entire posterior soleus was now exposed.
In the superficial dissection of the:
proirh.czl (superior) wo thirds of the postenor soleus, both the proximal and
distal attachments of the fiber bmdles of the most proximal row couid be phed.
In the subsequent mws ody the posterior ends of the fiber buadles were visible
for pinning as shown in Figure 4.5.
diml third of the posterior soIeus, the muscle beliy aanows, aliowiog more
compiete exposure of the fiber bmcües. These hrbundles were pinned at their
postenor ends and at two to three sites along their curved course as shown in Figure 4.5. The antenor attachment sites of the nber bundes could not be seen at
this Ievel of dissection.
Figure 4.5. Pinneci fiber bundles of posterior soleus, posterior view. Note that the superior row of fiber bmdles were pimeci at both attacbment sites. In the subsequent rows OP the superior two third of soleus oniy the posterior amchment site codd be pinned. In the distal (iderior) third the fiber bundies are pinned in maitiple locations. In this picture sample fiber bunaes are indicated with soiid iines, Specimen orientation: S = superior, 1= inferior, Med = medial, Lat = Iaterai.
In the deep dissection of the:
proximal nvo thirds of the muscle, each pinned fiber bundle was traced to its
attachent to the antenor aponeurosis. The termination of each fiber bundle- was
pinned with the same color of bead as used in the superticid dissecticin. Once
pinned, the nber bunde itself was removed to facüitate the tracing of adjacent
nber bundies. The specimen was photographed when aü the selected nber
bundles had ken pinned at theù anterior attachent site.
distaf third of the muscle, each phed nber bunde was traced to its attachent to
the antenor aponeufosis. The site of termination was pinned with the appropriate
color of bead and the specimen photographed. In the proximal two thirds of the mnscle, the fîber bundles have a hear course and were pinned at two sites, their posterior and aaterior attachments. In the distal third of the muscle, the fiber bundles were, and therefore each fiber bundle was pinned at multiple locations between the attachmcnt sites. The distal part of posterior soleus was cootinuous with the marginal soleus.
One set of photographs (as descriid in Section 4.1.2) was taken of the postenor aspect of the specimen and another set of photographs was taken of the posterornediai aspect of the specimen at both superficial and deep Ievels of dissection of the posterior soleus.
4.13.4 Anterior Soleus
The fiber bundles of the anterior soleus span between the median septum and anterior aponeurosis. The posterior aspect of the anterior soleus and median septum were hadypartiaLiy exposed due to the removal of the fiber bundles of the posterior soleus in the previous dissection. In order to get complete exposure of the postenor aspect of the anterior soleus, the antenor aponeurosis was removed as necessary. Each identified fiber bundle was pinued at both ends and at up to two intervening sites with the same color of bead as shown in Figure 4.6.
A total of one hundred fiber bundles were pinned anci photographed on four levels of senai dissection. At the termination of this dissection, the crurai fascia covering the deep posterior cornpartment of the Ieg was exposed. One set of photographs of the posterior aspect of the spechen was taken at each level of serial dissection. 4.6. Pùtned Kber bundles of the anterior soleus, posterior view. Note that individd fiber bundles are indicated by a solid line and that they attach in the miàiine to the median sep- 0. Spedmen orientation: 1= Merior, Med = medial, Lat = lateral.
4.1.4 Digitization
The photographie images hmall hree cameras were transferred to CPROM.
Adobe Photoshop 5.0 was used to import and visualize the images on the compter screen. Sigma Scan Image (Jandel Scientific) was used to digitize and record the x and y coordinates of the:
center point of the baU bearings on the caübration devices.
center point of the pin heads on the beaded specimens.
4.1-4.1 Digitization of the baseplate
Each bail bearing on the base plate was assigned a number (1 to 50) that remained consistent on ail images. Two arrows engraved into the baseplate assisted with orientation of the baseplate. Digitization proceeded in numerical sequence, so that the appropriate coordinates were recorded for each bail bearing as shown in Figure 4.7. Any ball bearing not vÎs%le on a particdar image was coded as a missing value. 4.l.4.2 Digitbation of the vdume plate
Each baiI beating on the volume plate was assigned a consecutive number hm
63 to 77, and each mark on the four posts was assigned a number (78 to 90) as show in
Figure 4.7. The baU bearings on the plate and the markings on posts were digitized.
BASEPLATE Camera 1
Camera 2
I Pole
Fi4.7. Recordhg sheet showhg the nmkring of the eoordinates of the baseplate and volume phte. To view the placement of the volume plate on the basepIa@ see mgnre 4.l. 4.1.43 Digitization of the mkerchisters
The bdl bearings embedded in the marker ciuster located at the medial epicondyle of the femur were numbered hm 51 to 56 in a clockwise fashion hm an arrow engraved into the marker cluster. Similady, the bail bearings in the marker cluster located at the medial mdeolus of the tibia were numbered hm57 to 62 (see Figure 4.8).
Digitization proceeded in numerical sequence, so that the appropriate coordinates were recorded for each baii bearing. Any baii bearing not visible on a partictiiar image was coded as a rnissing value.
The marker clusters had a flat side and a screw side. The screw side had the bone pin mounting mechanism attached to it. Digitization was camed out €rom the screw side of the disc in a clockwise manner fiom the engraved arrow. If, on au image, the tlat side of the disc was superficiai, then the appropriate visuai transformation was made so that digitkation proceeded counter cbckwise as if the screw side of the disc was superficiai.
This kept the numeration of points consistent.
4.1.4.4 Digitization of the serial dissections
In preparation for digîtkation, every pin in the center of a colored bead was
numbered on the dmwings of the pinned specimens. A recordhg sheet was designed for
each Ievel of seriai dissection as shown in Figure 4.8 that included:
a diagram of the specimen with numbered pins and a sùnüarly numbered
coordinate recording chart;
a diagram of the baseplate with nnmbered bail bearings; and
diagrams of the two marker ciusters with nmnbered bdbea~g~ Camera 1 1
Camera 3 MARKER
Medial malleolus
Figare 48. Recordhg sheet for each ledof senDaidïssecüon. Note that the shsheet dows recoràing of the coordinates of the basephte, marker ciusters and beaded pin heads on the specimen. There is also an ares in which to dmand aumber the beaded phheads of the specimen. For each IeveI of serial dissection there were either three or six images on the CD-
ROM, depending on whether the specirnen was photographed hmone or two aspects by each of the three cameras. The recording sheet of each level of dissection was color photocopied so there was a correspondhg map for each image on the CD-ROM.
The recording sheet was used to indicate the points @ail bearingslpins) that were visibleloot visible on a CD-ROM image. Any point(s) that could not be seen on the baseplate, marker clusters or specirnen was marked with an "X". The numeration of the points on the spreadsheet matched those on the recording sheet. This recording sheet couid then be used to make sure that:
visible points were digitized in the correct numerical sequence; and
hidden points were indicated as rnissing values on the spread sheet.
For every image, the center of each of the visible baU bearings and pin heads was digitized in numerical sequence as indicated on the recording sheet. Hidden points were entered as -1.1 11 1 on the spreadsheet (no namericaI value, place holder ody). Each spreadsheet was carefhily narned and saved as a text file for use in the Direct Linear
Transformation Program that converted the 2-D points into 3-D points.
4.1.5 Reconstruction of digitized data fkom 2-D to 3-Dcoordinates
Data reconstruction From 2-D to 3-D coordinates was canied out by adapting photogrammetric methods descrjtbed by Bail and Pierrynowski (1988, 1995). This is
Merdesrnid in Appendices A and B.
The main steps of the procedure inciude the foiiowing:
Dura @ut Read files containing digitized 2-D data hmail images of the calibration devices and send dissections. Culibrarion procedure usîng Direct heurTr~onnatiun (DLT) Heven camera parameters (internai and extemal) were determined for each camera using the non-iinear least squares best-fit approach. New DLT parameters were calculated for each Ievel of dissection, taking into consideration the transformation (movement) of the cameras relative to the base plate. Rigid body trackhg methods were used to determine the transformation of the cameras. 3-0reconstruction of the coordinates Using the new DLT parameters and the digitized 2-D coord.inates, 3-D coordinates were computed for the calibration devices and the muscle fiber buodles. In order to cornpute the 3-D coordinates from the 2-D coordinates it was necessary that the data point be digitized in at least two out of the three images photographed for each level of serial dissection. Trachg of the marker clusters The coordinates of the bail bearings on the marker clusters were tracked for each level of dissection and the results used to traasform the 3-D coordinates back to the first level position. This enabled stacking of aü the Ievels of senal dissection and mapping of the coordinates in 3-D as seen in situ. Rigid body tracking methods were used to determine the transformation of the marker clusters. Input connection matrix tu delineate eachfiber bundle LUie segments were used to connect the coordinates belonging to each individual fiber bundle- When the comection ma& for the entire muscle had been entere.d it was possible to visualize, in 3-D,the fiber bundle architecture for the whole muscle and its component parts.
4.1.6 Modehg the sofeus muscie with B-spline soüds
A muscle model, osing deforniable B-sphe solids, was developed to visualize the intemal architecture of the human soleus muscle in 3-D (Ng-Thow-kg et al., 1998a;
Ng-Thow-Hing et al., 1998b) and to measure architectural parameters throughout the volume of the muscle. B-sphe solids are codigured as 3-D vector fimct.011~that cm pafameterize an enclosed volame and its extemal bomdary daces, such as the posterior, anterior and marginal parts of the soleus muscle. Any point within the volume of the muscle cm be referenced. The steps of the process are summarized below.
Data input Read files containhg 3-D coordinates and co~ectionmatrices of the fiber buadles of the soleus muscle obtahed by anatomicai photogrammetry (see Section 4.1.5). Data fltting process Using the 3-D coordinates, a continuous volume sampling fiuiction was constructed that defïned the control points on the surface and within each muscle Part- The three B-sphe solids thus created (that is, one for each part of soleus: antenor, posterior and marginal) were joined to rebuiid the whole muscle. 30 display offlber orientation ho-curves and iso-surfaces can be extracteci fiom the B-spline solid and used to generate streamiines that enable visualization of individual muscle fiber bundles or boundary surfaces as shown in Figure 4.9. Streamlines, comecting appropriate control points, were generated to represent individuai fiber bundles in ail thtee parts of soleus. Additional fiber bundles were generated, hmthe onginal fiber data set fitted to the 8-spline soiid, using a Sobol sequence. The Sobol sequence is a quasi- random sequence where the points are chosen in a rnanner that distributes the fibers evenly across the soüd as shown in Figure 4.10. As the number of streamlines is increased, the newer fibers are generated between the space of existing fibers, aever generating the same parameter values twice.
Figure 49. h-curves and bsdacesgenemted from a B-spiine solid, (Reproâuceù with permission hmNg-Thow-Hing (2001)) Fiber bundle length (mm) was obtained by using numerical integration or by summing the Iengths of the line segments joining sampled points of each fiber bundle. As the numbers of sample points increases, the length of the summed he segments converges to the mearc length. Meusurement of angle of pennatiun The point of attachment of the nber bundle to the iso-surface, representing the aponeurosis, is three-dimensionai. The angle of pemation was cdcuiated at the attachment site at each end of the fiber bundle by rneasuring the angle the fiber tangent makes with the local tangent plane as shown in Figure 4.1 1.
100 Rbres 500 fibres
Figure 4.10. Ceneration of liber bandles usiag the Sobol sequence, (Reprduced with permission hmNg-Thow-Hing (2001))
of fîber where it Isis
3, and V2arc vectacs that a =Angie betwetn tangent vector d&nc the tangent plruie of the of nber bmdIe and tangent plane of muscle sucfàce at the point where nmscfe mdwe at point where tïk bunde meets aponeurosis
Figare 4JlA Sebernatic illustration of the mersurement of angle of pemaüon using the B- sphe mosde model. Fiber length and angle of pemation (at both ends of the nber bundIe) were recorded for 100 fiber bundles distriiuted throughout marginal soleus as shown in Figure
4.12A, 100 fiber bundes in posterior soleus (see Figure 4.12B) and 200 nber bundles distri'buted throughout four Layers of anterior soleus (see Figure 4.13).
tangent vector
Figure 4.11B. Measmement of fiber bdeIength (mm)and angle of pennation (degrees) hmthe B-@ne muscle modei. The fiber Iength and angle of pemation are üsted respecüveiy bdde each fiber bde(aber veetor). (Reproduced with permission from Ng-Thow-Hing (2001)) Most proximal Most prod fibdar attachment fiMar attachent Soperior t
A. Proximal end of dcaneal tendon
Figare AU. Nmbering scheme and location of fiber bmidles (streamlines) used to record fiber le@ and mgtes of pemtion. A. Right mugiaal deus, posterornedial view. B. Right posterior sok- posterior view. Superior
septum A.
Figure 4J3. Numbering scheme and location OFober bandles (stffamlgies)used to record fiber length and angles of pennition of right antenor solem, antenor vie- A. Most posterior layer. B. Most anterior Iayer. The mean, standard deviation, and range of nber Iength and ang.Ie(s) of pemation were caldated for the following regions of soleus:
the mediai and lateral fiber bundles of the proximal, middle and distai thirds of
the marginal soleus;
the medial, middle, and lateral fiber bundes of the proximal, midde, and distal
thirds of the posterior soleus; and
the medial and lateral fiber bundles of the tip and proximal, midde, and distal
thirds of the antenor soleus.
Marginal soleus No. of Posterior soleus No. of Anterior soleus No. of fiber fiber fiber bundles bmdtes bundles Proximal 1/3: Proximal 113: Tip: Laterd 22 Laterai 4 Lateral 5 Medial L8 Middle 6 Mediai 5 Middle 1/3: Medial 4 Proximal ln: Lateral 16 Middle ln: Lateral 9 Mediai 18 Lateral 7 Medid 6 Distai 113: Middle 8 Middle L/3: Lateral 11 Medial 8 Laterai 5 MedÏai 15 Distal 113: Medial 5 Laterd 5 Distai 11'3: MiddIe 4 Lateral 5 Medial 4 Medial I t
Table 4.1. Cornputer rndel: Number of fiber bundles in -ch subdivision of the marginai, posterior and anterior soleos nsed for data amùysis, Only the most anterior tayer of anaor deusis hciuded, since it is the ody fayer accessed by the other data coiîectïon techniques. 4.2 Architectaral panmeters of the cadaveric soleus mriscle: manual memement
Fm-four soleus muscles were removed from 3 1 cadavers with average age 79 I
10.3 years. In total, 26 femde (16 nght (R)/10 left (L)) and 28 male (16R112L) specimens were obtahed. The legs from which the specixnens were obtained had no evidence of muscdoskeletal deformity and the ankie joint was fixed in the anatomical position (the foot at 90 degrees to the leg). AU specimens were examined to document the architectural parameters of the enthe soleus. To dow quantification of architectural parameters of the marginal, anterior, and posterior parts of soleus muscle, Mer dissection was carried out on nght and Ieft soleus muscles of 5 cadavers (that is, 5 pairs of specimens).
Ail 54 embalmed soleus muscles were cleaned by removing ûdjoining loose co~ectivetissue. Muscle length (cm) was measured lateraily, centrally, and medidy hmthe most proximal fibuiar attachment; the site of the neurovascular bunde passing deep to the fibrous arc& and the medial attachent to the soleal line of the tibia to the distal site of attachent to the caicawai tendon (see Figure 4.14). Figure 4.14. Measureinent of deus musele length. From: A = most pmximai fibular attachent; B = site of neurovascular peàide at fibrous arch of soleus; C = medial end of soleal Ine of tibia. To: X = distal attachment of muscle beüy to calcaneaï tendon.
Leg Iength (cm)was measured as the distance between the anterior superïor iüac spine and the base of the medial maüeolus. The Correlation Coefficient (r) was calcuiated for leg length and muscle leogth. Each muscle was inspected to determine the presence of marginal, antenor, and posterior parts.
