Open PSU Thesis Laura Mendez

The Pennsylvania State University

The Graduate School

College of Health and Human Development

GASTROCNEMIUS MUSCLE PENNATION VARIATION

A Thesis in

Kinesiology

Laura Ximena Mendez Guevara

 2015 Laura Ximena Mendez Guevara

Submitted in Partial Fulfillment of the Requirements for the Degree of

Master of Science

May 2015

The thesis of Laura Ximena Mendez Guevara was reviewed and approved* by the following:

John H. Challis Professor of Kinesiology Thesis Advisor

Robert B. Eckhardt Professor of Developmental Genetics and Evolutionary Morphology

Stephen J. Piazza Professor of Kinesiology Graduate Program Director

*Signatures are on file in the Graduate School

ABSTRACT

Pennated muscles have their fibers attaching obliquely to their tendon forming an angle which is referred to as the pennation angle. Pennation angles change with muscle length, muscle force, and contractile velocity. The aim in this study was to further understand the function of pennation angle variations during different muscle actions of the gastrocnemius muscle in vivo. The direct action of the gastrocnemius muscle can cause ankle and knee motion. Both heads of the gastrocnemius were imaged in vivo using ultrasound during muscle actions in a dynamometer while ankle moments were recorded. These data were collected for twenty-four healthy subjects (age: 25.8 ± 5.2 years; mass: 68.0 ± 14.6 kg; height: 1.69 ± 0.12 m). Ultrasound images were taken at nine different ankle angles for maximal static plantar-flexions, and for three different angular velocities for dynamic contractions. Both tests were performed with the knee extended and the knee flexed. The ultrasound images were used to measure pennation angles during the static and dynamic tests. Analyses were performed to assess differences in pennation angle between ankle angles and between gastrocnemius heads in the static test, and between the static and dynamic tests. Correlations were analyzed between pennation angle and the inertial parameters of the shank, and ankle moments. A muscle model which included pennation angle in the calculation of tendon force was evaluated based on the experimental data. There were no statistically significant correlations between pennation angle and the segmental inertial parameters, or with normalized peak ankle moment at the two knee angles. Differences in ankle moments between the two knee conditions were not statistically significantly different. The model presented similarities with the experimental data with the knee flexed but not with the knee extended. The predicted ankle moments were higher compared with the experimental data with knee extended, and with the knee flexed the predicted moments were higher than the experimental data in plantar-flexion and lower in dorsi-flexion. Coefficients of variation presented small variability in pennation angle between subjects. Pennation angles between the gastrocnemius heads were not statistically significantly different for both knee conditions. Pennation angles in static and dynamic contractions presented statistically iii

significant differences where in general larger pennation angles were found for the static conditions for all ankle angles. In some cases the lateral head presented larger pennation angles for the dynamic condition compared with the static condition. This study helped in the understanding of in vivo pennation angle changes and is the first study to examine pennation angles and segmental inertial parameters, and to compare pennation angle between static and dynamic conditions for different ankle angles within the normal ankle range of motion.

TABLE OF CONTENTS

List of Figures ...... vii

List of Tables ...... x

Acknowledgements ...... xi

Chapter 1 - Introduction ...... 1

1.1 General Introduction ...... 1 1.2 Purpose of the Study ...... 1 1.3 Specific Aims ...... 2 1.4 Study Overview ...... 5 1.5 Thesis Structure ...... 5

Chapter 2 - Literature Review ...... 6

2.1 Overview ...... 6 2.2 Muscle Mechanical Characteristics ...... 6 2.2.1 Force-Length Relationship ...... 6 2.2.2 Force-Velocity Relationship ...... 9 2.2.3 Muscle Architecture ...... 13 2.3 Muscle Pennation ...... 15 2.3.1 Variation between Muscles ...... 15 2.3.2 Variation within Muscles ...... 17 2.3.3 Variation during Movement ...... 20 2.3.4 The influence of Training ...... 22 2.3.5 The influence of Aging ...... 24 2.4 Triceps surae Characteristics ...... 26 2.4.1 Anatomy ...... 26 2.4.2 Architecture ...... 28 2.4.3 Function ...... 31 2.5 Summary ...... 33

Chapter 3 - Muscle Model ...... 34

3.1 Overview ...... 34 3.2 Model Structure ...... 34 3.3 Contractile Element ...... 35 3.4 Series Elastic Element ...... 36 3.5 Muscle-Tendon Complex Length and Moment Arm ...... 37 3.6 Muscle Pennation ...... 40 3.7 Model Parameters ...... 41 3.8 Simulations...... 42 3.9 Summary ...... 43

Chapter 4 – Methods...... 44

4.1 Overview ...... 44 4.2 Subject Recruitment, Characteristics, and Anthropometry ...... 44 4.3 Shank Inertial Parameters ...... 45 4.4 Ultrasound and Gastrocnemius Measurements ...... 47 4.5 Biodex Isokinetic Dynamometer Tests ...... 50 4.5.1 Isometric Test Protocol ...... 51 4.5.2 Isokinetic Test Protocol ...... 51 4.6 Muscle Architecture Measurements ...... 52 4.6.1 Isometric Data Analysis...... 52 4.6.2 Isokinetic Data Analysis ...... 53 4.7 Pennation angle Model and Experimental Data ...... 54 4.8 Statistics ...... 54 4.9 Summary ...... 54

Chapter 5 – Results ...... 55

5.1 Overview ...... 55 5.2 Anthropometry ...... 55 5.3 Pennation Angle and the Peak Isometric Moment...... 58 5.4 Peak Isometric Moment–Ankle Angle Relationship with Knee Angle Changes ...... 60 5.5 Inter-subject Pennation Angle Variability...... 63 5.6 Pennation Angle for Static Condition Compared with Isokinetic Conditions ...... 66 5.7 Summary ...... 68

Chapter 6 - Discussion ...... 69

6.1 Overview ...... 69 6.2 General Findings in the Study ...... 69 6.3 Discussion of the Results ...... 71 6.4 Limitations in the Study ...... 74 6.5 Future Research ...... 75 6.6 Conclusions ...... 76

References ...... 77

Appendix – Informed Consent ...... 82

LIST OF FIGURES

Figure 1.1. Hypothetical muscles with a parallel fibered muscle (A) and a pennated muscle (B), where the muscles have the same volume. Red lines represent the longitudinal and transverse axis through the center of mass of the segment...... 3

Figure 2.1. Force-length curve determined by Gordon et al. (1966) contrasted with the overlapping of the actin and myosin fibers (modified from Gordon et al., 1966). …………...... 8

Figure 2.2. Velocity-force relationship found by Hill (1938). Circles represent experimental data at 0 ºC, and the curve was found by the equation (P + 14.35) (v + 1.03) = 87.6. It can be seen the accuracy of the “characteristic equation” (taken from A. V. Hill, 1938)...... …………...... 10

Figure 1.1. Different velocity-force relationships of the cat medial gastrocnemius (MG) and soleus (SOL) depending on the velocity definition A) is velocity per average fiber length, B) is sarcomere length and pennation angle, and C) is muscle length. P(0) is the maximal isometric force and L(0) is the optimum length (taken from Spector et al., 1980). ……………………..... 11

Figure 1.2. Where w is muscle width, t is muscle thickness, and the arrow indicates the amount of muscle shortening. A) muscle at rest, B) is a low-force contraction, where fiber rotation is large, muscle thickness increases and gear ratio is large, allowing for velocity, and C) is a high- force contraction, where fiber rotation is small, muscle thickness decreases, and gear ratio is close to 1, allowing for force production (taken from Aziz et al., 2008). …………………………...... 19

Figure 1.3. Planimetric muscle model assuming constant muscle thickness t and linear fiber length Lf. ABCE is the muscle at rest, ABDF is the contracted muscle, a and b are the pennation angles (taken from Maganaris et al., 1998). …………………………………………………..... 20

Figure 1.4. Muscle architecture difference between elderly (A) and young (B) men. Where t is muscle thickness, Lf is fiber length and θ is pennation angle (figure modified from Figure 2 in Narici et al., 2003). …………………………………………………………………………...... 25

Figure 1.5. A) Gastrocnemius, and B) soleus (modified from Figures 1 and 2 of Chow et al., 2000). ………………………………………………………………………………………...... 27

Figure 3.1. Schematic representation of the muscle model, where CE is the contractile element, θ is the pennation angle of the muscle fibers, and SEE is the series elastic element. ……………………………………………………………………………………...... 34

Figure 3.2. Isometric muscle fiber force-length relationship. Force is represented as a function of fiber length, peak force is found at optimum length (LF,OPT)...... ………...... 36

Figure 3.3. Extension-force relationship of tendon. The y-axis represents the extension of the tendon at a given muscle force and FT is the force of the tendon as a fraction of the maximal force that can be applied to the tendon. ....……….……………………………………...... 37

Figure 3.4. Joint angle definitions by Grieve et al. (1978). ..……………………...... 38 vii

Figure 3.5. Muscle-tendon complex length-ankle angle relationship for the gastrocnemius muscle. ……...……………………………………………………………………...... 39

Figure 3.6. Moment arm-ankle angle relationship for the gastrocnemius muscle...... 39

Figure 3.7. Representation of modeled pennated muscle, where FT is the force at the tendon, LF is the muscle fiber length, T is the muscle thickness, θ is the pennation angle, LT is the tendon length, LMB is the length of the muscle belly, and LMTC is the muscle-tendon complex length...... 40

Figure 4.1. The measurements of the leg. …………………………………………………….... 46

Figure 4.2. Gastrocnemius measurements. Where 1) origin of both heads, 2) intersection of the Achilles tendon with the heads of the gastrocnemius, and 3) edges of calcaneus on the lateral and medial sides. …………………...……………………………………………………………...... 48

Figure 4.3. Identification of the separation between the heads of the gastrocnemius (LG is the lateral head, and MG is the medial head) using the ultrasound image. ………………...……..... 48

Figure 4.4. Ultrasound probe positioning on the leg, with subject in the Biodex dynamometer...... …………...... 49

Figure 4.5. Ultrasound machine and Biodex dynamometer set-up. ..……………………...... 49

Figure 4.6. Biodex testing with A) Knee extended at 0° and B) knee flexed at 90°...... …………………...... 50

Figure 4.7. Illustration of ankle angle definition, where the ankle angle (φANKLE) used was defined as φANKLE = θ - 90°...... ………………………………...... 51

Figure 4.8. Ultrasound image of gastrocnemius medial head indicating the muscle architecture parameter measurements. TSs and TSd are the superficial and deep aponeuroses respectively, t is the muscle thickness, Fl is the fascicle length, and θs and θd are the pennation angle of the fascicle with respect to the superficial and deep aponeuroses respectively...... 53

Figure 5.1. Pennation angle and center of mass for each subject for the lateral head at 0º knee angle...... 57

Figure 5.2. Pennation angle and radius of gyration on the transverse axis presented for each subject for the medial head at 0º knee angle...... 5¡Error! Marcador no definido.7

Figure 5.3. Moment-pennation angle relationship for the medial head at 90° (blue) and 0° (red) knee angles, solid lines reflect linear trend lines...... 59

Figure 5.4. Moment-pennation angle relationship for the lateral head at 90° (blue) and 0° (red) knee angles, solid lines reflect linear trend lines...... 59

viii

Figure 5.5. Peak moment-ankle angle relationship at 90° (flexed) and 0° (extended) knee angles for the muscle model using the group mean pennation angles...... 60

Figure 5.6. Peak moment-ankle angle relationship at 0° (extended, solid line) and 90° (flexed, dashed line) knee angles for the group mean isometric peak moment with the standard deviation...... 61

Figure 5.7. Peak moment-ankle angle relationship for the knee flexed comparing the muscle model with the mean experimental results...... 62

Figure 5.8. Peak moment-ankle angle relationship for the knee extended comparing the muscle model with the mean experimental results...... 62

Figure 5.9. Pennation angle-ankle angle relationship of both gastrocnemius heads for the group mean and standard deviation for the isometric testing at 0° knee angle...... 63

Figure 5.10. Pennation angle-ankle angle relationship of both gastrocnemius heads for the group mean and standard deviation for the isometric testing at 90° knee angle...... 64

Figure 5.11. Pennation angle-ankle angle relationship for every subject (dotted lines) and the group mean (solid line) for the medial head at 0° knee angle...... 65

Figure 5.12. Pennation angle-ankle angle relationship of the medial head for the static and dynamic conditions at 0° knee angle...... 68

LIST OF TABLES

Table 2.1. Similarities of pennation angle of muscles in a synergistic group and differences between antagonistic groups. Semitendinosus (ST), semimembranosus (SM), biceps femoris long head (BFl), biceps femoris short head (BFs), rectus femoris (RF), vastus medialis (VM), vastus lateralis (VL), vastus intermedius (VI) (modified from Table 1 in Wickiewicz et al., 1983)...... 16

Table 1.1. Pennation angle for the leg muscles by joint group. Some muscles in a group presented different values and are indicated (modified from Appendix A-1 in Yamaguchi et al., 1990). ………………………………………………………………………...... ………………...... 17

Table 1.2. Architectural characteristics of the gastrocnemius human muscle (medial head GM, and lateral head GL) (taken from Huijing, 1985). …………………………………………...... 28

Table 1.3. Architectural characteristics of the triceps surae (gastrocnemius medial head MG, gastrocnemius lateral head LG, and soleus Sol) (taken from Kawakami et al., 1998). ……...... 30

Table 3.1. Muscle specific model parameters...... ………………………………..……...... 41

Table 3.2. Model general parameters. ..………………………………………………..……...... 42

Table 4.1. Subject characteristics and physical activity. ……………………………..……...... 45

Table 4.2. Subject characteristics (mean ± standard deviation)...... …………………...... 45

Table 5.2. Correlation between pennation angle and segment inertial parameters. ..……..……. 56

Table 5.3. Correlation between pennation angle and ankle moment at 10° ankle angle for the medial and lateral head of the gastrocnemius at two knee angles. ………………………..……. 58

Table 5.4. Group coefficients of variation expressed as percentages for each gastrocnemius head at two knee angles for nine ankle angles...... ……………………………..…….. 64

Table 5.5. Largest and smallest pennation angles for both gastrocnemius heads at two knee angles for nine ankle angles...... …………………...... 66

Table 5.6. Pennation angles for static and dynamic conditions at each ankle angle for both gastrocnemius heads at two knee angles...... …………………...... 67

ACKNOWLEDGEMENTS

I would like to thank my thesis advisor John Challis for serving as my mentor in this process. I learned many things thanks to you and it was a great experience.

Thank you also to Dan Gales, Curtis Kindel, Samuel Masters, Rebecca Rogers and Justin Wager for all the support, help, and advice during this process.

I would like to thank all the undergraduate research assistants who volunteered their time and helped me with the data collection and measurements; this would have been a longer process without their help.

Special thanks to all volunteers in this study, for giving your time for muscle research.

I would like to thank my thesis committee composed by Robert Eckhardt and Stephen Piazza.

Thank you to all friends whom supported me along the way.

I would like to thank my family and especially my mother and father for your continuing support, patience, and guidance thought this process, and to my brother who always believed in me.

Chapter 1 - Introduction

1.1 General Introduction Muscles have the ability to produce body motion and examining their function in human movement can help further our understanding of the co-ordination of muscles, injury prevention, and improve rehabilitation and strength training protocols.

Muscle architecture has been studied not only to understand muscle function but also to improve musculoskeletal models. However, many of the studies have been on cadavers which potentially limit the understanding of the importance of muscle architecture on muscle function in vivo. With new technologies that allow the in vivo measurement of muscle architecture, the understanding of the influence of muscle architecture has increased.

The muscle architecture parameter that has received the most attention is fascicle length, and important finding have been reported. However, pennation angle has received less attention although it is known to be related to the maximum muscle force transferred to a muscle’s tendon, changes with movement, has great plasticity adapting to training regimens, and also changing with aging. Due to this, pennation angle merits more investigation to further understand its function in muscles.

The gastrocnemius muscle is part of the triceps surae complex which is responsible for plantar-flexion of the ankle. The gastrocnemius is a superficial muscle and therefore easy to visualize with ultrasound imaging, and has two heads which present differences in their respective muscle architecture. These two features make the gastrocnemius muscle a good candidate for the investigation of pennation angle function.

1.2 Purpose of the Study The pennation angle changes within a muscle when it is contracting, which raises the question of how different are the pennation angle changes between different 1

contraction types and how do these vary between subjects? Considering this, the purpose of this study was to measure pennation angles in vivo for both heads of the gastrocnemius muscle for static contractions with varying muscle lengths and dynamic contractions at different angular velocities. Along with pennation angles, the fascicle lengths, muscle thicknesses, ankle moments, and anthropometric data were measured. These measurements were taken in healthy subjects.

1.3 Specific Aims There were five aims in this study.

1. The first aim in this study was to investigate if there is a relationship between segmental inertial parameters and the pennation angle of the fibers of the muscles comprising the segment.

Considering two hypothetical limbs with the same mass having the same volume, where one is a parallel fibered muscle and the other is pennated then this could result in different inertial properties of the limb (Figure 1.1). The center of mass would be higher in the pennated muscle, as more muscle mass would be distributed closer to the proximal end of the segment. The longitudinal moment of inertia would be greater for the pennated muscle as the pennation would distribute more of the muscle mass further away from the longitudinal axis than occurs in the paralleled fibered muscle. With the transverse moment of inertia if more mass is distributed higher in the segment this may increase the moment of inertia of the limb for a pennated muscle compared with a parallel fibered muscle, but if the moment of inertia is referenced to the center of mass of the segment and this is higher in the pennated muscle this may compensate for the more proximal distribution of muscle mass. These potential relationships will be examined with the data collected in this study.