Volume (& of the entire soleus and each of the component parts, marginal, antenor, and posterior, were recorded by measuring the amount of water displacement that occurred on addition of muscle tissue to a graduated beaker coniainiag water. The volume of margmal, anterior, and posterior soleus was expressed as a prcentage of the total volume of the muscie, 42.3 Manul measurement of fiber bonde Iength and angle of pedonof the margfnd, anterior and posterior soIeus
Five pairs of specimens, From the 54 soleus specimens described in Section 4.2.1. were selected for more detailed architectural study.
42.3.1 Marginal so1eus
In each of the specimens 25 to 41 fiber bdles of the marginal soleus were identified and teased apart around the circderence of the muscle. The begllioing and end of each fiber bundle were pinned with the same color of bead. The length of each fiber bundle (mm) was measured by followhg the curvature of the bunde as shown in
Figure 4.15. The angie of pe~ationof each fiber bunde was measured in degrees relative to its attachment to the posterior aponeurosis.
Fipare 4.E Mandmeasurement of fiber length (n)and angie of pemtion (Be) of marginal soleus. PA = posterior aponeurosis. 4.2.3.2 Posterior soleus
To expose the fiber bundIes of the postenor soleus, saginal incisions extending through the muscle belly between the anterior and postenor aponeuroses were made in the medial, central, and lateral part of the muscle. Five to sixfiber bdeswere traced in the central incision site and three fiber brmdles were traced in each of the medial and fateral incision sites of postenor soieus. The ends of each fiber bundle were pimed with the same color beads. Fiber bundk length (mm) was measured. The antenor and posterior angles of pennation were measured in degrees, the former relative to the anterior aponeurosis and the latter relative to the postenor aponeurosis as shown in
Figure 4.16.
Posterior Soleus 1 AlUr APON.
Figure 4.16. Manoal messiirements of posterior soleas. A. Sites of sagittat incisions (1-3). B. Memirement of &r Iength (EL) and angles of pemation (&and h). PostJAnt, Apon, = posterior / anterior aponelllosis. 4.233 Anterior solens
EIeven to twenty-FeBber bundles of the anterior soleus were identined on the anterior surface of the muscle. Each fiber bundle was traced between the median septum and antenor aponeurosis, teased apart and pinned with the same color beads. Fiber length
(mm) was measured and the angle of pennation (degrees) was measured relative to the median septum as shown in Figure 4.17.
Figure A17- Manual mensurornent of fiber Iengtù (FL) and angles O€ pemation (&) on the medial and laterai sides of the median septum.
4.2.3.4 Anaiysis of menual measurernents
The mean, standard deviation, and range of fiber length and aagIe(s) of pemation were cdcuiated for:
the medial and lateral fiber bundies of the proximal, middle, and distal thirds of
the marginal soleus:
the medial, middle, and latelal mer bundles of the proximal, middle and disral
thirds of the posterior soleus; and
the meclid and lated fiber bundes of the tip and proximal, middle, and distd
thirds of the anterior soleus. 4.2.4 Comp8PiSon of architectural parameters obtained by manuai meanirement and hmthe computer model The mean, standard deviatioa, and range of fiber length and angle(s) of pe~ation were cdcuiated for the same subdivisions of the marginal, anterior. and postenor soleus as described for the manual rneasurements (see Section 4.2.3.4). The similarities and differences of the descriptive statistics are discussed. Since the angle of pemation was recorded in 2-D when measured manudly and in 3-D with the computer rnodel, cornparison of redts is not directiy possible. Statisticai analysis was not carried out, since the computer model was based on one specirnen.
43 In vnto imaging
43.1 Ultrasound study
4.3.1.1 Subjects
Ultrasonographic studies were carried out on 35 normal healthy voiunteers (16
fernales, 19 males) with no history of musculoskeletal injury. Subject age mged nom
IO to 92 years, with a mean age of 44 years. Informed written consent was obtained hm
each subject. The University of Toronto Human Subjects Review Cornmittee approved
this study (protocol reference #1859). See Appendix C for Ethics Document and Subject
Consent Form.
4A13 Shidy protoc01
The study protocol was developed as part of an eight-month pilot snidy during
which thne live subjects and cadavenc specimens were scanned to determine optimum
and reproduciile scdgplanes for each part of solens. The scanning and recordhg
protods descrïbed below were assembled based on the results of the pilot study. A Toshi'ba SSH-140A real theultrasotmd scanner with 5 MHz or 7.5 MHz linear array traasducer was used for the study. An Agfa Unpax System (Pax System) processed the information.
After signing the consent forni, the age and leg Iength of the subject were recorded Leg length (cm)was measured hmthe anterior superior iliac spine to inferior end of medial rndeolus.
For scanning, the subjects were positioned prone on an examinhg table with their lower bbsextended muscles relaxed and feet resting over the edge of the table at aa angie of 90 degrees to the leg. A total of five sites in the soleus were scanned. At each site the leg was scanned fint with the muscle relaxed, and then with the muscle in a state of maximal vofuntary contraction. For scannllig in the contracted state, subjects were requested to produce and sustain full plantar flexion of the ankle. We attempted to obtain a total of twelve images of soleus for each leg. The scanniog site(s) and planes wilI be described for each part of the soleus. In order to visuaüze fiber bundles throughout their entire length, the transducer needs to be placed in the pIane of fiber bundle orientation.
To locate the scaaDing sites for posterior soleus, a horizontal hewas drawn from the apex of the head of the fibula to the medial tibia1 plateau. A vertical line was then drawm hmthe horizontal iine to the midpoint of the attachent of the calcaneal tendon to the calcaneus bone. The rniddle and distal tbirds of the vertical hewere identified,
Using a 5 MHz hear array tramducet in the sagittal plane, a total of 6 scans (3 of
~Iaxedmuscl& of contracted muscle) were obtained from 3 sites. The scan sites as shown in Figme 4.18 were located at the Ievel of: the middle of the vertical he(A) the distal third of the vertical he(B) the middle thud of the vertical Liae Iateral to rnidline (C)
Figure 4.18. Location of the sonographic scanning sites of posterior soIeirs, posterior view. A, B and C are described above.
To Iocate the scanning sites for the anterior soleus, a 5 MHz hear array transducer was placed on the media1 aspect of the leg in the coronal plane. Fit, the full extent of the median septum was identified and then the locations of the proximal and middIe ihirds of the median septum were established. With the transducer in the coronai plane, a total of 4 scaos (2 of reiaxed muscle42 of contracted muscle) were obtained bm
2 sites. Anterior soleus imaging was codined to the medial half of the bipe~atefeather.
Scanning of the lateral side of anterior soleus was unsuccessN due to the limitation of probe penetration. The scaa sites (Figure 4.19) were located at the leveI of the:
proximal third of the median septum (A); and middle third of the median sephun (B)
figure 4.19. Location of the sonographie seanning sites of anterior soleus, medial view. A and B are describeci above.
The marginal fibers could not be viewed in their entirety in any one plane because of their cwed orientation. Using a 7.5 MHz linear array transducer in the axial plane, it was possible to locate some cenvally located marginal fibers passing between the medial edge of the posterior aponeurosis and the medial border of the tibia These fibers could not be identified consistentiy and therefore were not included in the study.
43.13 Measurement of architectural parameters €rom ultrasound scans
Fiber bdelengths, angIes of permation, mrd muscle thickness were measured hma total of 840 scms using a scaled der and a protractor. A cleariy visible fiber btmdle surrounded by its comective tissue covering was identified on each scan. The fiber bundle and the apoaeuroses of attachent were taped usiag thin Letraset tape
(I/W7thiclmess). In the posterior soleus the nber bmdies span between the antenor and posterior aponeuroses, and in the anterior soleus the nber bundles span between the median septum and anterior aponemsis. AU variables were measured independentiy by two hvestigaton.
Fiber bdelength (mm) was measured dong the marked nber bundle as the distance between its aponeurotic attachments as shown in Figure 4.20.
In the posterior soleus fwo angles ofpennution (degrees) were measured for each
fiber bmdie. Angle BA is the angle of insertion of the fiber bundle into the anterior
aponeurosis and angle 4 is the angle of insertion into the postenor aponeurosis. The hs
and BAp angles of the fiber bundies of the antecior soleus were meamred as the angle
between the point of insertion of a fiber bundle into the median septum and antenor
aponeurosis respectively as shown in Figure 4.20.
Muscle thickness was rneasured in mm, at the center of each scan, as the
perpendicular distance between the two aponeuroses to which the muscle fber bundles
attach (Fig. 4.20). For posterior soleus the rneasurement was made between anterior and
posterior aponeuroses. Anterior soleus measurements were confined to the medial hdf of
the bipemate feather i.e. between the median septum and antenor aponeurosis. Scanning
of the lateral side of the feather was attempted, but fiber bundles couid not be imaged in
their entirety. Figure 4.20. Measurement of architectural parameters trom uitrasoaad seuis. A. Schematic illustration. B. Relaxed &rasornid scan, sagittaI plane. C Contracted uitrasound scan, phne FL = fiber bande Iength; MT = mnsele thickness; &, &, OW, & = angics of pennation; Post = posterior aponePMSiS', Ant = antecior aponearosia White line on B and C denotes fiber bundIe. Students' paired cornparison t-tests were used to evaluate ciifferences between relaxed and contracted fiber bundle length, muscle thickness, and antenor and posterior angles of pemation. Signincant Merences were identified where the pvalue was less than 0.05. Percentage changes in architectural parameters are calculated as
Absolute dgernce between relaxed and contracted values x 100 Relaxed value
Percentage changes in architectural parameters on contraction withia and among muscle parts were compared. Initial exploration of data was carried out using univariate analysis of variance, which was foilowed by multivariate analysis of variance for repeated measures. Sources of signifi~cantvariation were idenfified with the Waller-Duncan k- ratio t-test and Tukey's HSD test. The Pearson correlation coefficient was used in idenmg correlated variables. Architectural parameters and percentage changes were repoaed as mean values * standard deviation (SD).
For the male and female subject groups, measuns of centrai tendency were cdcdated for every architectural parameter at each scanning site, Percentage differences were recorded as
Average male value - average fede value x 100 Average female value
Gender Merence and consistency of ihis clifference amss sites were statisticaliy andyzed using rnultivariate analysis of variance (MANOVA; p < 0.05).
43.2 Magnetic resonsnce imapiirg: Pilot study
Magnetic resonance imaging studies were piloted on 3 normal healthy volunteers with no history of mdoskeletal injury- The images were obtahed using a General Eleceic Signa 1.5 Tesla Scanner. The University of Toronto Human Subjects Review
Cornmittee approved this study (protocol reference #1859). See Appendk C for Ethics
Document and Subject Consent Forrn.
Subjects were placed into the scanner in a supine position with the knee, ankle and fmt in the matornical position. The ankle and fmt were supported in this position by piiiows and foam wedges and held in place with Velcro straps. Three-dimensional gradient echo axial images of 6 mm continuous senes were done through the soleus muscle ht, with the muscles relaxe& Sagittal images were obtained to visuaiize the fiber architecture of posterior soleus, and corond images were obtained to visualue the fiber architecture of anterior soleus. With the muscle relaxed, fiber bundle architecture could be visuaiized in some subjects. In other subjects, finding the optimum image planes was ciifficuit and very time consuming. Despite numerous attempts, imaging of muscle architecture in a state of maximai voluntary contraction was not possible due to movement artifact related to muscle fascicdations. Therefore, it was decided not to pursue the MRI part of the study at this the.
4.4 Cornp~on/mdysisof data obtained €rom cadaver studies and uI vivo data obteiaed by ultrasornid
Ultrasonopphic and cadaveric measurements are repocted as mean Istandard deviation (SD). Percentage differences of fiber length and angle of pe~ationin cadaveric and relaxed Living muscle were caicnlated Data hmultmsonographic scans were matched with correspondhg data hmcadaveric specimens (manual measurement).
Groaps were weighted equally irrespective of the nomber of measurements taken at a given location. Mdtivariate analysis of variance was canied out to iden- the presence of variation in muscle architectural parameters between cadaveric and iive muscle. Analysis was canied out on the entire soleus and on the individual muscle parts Results indicating sigaificant variation (p<0.05) were meranalyzed using the Tukey's post- hoc cornparison test.
45 Comparisonlanalysis of data obtained by computer modelling, manoal measnrement and by tùtrasound
The mean, standard deviation, and range of fiber length was compared for the regionai subdivisions of antenor and postenor soleus measured using aiI three methods: computer modehg, manual measurement, and ultrasound. Funher statistical analysis of
£iber Iength was not done since the data fbm the computer model was fiom one
Angle of pemation measurements cmot be compared for the three methods since the manuai measurement and ultrasound data is two-dimensional (see Figures 4.16 and 4.20) and the computer modelling data is three-dimensionai (see Figure 4. I 1A). Chapter 5: Results
Soleus architecture: Modehg of cadaveric muscle
The results of the computer modelling are divided into:
three-dimensional(3-D) visuaikation of soleus muscle architecture;
documentation of fiber length and angle of pennation throughout the volume of
marginal, antenor, and posterior soleus; and
descriptive statistics of fiber length and angle of pe~ationfor regional
subdivisions of soleus. (The regionai subdivisions are the same as those used for
the cadaveric manual measurements and ultrasonographic studies as shown in
Table 4- 1.
Three-dimensiond visu~tionof soieus muscle architecture
The computer model dowed full reconstruction of di parts of the soleus muscle
the digitized data The three-dimensional (3-D)model is Mymanipulatable allowing visualization of the muscle fiber bundles from any angle. The Eiber bundles are displayed throughout the volume of the muscle and can be animated io show sequential arrangernent of fiber bundes hmdistal to proximal.
The computer model contains B-sphe solids that have been built using continuhg volume sampie function. The B-sphe solids can capture detailed muscle architecture in 3-D. ûnce the original digitized data has been entered into the model, any ntrmber of additional fiber bimdIes cm be generated by creating streamlines (mer bundes). Since streamlines have an analyticd expression, the physical characteristics of the aew fiber bundles can be computed, added to the B-spline solid, and visuaüzed The new nber bundles thus added are distniuted evedy throughout the volume of the muscle part, Thousands of muscle hrbundles may be included to help vimalize the intemal architecture. This process would be very time consuming and tedious if done manually on the specimen. For a complete description of the mode1 and its machernatical coostnict refer to Ng-Thow-Hing's PDthesis (200 1).
Colorkation options are extensive both for the fiber buncües and background.
Adding color to mer bundles in different parts of the muscle or to individual rows or layea of fiber bundles permits clear visualization of the architecture.
Still fiames fiom the computer program have been reproduced in black and white, bmmany views, to show the following for the marginal (Figure 5.1). posterior (Figure
5.2), and antenor (Figure 5.3), soleus of the nght leg:
streamlines (loosely packed)
streamlines (densely packed)
template (original data set)
Figs. 5.1 to 5.1 are of the same specimen.
The fiber bundles of marginal soleus are cwed and directed anterosuperiorly dong the medial and laterd margins of the muscle, but are ahnost vertical proximaliy.
The fiber bundes of marginal soleus were thin on dissection and were modeiied as one layer.
The posterior soleus was seen consisting of densely packed fiber btmdies modeiled in rowslcolumns. The nber bimdles pas from anterosuperiorly to posteroinferiorly. Streamlines can be generated to increase the number of rows audlor the number of £ibers in each row.
The bipemate anterior soleus was modelied in iayers. The original data set is based on four layers of senal dissection. Using the streamline hction new Iiber buadles can be added to existing layers adto form new layer(s). The length of the anterior soleus, as a whole, increased hmposterior to antenor when seridy dissected.