2. The second aim of this study was to investigate the relationship between muscle pennation angle and peak moment the subjects could produce.

There is evidence in the literature that muscle fibers in larger muscles tend to have larger pennation angles (Kawakami et al., 1993), and should therefore be a positive relationship between the measured peak moment and the muscle pennation angle. The data from this study will permit examination of the strength of this relationship.

3. The third aim in this study was to investigate the influence of changing the knee angle on the moment–ankle angle relationship of the plantarflexors.

The gastrocnemius is a bi-articular muscle acting on the knee and the ankle. As the knee angle is changed the length of the gastrocnemius changes and therefore the 3

position on its force-length curves is changed. If a muscle is on a different portion of its force-length curve, then the force it can produce will change, in the case of the gastrocnemius altering the moment at the ankle joint. The moment at the ankle joint is predominantly cause by the action of the soleus and gastrocnemius, as the soleus is uni- articular then with knee angle changes its contribution to the ankle joint moment will remain the same. There is evidence in the literature that knee angle changes alter the moment generated by the gastrocnemius (Sale et al., 1982), as evidenced by a change in the ankle plantar-flexion moment. The manipulations of knee and ankle angle in this study will permit examination of this relationship.

4. The fourth aim in this study was to study the inter-subject variability of the pennation angle of the gastrocnemius fibers.

Zajac (1989) has suggested that pennation angles only need to be accounted for with pennation angles of 20° or greater. It is feasible that some subjects have pennation angles greater than this threshold, while others do not. Indeed it is feasible that for some joint configurations the pennation is below this threshold, while for other configurations of the same subject the pennation angle may exceed this threshold. This study will examine these potential phenomena.

5. The fifth aim in this study was to examine how pennation angle changes during isokinetic actions compared with static conditions.

According to the force-velocity properties of muscle, as the speed of muscle shortening increases the muscle force decreases (Hill, 1938). During an isokinetic joint action as the joint angular velocity increases the muscle fibers will shorten at higher velocities and therefore produce less force. If the plantar-flexion muscles produce less force then the Achilles tendon will stretch less. Therefore if static and isokinetic conditions are compared for the same joint angle, and therefore the same overall muscle- tendon lengths, then the fibers will be longer and pennation will be less (pennation angle

varies with muscle length) during isokinetic conditions compared with the static conditions. Dynamometry combined with ultrasound imaging will allow comparison of pennation angle under static and dynamic conditions.

1.4 Study Overview The medial and lateral head of the gastrocnemius muscle were imaged in vivo using ultrasound. The ultrasound images were taken at nine different ankle angles for maximum static plantar-flexion contractions, and for three different ankle angular velocities during the dynamic contractions, both tests were performed with the knee fully extended and the knee flexed at 90°. The ultrasound images were used to measure pennation angle, fascicle length and muscle thickness for nine participants for the static test, and twenty-four participants for the dynamic test. The ankle moments were recorded for all tests with an isokinetic dynamometer. Statistical analyses were used to assess differences in pennation angles in the static test between ankle angles, and between the static and dynamic tests. Correlations were performed to understand the relationships of pennation angle with shank inertial parameters and with peak ankle moment. Coefficients of variation were used to observe pennation angle variations between subjects. A muscle model which included pennation angle in the calculation of tendon force of the gastrocnemius muscle was evaluated based on the experimental data.

1.5 Thesis Structure In this thesis, Chapter 2 contains the review of literature, including muscle mechanical characteristics, definition of muscle architecture, important characteristics of pennation angle, and a description of the function and characteristics of the triceps surae complex. Chapter 3 contains the description of the muscle model. Chapter 4 presents the methods used in this study for collecting data, and includes the description of the subjects participating in the study, description of the equipment used, and the definition of muscle architecture parameters measured. Chapter 5 presents the results of the study. Finally, Chapter 6 is the discussion of the findings of this study, and ends with the study conclusions.

Chapter 2 - Literature Review

2.1 Overview This chapter contains a review of literature about the mechanical properties of muscle, muscle fiber pennation angle, and the triceps surae muscles. Section 2.2 addresses the muscle mechanical characteristics. Section 2.3 presents the characteristics of pennated muscles and muscle fiber pennation. Section 2.4 describes the triceps surae muscles and their function.

2.2 Muscle Mechanical Characteristics In section 2.2.1 the force-length relationship of muscles and muscle fibers are presents along with the characteristic curve of this relationship, section 2.2.2 discusses the force-velocity relationship of muscles and its derivation, and section 2.2.3 discusses the importance of muscle architecture and modeling.

2.2.1 Force-Length Relationship Banus and Zetlin (1938) investigated the force-length relationship of different cat and frog leg muscles in situ. They described the relationship of the changes in total and passive force due to changes in the length of the muscles. The relationship between muscle length and the passive force was exponential. The total force curve for all five muscles showed an initial linear increase in total force with increasing length. At approximately 90% of the maximal physiological length the muscles showed three different patterns of force production, either continuing in a linear fashion, or a plateau, or a concave curve. This study was one of the earliest to attempt to determine the force- length properties of muscles.

Ramsey and Street (1940) examined the force-length relationship of isolated frog muscle fibers. They wanted to determine the lengths at which a muscle can develop force. They defined the resting length of the fibers as the length at which the maximum force was produced, now typically referred to as the optimum length. The passive force: started 6

at lengths slightly greater than the resting length, were due to connective tissue, and increased with increasing length in an exponential fashion. The muscle force produced with increasing length was parabolic in shape with no force produced below lengths of 50% of the resting length, and beyond 200% of the resting length.

Gordon et al. (1966) studied the force-length relationship of sarcomere using isolated fibers from frog muscles. The force-length curve had a characteristic shape (Figure 2.1). Force was developed at sarcomere lengths greater than 1.3 μm, but not beyond 3.65 μm. The peak of the force-length curve had a plateau between sarcomere lengths of 2.05 and 2.20 μm, which was defined as the optimum length. The shape of the force-length curve was explained by the amount of overlap of the thin actin filaments and the thick myosin filaments (Figure 2.1), which determines the number of cross-bridges that are formed. At the optimum length an optimum filament overlap is reached creating a maximum number of force producing cross-bridges and therefore a maximum amount of force is produced (points 2 and 3 in Figure 2.1). At lengths shorter than the optimum length fewer cross-bridges are formed, and above optimum length fewer force producing cross-bridges are formed as there is less overlap between the two sets of filaments.

Gareis et al. (1992) examined the differences in the force-length curves associated with the variety of architecture found in nine different cat muscles. The muscles were electrically stimulated in situ to determine the force-length properties of the muscles. The developed force curves were classified into three categories: symmetric, asymmetric, and a special case for tibialis anterior. All muscles had low-level passive force before reaching their optimum length, after this point the passive force increased in an exponential fashion. For the total force, some muscles presented an increase linear force with elongation, others presented a plateau at the optimum resting length followed by another increase in force due to the passive components, and other muscles presented an initial increase in force followed by small decrease at optimum length and an increase with further elongation until reaching failure point. They attributed these differences to

different functional requirements of the muscles being matched by different architectural features.

Figure 2.1. Force-length curve determined by Gordon et al. (1966) contrasted with the overlapping of the actin and myosin fibers (modified from Gordon et al., 1966).

The force-length relationship of muscles has been extensively studied, from the level of the sarcomere, to muscle fibers, to whole muscles. The active developed force curve can be described as parabolic in shape, which has a peak at a characteristic length - the optimum length. The force-length curve of whole muscle is in part determined by the

force-length properties of the sarcomere but is also influenced by architecture features of the muscle, as will be outlined in subsequent sections.

2.2.2 Force-Velocity Relationship Fenn and Petrilli (1931) reported the force-velocity relationship of limb movement. They analyzed the displacement-time curves of arm swing and leg swing in order to estimate limb velocity and acceleration. For the leg swing experiment the subject was allowed to do a free swing, and a quick release swing. The kinematics of the leg was used to approximate the force-velocity curve. The curve for the leg experiment described a decrease in angular acceleration (proportional to force) with increasing leg velocity, although at the beginning the decrease was less pronounced than at the end of the curve, which they attribute to reflexes. The quick release curves were taken as the maximum force at a given velocity. The difference between the quick release and the free swing force-velocity curves showed that the muscles produce force until they reach their maximum and then they lose force as describe above. It was also found that high initial force had a larger velocity loss than lower initial force.

In his classic 1938 paper, A. V. Hill described the force-velocity relationship of isolated frog sartorii muscles. He measured the heat and force of the muscles while contracting and relaxing against a load. He found that after stimulating the muscles isometrically and then letting them shorten under a load, there was a quick heat production. This increase in heat rate was proportional to the velocity of shortening, where under large loads the heat rate was small (low velocity), while under small loads the velocity and heat rate were greater. Considering these facts he described the rate of extra energy liberation as (P + a) v which has a negative linear relationship with the load. With this relationship he presented the “characteristic equation” for the velocity of shortening: (P + a) (v + b) = constant, where P is the load, v is speed of shortening, a is a constant describing the shortening heat per length of shortening, and b is a constant describing the increase of energy liberation rate. The constants a and b were found by fitting the curve of load-velocity (Figure 2.2). The previously held idea that muscle

“viscosity” was the factor giving the force loss with shortening velocity was dismissed given that this hypothesis cannot explain the heat and energy liberation during shortening. Subsequently Hill rejected the idea that the coefficients a and b were related to energy liberation (Hill, 1964).

Spector et al. (1980) studied the characteristics of the cat soleus and medial gastrocnemius muscles. The maximal isometric force, maximal velocity of shortening and the force-velocity properties for each whole muscle were determined in situ. The muscle architectural characteristics (muscle length and pennation angle) were measured. They found that the absolute tension produce by both muscles was different, but by normalizing with respect to the physiological cross-sectional area of each muscle, the specific tension was not different. They found that the shortening velocity was greater for the medial gastrocnemius compared with the soleus when they considered the difference in pennation angle between the two muscles. The force-velocity relationship of both

muscles is different and the dissimilarities varied depending on the velocity definition used (the average fiber length, sarcomere length and correcting for the pennation angle, and as muscle length per second) (Figure 2.3). They proposed that during walking and running the medial gastrocnemius can keep producing force at higher velocities than the soleus, and that these differences are due to the differing force-velocity properties and architecture of each muscle.

Figure 2.3. Different velocity-force relationships of the cat medial gastrocnemius (MG) and soleus (SOL) depending on the velocity definition A) is velocity per average fiber length, B) is sarcomere length and pennation angle, and C) is muscle length. P(0) is the maximal isometric force and L(0) is the optimum length (taken from Spector et al., 1980).

Ichinose et al. (2000) described the force-velocity relationship of the human vastus lateralis muscle fibers (fascicles) during knee extension at different isokinetic velocities. The maximum isometric moment was measured at different knee angles, and the isokinetic moment was measured at two different joint angular velocities. The fascicle length and pennation angle were measured in ultrasound images. Tendon force (Ft) was computed from:

The fascicle force (Ff) was computed from:

s s

s θ

where PCSA is physiological cross-sectional area, and θ is the pennation angle. It is important to underline that for the Ff they assumed that the force contribution of the vastus lateralis is proportional to its contribution to the total quadriceps PCSA. Fascicle shortening rate and fascicle force were different at different angular velocities, and the peak fascicle velocity was reached at different knee angles with the different angular velocities, due to variations in tendon stretch, although it was reached at the same optimum fascicle length. Fascicle force-fascicle velocity curves were different with changing joint angular velocity, at higher angular velocities fascicle velocity was also higher but produced less force compared with slower angular velocities.

The force-velocity relationship has been described under different conditions. It is clear that there is a decrease in force associated with an increase in shortening velocity. Depending on the architectural properties the muscles will have a different curvature of their force-velocity curve, with different active ranges.

2.2.3 Muscle Architecture Muscle architecture comprises the muscle design or muscle arrangement at a macroscopic level which include the muscle fiber organization, muscle volume, muscle length, muscle and fiber physiological cross-sectional area, the muscle thickness, and the form of the tendinous sheets. The purpose of this section is to review the importance of muscle architecture in muscle function.

In their review Lieber and Fridén (2000) presented the muscle architecture- function relationship of skeletal muscles. The general definition of muscle architecture given by Lieber (1992) is “the arrangement of muscle fibers within a muscle relative to the axis of force generation”. Fibers can be oriented parallel to the pulling axis (parallel muscles), at an angle relative to the pulling axis (uni-pennated muscles), or at several angles relative to the pulling axis (multipennated muscles). They identified the important architectural parameters as muscle length (distance from the origin of the most proximal fibers to the insertion of the most distal ones), fiber length (usually fiber bundle or fascicle length), pennation angle (usually the average of the angle formed between the superficial fibers and the pulling axis), and physiological cross-sectional area. The physiological cross-sectional area (PCSA) can be calculated from the other parameters and is proportional to the maximum force generated by the muscle:

s ss s θ

where is the muscle density. The force applied to the external tendon in pennated muscles diminishes by a factor of s θ compared with muscles with parallel fibers. However, muscle architecture only has effects on the extrinsic muscle properties and does not affect the shape of the force-velocity and force-length curves of the individual fibers. Muscle architecture in many cases can determine the specialization of muscle groups.

Infantolino et al. (2012) investigated the arrangement of fascicles in the first dorsal interosseous muscle of human cadavers using high resolution magnetic resonance imaging. They demonstrated that fascicle arrangement is complex, and that there is no uniformity in their length within a muscle. Fascicle lengths were shorter than muscle length implying that there should be overlap of some fascicles, with some of the fibers having in series arrangement. Given the differences between fascicles comprising a muscle they should have different properties, and the analysis of only one fascicle may not be appropriate to infer the properties of the whole muscles or the other fascicles.

Otten (1988) reviewed models of muscle pennation. With models of muscle architecture it is possible to estimate muscle characteristics that are difficult to measure in vivo, and they can give functional explanations of the form and design of muscles. In these models muscle volume is kept constant, which has been proven to be true (Matsubara and Elliott, 1972). Knowing that muscle volume remains constant during contraction, it has been presented that the force that a pennated muscle can produce is dependent of the fibers pennation angle, muscle length, and muscle width. Although, muscle force and the ratio of displacement of the tendon to the fiber shortening distance are highly dependent on fiber pennation angle, the muscle work is independent of fiber pennation angle. However, muscle work has to be equal to total fiber work, and under these conditions, in a simple unipennated muscle, the muscle shortens while its thickness remains the same. Fiber curvature is also possible while the muscle is contracting. This can happen in pennated muscles with two tendinous sheets. When the tendinous sheets can stretch, muscle curvature is needed in order to keep a constant volume and maintain work. Muscle curvature can change the muscle properties, and it is an important parameter to consider when modeling pennated muscles. He concludes that although using models that simulate the muscle behaviors are good (for example using springs and dampers), they do not allow explaining the function of muscle architecture. While with models that include muscle architecture and their mechanical properties it is possible to gain understanding of the functional properties of muscles relative to their architecture.

Muscle architecture influences the function of the muscles. The most important architectural parameters are muscle fiber or fascicle length and pennation angle. With these parameters many characteristics of muscle can be determined. However, muscle architecture is complex and it is important to consider each muscle individually when analyzing muscle function.

2.3 Muscle Pennation Section 2.3.1 discusses the pennation angle variation between different muscles, section 2.3.2 discusses the pennation angle variation within the same muscles, section 2.3.3 discusses how pennation angle varies with movement in a muscle, section 2.3.4 discusses the effects of different training regimens on changes in pennation angle within the muscles, and section 2.3.5 presents the influence of age on pennation angle of the muscles.

2.3.1 Variation between Muscles Wickiewicz et al. (1983) measured fiber length, sarcomere length and pennation angle of 27 knee and ankle muscles from three human cadavers. Fiber length and pennation angle presented uniformity within a muscle for the majority of muscles analyzed, meaning that along the muscle the fibers act in the same manner. However, the soleus, the vastus medialis obliquus part and the vastus lateralis obliquus part were an exception presenting portions within the muscle with differences in pennation angle. The different muscles studied presented marked differences in fiber orientation and angles, however there was no notable differences between the three legs. They did not discuss this but from their Table 1 it is possible to see that muscles in synergistic groups share similar pennation angle and they tend to be different compared with the antagonistic group (Table 2.1). The limitations of their study include that they worked with cadavers for whom the characteristics were not presented, and that the sample size was small.

Yamaguchi et al. (1990) presented a compilation of muscle parameters of the human muscle-tendon complexes. The majority of the reported measures were made on cadavers. For the leg muscles, pennation angles could be identified (Table 2.2). For the hip muscles some measurements were not consistent, for example for the gluteus minimus some studies measured a pennation angle of 10 º, while others gave a pennation angle of 21 º. The knee and ankle muscles (gastrocnemius medialis, gastrocnemius lateralis, and plantaris) also had some inconsistency between measurements. The limitation of this data-base, and probably one cause of the inconsistencies, is that some measurements were made on cadavers with different characteristics indicating the potential for high inter-subject variability.