To view a video clip of the three-dimensionai architecture of the entire human soleus muscle, refer to the lab Web Site: http://dante.med.utoroato.ca/skeletalmusc~e/
The text continues on page 108. Most proximal Scale: fibuiar attachent rn
A. caicaned tendon
Figure 5.î. Cornputer modelling of right marginal s01eas Streamh'nes (10nber bundtes): A. Posterior view. B. Anterior view. Superior
Med
Figure 5.l. Cornpater modellinp of cight marginal deus (continued). Stcmdhes (100 nber bundles): CcPosteromedîai view. D. Posterolateral view. Supenor
Latex iledial
Figure 5J. Cornputer modening of cight marginal soleap (continued). Streamlines (100 fiber budes): E. Anterornediai view. F. Antecolaterai view. Superior Sunerior
Mec
Figure 5.ï. Cornputor modeilhg of right ma@d deus(continued). StreamHnes (Iûû fiber bnndes): Go Posteromperior view. H. Superornedial view. Superior Superior
hferior
1. Supenor
Fignre 5.l. Cornputer modeilhg of right marginal soleus (continued) Template: K. Posterior view. L. Postemlateral view. Most proXinial fibalar attacbmeat Figare 5.2. Cornpater modehgof right posterior deus (continned). Streambes (100 6ber bmidles): E, Medial view, F. Lateral view. G, Anterohteral view. H. Posterornedial view. 1. Inferior
Figure 5.2. Cornpater modeninp of right posterior deus(continued). Streamünes (400 6ber bundIes): 1. P-or view. J. Postecolaterai view. Superior Superior
Figme 5.2. Computer modelüag of rigùt posterior soleus (continueci). Template: K. Posterior viea. L. Lateral view. Infenor =. -\ Median B. septum
Figure 5.3. Cornputer madeilhg of rîght anterior soleos. Streamiines (100 fiber bandes) for cach laye5 where hyer 1is rnost posterior and layer 4 is most nnteriw; a posterior view is show of esch layer. A. Layer 1. B. Layer 2. Superior
Figure 53. Cornputer modehg of right anterior deus(continued). Streamhes (100 fiber bundles) for each layer, where layer 1 is m& posterior and Iayer 4 is most anterior. A posterior vïew is shown of =ch Iayer. C Layer 3. DDLayer 4. Snperior
Cornpater modeIIhg O€ right anterior Shamihes (400 fiber bundles): E, Po vie Superior
Figare 5.3. Cornputer modeIling of right anterior soleus (continueâ). Template: G. Posterior view. H. Anterior view. 5.Documentation of soleus muscle mchitectnre
The nber bundie Iength and angies of pennation, for the attachent sites of both ends of the fiber bundle, were recorded using the B-spline soüds program. For the
marginal and posterior soleus 100 fiber bundles (strearnlines) were measured. For the
anterior soleus 50 mer bunàies in each of the 4 Iayers were documented. Each fiber bundle is numbered and the architectural parameters documented in a table. For the
marguiai soleus see Table 5.1 and Figure 5.4, for posterior soleus Table 5.2 and Figure
5.5, and for anterior soleus Table 5.3 aad Figure 5.6.
The compter modehg has aiiowed for measwement of the fiber length and pe~ationangles in 3-D space. Ali previously cited data in the iiterature has been
measured in 2-D,ushg a protractor, caliper andlor deras the rneasuriag devices. Snperior
Figure 5.4 Nmbered Bber bdesof right marginal soleus, posterornedial view. Fiber bmdies are referred to by nmnber in Tabk 5.l. 63, 6 @A (degrees) (degrees) (degrees) 28.39 34.78 16.29 2532 =O9 4333 47.38 54.83 80.69 46.60 63.13 5190 31.83 84.69 269 82.41 10.16 66.60 28.39 6.63 36-14 1321 41.03 4337 3832 73.18 21.74 28.75 1 t3 18.01 1427 23.08 35.05 25.77 46.4 1 3221 53.5 1 491 1 5552 45.94 45.76 50.1 1 38.98 53.94 40.08 5 1.66 45.92 $6.8 1 5280 47.35 5038 57.72 4928 6273 43.38 58.04 48.30 55.89 45.49 58.10 36.52 60.08 38.48 64.35 17.50 67.00 t 4.32 59.1 1 3t.80 47.6 1 2.44 483 16.68 59.83 l2lI 66.93 1311 65.97 t65t 60.58 26.41 5733 4954 6133 33.30 66.0 1 23.07 7057 2639 79.97 3031 87-08 13.60 76.03 6.7 1 60.69 10.44 56.69 t3.90 ai38
Table 5.î Computer model: 3-D angles of pennation and fiber le@ mesparenena of the fiber buadles of the right marginal soleus. 6 = angle of pmation meaPared dative to the posterior aponeumth; BA = mgie of pennation measured relative to the anterior aponeurosis; PB = nber bmidie. Figure 5.5 Nmnbved fiber bmdles of right posterior deus, posterior view. The rows of fiber bandles are also nmnbered at the mq@s of the mude. Fiber bmides are dedto by nmnber in Tabie 5.2. FB Length FB Length 6 $4 @A Nurnber (mm) (degrees) 'degrees) Nurnber (mm) (degrees) 15.77 21-72 l6.lO 18.12 8.03 15.75 1.23 13.92 939 16-19 11.28 1731 17.66 17-48 17.47 17.62 20. 17 19.01 19.99 18-08 27.48 23.9 1 27.44 23.00 23.03 19-93 8-78 1266 7.02 11.63 834 1 1-72 1 1 .O3 1366 15.96 15.18 1956 16.9 23.1 1 18.05 15.54 9.60 27.m 30.12 23.42 25.98 1456 16.85 13.61 t 4.08 128 12.75 1 1-62 1248 16.17 14.99 19.21 IS.26 17.80 14.55 2435 2.70 2638 39.% 27.69 3456 20.65 Y)Qd 19.88 20.08 1854 18.08 17.06 17.83 19.15 t 756 19.19 1355 4.70 851 2539 11.71 25.40 393 1 29.79 34.60 24.76 26.60 22.88 2131 2052 16.63 17.6 1 13.05 14.79 1150 10.97 8.82 5.89 532
Table 5.2 Cornputer model: 3-D angles of pemation and fiber length meaniremen& of the fiber bandles of the t=ightposterior soleos, += ange of pemation meddative to the posterior aponearoSs, ûA= meof pemation measured relative to the anterior aponemosis; PB = nber baudle, Superior
Superior \ -;.
Inferior B.
Figure 5.6 Nmbered fiber bandles of right anterior soteus, postecior vkws. A. Layer 1. B. Layer 2. The ïayers are ammged seqpentiaRy so that rayer 1is most posterior. Fiber bundles are referred to by nmnber in Table 53A. Length 4P &is Length O! afs (mm) (degrees) (degrees) (mm) (degrees) (degrees) 4.56 2.23 4.54 0.53 459 935 4.68 5.03 4.8 1 6.8 1 499 8.40 534 9.87 558 11.26 6.04 1362 6.67 13.94 750 t S. 19 859 16.32 10.02 17.18 1 1.87 1 758 14.22 17.25 17.16 15.89 20.70 133 24.40 959 27.40 5.7 1 30.37 1.59 33.67 3.40 33.% 15.77 2738 4.49 20.47 4.05 16.58 7.88 t4.84 10.69 14.36 13.01 14.63 14.98 15.43 16.68 16.65 18.15 18.27 19.46 20.29 20.65 22.73 21.81 5.57 23.1 1 2875 24.9 1 30% 27.23 32.49 30.06 34.11 3382 35.49 34.10 36.7 1 3272 37.93 3.59 3939 2651 40.9 1 24.33 4249 23. l? QI .?2 US6 35-77 2333 36.75 24.12 20.46 25.37 17-78 26.8 1 17.66 2830
Table 53A Cornputer modek 3-D angles of pemation and fiber length messurements of the fiber bundles of the right anterior soleus, layers 1and 2 & = angle of peonation mernired relative to the anterior aponeumis; hS= angle of pennation measured relative to the median septum; EB = fiber bundIe. Superior Superior
Fi- 5.6 Numbered fiber bmdles of right anterior soleus, posterior views (continued). C. Lager 3. D. Layer 4. The layers are arraaged seqllentialiy so thrt Iayer 4 is most mtenor. Fiber bundles are referred to by nmnber in Table 53B. O! 4a Length @)AP 8ks (degrees) (degrees) (mm) (degrees} (degrees) 6.67 634 2639 6.68 1938 850 11.97 'm24 7.95 t7.28 10.08 17.05 30.26 7-53 19.89 11.57 21.27 32.28 6.1 1 20.97 13.02 2451 34.21 4.43 21.04 14.47 26.79 3597 3.13 2039 15-91 2824 37.5 1 374 19.22 1733 2898 38.8 1 3.72 17.65 18.70 -9.15 39.85 6.7 1 15.73 10.00 28.85 40.62 12.79 13.47 21.18 28.15 41.13 23.78 10.85 22 16 27.12 41 37 4039 7.81 228'7 25.80 4126 51.19 4.24 23.24 24.19 41.12 4652 0.05 23.17 22.34 40.68 38.22 5.27 22.60 20.28 40.06 3 1.07 11.34 2152 18.13 3933 14.90 16.78 20.08 15-98 3858 19.44 18-73 1 8.7 1 14.69 37.% 14.83 16.69 1755 15.80 37-44 10.8 1 13.24 16.64 23.33 36.99 73 1 9.72 16.02 34.68 3659 4.34 6.43 1 5.70 3.42 3621 1 -92 333 15.68 26.1 1 35-89 0.1 1 0.28 15.95 25.68 35.46 1 .O7 2.50 16.48 26.37 35.05 1.61 3.18 l724 27.45 34.62 153 1.17 18.19 2854 34.16 1.O4 1 .a7 t 9.30 29.45 33.68 0.62 2.76 20s 29.98 33.2 1 1 .cc 3.78 21.89 29.97 3m 345 4.W 23.24 3338 3.75 3.60 -24.80 27.60 32.09 3.65 380 26.36 24.9 t 3196 1-47 300 D.89 21.90 31.99 1.96 155 9-23 19.02 3312 5.12 1 -43 3039 1650 373 8.03 158 3139 1451 32.46 1 0.73 1-94 3235 1333 393 13.23 230 3- 1'9s 39258 1555 326 33.63 1431 3247 13.70 4.25 3421 18.17 3222 1 9.68 5.50 34.78 27.23 3L8t 2 1 -45 7.09 3538 4201 38.23 2293 9.12 36.10 44.67 30.47 24.00 1 1.78 36.89 36.6 1 2953 24.43 t 535 36.87 30.96 2842 2392 20.24 32.73 27-75 27.15 $307 26.84 23.8 t 3.86 3-74 189- 33.88 17-11 24.7 1 2421 13.02 34.18
Table 5sCornpater mdek 3-D angles of petmation and fiber length meanvements of the fiber bundes of the right anterior soleus, laps3 and 4. BAT = angie of pemation mesudrelative to the anterior apone~, bS= angle of pemation mdrelative to the median septmn; FB = mer bmdIe, 5.13 Stmmmy of mdearchitecturai parameters: Fiber bundle Iength and mgle of peunation
The mean, standard deviation, and range of 6ber length and aogie(s) of pennation were cdculated for the regions of soleus. The regional subdivisions are the same as those used for the cadaveric (manoal measurements) and uitrasonographic studies.
5.1.3.1 Marginal soleus
The average fiber bundle length was found to be between 30 mm and 34 mm, but it should be noted that the shortest fiber bundle was 16 mm and the longest 45 mm (see
Table 5.4). A trend of decreasing average fiber bundie length fiom proximal to distal was observed on the medial side of the marginal soleus.
Marginal soleus ISD Range 1 (mm) / j%erbundles
Middle 113: Lateral Mediai
Table 5.4. Cornputer model: Fiber bmdie length of right marginal soleus Average €ber bunde Iength (FL)f standard deviation (SV) and range is reportecl €or the medial and laterai parts of the proximal, midàïe and distal thirds of the marginal soleus. (N = 1 specimen)
The aogle of pemation measarements were diverse ranging hm3 to 88 degrees
posterïorly and 7 to 88 degrees anteriorly (see Table 55). The average anterior angle of
pennation was pater than the average posterior angle of pemation for aii ngions of
marginal soleus. Table 5.5. Cornputer moùel: 3-D angle of pennation of dght marginal deus measured relative to the posterior apoaeiuosis (6)and to the anterior aponeurosis (OA ). Average aiigle of pennation (AP)f standard deviation (SD)and mgeis reported €or the medial and lateral parts O€ the pmximai, middle and distal thirds of the marguial soleus. For disaibution of fiber bundle sampling, see Table 5.4.
5.1.3.2 Posterior soleus
The average fiber bundle Iength of posterior soleus was in the range From 33 to 44 mm, with the shortest fi'ber bmde having a Iength of 3 1 mm and the longest 45 mm as seen in Table 5.6. The middle (central) part of the proximal, middle, and distal thirds had the longest average fiber bdelength, followed by the laterai part. The medial part tended to have the shortest average fiber bundle Iength in aIJ thirds of posterior soleus.
The average antenor angle of pennation was between 6 and 29 degrees as measarpd in 3-D relative to the tangent plane as seen in Table 5.7. The average posterior angle was between 8 and 24 degnes. The anterior angle ranged hm1 to 35 degrees and the posterior angle 4 to 30 de-. Proxima1 113: Lateral Middle Mediai - - Middle 1/3: Lateral Middle Medial
Table 5.6. Cornputer model: Average fiber bande length O€ right posterior deus. Average fiber bundle Iength (FL) fstandard deviation (SD) and range is
reported for the lateral, middIe and mediai parts of the -proximal, middle and di&i thirds of the po&rior soleus. (N = 1 &cimen)
-- - Posterior soleus Range (degrees) (degrees)
Proximal 113: Laterai 15.6 * 0.9 17.7 * 1.9 15-17 16-20 Middle 7.5 I2.3 8.3 I4.2 5-12 4-15 Mediai 6.3 I6.2 f 1.0 I2.1 1-14 8-13 Middle Ln: Laterai 13.21 1.8 11.212.7 12-17 7- 15 Middle 15.4t7.5 ( 17.5164 Mediai 1 16.7t1.8 10.112.6 ( 14-18 Distal 1/3: Laterat 22.3 * 6.6 2 1.9 * 7.6 13-30 9-27 Middle 29. 1 k 5.2 24.0 I5.0 24-35 18-30 Mediai 17.9k2.6 7.911,9 16-21 6-1 1
Table 5.7. Cornputer model: IDanterior (8'and posterior (&) mgle of pennation of right posterior soIeus. Average angle of pennation f standard deviation (SD), and range is reported for the lateraï, rniddie, and mediai parts of the proha&micidi6 Pmi distai thircLp of the pasterior soleus. The anterior angïe of pemation (BA) is medreiaüve to the attachment of the îi'ber btmdles to the anterior aponenrosis and the posterior angle of pennatiou ($.)is measund dative to the attachment of the Wer bondies to the posterior aponearosfs, For distribution of fiber bundle sampling, see TaMe 5.6. The average fiber bunde length was between 30 mm and 40 mm with a range
ûora 25 to 41 mm as seen in Table 5.8. The shortest fiber bundles were iocated in the distal third. The lateral side of the muscle had longer average nber lengths than the media side. This trend, although preseat in ail the regions of anterior soleus, was most
~rominentin the proximal aud middle thirds of the muscle.