Kawakami et al. (2006) investigated the relationship between pennation angle and physiological cross-sectional area (presented as muscle thickness) in vivo for the human triceps brachii, vastus lateralis, and gastrocnemius medialis muscles, all of which have different functional roles. The pennation angles were measured in ultrasound images as

the angle between the fascicles and the deep aponeurosis of each muscle. There were statistically significant differences in pennation angle and muscle thickness between the muscles, as well as between female and male muscles. They also found a positive relationship between pennation angle and muscle thickness.

Table 2.2. Pennation angle for the leg muscles by joint group. Some muscles in a group presented different values and are indicated (modified from Appendix A-1 in Yamaguchi et al., 1990). Muscle group Exceptions to group value Pennation angle (°) Hip muscles 0-15 gluteus minimus 5-21 obturator internus 0-25 Hip and knee muscles 0-10 semimembranosus 15-20 Knee muscles 0-10 biceps femoris short head 15-25 Knee and ankle muscles 5-25 Ankle muscles 5-16 flexor hallucis longus 10-20 tibialis posterior 14-26 soleus 20-30

Studies have shown that there is a wide variation in pennation angle between muscles. These differences are more noticeable between antagonistic groups, but even between muscles with the same function there are differences. Some muscles tend to have small pennation angles while other have large pennation angles. It seems also that bigger muscles (thicker) have greater pennation angles.

2.3.2 Variation within Muscles Narici et al. (1996) described the changes in muscle architecture during isometric contractions of varying intensity. They imaged the human gastrocnemius medialis muscle and measured pennation angle, fiber length, and muscle thickness in vivo along the longitudinal axis of the muscle, and medially and laterally from this point at rest to a 17

maximum contracted state. During the isometric contractions, pennation angle linearly increased with force fraction from rest to maximum isometric force, and there were no significant differences of pennation angle between probe positions during contraction. Pennation angle at rest and at maximum isometric force were not statistically significantly different between probe positions on the belly of the muscle. This suggests homogeneity of the entire gastrocnemius medialis muscle in terms of the pennation angle changes with increasing muscular force.

Maganaris et al. (1998) performed a similar experiment but they measured architectural changes in vivo of all the human triceps surae complex (gastrocnemius lateral and medial heads, and soleus). The architectural changes were measured for isometric contractions at different ankle angle positions, and for different force levels at a neutral ankle position. Ultrasound scanning was done on the lateral, mid-sagittal, and medial sections for the proximal, central, and distal parts of the muscles belly. There were no statistically significant differences in pennation angle, fiber length, and muscle thickness, between the scanned regions for the three muscles. During graded isometric contractions at neutral position, pennation angle increased and fiber length decreased as a function of force for all three muscles. Pennation angle for the medial gastrocnemius increased from 22.3 ± 2.0° to 42.5 ± 2.2°, and had larger pennation angle than the lateral gastrocnemius. In the lateral gastrocnemius pennation angle increased from 11.3 ± 1.2° to 38 ± 2.4° and had the greatest percent of change (245%), and in the soleus there was an increase from 25 ± 2.6° to 40 ± 3.3°. They concluded that the architecture of the triceps surae complex is homogeneous within each muscle, and that there are also changes in architecture with force level in all three muscles.

Azizi et al. (2008) measured the effects that muscle shape changes while contracting under different loads have on the architectural gear ratio (muscle fiber velocity to whole muscle velocity) in a pennated muscle. They did in situ velocity measurements of the lateral gastrocnemius of the wild turkey. During contraction the shortening velocity of the muscle-tendon unit was higher than the velocity of the muscle 18

fiber. Muscle thickness changed in magnitude and direction depending on the force produced, where at low-force the muscle thickness increased and at high-force it decreased, these thickness changes go along with muscle width changes so that muscle volume is kept constant (Azizi et al., 2002), where a decrease in muscle thickness gives an increase of muscle width. Pennation angle increased during contraction, but the magnitude depended on the muscle thickness, with more rotation at low-force contractions, and rotation decreasing with increasing contracting force (Figure 2.4). At low-force the muscle velocity is amplified, while at high-force muscle fascicle and whole muscle velocity are similar. They concluded that pennated muscles have this variable gearing which might be a mechanism to improve muscle performance over different demands adjusting for the need of speed or force, similar to the gears on a bicycle.

Figure 2.4. Where w is muscle width, t is muscle thickness, and the arrow indicates the amount of muscle shortening. A) muscle at rest, B) is a low-force contraction, where fiber rotation is large, muscle thickness increases and gear ratio is large, allowing for velocity, and C) is a high- force contraction, where fiber rotation is small, muscle thickness decreases, and gear ratio is close to 1, allowing for force production (taken from Aziz et al., 2008).

Pennation angle within muscles remains moderately homogenous along the muscle belly. However, there are significant pennation angle changes occurring as the muscle contracts. Pennation angles change also as a function of the force produced, and the magnitude of the change depends on the magnitude of the force applied, which is useful for regulating between force production and velocity.

2.3.3 Variation during Movement In their work, Maganaris et al. (1998) compared the architectural changes of the triceps surae muscles during isometric contraction at different ankle angles, with those predicted by a planimetric muscle model (Figure 2.5) extensively used for the determination of pennated muscle parameters. At rest and during maximum isometric force at different ankle angles, pennation angle and fiber length were ankle angle dependent in the three muscles, where with plantar-flexion pennation angle increased and fiber length decreased. However, at rest pennation angle was smaller and fiber length was larger than in the contracted state, and muscle thickness remained constant for all ankle angles. Nevertheless, muscle thickness was constant for the medial gastrocnemius between rest and contraction, but the thickness increased for the lateral gastrocnemius and soleus from rest to maximum voluntary contraction. There were significant differences between the model and the measured architecture parameters, and this casts doubt on the applicability of the planimetric models to describe muscle architecture dynamics.

Figure 2.5. Planimetric muscle model assuming constant muscle thickness t and linear fiber length Lf. ABCE is the muscle at rest, ABDF is the contracted muscle, a and b are the pennation angles (taken from Maganaris et al., 1998). 20

Reeves and Narici (2003) studied the behavior of the human tibialis anterior muscle architecture in vivo during maximal isometric dorsi-flexion at different ankle angles, and during muscle shortening and lengthening at different isokinetic velocities. Similar to Maganaris et al. (1998), they found that fascicles shortened and pennation angle increased with changes in ankle joint angle (dorsi-flexion). They also found that during concentric muscle actions at high angular velocities the fiber length was longer compared with their length during isometric contractions, therefore pennation angles were smaller compared with the pennation angle of the same muscle at the same joint angle during an isometric muscle action. In contrast during eccentric muscle actions, the fibers behaved “quasi-isometrically”. During shortening at increasing angular velocities the muscle produced less force than under maximal isometric conditions due to its force- velocity properties, meaning that the fibers shorten less because the reduced force cause tendon stretch, reducing the pennation angle. This reduction is advantageous for the muscle since it reduces the reduction of force that is transmitted to the tendon.

Lichtwark et al. (2007) considered the changes of human medial gastrocnemius muscle architecture in vivo during walking and running. They matched the walking and running cycles with the changes in fascicle length and pennation angle at three different sites on the muscle belly (proximal, midbelly, distal). There were no statistically significant differences between the three sites for fascicle length and pennation angle, however measurements were closer to each other when running compared with walking. There were statistically significant differences between walking and running for both fascicle length and pennation angle. It seems that during the loading phase of walking the muscle fibers behave almost isometrically (minimal changes in fascicle length and pennation angle), while there is a significant decrease in fascicle length and an increment in pennation angle during running. They claim that this difference means that while running the fibers are producing positive work, but they still work at an optimal shortening speed, so the series elastic element plays a greater role in the muscle-tendon

complex shortening than do the fibers, allowing them to produce higher forces as they act isometrically rather than concentrically.

In summary, pennation angle changes with movement of the joints and the corresponding changes in muscle length. In leg muscles pennation angle increases as joint angle changes towards the line of pull of the muscle during isometric contractions, however when comparing between different movements, there are differences in pennation angle changes depending on the load on the muscle. Also, the behavior of muscle fibers during isokinetic movements is significantly different for concentric versus eccentric contractions, where muscle fibers seem to adapt to faster shortening, reducing pennation angle and increasing fiber length with increasing angular velocity, in contrary when lengthening the muscle fibers seem to not undergo significant changes in pennation angle and fiber length. This happens because during lengthening of a muscle the forces are greater and the tendon has to stretch more, which gives small muscle and fiber length changes compared with a concentric contraction where the muscles have significant length changes.

2.3.4 The influence of Training Aagaard et al. (2001) described the architectural and morphological changes of the human vastus lateralis after 14 weeks of strength training. Anatomical cross-sectional area, volume, fiber cross-sectional area, and pennation angle increased after heavy- resistance strength training, and the maximal muscle strength also increased. They attributed the increase of muscle fiber cross-sectional area to the pennation angle increase, allowing it to be greater than the anatomical cross-sectional area increase. Pennation angle and muscle fiber cross-sectional area changes would be responsible for the increase in muscle strength. It is also evident from this study that muscle architecture has plasticity and it becomes important to consider this when examining the changes in muscle strength due to strength training.

In contrast, Blazevich et al. (2007) investigated the effects of eccentric and concentric resistance training on muscle architecture of the human vastus lateralis muscle. The effects of concentric and eccentric training were evaluated independently. The changes were followed during a 10 week training period, and after 3 months of detraining. Peak moment, quadriceps volume, physiological cross-sectional area and muscle thickness increased with both types of training. Muscle length increased after 5 weeks of training, however, both types of training induced fascicle lengthening, suggesting that fascicle length changes depend on factors different from contraction mode and velocity. Pennation angle increased during the whole training period and presented a positive relationship with muscle size, suggesting that pennation angle adapts to muscle hypertrophy and might be a response to the space constraints in the muscles. Also, pennation angle adaptations were retained after the period of detraining. They proposed that changes in pennation angle are responsible for the increase in strength given that more contractile elements can attach to the aponeurosis and also because this promotes an increase in the architectural gear ratio allowing the fibers to work closer to their optimum length.

Reeves et al. (2009) studied the adaptations of the vastus lateralis muscle architecture to eccentric only and conventional training (eccentric and concentric contractions). Peak moments were analyzed for isometric contractions and different isokinetic speeds. Fascicle length, pennation angle and muscle thickness were measured in vivo. There were statistically significant differences in the architectural adaptations between the eccentric and the conventional training groups. There was a larger increase in fascicle length with eccentric training than with conventional training, but there was no statistically significant pennation angle increase with the eccentric training compared with the statistically significant increase in the conventional training group. In general architectural adaptations were greater for the eccentric training group. Each group increased the peak moment for the direction of the contraction they were trained for, but not for the other type of contraction, and isometric strength increased in both groups in a similar way. They concluded that it is surprising that during eccentric training pennation 23

angle did not increase significantly since this training presents a higher mechanical stress state for the muscles. This suggests that the adaptations for adding sarcomeres in-series and in-parallel might be different. Muscle load being important for fascicle length but not for pennation angle. There might be other mechanisms allowing the muscles to gain strength.

Muscle architecture is plastic and there are notable adaptations happening within the muscles due to periods of strength training. Studies show that with concentric strength training pennation angle increases, and is related to muscle shape changes. An increase in pennation angle is partially responsible for strength increases after a period of training, and there is not a direct relationship between pennation angle changes and fiber length changes with strength training.

2.3.5 The influence of Aging The changes in pennation angle with age were studied by Binzoni et al. (2001). The medial gastrocnemius architecture was analyzed in people of 0-70 year of age. There was a continuous increase of pennation angle with age from 0 to adolescence, followed by a stable value from that age on. However, they were unable to fit a trend to their data. There was a strong linear relationship of pennation angle with muscles thickness, and of muscle thickness with tibia length, which implies that pennation angle might increase with age following the same trend as bone growth, likely explaining why after the growth spurt pennation angle remains at a stable value. The limitation of this study is that they did not consider level of activity of the participants which might explain some of the spread of the data.

The upper age limit of the relationship described above was investigated by Narici et al. (2003). The medial gastrocnemius of active elderly participants of age 70-81 years was studied in vivo for: muscle anatomical cross-sectional area, volume, fiber length and pennation angle, and were compared with a younger population (27-42 years). All measured parameters were smaller in the elderly, indicating that there is a change in 24

muscle architecture with age (Figure 2.6), representing a loss of sarcomeres in-series and in-parallel. With reduce pennation angle there is less contractile tissue along the aponeurosis and this goes along with a reduced physiological cross-sectional area.

Figure 2.6. Muscle architecture difference between elderly (A) and young (B) men. Where t is muscle thickness, Lf is fiber length and θ is pennation angle (figure modified from Figure 2 in Narici et al., 2003).

In contrast to the findings of Binzoni et al. (2001), Bénard et al. (2011) did not find any statistically significant difference between the pennation angles in the medial gastrocnemius of children between the ages of 5 to 12 years. They used a novel 3-D ultrasound reconstruction of the muscle and found that the children did not present pennation angle differences. However, other parameters increased with age (muscle- tendon complex length, physiological cross-sectional area, aponeurosis length, and fascicle length), suggesting that between the ages of 5 to 12 the fascicle length and aponeurosis length explain the increases of muscle length.

There is evidence that pennation angle changes with age. Some studies show that pennation angle increases with age until the growth spurt, however there seems to be some inconsistencies between studies, and perhaps at certain ages there is not a significant change in pennation angle. However, there are only a few studies examining

pennation angle in children and more research should be done on this area. In contrast, for elderly it was found that there is a decrease in pennation angle along with a reduction of other muscle parameters, which indicates that there is a reduction of the amount of muscle tissue with age, and this is one of the reasons for the loss of force in the elderly.

2.4 Triceps surae Characteristics Section 2.4.1 presents the anatomy of the triceps surae muscles, section 2.4.2 discusses the architecture and differences between the triceps surae muscles, and section 2.4.3 discusses the different functional roles of the triceps surae muscles.

2.4.1 Anatomy The triceps surae (triceps = three, and surae = calf) complex is composed of the gastrocnemius, soleus, and plantaris muscles (Cael, 2010). The gastrocnemius is the most superficial muscle in the triceps surae complex. It is divided into a medial head and a lateral head, and it is the most prominent at the back of the lower leg (Figure 2.7A). The medial head is the larger of the two and has an origin on the posterior medial part of the femoral condyle, and the lateral head has an origin on the posterior part of the lateral femoral condyle. Both heads attach to a tendinous expansion (aponeurosis) which surrounds their anterior and posterior surfaces. The soleus is located deep to the gastrocnemius and is broader. It has an origin on the posterior surface of the tibia and the posterior proximal head of the fibula. Some of its fibers have an origin on the deep surface of the aponeurosis which are bipennated and insert on an intramuscular tendon. The soleus is usually divided in superficial and deep about its aponeurosis (Figure 2.7B). The plantaris is deep to the lateral head of the gastrocnemius and is the smallest of the three muscles; it has a longer tendon than its muscle belly. It has an origin on the distal part of the lateral line of the femur. The gastrocnemius and the soleus converge onto the Achilles tendon which has an insertion on the posterior surface of the calcaneus, while the plantaris has been found to have an insertion on the Achilles tendon or on the soleus tendon for some individuals (Buarque de Gusmão et al., 2011). The three muscles perform plantar-flexion of the ankle, with major contribution of the gastrocnemius and 26

soleus. The gastrocnemius also assists in flexing the knee, being a bi-articular muscle. Usually, given that the plantaris is small and the gastrocnemius is divided in two heads, the triceps surae is often referred to as only the gastrocnemius and soleus (Cael, 2010; Gray, Williams and Warwick, 1980). The Achilles tendon is one of the largest tendons in the body and its superficial location makes it easy for examination. Under ultrasound imaging it can be seen as a bright organized fibrillar structure, which makes easy to identify any tendon pathology. A normal Achilles tendon is measured to have a thickness (in the anterior-posterior plane) no larger than 6 mm, if greater the patient probably suffers of Achilles tendinosis (Reach and Nunley, 2009).

Figure 2.7. A) Gastrocnemius, and B) soleus (modified from Figures 1 and 2 of Chow et al., 2000). 27

2.4.2 Architecture Huijing (1985) characterized the architecture of both heads of the gastrocnemius muscle on human cadavers. Both heads had a high degree of pennation, but there were differences between them. The lateral head had fibers with more sarcomeres (greater fiber length) than the medial head, but the medial head fibers had larger aponeuroses, the fibers were more pennated, and the muscle had a larger volume, which gave a larger physiological cross-sectional area (Table 2.3). The medial head had a smaller muscle length range, but both heads had a greater muscle length range than their fibers, which was expected for highly pennated muscles. The large physiological cross-sectional area of both heads allows the muscle to generate high force, while the pennation angle allows it to exert this force over a small length range.

Table 2.3. Architectural characteristics of the gastrocnemius human muscle (medial head GM, and lateral head GL) (taken from Huijing, 1985).