Anterior soleus Average FL k SD Rmge Nuder of (mm) (mm) fiber bundles Tip: Laterd 1 36.6 t0.6 1 36-37 1 5
Middle 1/3: Laterai 38.6 I1.9 36-41 5 Medial 32.3 * 0.2 32-33 5 Distd 1/3: Lateral 30.3 I3.1 26-34 5 Mediai 29.6 I2.9 24-33 11
Table 5.8. Computer model: Fiber bundle length of right anterior soleas. Average fiber bundie Iength (FL)f standard deviation (SD)and range is reported for the lateral and medial parts of the tip and proximal, mlddïe and dtotal tbirdp of the posterior deus (N = 1spceimen)
The average angle of pemation relative to the median septum was between 15.6 and 18.2 degrees and relative to the anterior aponeurosis 2.2 to 32.2 degrees as seen in
Table 5.9. The greatest range and largest standard deviation was found in the laterai aspect of the proximal third of anterior soleus Average AP ISD Range (degrees) (degrees) 0, a.P @OIS 67AP Tip: Medial Laterai Proximal 1/3: Medial Laterd
Table 59. Computer model: 3-Dangie of petmation of Rght anterior soleus relative to the me&n septum (Our ) and to the anterior aponeurosis (OM). Average angie of pemation (AP)f: standard deviation (SD)and range is reporteci for the lateral and medial parts of the tip and proxhai, dddle and distal thirds of the anterior soleus For distribution of fiber bande samphg, see Table 5s.
5.2 Soleus architecture: Manuai measurement of cadaveric mude
The results of the manual measurements of the architectural parameters of the
soleus muscle are:
reported for the muscle as a whole (gros morphological characteristics); and
detailed for each individual part (anterior, postenor, and marginal).
The gros morphological chmcteristics studied inciuded musde length and
voIame of the soieus muscle. The length of the muscle beliy was measured in 3 locations
dong the site of ongin, Iaterally, rnedidly, and centrally as seen in Figare 4-14 and the
volume was obtained using the water displacement technique (see Section 42.2)- The average mascle length of soleus varies regionaily. As expecteà, the lateral aspect of the muscle which attaches to the head of the Bula is the longest and the part attaching to the medial aspect of the soleal line of the tibia is the shortest as seen in Table
5.10.
Site Average ML t SD Average ML as % of Number of (cm) kglength ISD Spechens Lateral 3 1.O t 29 (26-39) 35.7 * 2.3 54 Centrai 27.3 î 3.0 (23-34) 3 1.4 I2.3 54 Medial 21.712,9(16-28) 24.9 I2.8 54
Table 5JO. Manuai measurements: Average soleus muscle beiiy Iength. Average musde length (ML) *standard deviation (SD)and range ( ) is reported for 3 sites of measurement. Raufts are also expressed as percentage ofleg lengtb.
From Table 5.10, it should be noted that there was a 9.3 cm difference in average
Iength of the muscle beliy between the mediai and lateral measurement sites. Differing lengths of the muscle beliy in different regions of the muscle make it important to state precisely the site where muscle length is measund. Correlation between leg length and muscle Iength measurement was poor (r = 0.2). Anterior, posterÎor, and marginal parts were present in aU specimens examined.
The volume of each of the parts of soleus (n = 2 specimens) are listed in Table
5.1 1. The total volume of the two specimens differed by 138 cm3, but in both specimens postenor soleus had the greatest volume, followed in descending order by the antenor and marginal parts respectively. Soleus Volume (cd) % of total volume Specimen I Specimen 2 SpecMen I SpecOnen 2 Posterior 230 154 64 69 Anterior 92 41 25 18 Marginal 41 30 Il 13 Entire muscle 363 i 225 100 100
Table 5.U Manual measurements: Volume of the anterior, posterior and marginal deus.
The accuracy of these volume measurements was questionable, since on prelimulary measurement, before and after addition of moistening fluid, the volume of the triceps surae (gastrocnemius, soleus and plantank muscles) increased on average by
32 mi. The amount of fluid injected in the ernbalming process may have also infîuenced these resdts. The percentage of totd volume of each part of soleus was consistent in the two specirnens, assurning that the fluid was absorbed similariy in ail parts of the muscle.
52.2 Summary of muscle architectural parameters: Fiber bondie Ieagth and angle of pennation Ftkr bundle length and angle of pemation measurements for the marginal, posterior, and anterior soleus are sumrnarised in present section. To review the methodology of fiber bunde length and angle of pe~ationmeasurement, see: Figures
4.15 (marginal part), 4.16 (posterior part) and 4.17 (antenor part).
522.1 Marginal soleos
The nber bundles of the marginal soleus were found to have average length of 21-
26 mm, but as indicated by the mesures of dispersion (that is, the standard deviation and range) the longest fiber brmdle may be up to 3 Qnes the length of the shortest &r bundle meosnred in a particdar region (see Table 5-12). The average fiber length decreased fimm proximal to distal, especiaüy on the medial side of the marginal soleus.
This trend was noted in the averaged data and in 9 out of 10 individuai specimens.
Margid soleus Average FL ISD I specimens
Middle 113: Latetal 25.1 ~7.1 13-45 10 Medial 24.1 I 5.1 16-43 10 Distai 113: Lateral 24.1 & 5.9 12-40 10 Medial 21.1 k4.8 12-36 1 10
Table 5.12, Manual mewurements: Fiber bnndle length of marginal solens, Average Bkr bundle Ienm (FL)I standarà deviation (SD)and range is reported for the mediai and lateral parts of the proximal, &dde and distal thiràs of the marginal soleus.
The angles of pemation in the marginal soleus were diverse and mged from 2 to
90 degrees as seen in Table 5.13. The average aagle of pennation was found to be betwwn 33 and 43 degrees, with the smdest average angle observed in the mediai aspect of the middle thkd and the largest in the proximal and middle thirds of the lateral aspect.
The average angle of pennation increased hmthe middle third to the distal third on the mediai aspect, but in contrast, on the lateral aspect the average angle of pennation decreased distally. Individuai &ta aIso supported this trend with pemation angle hmasing on the mediai aspect from the middle to the distai thirds in 7 out of 10
Speamens and decreasing on the laterai aspect in 8 out of 10 specimens. Average AP * S'1 Range (degrees) (degrees)
Middle 1/3: Lateral Mediai
-
Table 5J3. Manuai measurements: Angle of pennation of marginal solens. Average angie of pemation (AP)t standard deviation (SD) and range is reported for the medial and lateral parts of the proximal, midàïe and distai thirds ofthe margind soleus. The angle of pennation is measdrelative to the attachent of the fiber bandles to the posterior aponeurosis (see Figure 4.15). For distribution of fiber buadie sampüng, see Tabk 5J2.
The average angle of pemation increased from the middle third to the distal thlrd
on the medial aspect, but in conhast, on the laterai aspect the average angle of pennation
decreased distaily. Individuai data also supporied this trend with pennation angle
increasing on the mediai aspect From the midâie to the distal thirds in 7 out of 10
specimens and decreasing on the laterai aspect in 8 out of 10 specimens.
It shoufd be noted that the greatest range in data occurred in the proximai third
where the angle of pemation ranged between 4 and 90 degrees. The proximal third of
marginal soleus is fan-lüce in shape, having mediai and lateral fiber bnndies that merge
on the superior aspect of the muscle. The fiber bundles of the superior aspect were
onented verticdly or almost verticalty to the posterior aponeurosîs, resuiting in large
pennation angies, up to 90 degrees. The angle of pemation of the medial and laterai nber
bundles increased on approaching the superior aspect of the muscle. 5.2.2.2 Posterior soleus
The observed average mer bundle length of the posterior soleus was 20-28 mm as seen in Table 5.14. The midde (central) fiber buadles of the proximal, midde, and distal thicds had longer observed average fiber bundle length than the mediai and lateral fiber bundles. In 6 out of 9 specknens, the midde fiber bundles were found to be equd to or longer than their medial and lateral counterparts. The laterai, middle, and medial nber bundes of the distd thud had shorter average fiber bunde length than the proximal and midde tbirds.
Posterior soleus Average FL ISD Range Nwnberof Nwnber of (mm) (mm) specimens fiber bundles Proximal 1/3: Laterai 9 Middle 19 Medial 9 Middle in: Lateral Middle Medial Distal 1M: Laterai Middle Medial
Table 5-14- Manuai measorementS.. Fiber bmdie le@ of posterior soIens, Average fiber bandie iength (FL)*standard deviation (SD)and range is reporteci for the iatemî, middle and mediaï parts of the pmxhai, midàïe and distal thirds of the pasterior soleas.
The average antenor angle of pennation was fomd to be between 25 and 38 degrees and the average posterior angie between 21 and 29 degrees as seen in Table 5.15.
The average antenor angle tended to be pater than the average posterior angie, except in the medial distd part of the posterior soleus. The average anterior aogle of pemation was greatest in the laterai nber bundles of the proKimal, middle, and distd thirds of the posterior soleus. However, the average posterior angle of pemation is greatest in the laterd, rniddle, and medial fiber bundles of the micide third of the posterior soleus. The antenor angle of pennation ranged hm 5 to 60 degrees, whereas the range of the posterior angle of pemation was about 10 degrees Iess, that is, hm7 to 5 1 degrees.
Posterior soleus Average AP ISD Range (degrees) (degrees)
Proximal ln:
Middle Mediai Middle 113: Lateral Middle Medid Distal In: Lateral 30.5 I10.2 Middle 24.9 I9-9 Mediai 26.8 * LIS
Table 5.15. Manual rneasorements: Anterior (OJ and posterior (6)angle of pennation of posterior solens. Average angle of penrution (AP) t standard deviation (SD), and range is reported for the lateral, &dcMe and medial parts of the pmrsimal, middle and distai thlrds of tbe posterior soleus. The anterior mgïe of pennation (BA) is measared relative to the attachment of the fiber bmdles to the anterior aponearosis and the posterior angle of pemation (Ois measured relative to the attachment of the fiber bmdles to the posterior aponenrosfs (see Fignre 4.l6). For distrifiution of Wer bdesampling, see Table 5.14. 5.2.2.3 Anterior soleus
The average nber brmdle length was between 23 and 31 mm as seen in Table
5.16. in aii parts of the anterior soleus the lateral side had longer average fiber length than the medial side. The difference was greatest in the proximal and middle thirds of the muscle. This trend was present in the proximal third in 8 out of 10 specirnens and in the middle third in ail ten specimens. Fiber bundle leogth varied hm11 to 57 mm, with the shortest fiber bundes located in the distai third of the anterior soleus (see Table 5.16).
Tip: Lateral Medial Proximal 1/3: Laterd Mediai
Distal 113: Lateral Medial
Table 5.î6. Manual measurements Fiber bondle Iength of anterior soleus. Average fiber bande length (FL)t standard deviation (SD)md range is reported for the latual and mediaï parts of the tip and pmximaï, middle and distril thMs of the posterior soleus.
The average angle of pe~ationof anterior soleus, as measured relative to the median septum, was between 21 and 47 degrees as seen in Table 5.17. The average angle of pennation was Iargest in the middle ihird, fonowed in decteasing order by the proximal and distal thirds and the tip. In aIi 10 spechneas, the fiber bundles of the pmximal and middle thùds had greater pennation angles than those of the dis& third and tip. Anterior soleus Average AP IS. Range (degrees @us) (degrees) T Tip: Medid Laterai Proximal 1/3: Medial Lateral Middle 1B: Medial Lateral
-.
Table 5.17. Manual measurements: Angle 00 pennation of anterior soleus reiative to the median septum (&s). Average angle of pennation (AP)I standard deviation (SD)and range is reporteci for the mediai and lateral parts of the tip and pmrpUnai, middle and djstai thirds of the anterior soleus. Nore that the ungk of penndion is memured re&e to the kehment of themer bundles to the median septum us shown in Figure 4.I7. For distnbution of riber bundle sampüag, see Table 5.16.
53 Soleus architecture: In Mvo dtrasound
The resuits of the in vivo measurements for the architecturai parameters of the soleus muscle are reported for each individuai part (anterior and posterior). To review the methodology for fiber bundle length, angle of pemation and muscle thickness measmement, see Fgtue 4.20. For scanning sites, see Figures 4-18 and 4.19.
5.3.1 Pusterior solens
The average relaxed fiber bdelength was 30 to 34 mm, with the longest
average nber brinde length in the middie of the midde third of posterior soleos as seen in
Table 5-18. The average Ber bunde Iength decreased distally. The middle nber bundles În the middle third of the posterior soleus shortened 23% on contraction, whereas the remaining sites stodied shortened by about 20 percent on contraction.
A* Posterior Relaxed (mm) Contracted (mm) 4& Shortening sohs *sD +D +sD 1 1 L1 Middle 1/3: Laterai 33 *9 2618 21 123 Middle 34t 11 26 *7 24 ~21 Distal 1/3: Middle 30 + 8 24*7 20 I20
Posterior Relaxed Contracteà Soleris 1 Number of Nimber of Numberof Numiber of spechens fiber bundles specimens fiber bundles Middle 1/3: Laterd 57 57 51 51 Middle 64 64 56 56 DistalU3: Middle 63 63 54 54
Table 5J8. In vivo ultrasonnd: Am Fiber bundle Iength of posterior soleus. Relaxed and contracted average fiber bundle Iength Istandard deviation (SD) and pcent decrease in Wer length on contraction is reporteci for the laterd and mîdâie &berbundles of the midàîe third and for the middle fiber bundles O€ the distai third of the posterior soleus. B. Distribution of fiber baode sampling.
Muscle thicktess increased on contraction an average of 1 mm in the distal W of postenor solens, and 2 mm in the middle third as seen in Table 5.19. The average pcrcentage hcrease in muscle thickness was variable, with the lateral part of the middle third becoming 18 percent thicker on contraction. Posterior Reiaxed (mm) Contracted (mm) % lncrease Soleus ISD ISD ISD Middle 1B: Lateral 11 13 1313 181 15 Middle LI 13 13 14 18 I16 Distal 1M: Middle il 13 1213 9~15
Table 5-19. In vivo ultrasouud: Muscle thickness of posterior soleus. Relaxed and contracted average mdethickness Istandard deviation (SD) and per cent incmase in thickness on contraction is reported for the lateral and midde fiber bruidles of the midà.Ie third aad for tbe middIe fiber bundles of the distai third of the posterior soleus. For distribution of Iiber bundle sarnpling, see Table 5.18-
The average relaxed antenor angle of pennation was i tu 2 degrees pater than the posterior angle. The percentage increase on contraction in both the anterior and posterior angles of pe~ationwas greatest in the middle third of the muscle as seen in
Table 5.20.
Posterior Relaxed (degrees) Contracted (degrees) % lncrease soleus tSD LW *SD .- -I l -- - - @A OP @A & -.- - - @A OP Middle ID: Laterai 22*6 20k6 33111 31112 50159 55*6i Middle 2217 2017 32110 31110 45146 Sh58 Distal 113: Middle i24t6 2316, 33111 33*12 38t42 43154
Table 5.20. In vivo dhssound: Antenor (OA) and posterior (Oangle of pemation of posterior soleas. Average a@e of pemation * standard deviation (SD)and per cent increase on contraction is reportecl for the laterai and &ddle fiber bundles of the middle third ad€or the middie fiber baodies of the di9ial third of the posterior soleus. The anterior angle of petmafion (BA) and the posterior angle of pemation (9) are measured dative to the attachment of the fiber btmdles to the anterior and posterior aponearoseî respe&vely (see Figure 420). For distribution of über bundle samphg, see Table SJS. The average length of the medial fiber bundles of the proXimai and middle third of anterior soleus were found to be similar, that is, within I mm. On contraction, the mer bundles shortened by 17% as seen in Table 521. A. Anterior Relaxed (mm) Contracted (mm) % Shortening Soleus ISD *SD *SD Proximal 113: Medial 3019 25 19 17 123 Middle 1/3: Mediai 29 I10 24~9 14 I29
Reluxed Contracted 1 AnteriorSoleus / Numberof Nmberof Numberof Nwnberof 1 specimens fiber bdles specimens fiber bundles Proximal 1/3: Medial 53 53 47 47 Middle 1/3: Medial 58 58 53 53
Table 5.21. In vivo dûamund: A. Fiber bunde length of anterior soleus Relaxed and contracteà average Rber bundle length standard deviation (SD) and per cent hrease in libv length on contraction is reporteci for the medial fiber bmdles d the proximal and middle tbirds of the antenor deus. B. Distribution of fioer bdesampiing.