Kawakami et al. (1998) characterized the triceps surae architecture of humans in vivo at different ankle and knee angles (Table 2.4). Changes in fiber length with movement were different for the three muscles. The muscles had longer fibers when the ankle was flexed and the knee was extended and shorter fibers when the ankle was extended and the knee flexed. The lateral head of the gastrocnemius had the largest fibers, followed by the medial head and the soleus. The larger fibers in the lateral head 28

might indicate that it is built for velocity. The medial head was highly pennated and together with short fibers its architecture suggests that it might have a greater force potential than the lateral head. The fibers in the medial head showed the greatest changes in pennation angle. The level of activation (passive and maximal isometric contraction) produced differences in the architecture of the muscles. With plantar-flexion the changes in fascicle length of the medial and lateral gastrocnemius were smaller; this might be an adaptation to the increasing pennation angle, which allows more tendon excursion with less fiber shortening, and a decrease in tendon length change due to decreased force. They propose that the great variation in muscle architecture between the muscles reflect their different roles in movement, and that the different changes in the architecture parameters between the muscles at different angles reflect the different capacities for the muscles to produce force.

There is also variation in muscle architecture between genders as identified by Chow et al. (2000). They used ultrasonography to measure the muscle architecture of the medial and lateral head of the gastrocnemius, and the anterior and posterior parts of the soleus at a neutral ankle position. They positioned the ultrasound probe at 10 different sites to be able to have clear ultrasound images of the gastrocnemius and soleus muscle architecture. Females presented longer fibers while males had greater pennation angles and muscle thickness for all the parts of the muscles. Pennation angle was the most different architectural parameter between males and females. They suggested that the differences in architecture could be related to differences in function between females and males, for example greater endurance in females, compared with greater force production capacity for males, however more studies are needed to corroborate this conclusion.

Triceps surae architecture varies between the muscles comprising this group. These differences allow the muscles to have different force-length properties and force- velocity properties, which allow them to have different functions. In general the triceps surae muscles are highly pennated, present short fibers and have large physiological 29

cross-sectional areas, which are built for force production, agreeing with their role in plantar-flexion. There are also marked gender differences in muscle architecture, which implies that female and male muscles are adapted to function in different ways.

Table 2.4. Architectural characteristics of the triceps surae (gastrocnemius medial head MG, gastrocnemius lateral head LG, and soleus Sol) (taken from Kawakami et al., 1998).

2.4.3 Function Sale et al. (1982) demonstrated in vivo that the force that the triceps surae can produce is affected by the joint angle. They had subjects perform plantar-flexion and dorsi-flexion while either electrically stimulating the muscles or asking subjects to produce maximum voluntary contractions with the knee flexed and completely extended, while measuring ankle joint moment and electromyographic activity. The plantar-flexion moment was greater when the muscle was stretched (ankle at a dorsi-flexion angle), and the optimum lengths of the muscles were found to be at a dorsiflexed position. As the gastrocnemius is a bi-articular muscle, flexing the knee produced a greater decrease in moment while plantar-flexing compared with the decrease observed when the knee was extended. These observations were similar between electrically stimulated and voluntary contractions. When the triceps surae were stimulated it was possible to determine that they account for approximately 70% of the total plantar-flexor moment, making them the main responsible for the plantar-flexion of the ankle.

In the study of Huijing (1985) a difference in the architecture of the heads of the gastrocnemius was evident (sub-section 2.4.2). With the geometry of the muscle heads, the force-length relationship was described as well as the relationship for the whole muscle. He found that the relative force that each head of the muscle produced was dependent of the muscle length, for example the contribution of the lateral head to the isometric force was 30% at optimum muscle length, but it was 100% at longer lengths. However, both heads presented similar physiological length ranges. Their large physiological cross-sectional area allowed them to generate high forces and, as mentioned before, their architecture allow the muscle to generate high forces under a small length range, which is suitable for this bi-articular muscle that moves the ankle and the knee, since this characteristic allows the muscle to transport power between the two joints without having a great shortening.

Out et al. (1996) studied the effects of triceps surae muscle model parameters on the ankle moment-ankle joint relationship. They performed a sensitivity analysis of the moment-ankle joint relationship for variations in several of their muscle model parameters. The model presented a decline in moment with increasing plantar-flexion angle, and presented the different effects on this relationship with changes in knee position. Also, the model had a high sensitivity for the following parameters: the length of the series elastic element under zero force (lslack), the mean moment arm for the ankle angles between 0 and 2.5 radians, the maximum force of the muscles (Fmax,TOT), and the optimum length of the contractile element (lce,opt). For lslack and Fmax,TOT the values were found by optimization, which did not allow a clear conclusion about the effect of these parameters on the moment-ankle angle relationship of the muscles, however changes in lslack shifted the curve along the angle axis since this parameter has a strong influence on the optimum ankle angle (ankle angle at which maximum moment is reached). The lce,opt parameter had the largest effect, where changes in this parameter were reflected in great shape changes of the moment-ankle angle curves producing shifting of the optimum ankle angle, especially for shorter lce,opt. They demonstrated that muscle models can fit the real experimental data of the triceps surae, and which muscle model parameters had the greatest influence on the muscle model function.

Gallucci and Challis (2002) demonstrated the effects of changing the ankle angle on the function of the gastrocnemius muscle for knee flexion while performing isokinetic leg curls. Since the gastrocnemius is a bi-articular muscle, its length is affected by both changes of the ankle joint and the knee joint. The knee moment was larger when the ankle was dorsiflexed. Changing the length of the muscle changed the point on the force- length curve where the muscle was acting, thus the force production capacity for knee flexion changed with muscle length. When the muscle was longer (dorsiflexed) the moment produced was greater.

The triceps surae muscles plantar-flex the ankle, however it has been demonstrated that changes in the joint angle also affect the function of the muscles. The 32

optimum length of the muscles and the maximum moment at the ankle joint have been found to typically be at a dorsiflexed position, and the force that these muscles can produce diminishes with plantar-flexion. Not only the ankle angle affects their function, changing the knee angle also has an effect on the bi-articular gastrocnemius, where with knee flexion the muscle typically loses force production potential which is reflected by a decrease in moment at the ankle, the same is seen if the ankle angle is changed along with changes in knee angle. Triceps surae muscle function can also be modeled, these models give accurate predictions of muscle function in vivo if the muscle data used for the model parameters are based on real architectural measurements.

2.5 Summary Muscle architecture is a determinant of muscle function and has an effect on the mechanical characteristics of the muscles. The most important muscle architectural parameters are fiber length and pennation angle. Pennation angle changes during movement, and as a consequence of concentric strength training and age, and is significantly different between muscles, however fiber pennation typically remains homogeneous within a muscle. For the muscles in the triceps surae complex (gastrocnemius and soleus) there are important architectural differences not only between the gastrocnemius and the soleus, but also between the two heads of the gastrocnemius, which are proposed to be related to different functions. Also the length of the tendon under zero force has been identified as an important parameter determining the muscle function. However, there is not a clear understanding of the function of pennation angle changes, and more research needs to be done to understand how these differences are related to the muscle function.

Chapter 3 - Muscle Model

3.1 Overview In this chapter a model of the triceps surae, its elements, and parameters are described. In section 3.2 the structure of the muscle model is described and its elements defined. In section 3.3 the contractile element is described along with its characteristics. In section 3.4 the series elastic element is described. In section 3.5 the relationship between the changes in muscle length with ankle and knee angles are described, and used to define the muscle moment arm about the ankle joint. In section 3.6 fiber pennation angle calculations are described. In section 3.7 the parameters used for the model are given. In section 3.8 the simulation process of the muscle model is presented. Finally, section 3.9 is a summary of this chapter.

3.2 Model Structure This model was used to calculate the isometric ankle moment-ankle angle plantar- flexion relationship. Each modeled muscle was divided into two elements (Figure 3.1). A contractile element (CE) which represented the contractile behavior of the muscle fibers, and a series elastic element (SEE) which represented the elastic behavior of the tendon. The elastic behavior of the cross-bridges was not considered, since the energy stored in the cross-bridges is small compared with the energy stored in the tendon, and its effect was therefore neglected (Flitney and Hirst, 1978). The lengths of the CE and the SEE together made up the length of the muscle-tendon complex (LMTC).

Figure 3.1. Schematic representation of the muscle model, where CE is the contractile element, θ is the pennation angle of the muscle fibers, and SEE is the series elastic element. 34

The force that the muscle fibers produce ( ) was defined by,

Where q is the current active state of the muscle which can vary between zero and one (maximal active state), is the maximal isometric force that the muscle can produce, is the fraction of the maximal force that the fiber can produce at its current length , and is the fraction of the maximal force that the fiber can produce at its current velocity . For the analysis undertaken here the active state was assumed to be maximal (q = 1), and only isometric cases were examined so , therefore the equation was simplified to,

The force applied to the tendon ( ) is a function of the pennation angle ( ) of the muscle,

The resulting moment ( ) at the joint caused by the muscle is,

Where is the moment arm of the muscle at the joint for a given joint angle ( ).