The average relaxed muscle thickness was the same in the medial portions of the proximal and middle third of the antenor soleus. Average muscle thickness increased by
1 mm on contraction as seen in Table 5.22. Relaxed (mm) Corttructed (mm) ISD 1 +SD
Middle ln: Medial
TabIe 5.22. In vivo dtrasound: Muscle thickness of anterior so1eus. Rddand contracted average muscie thickns Istandard deviation (SD) and per cent increase in tbickness on contraction is reported for the medial fiber bundks of the proximal and midàie thirds of the anterior soleus. For distribution of fiber buttdle sampüng, see Table 5.21-
The average relaxed medial (&) and laterai (&) angles of pennation ranged from 15 to 18 degrees as seen in Table 5.23- On contraction, the percentage increase in both angies of pemation was pater in the proximal third than in the rniddle third of anterior soleus.
Anterior Relaxed (degrees) Contructed % Increase Soleus iSD [degrees)* SD ISD &s eAp Bks eAp &s 6)AP 4 Proximal 113: Mediai 16~5 1514 2217 2Lk6 38143 40k49 Middle 1/3: Medial 1816 16~5 2419 2219 33153 38k60
Table 5.23, In vivo uitrasound: Medial (bLs) and lateraï (&) mgles of pemation OF the mebirrl Mf of the anterior soieus. Average reiaxed and contracteà angies of pe~atîonI standard deviation (SD), are reporteà For the mediai fiber bondles of the proximal and middle thirds of the anterior solens The rneriull angk of penllObCon(&s) i;r measured rewve to the at&ciunent of the fiber bdsto the median septum, adthe tatemi ong?e of pendn (&) i;S measured mlirtive to the attachent ofthefiber bunàtes to the unterior upone~~~sis(see Figm 42û). For distribution of fiber bundie sampling, see Table 5.21.
53.3 StaListicai analysis of in vivo data
The architectnral data hm relaxed and contracted muscle were anaiysed by individual scanning site and by grouping the data for anterior and postenor solens. The data are summarized by scanuing site in Tables 5.18 to 5.23-
As correspondhg data hmthe left and right Iegs of the same subject were not si@cantIy different (p c O.OS), aii resuits in this paper refIect the averaged data hm both legs. Initidy the data obtained from ail the subjects that underwent dtrasonographic examination were analyzed and then the data were analysed by sex.
There was no correlation between Ieg length and any of the three architectural variables measured.
Fiber bundle Iength and muscle thickness measurements were found to be consistent to + 1 mm and angles of pennation to r 1 degree when measurements were done independently by two individuals.
5.33.1 Relaxed muscle
The posterior soleus was 29 per cent thicker than anterior soleus. In addition, the angle of pennation of postenor soleus was 24 per cent greater &an that of antenor soleus
(p c 0.0001). The fiber bundle length was not significantly diffennt between posterior and anterior soleus,
No statisticaily signifcant ciifference of fiber Iength, angle of pennation, and muscle tbickness was found within or among the individual scanning sites.
5.3.3.2 Contracted muscle
On contraction of the soleus muscle as a whole, nber bunde Iength decreased sipnincantly (p < 0.0001), angles of pe~ationiacreased signXxcantIy (p c 0.0001) and musc1e thickness oicreased signincantiy (p < 0.02).
Next the data for anterior and postenor soieus were maiyzed Percentage changes of architecturai parameters for the anterior and postenor soleus are summarized in Table 5.24. Absolute changes in muscle thickness and aagies of pe~ationdiffer signincantly between anterior and posterior soleus (p < 0.0009). However, no si@cant differences were found for fiber length, angle of pemation, or muscle thickness of anterior and posterior soleus when pemntage ciifferences on contraction were anaiyzed. Although not statisticaily signincant, the percentage of fiber bundle shortening and muscle thickness and angles of pe~ationincrease was found to be greater in posterior soleus.
Change on Posterior Anterr'or l Contraction Soleus Soleus % Fi'ber bundIe shortening ISD 1 I9I2l 1 16k27 % Thickness increse ISD I 96 Angle of pennation (8) Iincrease * SD pennation (8) increase IS.
Table 5.24. In vhw dtrasound: Pwczntage changes in fiber bundle Iength, muscle thickness and angles of petmation of anterior and posterior soleus, Angle of pennation measured relative to anterior aponeurosis (8'). pasterior aponeurosis (&), median sep- (&).
No statisticaiiy significant differences were found in percentage change for fiber bundle length, muscle thickness or angle of pemation on contraction, when compared within or among individual scanniog sites.
In the soleus muscle of males and fernales the Merence between the overd fi'ber bmdle Iength was statistically signiticant @ c 0.05). Fernales were found to have longer average fiber bunde length in ail paris of the muscles examined, except in the laterd part of the postenor soleus (Table 5-25). Fihr bundle length ui the femaie varied more than in the male as shown by the greater standard deviations.
Scan Location Posterior Middle 1/3: Lateral Middle
Distal 113: Middle - - Anterior Proximal 1/3: 3 1.7 & 10.0 28.0 I7. 1
Middle U3: 30.0 I9.7 27.7 I9.7
Table 5.25. In vivo ultrasoand: Fiber bunàïe Iength of the anterior and posterior deus of maies and females. Relaxed average fiber budeIength (FL)t standard deviation. For sites of seenq see Figures 4.18 and 4.19.
The larges percentage difference of fiber length between males and females was in the midiine of the postenor soleus (middle: 13 per cent and distal: 9 per cent) and in the proximal antenor soleus ( 12 per cent), see Table 5.26.
The angle of pennation measurements (BA and Op)in the soleus muscles of males
and females were significantiy different @ < 0.05). Males wen found to have greater average angles of pennation (Ba and 6)in aU parts of the soleus as seen in Table 5.27.
The Largest percentage ciifference of angle of pennation between males and females was
in the posterior soleus (see Table 5.26)- SoIeus No. @legs No. of legs Scm 1 file 1 mule Location Posterior Middle 1M: 1 27 1 37 Laterai Middle
1 Distai ln: I 1 24 1 33 1 Middle
Anterior 26 27 Proximal 1/3:
27 3 1 Middle 1/3:
Table 526 In vivo ultrasound: Percentage difference between the architectural parameters of the anterior and posterior deusof males and Cemales. A positive per cent Merence iodicates tbat male data > female data, and negative pet cent merence indiates male data c temale data. Measur~ments of fiber bundle length (PL),mde thidmess (MT) and angles O€ pennation O€ posterior soleus BA and 6 and anterior soleus hsand are shown in Figure
Soleus Scan 1 Female (degree~)~1 Mule (degrees) Location @A 9~ @A OP Posterior Middle 113: Lateral 19.0 2-0 18.0 I6.2 24-0I 3.0 18-0* 6.2 Middle 19.0 I3.0 17.6 I6.5 24.1 * 4.0 22.2 I7.1
DistaI U3: Middle 21.1 13-0 20.5 *5.8 25.4 13.0 24.4*6.5
Bks @AP 8Ms @M Proximal 1/3: 15.7 + 2-0 13.8 * 4.0 17-0* 2.0 163 * 4-0
Middle ln: 1 169 I2.0 1 15.1 A 4-0 1 18.2 I2.0 1 17.8 I 6.1
Table 527. In +O dtrasound= Angles of pennation of the anterior and posterior deus O€ maies and fernales. Location of arsgies BA, &, & and Bu are show in Figure 4.20. Muscle thickness of the soleus muscie of males and females was signincantiy different (p < 0.05). Males were found to have greaiet average muscle thichess in ail parts examine& except in the distd part of the anterior soleus as seen in Table 5.28. The greatest percentage ciifference of muscle thickness between males and females was in the posterior soleus (see Table 526).
Scan MT (mm) Location Female Male Posterior Middle 113: Lateral 9.4 * 2.2 1 1.8 * 2.8 r Middle 10.7 I3.0 12.1 I3.6 MiddleIn: 1 10.8 t 3.3 1 11.712.8
Middle in: 1 8.2 12.3 1 8.0 12.2 1
Table 538 In vivo uitrasound: Musde thickness of the anterior and posterior soleus of maies md fmales. Reiaxed average musde thickness (MT)I standard deviatioo.
No measurements are presented in this paper to support the non-pdel positions of the anterior and postenor aponeurosis but this was frequentiy observed, especidly
5.4 Solens architecture: Cornparison of manual (cadaveric) and in vivo measuremenfs Mean fiber bundle Iengths and angie(s) of pe~ationas measured for anterior and posterior soleus hmreIaxed and contracted in vivo muscie and hmcadaveric muscle are shown in Table 5.29. Aiso summarized is the percentage by which the cadaveric architectural parameters differed from relaxed in vivo parameters. A cornparison of cadaveric fiber lengths with the m vivo measunments shows that
in both anterior and posterior soleus, the cadaveric nber length lay between that of the
relaxed and contracted value hmthe living tissue. In the antenor and postenor soleus,
the cadavenc values were not significantly dBerent hmeither the relaxed or contracted
in vivo measurements. Within in vivo posterior soleus, contracted fiber lengths were
shown to be significantly @ c 0.05) shorter th relaxed nber lengths as seen in Table
5.29-
Aii angles of pemation measured in vivo in contracted anterior and posterior
soleus were significantly greater than in the relaxed state @ < 0.05). in the cadaver, the
antenor and postenor angles of pennation of posterior soleus lay between each of the
relaxed and contracted in vivo values. However, the angle of pennation of anterior soleus
was greater than both the relaxed and contracted values. In the antenor soleus the medial
cadavenc angle was significantly @ c 0.05) greater than the medial relaxed angle.
1 pometer ( ~olcvr 1 in viw: In vivo: 1 Cadcnteric 1 % dgerence Relaxed Contracted 1 J Fiber length Posterior 29-7 I1 1.1 " 20.4 I6.1 25.0 I4.1 Lb -15.8 Anterior 26.9 I7.7 " 20.8 I8-6 " 26.8 I5.8 " -0-4
@A Posterior 23.7 * 63 35.5 t 9.7 30.3 * 73* +27.8 6 Posterior 22.2 I7.2' 34.2 I103 25.2 t 4.6 ab +13S hs Anterior 16.5t5.4" 2~St7.6~46.1fll.0c +179.4 ~AP Anterior 14-4 & 53a 23.6 I7.0 NM -
Table 5.29. Fiber bundle length and angle of peman'oa in cadaveiie and in vivo anterior and posterior soleus. Percentage clifference caldated by comparing cadaveric with relaxeci in vivo values. Nmaber of observations (in vivofeadaveric): PS(10/46), AS(10/80); NM not measured. The superscript letters are used to indiente the presence or absence of ststish'cal signincance (maltivariate 8tLBtysis of -ance) between in viiw ceiaxed, in Mro contracted and cadavenecfiber tength and angIes of pemation. I€ the superscrQt Ietters in a roa diffkr, then the redtis statistically signüïcant If the Ietter is repeated, there is no staüsticai sigdcance, 5.5 Soleos architectme: Cornparison of computer modeilhg (cadaveric), manual (cadaveric) and in vivo measorements
The average fiber bundle length data for each region of the postenor and anterior soleus are summarized in Tables 5.30 and 5.31 respectively. The average fiber bundle length is longest in the muscle used for the compter model, foiiowed by the relaxed in
MVO measurements, and shortest in the cadaveric specimens mmually measured The range and standard deviation may be least for the computer model since it is based on one cadaveric specimen. In cornparison, IO cadaveric soleus muscles were maauaily measured and both legs of 35 live subjects were scanned The specimen dissected for the computer model was very large. Average muscle length of the lateral side of the manuaiiy measured soleus was 3 1.0 cm with a range of 26 to 39 cm (see Table S.IO), whereas the modelied specimen had a lateml muscle length of 37.0 cm. In addition, in
Table 5.30 the average fiber buadle length of the modelIed muscle exceeds the upper range of the fiber bundle length reported for the manually measured specimens.
The cadaveric specimens measured manudly, although Fixed in situ, had the shortest average Eiber bundle length and the range was at the low end of the spectnim when compared to in vivo resufts. Posterior Càdaver(cornputer ) CiukveF(m41tual) In vivo(uIh.asound) soleus FL ISD(Range) FL IS.ge) FL ISD (Range) (mm) (mm) (mm) Relaxed Contracted ProximaI 1/3: Lateral 40.3 I2.2 (38-43) 23.0 + 6.8 (11-3 1) - - Middle 43.5 * L .1 (42-45) 27.9 I70 (1 5-43) - - Medial 38.4 i L -3 (37-40) 23.6 r 4.6 (15-3 1) - - Middle 1/3: Lateml 42.2 * 1.2 (41-44) 24.2 I6.8 (15-34) 33 r 9 (15-61) 26 I8 (10-48) Middle 42.5 I1.5 (4 1-45) 27.6 I4.8 (20-37) 34 I1 1(16-66) 26 I7 (1 1-50) Mediai 33.9 * 2.2 (3 1-38) 24.5 I4.7 (15-30) - -
I Distai in: ' Lateral 37.8 I2.4 (35-41) 21.8 I7.2 ( 10-32) - - Middle 39.411.3(38-41) 23.514.3(15-32) 3018(13-49) 2417(12-48) Media1 32.9 r 1.O (32-34) 20.6 6.9 ( 10-30) - -
Table 530. Cadaver (computer), cadaver (manual measurement), and in vivo dtrasound: Average f'iber bundle length of pasterior soleus. Average fiber bundle length (FL) * dandani deviation (SD)and range is reporteci.
In vivo(uItrmound) FL * SD (Range) (mm) Relaxed Contracted Tip: Laterai Medial proximri~in: Lateral Mediai Middle in: Lateral Medial Oistal1/3: Laterai Mediai
Table 531. Cadaver (computer), cadaver (manuai measurement), and in vivo altramund: Average fiber bdeIength of anterior deus. Average fiber bmaele* (PL)I standard deviation (SV) and range is reported. Chapter 6: Discussion
6.1 Vialization of muscle architecture ushg a B-sphe soiids model
To date, no study has docurnented muscle architecture throughout the volume of a muscle. Visualization of muscle architecture has ken iirnited to two-dimensiond (2-D) pianes using sectioned cadavenc muscle (Tnenschik and Loetzke, 1969; Wickiewin et al., 1983; Friederich and Brand, 1990) or in vivo ultrasound (Kawakami et al., 1998;
Magmaris et al., 1998). Anatomicai photogrammetry, in conjunction with B-sphe modebg, has enabled the creation of a three-dimensional manipulatable model of an enth soleus muscle from one cadaver. The soleus musde can be viewed:
in its eatirety,
as marginal, anterior, and posterior parts or,
as individual rowsllayers of mer bundies within the marginal, anterior, and
posterior parts.
One of the advantages of using B-spline modelling is that it can mathematicaily extrapolate the onginal data set (template) to mate any number of fiber bundies
(streamIines). This feature enables viewing of the fiber architecture at various Ievels of compIexity.
The mode1 is designed to permit the addition of connective tissue elements such as aponemses, septa and tendons and the underiying bony skeleton, including the ankle
(taid)joint. 1t is hoped that in subsequent snidies these &ta will be collected m addition to the fiber bnndie data, 6.2 Memement of architectnral prameters of human mde
Fiber bundle Iength and angle of pemation has been measured using:
fuced cadavenc tissue (Tnenschik and Loetzke, 1969; Cutts, 1988; Spoor et al.,
199 1),
rnacerated fixed cadavenc tissue (Wickiewia et ai., 1983; Fnederich and Brand,
1990), and
dtnsonography in vivo (Henriksson-Larsen et al., 1992; Rutherford and Jones,
1992; Kawakami et al., 1993; Herbert and Gandevia, 1995; Kuno and Fukunaga,
1995; Narici et al., 1996; Fukunaga et ai., 1997; Ichinose et al., 1997; Ichinose et
al., 1998; Kawakami et ai., 1998).
The plane of section of the cadavenc muscle and the angle of the ultrasound tmsducer must be such that the fiber bundles can be seen in their entirety between attachment sites. In these previous snidies fiber bude length has ken measured manually fiom cadaveric tissue and ultraSound scans using a der and/or caüpers.
Si~nilarly,the angle of pe~ationbas been measured using a protractor. This method resuits in a 2-D conceptuiiüzation of muscle; muscle, however is a three-dimensional structure that can have a complex nber arrangement. Furthemore, the locations of the measured mer bundles are often not SpeCir~calIystated, Ieading to dificulties in the interpretation of dts.
The B-sphe solid, in conjunction with anatomic photogrammetry, provides a complete threedirnensionai (3-D) mode1 of the fiber bundles throughout the volume of the soIeus. The Iength and the two angles of pemation (at the attachment site of each end of the mer bunde) can be measured in 3-D space using the B-spline model. Large numbers of streamlines can be quantined using the nber bundes of the original template.
By dennition, the angle of pennation is the angle at which the muscle fibers are onented to the Linc of force generation of a muscle (Wickiewicz et al., 1983).
Wickiewicz et al. (1983) estimated a line of force and approximated the angles relative to that line using a protractor. When measuring pemation angle in complex muscles, such as the soleus, the angle is usuaüy measured relative to the aponeurotic attachent of the fiber bunde (Tnenschik and Loetzke. 1969; Alexander and Vernon, 1975; Maganaris et al., 1998). Measuring the angie of pemation relative to a single Line of action for the entue posterior soleus would be difficult. Furthemore, if the line of force is estimated for a muscle, it shouid be ciear where the iine is iocated and in what area of the muscle the angie measurements were made.
In 3-D,the angle of pemation is the angie between the tangent vector of the fiber bunde and the tangent plane of the muscle surface at the point where the fiber bundle meets the aponeurosis (see Figure 4.1 LA). Traditionaîiy a fiber bundle is traced to its attachment on the aponeurosis, the protractor is aügned with the aponeurosis and the angle to the fiber bundie is measured. Angles measured relative to the tangent plme in three-diwnsions cannot be compared to traditional measurements in two-dimensions.
Aithough vimalization and caicdation of saictmd parameters in three dimensions is standard practice in engineering, this has not ken the case with human or animal muscle.
In our study, by obtaining 3-D coordinates at the fiber attachent sites, it bas been possible to document the architecture throughout the entire muscle. Muscle modeis reponed in the litemtm are generally hear and unable to incorporate cornpiex muscle architecture and 3D data Continued development of the B-spline mode1 to include connective tissue elements and bone may provide a new 3-D approach to viewing and understanding skeletd muscle.
63 Architectnral parameters of cadaveric hnman soleus muscle
The data available in the literature regarding muscle Iength, volume, mer bundle length and pennation angle (see Tables 2.3 and 2.4) will be discussed relative to the results of this snidy.
63.1 Musele length
Wickiewicz et ai. (1983) rneasured soleus muscle length between the most proximal and distal muscle fibers and found the average length to be 30.9 cm (n = 2). In this study, using the same measurement technique as Wickiewicz et al. (1983). the average muscle length was 31.0 cm (n = 54). Friederich and Brand (1990) rneasured muscIe length hmthe centmid of origin to the centroid of insertion and found the average Iength to be 35 cm (n = 2). However, the locations of the centroids were not defïned. Spoor et al. (1991) documented an average muscle length of 27.5 cm, but did not specq the site of measurement. In the present thesis, there was a 10.7 cm merence between the kemeasurement sites of muscle Ieogth (mediai. median, and lateral). indicating the importance of describing the specific location of the site.
6.3.2 MPscIevoIume
The volume of the entire soleus muscle (excluding tendon and other connective tissue elements) as reported in the fiterattue ranged hm98 an3 to 328 cm3 (n = 8)
(Tnenschik and Laetzke, 1969; Wickiewicz et al., 1983; Spret al., 1991). In this thesis, the average muscle volume was 294 cm3 (n = 2). but it was also fodthat by moisteniag the specirnen the previous evening the volume increased when measured the next rnoming. In addition, the variable amount of fluid absorbed during and after the embalming process, and the variable amounts of remainhg comective tissue elements may &O influence the volume measurements. As a result, there are many potential sources of emr when conside~gthe volume of cadaveric muscle.
In our study, as weii as in Trzenschür and Loeake (1969) and Spoor et ai.(1991), it was found that postenor soleus had a pater volume than anterior soleus. Marginal soleus, as defined in this study, had the least volume. The volume of marginal soleus has not been previously measured It should be noted bat marginal soleus bas not ken previously defmed.
6.33 Fiber bondle length
Haines (1932), Witkiewicz et al. (1983), and Friederich and Brand (1990) reported a single measurement of average fiber length for the entire soleus ranging hm
19.5 to 34.0 mm. A total of five specimens were studied (see Table 23).
The posterior and anterior sofeus were documented separately by Trenschik and
Loeake (1969) and Spoor et al. (1991). The posterior soleus as a whole was found to have an average fiber length of 28.6 and 25.8 mm respectively. In the present thesis, the posterior soleus was divided into nine parts with average fiber length for the manuaily measured specimeas ranging hm 20.6 to 27.9 mm (see Table 5.14). The central
(middle) fiber bmdles throughout the postenor soleus had the Iongest average fiber bundle Iengths. Spoor et ai. (1991) reported a Ionger average fiber buadle length (26.7 mm) for anterior soleus than for postenor soleus, but Trenschik and Loetzke (1969) reported a shorter average fiber bundle length (27.8 mm) for anterior soleus compared to posterior soleus. Io our study, the anterior soleus was divided into eight parts, The average nber length for the manuaiiy measund specimens ranged hm23.6 to 3 1.1 mm. with the laterai side having a longer average fiber length than the medial side. The marginal soleus has not been previously studied The fibet bundles of marginal soleus. connecting the edges of the posterior aponeurosis to the antenor aponeurosis and to the tibia and nbula., were found to have an average fiber bundle length of 2 1.1 to 26.2 mm.
The average nber buadle Iength decreased from proximal to distal, most noticeably dong the medial aspect.
The B-spline mode1 of the soleus dissected in situ had longer average fiber bundle length for ail the regions than the manually rneasured specimens. Average fiber bundle lengths of posterior soleus ranged lrom 32.9 to 42.5 mm, anterior hm29.6 to 40.2 mm and marginal hm29.6 to 33.7 mm. The standard deviatîon is also Iess in all regions snidied, perhaps because at present the modeiling results are based on one specimen thus reducing the effect of variability between specimens
6.3.4 Angle of pnnation
The angle of pemation measurements discussed in this section of the thesis are two-dimensional. The angles of pennation were obtahed hm cadavenc specimens. mamally measured, and fiom in vnto ultrasonography. The 3-D angles of pennation obtained fiom the cornputer mode1 cannot be compared to the 2-D data.
Average angle of pennation for the solens muscle (region not specified) was rrported by Alexander and Vernon (1975): 20 degrees (n = 1); Witkiewicz et al (1983): 25 degrees (n = 2); Cutts (1988): 19 degrees (n = 3) and Friederich and Brand (1990): 32 degrees (n= 1). See Tables 2.1 and 2.3.
Trenschik and Lmtzke (1969) found the average angle of pemation of the postenor soleus to be 20 degrees and the antenor to be 25 degrees. Spoor et al. (1991) reported an average pemation angie of 34 degrees for postenor and 31 degrees for antenor soleus. In our study, the range of average anterior and posterior angles of pemation has ken documented in nine parts of postenor soleus. The average anterior angle ranged km24.9 to 37.5 degrees, and the average posterior angle hm2 1.6 to 28.5 degrees. The average anterior angle was greater than the average posterior angle in the proximal and middle thirds of posterior soleus. For the six regions of anterior soleus, the average angle to the median septum ranged from 2 1.5 to 46.8 degrees. The average angle of pennation was largest in the middle third of anterior soleus. The average angie of pe~ationfor the six regions of the marginal soleus ranged hm32.9 to 42.8 degrees.
The lateml aspect of the proximal and middie thirds of marginal soIeus had greater average angle of pennation ihan the comsponding regions medially. In the marginal and anterior soleus, some fiber bundles were close to being horizontal while others were almost vertical. The distribution and extent of variation of the angle of pemation within the parts of soleus has not been previously documented.
6.4 Architectural parameters of in vivo huma0 soleas moscle
In the present thesis, sonographic data of posterior and antenor soleus was collected hm35 subjects, 19 males and 16 fernales. Mamganis et ai. (1998) and
Kawakami et ai. (1998) each scanned the posterior soleus of 6 male subjects. 6.4.1 Anterior and posterior soieus
The average relaxed and contracted fiber lengths of the postenor soleus were fomd to be somewhat shorter than those reported by Maraganis et al. (1998) and
Kawakami et al. (1998). Kawakami et al. (1998) reported the longest average relaxed nber Iength of 38 mm, foIlowed by Mamganis et ai. (1998) at 35 to 37 mm. In this thesis, average fiber length of posterior soleus ranged from 30 to 34 mm depending on the region. On contraction, the average fiber bundle length was reduced by 6 to 8 mm.
Kawakami et ai. (1998) and Maraganis et ai. (1998) reported a reductioa of 12 mm and
5.2 to 5.8 mm respectively. It should be noted that Kawakami et al. (1998) studied ody one site in the posterior soleus.
Both in our study. and in Maraganis et al. (1998). two angles of pe~ationwere measured, but Kawakami et al. (1998) only reported the mgle relative to the postenor aponeurosis. In our study, the average anterior angle of pennation was larger than the posterior angle. The relaxed average angles of pennation obtained in this thesis (20 to 24 degrees) closely resembled the average angie reported by Kawakami et al. ( 1998): 23.8 to
25.0 degrees, and Maraganis et al. (1998): 21 degrees. On contraction, the average pemation angle increased by 9 to 11 degrees in our study. by 19 degrees in Kawakami et al. (1998) and 15 to 16.6 degms in Maraganis et I (1998).
Average muscle thichess of relaxed postenor solens in this study (1 1 mm) is less than the 14 to 16 mm reported by Maraganis et ai. (1998). On contraction, Maraganis et ai.. (1998) fond an increase of 6 to 7 mm in average muscle thickuess, but in this study an Încrease of oniy 2 mm was fomih Some of the Merences in dtsbetween this study and that of Maraganis et al. (1998) may be atmbated to the gender of the subjects (see Section 6.4.2). Maraganis et al. (1998) studied six male subjects with an average age of 28 * 3 years. In this study, there was a similar distniutioa of males and females
(average age of 44 years).
The average relaxed fiber bundle length of the medial side of the anterior soleus was 29 to 30 mm. On contraction the fiber bundes of anterior soleus shortened an average of 14-17 per cent of their relaxed length, whereas posterior soleus shortened 16 to 23 per cent. The average mer Iengths of anterior and posterior soleus were sùnilar, but the average angles of pemation of anterior soleus were les than those of the postenor soleus. Anterior soleus had average relaxed pennation angles between 15 and
18 degrees, and on contraction, the average angle increased to 2 1 to 24 degrees.
6.42 Gender diîferences
Overall, the muscle architechual parameters of fiber bundle length, angles of pematiori, and thickness are siflcantly different in males and females. The dichotomy in muscle architechiral properties between males and females is most prominent in the posterior soleus. in the three sites sampled in posterior soleus, males were observed to have up to 26 per cent thicker muscle, up to 27 per cent larger angles of pemation, and up to 13 per cent shorter fiber lengths on average than females. Therefore, the soleus of females has longer fibers, smaUer aagIes of pennation, and is not as thick as the soleus of males. Larger angles of pemation and pater muscle thickness in males than in females were dso observed in highly trained male and fernale athletes (Icbinose et ai., 1998; Abe et al., 1998)-
The differences in muscle architecturai pmperties between maies and females have sigaifi;cant irnpIicatioas with respect to force and velocity. Current explaaations of the relationship betweeo muscle architecture and function rest on the assumption that due to practical reasons, such as mobility, there is a nnite maximum mass or volume that is struchually possible for ail muscles (Witkiewicz et al., 1983). Larger peunation angles have ken argued to permit a greater degree of fiber packing (Gans and Gauat, 1991;
Rutherford and Jones, 1992), the net result of which is a larger overd force on a tendon for the same muscle volume. In turn, thicker muscle with otherwise similar properties would resuir in a larger force vector on the same tendon. In contrast, longer muscle fibers have more sarcomeres arranged in series, permitting greaier muscle excursion and contraction velocity (Witkiewicz et ai., 1983; Lieber, 1992). The observed larger pennation angles, thicker muscle and shorter fibers recorded in the soleus muscles of males would each contriiute to greater force generation in maies than in fernales. This may be an inherent gender ciifference like flexiility and skeletal structure.
6.5 Cadaveric and in vivo measurements of the architectural parameters
Architectural charactenstics (fiber Length and pemation angle) of cadaveric muscle differ fiom both relaxed and contracted in vivo muscle. Fiber bundles of cadaveric anterior and postenor sokus had lengths which lay between the values for reiaxed and contmcted in vnto fiber bundIe lengths.
Pemation angles (both anterior and posterior) in cadaveric postenor sofeus were found to lie between in vivo relaxed and contracted valaes. The pennation angle of the cadavenc anterior soleus was significantly greater than both relaxed and contracted h vivo angles. Note, however, that the anterior soleus was the deepest structure to be imaged and it codd only be scanned hmits mediai aspect. Slight changes in the positioning of the angle of the probe, especially in the proximal part of the muscle, may have led to an alteration in the nber pennation angle.
The observed architechual clifferences in cadavenc and in in vivo muscle may be attnîuted to many factors. Post-mortem skeletal muscle undergoes ngor mortis, a process that has been shown to cause a slow contraction in muscle fibers (Bendali, 195 1).
Bendall (1973) fuaher descnid that this contraction is minimal in comp~sonwith a
Living contraction, yieldmg ody a smaU fraction of the total work that can be performed by the Living tissue. It may therefore be possible that when cadavers are embalmed, their skeletal muscle becomes fixed in this state of pariid muscle contraction found during ngor mortis.
The embalming procedure may aiso have some effect on skeletal muscle tissue directly. Cutts (1988) has studied the effects of shruikage on skeletal muscle as a result of cadaveric fixation and found that a siWcant loss in muscle Iength occurs when muscks are fied in isolation €rom the skeleton but not when Fmed in situ on the skeleton. Most cadavers are subject to a standard embalming procedure More the intemal tissues are examine& as was the case in the present study. This. therefore, decreases the possibility that shrllikage of the whole muscle may have occurred as a result of kation. However, it is stiU possible that formaiin hation may alter the architecturai parameten withh the muscle itseif without aite~ggross muscle length.
Ushg ox muscle, Locker (1959)has shown that fornalin fixation after ngor mortis does not alter sarcomere length. Hooper aod Hegarty (1973), however, have fouad that fomaün fixation does cause an increase in the percentage of passively contracted £ibers in muscles previously excised from the skeleton. They therefon speculated that formalin fixation may increase the "irritability potentiai" of muscle or may cause shortenhg of surmunding connective tissue.
Mer possible reasons that architechual parameters of cadaveric muscle mer hmthose of Living muscle include rnethod of storage and changes in the tissue, such as denaturation of proteins, The position at which full cadavea, cadaveric parts, or individual muscles are stored rnay place consistent physical saaia on a muscle or muscle part and this couid lead to deformation of the tissue. As weil, long tem degradation of muscle tissue may slowly, throughout the course of storage, alter the architecture within skeletal muscle. It may be possible that changes to the contractile elements and connective tissues, on deinnemation, Her. For example the contraciile elements rnay take up the slack in comective tissue such as aponeurosis.
Therefore, when developing models of skeletal muscle based on cadaveric studies, the architecturai ciifferences between tive and cadaveric tissue should be taken in to consideration.
6.6 Architectural parameters and muscle modeilhg
Hill's model has provided the basis nom which most muscle models have ken developed. It has three elements. a contractile element (skeletal muscle), a senes elastic element (tendon, aponetuosis), and a parailel elastic element (epimysium, perimysiurn and endomysium). Data couected to date for our B-sphe model is for the contractile elements of the cadaveric soleus muscle. The data is in the form of 3-D coordinates and provides a complete pichrre of the muscle beiiy. Therefore, the model is representative of cadaveric muscle but codd be made to resemble in vivo muscle by adjusting the cadaverïc Ber lengtb and angle of pennation to those obtaiwd using in vivo ultrasod. The m vivo parameters are regionalized so that the detailed architecture of the modd can be maintained.
The measured architectural parameters include fiber bundle ïength and pennation angle throughout the volume of the marginal, posterior, and antenor soleus. The architectural properties of the muscle are the most detailed that have been coiiected to date-
The B-sphe mode1 aiiows for the generation of additionai 6ber bundles, streamlines, hmthe 3-D fber bundie coordinates of the seriaiiy dissected specimen.
Since skeletal muscle consists not only of fiber bundies but also of comective tissue coverings and neurovascular bundIes there is a limit to the amount of fiber packing possible within a given volume. To determine a reaiistic number of fiber bundles present in each part of soleus the diameter of individual fiber bundles and the amount of perimysium around each tiber bundle needs to be quantified. These data couid then be used to limit the maximum number of strramiines. in the present thesis it was found that too many streamhes obscured visuaikation of architechiral detaii, so that the number of streamhes was limited by architectural cldty.
Aponeuroses and septa are another component of skeletd muscle which could be included in the model. The anterior and posterior apneuroses and median septum could be added by positionhg these sheets relative to the fiber bunde attachent sites of the marginal, anterior and posterior soleus. Although the position of the aponeuroses and septa couid be extrapo1ated hmthe end points of the fiber bundles, more data needs to be couected on their physical propertÏes. Tu make our B-spline model contractile, it is possible to use relaxed and contracted in vivo data for the contractiie element. This would dow visualkaton of changes in architectural parameters on contraction. To model the aponeuroses and septa on contraction their physical pmperties must be detennined and added to the model. The ultrasonography of the contracthg soleus showed the complex movement of the aponeuroses and septa relative to the fiber bundfes and to each other, stresshg thek importance in muscle contraction. In addition, a map of 3-D coordinates of the underlying skeleton with muscleltendon attachent sites needs to be obtained.
The B-sphe model has been desigaed tu incorporate these elements and when complete may provide more insight into how complex muscles fwiction, where function may include more sophisticated factors other than simply the amount of shortening between origin and insertion. The correct fiber arrangements provided hmthe senaily dissected specimeo may dso dow funire studies to examine muscle contraction and subsequent force generation with accurate muscle pennation effects.
Traditiondy, muscuIoskeIetal software systems have modeued muscles as a single force vector, that is, by one straight he or a senes of he segments pieced together @elp and Loan, 1995). The direction of the force vector is determined by the muscle architecture. The muscle architecture is often based on the PCSA (Physiological
Cross Sectional Area) formula, which includes only one average angle of pennation and one average nber Iength for an entire muscle, neglecting the fact that pemation and nber
Iength cm Vary non-unifonnly throughom a multi-part muscle. This representation also fails to account for moments that are exerted about the üne of action, especially in cornpIex muscIes with large attachment sites (Van der Helm and Veenbaas, 199 1). Past analyses have used Cross Sectional Area caiculations based on muscle thickness (Ichinose et al 1998); others have used PCSA hcorporatuig angle of peunation aod fiber length (Wickiewin et al.. 1983). Brand et al. (1986) concluded that it is not possible to predict which one of the three specimens they studied wouid generate the most force based on PCSA. Fukunaga et al. (1996) presented data that "suggest that factors other than PCSA contribute to the force output potential of plantar £îexors and dorsiflexors in humans".
In the present thesis the B-spline model has shown the complexity of soleus architecture, suggesting that single fiber bundlelnber models do not provide adequate representation of the entire soleus. With the varied architecm throughout the marginal. antenor and posterior soleus it is dificuit to see how a few fiber bundles cm be used to model function of the entire muscle. Interaction between the contractile and comective tissue elements ükely result in complex transmission and summation of forces.
ModeIiing of the muscuioskeletai system with B-spline may provide fitrther insight into factors contnbuting to force output.
6.7 Functionai considerations
Some of the possible functionai aspects of the soleus are discussed below relative to the data obtained in the present study. The model is not capabIe of showing muscle contraction and therefore this discussion is Iimited to indirect evidence.
The human soleus muscle has been desrnid as an ankie plantar flexor and an
important anti-gravity muscLe for the maintenance of bdance when standing (Campbell et
al., 1973; Wfiams et aI., 1989; Sinnatamby, 1999). The marginal, posterior and anterior soleus, on contraction, interact through theù aponeuroses to contniute to these important fiuictions.
The marginal soleus fies around the periphery of the muscle and is attached to both the anterior and posterior aponeuoroses medially and lateraily but proximally Lies between the posterior aponeurosis and the tibia and fibula. The marginal fiber bundles are curved, except where they attach to the proximal aspect of the tibia and fibula. In the pilot ultrasonographic studies it was observed that when the marginal soleus contracted the distance between the tibia and postenor aponeurosis decreased. This suggests that on contraction of the fiber bundles of the marginal soleus tightened the posterior aponeuorosis. Sidarly the marginal soleus where it exteods between the anterior and posterior apooeurosis can, on contraction, tighten both these connective tissue sheaths.
This may take up the slack in the aponeuroses and maximize the eficiency of contraction of the posterior soleus and Merprovide a mechanism for the transmission of forces lateraiiy. The average angle of pennation of the marginal soleus to the posterior aponeurosis was found to be pater on the lateral aspect of the leg than on the medial aspect in the middle of the muscle, although no ciifference in fiber bundle length was noted.
The fiber bmdes of postenor soleus form rnost of the volume of the muscle and are aminged obliquely between the ancerior and posterior aponeuroses. The fiber bundies of marginal soleus are generally curved The soleus as a whole, but especially the posterior part, is characterized by a large number of short nber bundles packed into the muscle volume at relatively high angles of pennation. This makes the muscle ideai for generating high forces with Linle excursion (Lieber, 2000). in real time ultrasound, the anterior and posterior aponeuroses are seen to move as the fiber bundles of posterior soleus shortened and their peunation angles relative to the aponeuroses increased The anterior aponeurosis moved distaiiy and the posterior aponeurosis proximally. This arrangement of mer buadles and their extent medidy, laterally and distaDy suggests that the posterior soleus is capable of considerable force production, which can be utilized in stabilizing the leg on the foot while standing. In the posterior soleus, fiber bundle distribution was homogeneous with slightly longer mer bundes in the central region.
No distinct differences in the angles of pemation were noted on the medial and lateral sides of posterior soleus.
The anterior soleus, due to its anachment to the median septum and bipemate structure, cm potentiaily play a role in ankle doaifiexion. The median septum blends into the calcaneal tendon and in real time ultrasound, movement of the fiber bundles of anterior soIeus is seen relative to the median sephim. The median septum moves proximaüy on contraction. Also on contraction the pe~ationangle of the fiber bundles within anterior soleus increases by an average of 45 per cent in relation to the median septum Campbell et al. (1973) in an electromyographic study suggested that the medial and lateral aspects of soleus ciiffer functionaüy; with the Iateral aspect behg a stabilizer and the medial aspect king an ankle plantarflexor. Campbell et al. (1973) used surface electrodes on the mediai and lateral parts of soleus not concealed by gastrocnemius. The antenor soleus is more easily accessed hmthe medial side of the leg and it is possible that in Campbell et ai. (1973) some of the signal came hmthe antenor soleus suggesting plantar flexion activity. The Iatedy placed eiectrodes may have picked up signai from the marginal and posterior soleus only, indicating stabiüzing activity. Use of needle electrodes is iïmited by the large number of veins traversing the soleus.
Ultrasonography &O demoastrated the relationship between different muscles in the same compartment. When muscles in a compartment contract, they intluence each others extemal shape and demonstrate coordinated activity. For example, aponeuoroses of two muscles such as soleus and gastrocnernius lie adjacent and paraIlel to each other but yet on contraction move in opposite directions. The orientation of the muscle fiber bundles determines the direction in which the aponeurosis moves. Therefore, the influence and interplay of muscles and their aponeuroses in a compartment may also be important for normal fimction.
ültrasonographic studies of muscle contraction have focussed on concentric contraction. It would be of interest to determine how soleus architecture is changed on isometric and eccentric contraction. This couid aid in the understauding of the role of this muscle in the gait cycle.
Gender differences in the architecture of the soleus muscle were observed in the present thesis. The observed larger pemation angles, thicker muscle and shorter fibers recorded in the soleus muscles of males each contribute to greater force generation in males than in fernales. Femaies have greater muscle excursion and contraction velocity, resuithg in greater flexibüity. Differences in muscle architecture have been linked to athletic performance. For example, fascicle length of gastrocnemius and vastus lateralis have been reported to be longer in sprinters than in distance mnners (Abe et ai., 20).
Ako, sprint performance has been reiated to muscle fascicie Iength (Kumagai et al., 2000). This suggests that athletic ability rnay be Linked to the specinc muscle architecture of an individual.
Clinicaüy it would be intereshg to determine if there are any differences in muscle architecture in pathological muscle. for example. spastic muscle foUowing a stroke, spastic diplegia, or muscdar dystrophy. If differences were found they could be modelled using the B-sphe program. This would allow for better understanding of the functional deficits of these individuais and provide an avenue to test adaptive or corrective strategies. The B-spline model could also be used to determine which part(s) of soleus are best suited for surgical Oap procedures. The aim of the flap is to cover the affected area to promote healing, for example, after severe Iower Iimb trauma, but at the same time to maintain as much function as possible. Fascia1 entrapment could also aect
the function of the muscle. The contractile elements may be intact but if there are fascial,
for example, aponeurotic. restrictions the muscle cannot function nomaiiy. Soft tissue
restriction of plantar flexion could be further exiunined ultrasonographicaUy to detemine
possible sites of fascid restriction.
The human soleus muscle is a complex muscle with Little known about how the
marginal, anterior and postenor parts interact and what their functional roles may be.
"An understanding of the force trammission paths is tantamount to devefoping adequate
models of structure-function relationships in skeletd muscle. It dso permit5 more
sophisticated interpretation of the functional effects of injury ..." (Patel and Lieber,
1997). A contractile B-sphe model based on cadaveric and in vivo data may provide
some answea to these questions. Chapter 7: Conclusions
The conclusions are divided into two sections. The first section of conclusions are drawn from the computer modelling portion of the study and the second section bm the architectural data obtained for the human soleus.
Conclusions related to the proeess of cornputer rnodehg:
1. A three-dimensional(3-D) manipulatable mode1 and database of the architectural
parameters of a complete cadaveric soleus were created using anatomicai
photogrammetry in conjunction with B-spline rnodeiiing.
The fiber bundle architecture of soleus muscle cm be viewed as:
a whole,
marginal, anterior, and posterior parts, or
individuai mwsllayen of nber bundles within the marginal, anterior, and
postenor parts.
2. Existing data of the architectural parameten of the human soleus have been
signincantiy enhanced with the development, in this thesis, of three dimensionai
modelling and data collection techniques.
Conclusions related to the architeetoral data obtained hmthis study:
1. Architectural parameters have ken documented throughout the volume of soleus
in 3-D.
2. A database of the architectural parameters of rnanudy measmed cadaveric soleus
and relaxed and contracted in vivo soIeus was compiled 3. The architecture of the human soleus varies throughout the volume of the muscle.
Fiber length, angle of pemation and muscle thickness were non-dom within
the marginal, anterior and posterior soleus.
4. The fiber lengths of cadavenc antenor and posterior soleus and the angles of
pennation of posterior soleus were between those of relaxed and contracted in
vivo muscle. The angle of pennation of cadaveric mtenor soleus was greater than
both relaxed and contracted in vivo meslsurements.
5. On contraction, the soleus muscle fiber bundle Iengths decreased significantly
(p < 0.0001), angles of peanation increased significantly (p < 0.000 1) and muscle
thickness increased signif~cantly(p < 0.02). The percentage change of fiber
buncüe length, angle of pemation and muscle thickness on contraction varied by
muscle part.
6. The soleus of femdes bas longer fiben. smailer angles of pe~ationand is not as
thîck as the soleus of males (p c 0.05). Chapter 8: Future Directions
The study undertaken for this thesis has many possible friture directions, some of which are outhed below.
1. Develop a technique that would enable cornparison of 2-D and 3-D data. This
may be done by determining the 3-D force iine that would Lie in a specified
coordinate plane.
2. Further data collection to expand the capabilities of the B-splhe model. Data
collection to include:
coordinates of muscle fiber bundles throughout the volume of ail the muscles
acting on the aiMe joint;
coordinates of the location of tendons, aponeuroses and septa for each muscle;
the physicd properties of connective tissue structures such as tendon,
aponeurosis, septum etc.;
meastuernent of fiber bundle diameter and the amount perimysium around
each mer bundle;
coordinates of the bones of the underlying skebton and specific muscle
attachment sites; and
coordinates of the articular sudaces of the ankle joint (tibia, nbula, and talus).
2. Use the data coUected in I above to mode1 the entire moscuioskeIetai system of
the Ieg, including the ankle joint and the physicd properties of the tissues. 3. Coiiect ultrasonographic data for ail the Leg muscles in relaxed and contracted
States.
4. Based on the ultrasonographic resuits, make the B-spline model a volume
preserving contractile model capable of moving the ankie joint.
5. Use the B-spline model to assess the functioaal capabilities md force generation
of each muscle aad its component parts throughout planta and dorsiflexion of the
adde joint. Also mess the contribution of fasciai stmctwes to functionai
outcome.
6. Trace and coiiect data in the format of three-dimensional coordiaates on the
course of the nerves running throughout the volume of each muscle, using a
dissection microscope. The nerves would be added to the mode1 to provide
contraction of portions of the muscie by nerve stimulation.
7. Mode! pathologie muscle using ultnsound data coiiected fiom patients with
various muscle diseases, thus creating a tool to assess bction following surgicai
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Zuurbier, C. 1. and PA. Huijing (1992). "Muence of muscle geometry on shortening speed of fibre, aponeurosis and muscle." Journal of Biomechanics 25: 10174026. Appendix A: Photogrammetric 3-D Point Reconstruction Thne-dimensional (3-D) point reconstruction is a photogrammetric technique used to determine the 3-D spatial coordinates of an object fiom several two-dimensionai (2-D)images taken at different angles. The spatial coordinates can be of the intersechg points (or nodes) of a grid pattern iocated on the surface of an object as shown in Figure A. 1, or they cati be markers placed on the surface at dinerent positions. The 2-Dpoints from the photopphs are used dong with the camera positions to compote the 3-D coordinates of the nodes of the grid pattern or markers on the object surface. Although two camera images at minimum are required to reconstnict a 3-D image, three cameras are utiiized in the present work.
Image Plane 2
Figure AL Two-dimmianai reprrolatationsd gid pattern in image plaues (&, Y',k = 1,2 and 3 of the tùree-dùnensionai object m object space (X, Y, 2). Object or marker point (x, y, z) is projected to image points (u,v)~ (u, vk and (u, vh in the thephotographie images. Direct Linear Transfomation (DLT) Method For n imaging devices or cameras (n = 3 in present study), the Direct Linear Trmqfîomtatôn(DLT) method is utiiized to define a reIationship between points (x, y, z) in 3-D object space (X, Y, Z) and their 2-D coordinates in image pianes (Ut,Vd where k = 1, ..., n as foilows (Abdel-Aziz and Kama, 197 L, Manan and Ka- 1975, BaiI and Pierrynowski, L985; Nigg and Henog, 1999; Kwon, 2000) where x' is a homogeneous position vector which specines the 3-D coordinates of the object point, uk is a position vector which describes the 2-D coordinates of the correspondhg point on the image plane k of camera k, and Dk is the Direct Lùrear Transjiormarion (DLT)matrir of dimension 3x4 rtlating the coordinates of the 2-Dimage for camera k and the 3-D object point. Note that the operator ( ) converts a homogeoeous vector to its standard fom as descnied in Appendix B. DLT matrix 4for canera k cm be written as foilows
where the 11 parameters Li, .. . , Li are the DLT parameters and the twelfth parameter represents a gfobai scalar multiplier which is set to unity- The DLT matrix and its elements are discwed below in further detail. Expanding Eq. (A.2), we cm write the DLT relationship between (u,v), for camera k and point (x, y, z) as foiiows
Thos, for each of the three cameras there will be two equations and one set of DLT parameters as described in Eqs.(A.4), (A5) and (A.6) . DLT Matrix DLT matrix Difor cameni k is written again as folIows
The DLT parameters Li,..., Lii for camera k are defined by and are functions of the intemal md extemal characteristics of camera k. It is beyond the scope of the present thesis to define the exact nature of these relationships. Nevertheles, the internai and extemal charactenstics on which the DLT parameters depend are discussed below. Five Intemal Characteristics of Camera k The five intemal characteristics (il, i3 i3. i4 and is) are defined by the internai dimensions and characteristics of the camem as shown in Fig. A.2. Their velues are fixeà, that is, they do not change after each photograph is taken. The only way for the values of these charactenstics to change is for the lens in the camera to shift, a highly unlikely occurrence.
Light rays From object point
~ek Backplme (1mge Plane)
Figure ALCamera internai parameters,
il and iz are defined by the intersection of the principal ray with the image plane k. i3 is the perpeadicular distance Corn the Iens centre to the image plane. t is the focal Iength, that is, the distance hmthe lens centre to the focal point. is is a measure of the tüt of the image plane viz-a-& the plane of the lem centre. Six Exremat CharucteMcs of Càmera k The six extemal chatacteristics (el, e2, e3, eb es and e6) of the camera are variable, that is, their vaIues typidy change after each photograph is taken. This is due in part to canera movements caused by the shutter release, nIm advancement, etc. causmg minute changes in the camera orientation relative to the object king photographed- et, ez and e3 are the (X, Y, Z) coordinates of focal point relative to the global ongin on the base plane. e4, es and es are the camera orientations (a, r) which correspond to the camera elevation, azimuth and rotation relative to the camera centrai ray. As stated above, mathematical relationships exist between the eleven DLT parameters and the eleven internai and extemai charactenstics. However, these relationships are not needed for the calculation of the DLT parameters. htead, DLT parameter values are estunated in the DLT calibration and recatibration processes as descri'bed in detail below- Initial Camera Caliration - Estimation of Initial DLT Parameters To estimate the 1 1 initial DLT parameters Li, LZI --- . LI1 for each canera, photographs of the base plate and caübration plate are taken with each camera as shown in Fig. A.3. The plates are fabricated from clear acrylic sheet, and they contain equally spaced bail bearings. The base plate contains 50 bai1 bearings, and the calibration plate which is sihiated 20 cm above the base plate contains 15 bal1 beanngs.
Figure A.3, Base piate and caübration phte for DLT parameter estimation.
The bail bearings on the base plate and caiibration plate are controlpohts, in tbat their coordinates (x, y, z) Ui the object space (X, Y, Z) are known. Next, we write out agah the DLT equations for camera k as follows (A. 10)
From the cali'bration photo of each carneni k, we cm measure the 2-D location in the image plane (U,, Vd of each point (u, v), that comsponds to each of the 65 control points (x, y, 2). Dependhg on a partidar carnera's angle of view, one or more of the contrai points may be hidden and so the total nomber of points may be less than 65. For each camera, the measwed (u, v), locations and their corresponding control point (x, y, z) locations are tabulated in Table k1where Miis the total number of points ncorded in calibration photo k. Tabk A.1. Initiai dbratioa data for camera k
Control Point i xi Yi Ei Ui Vi L 2
Mk 1
We cm merrewrite Eqs. (A9)and (A. 10) in ma& fomi points as foilows for control points i = 1,2, ..., n where n = Mk
(A* 1 1)
Nonünear least square estirnates of the 1 1 initiai DLT parameters Li, L3 ... , Li1 can be obtained by solving Eq. (A. 11) iteratively using the datatabulated in Table A. 1 for each control point. Since each control point (x, y, 2) genecates a u and v value, and since there are II DLT panuneters to be estimateci, a minimum of 6 conml points are needed to estimate the DLT parameters. By using a Iarger number of control points, however, it is possible to improve the accuracy of the DLT parameter estimates.
Each time a new photograph is taken of the object of interest lying on the base plate for 3-D point reconstruction, there is a proaounced but undetemiined amount of camera shift due to nIm advancement, shutter movement, etc. which resuits in a change in the values of the six extemai chanctenstics. It shouId be noted that the five interna1 characteristics do not change hmcarnera shoot to shoot Thedore, after each shoot, it is necessPry to moday the DLT matrix before the 3-D coordinates of the object of interest on the base plate ean be detetrnined. Instead of recalculating the DLT matrix as carried out to estimate the initial DLT parameters (which additiondy requires the use of the caLiiration plate), a transformation rnatrix EI is uaedas follows
(A. 12)
where rm, rm, ..., rm represent the components of rotational shift and tx, tu and tz represent components of translational shift of the camera relative to the base plate after each camera shoot In its homogeneous form, mahic 8' is written as foilows and where the scaling factor of 1 is utilized
Thus for each camera k, it is necessary to track the shift in the 2-D location in the image plane (LIk, V,of each point (u,v), that corresponds to conml points (x, y, z) visible on the base plate from one shoot to the next Note that many of the control points will be covered by the object of interest, so that only 15 to 20 control points may be visible. NevertheIess, the components of the transformation mauix H can be caiculated by solving the following equation
(A. 13)
(A. 14)
where x' is a homogeneous position vector which specifies the 3-D coordinates of the control point (x,y, z) in object space, rit is a position vector (u,v), which descri'bes the 2-D coordinates of the corresponding point on the image plane k correspondhg to camera k. Expanding Eq. (A.14). we can write the relationship between (u,v), for camern k and point (x, y, z) as follows (A. 16)
(A, 17)
Just as we tabuiated the 2-D locations (u,v), corresponding to each of the control points (x, y, z) in the initial DLT calibration, we need to again compile a shorter table of visible control points (x, y, z) on the base plate and their coffesponding 2-D projections (u,v), in the image plane (Ut,Vd as in Table A.2. Mk is the total number of points corresponding to visible conml points in photo k. As stated above, many of the control points will be covered by the object and so the value of Mkmay be as low as 15 to 20.
Table A.2. Recaiibration for camera k
Again, nodinear Ieast square estimates of the vaiues of the 12 rotationai and translational components in transformation manDr H can be obtained by solvhg Eqs. (A. 16) and (A. 17) using the data tabulated in Table A.2. DLT Matrix Modification As stated above, it is necessary to modw the DLT matrix 4after each camera shoot, This is carried out as follows (A. 18) (A. 19)
3-D Point Reconstruction Fiiatly, we are able to calculate the 3-D coordinates of the markers on the object of interest on the base plate from the corresponding projections (u,v), on the each of the image planes or photos. k = 1 to 3. Again we mite the relationship between projected point (u,v), in the 2-D image plane and 3-D coordinates (x, y, z) for camera k as
Combining Eq. (A.21) for the three cameras, we obtaîn [il-)
Since the combined DLT mat& in Eq. (A.22) is not square, it can not be inverted to solve Eq. (A.22) directly. Instead, we mast solve Eq. (A.22) iteratively, using for example the Levenberg-Marquart non-linear equation solver in Mathematica, to obtam the 3-D coordioates (x, y, z) for each marker on the object of interest Appeadix B: Mithematics of Vectors and Mlatrices
A substantiai amount of matrix mathematics is utilized in Appendù A in the discussion of photogrammetric 3-D point reconstruction methods. For the non- mathernatician, a brief review of some of the most important concepts of vectors and matrices is presented here. Enth mathematics textbooks are devoted to this area, and many excellent textbooks are available that cover this subject for Merreference (Bransoo, 1970).
1. A matnt is an array of elements arranged in horizontal cows and vertical columns as
The foregoing matrix A has rn mws and n columns, and therefore is of dimension (mp). It is caiied a m by n matrix, or a mxn matrix. Matrices are usuaily denoted by a CAPITAL BOLDFACE Ietter. The entries of a rnatrix are called elements.
2. A special mat& containing ody a single colurnn is cailed a vector, and is normaiiy denoted by a smali bo1dface Ietter such as x where
The focegoing vector x has dimension n.
3. It may be necessary to convert vector x in its srmidard fom to its comsponding homogeneous vector x' . If vector x in its standard form and of dimension n is
then its correspondùig homogeneous vector x' of dimension n+ 1 is defined as where the operator ( )' converts a vector of dimension n to its homogeaeous form of dimension n+ 1. For exampie, if vector x Ui its standard form having dimension 3 is
then its corresponding homogeneous vector x' with dimension 4 is
4. In the converse, it may be necessary to convert homogeneous vector x' to its corresponding vector x in its standard fonn. If homogeneous vector x' of dimension n+ l is
then its cornpouding vector x h&ng dimension n in standard form is defmed as
where ( ) is the operator which converts the homogeneous vector of dimension n+ 1 to its standard form of dimension n. For example, if homogeneous vector x' with dimension 4 is then its corresponding vector x in standard form having dimension 3 is
(B.IO)
5. Addition or subtraction of two matrices may be performed if the two matrices bave the same number of rows and the same number of colwnns, The sum of two matrices A and B is defmed as the rnatrix C whose eIements are the sum of the corresponding elements of the inciividual matrices, or
Simifarly, the difference of two matrices is defined as the matrix whose elements are the ciifference of the corresponding eiements of the individual matrices. For example, if
6. Multiplication of two matrices is defined only for conformabIe matrices. Two matrices A and B are conformable in the order AB if the nucnber of columns in A equais the number of rows in B, that is, A is a nwt amtrix and B is a nxp matrix where the number of coIumos in A and rows in B is equd to n. For example, if A is a 2 by 3 matrix and B is 3 by I ma& (or vector) as foiiows then A and B are conformable in the order AB, since the number of columns in A equals the number of rows in B which is equai to 3. The product of conformable matrix A and rnahyr B is product matrix C, that is C = AB, where (i) rnatrk C has m rows andp columns, and (fi) qj which is the elernent in the i" row and j" col- of C is the sum of the products of the correspondhg elements in the ilh row of A and j" column of B, that is
For example, the product of conformable matrices A and B as given above is
x abc ax+by+cz y .=AB=[ efg ex+fy+gz ] z =[ ]
7. A square manix is a matru< that has as many rows as it has colurnns. It can be written as
The elements air, aa ... ,a, lie on the main diagonal and are caiied diagonal elements.
8. A unit or identify matrix I is a square diagonal matrk that bas unit elements on the main diagonal and zemes elsewhere, that is
(B.18)
9, The transpose marrix A' is obtained by changbg ail the rows of square rnatrix A into the columns of A'. If abc CB-19)
10. The determinant of a square ma& is a scalar quantity and is denoted by det A or
For a 2x2 matrix, the value of the determinant is the scalar quautity a, ,e, . For Iarger dimension matrices, one must fint determine the cofacttor Au of elernent a, by rnultiplying the term (-1)'+j and the minor Mv obtained hmA by removing the ith row andjth column. in other words, we fitform a submanix of A by crossing out both the row and column in which the element ab appears. We then find the determinant of the submatrix and rnultiply it by the number (- l)'? For example, to compute the cofactor of the element b in ma& A
we fmt obtain the submatrix in matrix A for element b which is
Then we calculate the determinant of the submatrix which equds em -kg. FinaUy, we compute the cofactor of element b which is
To find the determinant of manix A of any dimeasion, (i) pick a row or column, (hi for each element in the row or colmchosen, find its cofactor, and (hi mdtiply each element in the row or colmnn chosen by its cofactor and sum the dts. This smn is the value of the detenninant of the matrix. For example, we caldate the determinant of the following mat* A
by first selecting the elements in coiumn 2 to calculate the cofactors as follows det A = (5)(cof&ctor of 5) + (2)(cofactorof 2) + (-6)(cofactor of -6)
1 1. The adjoint of a matrix A is the transpose of the cofactor rnatrix of A, and is designated as adj A. For exampie, the cofactor ma& Ac of the foregoing matrix A is detemiined as follows
AC=
The adjoint ma& is the transpose of the cofactor matrix ACwbich is adj A = (A')'
The inverse manix A-' of square rnatrix A is dehed as foilows
A-' =-!-adj A; if detAf O det A
For the foregoing rnatrix A, its inverse A" is calculated as foiiows
A-' =LadjA det A r14 -20 5
If we multiply ma& A and its inverse A", we should obtaia the identity matrix 1. Universitg of Toronto
. - OFFICE OF RESEARCH SERVICES
PROTOCOL REFERENCE # 1869
July 18,1996
Dr. NI McKee lnstitute of Medical Science Fawlty of Medicine Room 6270, Medical Sciences Bldg. University of Toronto
Professor A* Agur Instime of Medical Science Faculty of Mediam Room 6270, Medical Sciences Wdg. University of Toronto
Osar Dr. McKee and Professor Agw:
We are writing to advise you tht the Unrversity of Toronto Human Subjects Review Cornmittee has extendeci approval to the research study entitted, 'Human Gasbacriemius and Soteus Musdes: Creation and Validation of 30 Cornputer Mode1 Redicting Wonal Capabiiiies* based on Ressarch Ethics Board approvals from Toronto Hospital and St. Joseph's Hospital- The appcoved infomiatlon sheat and consent form are attacheci.
Owing the course of the c~s88cch,any signifiamt deviaÈt*onsRom trie approved pratocul (tftat is, any deviatïon *ch wotdd lead to an incmase in rbk or a decmse in banefït to human subiects) andlot any unandfpated daveloprnentir within the tesearch should be brought to the attention of the ûffice of Research Se~*ces.
Best wlshes for the succ8ssful completion of your projecti
Swan Pilon Exeume Officer Human Subjects Review Cornmittee
cc: Vice Oean of Research Dt. W. iCuchatcyCc Toronto Hospital St. Joseph's HospitaI Dr. 3. wsdge INFORMATION mEET CONSENT FORM
Titie oPpmjeck Human GastrOcaemius and SoIeus Muscles: Moaand Validation of 3D Cornputer Mode1 Predictmg Functionat Capbilitits
1 have read and u~derstandthe ixûodon&cet bthe above mciy. 1have bca~given a qyof tbis Mfi3donshca to Eotep. TMs striby has b&n expiainai to mby Aime Agur. Dt. D. Salotlt~,or Dr, N. Mc- All rny Signatnrc of Parent or Guardi= (for mbjhaged 8-13]