3.3 Contractile Element The CE represented the muscle fiber contractile properties. The force produced by muscle fibers varies with their length due to the number of cross-bridges formed between the actin and myosin filaments of the muscle fibers. The maximal force a muscle fiber 35

can produce occurs when there is an optimum overlap of the actin and myosin and the maximum number of cross-bridges can be formed, and the length at which this happens is called the fiber optimum length ( ). The fiber muscle force-length relationship is showed in Figure 3.2.

Figure 3.2. Isometric muscle fiber force-length relationship. Force is represented as a function of fiber length, peak force is found at optimum length ( ).

Finally, is the fraction of maximum isometric force the muscle fiber can produce at a given length which is defined by,

Where w is the width of the force-length curve at either side of the optimum length.

3.4 Series Elastic Element The SEE represents the elastic properties of the tendon. The tendon elastic characteristics depend on the tendon strain (amount of tendon stretch relative to its 36

resting length) and tendon stress (tendon force to tendon cross-sectional area) (Figure 3.3). To model the change in tendon length with muscle force, the current tendon length was defined by,

Where is the current length of the tendon, is the resting (slack) length of the tendon, and c is the strain in tendon under maximum isometric force.

3.5 Muscle-Tendon Complex Length and Moment Arm The length of the muscle-tendon complex was derived from the equation based on cadaver data presented by Grieve et al. (1978). The definition of the angles is shown in Figure 3.4. The format of the equation is as follows,

Where A0, A1ANKLE, A2ANKLE, A1KNEE, and A2KNEE are constants. φANKLE and φKNEE are the ankle and knee angles, and φM.ANKLE and φM.KNEE are constants. Examples of the variation in muscle-tendon length for the gastrocnemius are shown in Figure 3.5.

Figure 3.4. Joint angle definitions by Grieve et al. (1978).

To find the moment arm at a given ankle angle ( ) (Figure 3.6), the first derivative of the LMTC respect to ankle angle was taken so moment arm was defined by,

Figure 3.5. Muscle-tendon complex length-ankle angle relationship for the gastrocnemius muscle.

Figure 3.6. Moment arm-ankle angle relationship for the gastrocnemius muscle.

3.6 Muscle Pennation Pennation angle was modeled in the muscle-tendon complex as a muscle fiber attached at an angle to its tendon (Figure 3.7).

For a parallel fibered muscle ( ) the length of the fibers is,

For a pennated muscle the fiber length can be computed, but it is based around the assumption that the volume of the muscle remains constant as it lengthens or shortens (Matsubara and Elliott, 1972). For the planar model used here for the volume to remain constant muscle thickness (T) must be assumed to remain constant. Therefore,

and then,

Where LMB is the muscle belly length. Pennation angle is then computed from,

3.7 Model Parameters The parameter used in this model have been described in the previous sections, here they are summarized. Values have been taken from Out et al. (1996) and the experimental data in this study. To follow Out et al. (1996) here the parameters are divided into muscle specific parameters (Table 3.1) and model general parameters (Table 3.2).

Here is found by the multiplication of sarcomere optimum length (2.69 μm) by sarcomere number.

Table 3.1. Muscle specific model parameters. Parameter Medial Head Lateral Head Soleus A0 (m) 0.437 0.438 0.286

(m) 0.044 0.059 0.043

(m) 0.377 0.387 0.246

PCSAREL 2/9 1/9 6/9

(N) 948 474 2843

Table 3.2. Model general parameters. Parameters

A1ANKLE (m) -0.046

A2ANKLE (m) -0.008

A1KNEE (m) 0.016

A2KNEE (m) 0.001

c (dimensionless) 0.04

w (dimensionless) 0.56

φM.ANKLE (rad.) 1.66

φM.KNEE (rad.) 2.36

3.8 Simulations The gastrocnemius heads were modeled independently. Two knee angles were used (0° - extended, and 90° - flexed), and ankle angles were used from 20° to -30° (from dorsi-flexion to plantar-flexion). Under isometric conditions the muscle forces were determined using the following procedure. From the ankle and knee joint angles the length of the muscle-tendon complex was computed. Initially muscle belly length was computed assuming the tendon was at its slack length, and from muscle belly length and muscle thickness muscle fiber length was computed. Given this muscle fiber length and using the force-length properties of the muscle the muscle force was estimated. Given this level of muscle force the amount of tendon stretch was computed and muscle fiber length recomputed. The muscle fiber force was computed for this revised fiber length, and once again the tendon length computed. This procedure was repeated iteratively until no changes in fiber or tendon lengths were recorded. Then, pennation angle was calculated from the muscle thickness and the muscle belly length for the gastrocnemius heads. Finally, the force at the tendon was determined from the calculated muscle force and pennation angle for the gastrocnemius heads.

The net plantar-flexion moment was computed by summing the product of each muscle force and its moment arm, for each analyzed set of joint angles.

3.9 Summary With this muscle model the contractile and series elastic components of the gastrocnemius muscle are modeled for an isometric contraction with changing ankle and knee angles. Each component of the muscle-tendon complex was modeled. Pennation angle was included in the muscle model to see the effects of fiber pennation in the overall ankle moment. Finally, the net moment-ankle angle relationship was found by summing the moments generated by both gastrocnemius heads and the soleus; simulated for a range of ankle angles and knee angles of 0° and 90°.

Chapter 4 – Methods

4.1 Overview This chapter contains the methods used in this study to examine muscle architecture in both heads of the gastrocnemius muscle. Section 4.2 describes the characteristics of the subjects and the anthropometric measures. Section 4.3 describes the shank measurements and the determination of the inertial parameters of the segments. Section 4.4 describes the ultrasound machine used to obtain the muscle images, the placement of the probe, and the leg measures made. Section 4.5 describes the Biodex dynamometer. Section 4.5.1 describes the isometric tests, and section 4.5.2 describes the isokinetic test. Section 4.6 describes the measures made of muscle architecture. Section 4.6.1 describes the measurements and analysis of architectural parameters for the images of the isometric tests. Section 4.6.2 describes the measurements and analysis of the muscle architectural parameters for the images for the isokinetic tests. Section 4.7 describes the comparison between the muscle model and the experimental data. Section 4.8 describes the statistical analysis. Section 4.9 is a summary of this chapter.

4.2 Subject Recruitment, Characteristics, and Anthropometry Subjects were recruited by direct contact with the University Park community. A screening questionnaire was sent to the potential subjects to determine their eligibility for the study. Subjects were selected between the ages of 18 and 40 years, and that had no right leg and hip injuries in the past three years. Twenty-four healthy subjects volunteered for this study including nine females and fifteen males. Their typical weekly physical activity was recorded. Table 4.1 gives the characteristics of each subject and Table 4.2 presents their mean characteristics. All subjects gave an informed consent to participate in this study, with the protocol approved by the Institutional Review Board (Appendix).

Table 4.1. Subject characteristics and physical activity.

Frequency Age Height Mass Subject Gender Activity (days per (years) (cm) (kg) week) 1 M 22 189.0 115.7 Basketball 4 2 M 21 164.0 66.2 Bicycle 3 3 M 21 175.0 73.3 Swimming 5 4 M 21 178.0 78.9 Racquetball/Golf 3 5 M 28 180.5 69.8 Soccer/Bicycle 5 6 F 23 152.0 56.0 None - 7 M 21 175.0 79.4 Gymnastics 6 8 F 40 155.0 56.3 Bicycle 5 9 M 22 188.0 82.1 Basketball 2 10 F 23 158.0 53.9 Running 3-5 11 M 30 174.0 78.9 Bicycle/Weights 3 12 M 24 163.0 55.8 Running 7 13 F 32 157.0 58.5 None - 14 M 32 181.0 83.6 Running 2 15 F 23 155.0 56.2 Lifting weights 2 16 M 25 169.0 56.9 Running 7 17 M 26 179.0 68.9 Tennis 1 18 M 22 165.5 67.6 None - 19 M 37 176.0 65.3 Lifting weights 4 20 F 23 150.0 50.6 Lifting weights 4 21 M 29 183.0 79.8 Bicycle 5 22 F 27 175.0 61.2 Weights/Walking 2-3 Group Exercise 23 F 22 162.0 68.4 3 Classes 24 F 25 156.0 49.5 Swimming 2

Table 4.2. Subject characteristics (mean ± standard deviation). Gender Age (years) Height (cm) Mass (kg) Male (n = 15) 25.4 ± 4.9 176.1 ± 8.0 74.8 ± 14.2 Female (n = 9) 26.4 ± 6.0 157.8 ± 7.3 56.7 ± 5.7 Group (n = 24) 25.8 ± 5.2 169.2 ± 11.8 68.0 ± 14.6

4.3 Shank Inertial Parameters To determine the inertial parameters of the shanks of each of the subjects in this study they were modeled as a series of truncated cones (Challis et al., 2012). Each leg was divided into eight truncated cones of equal height. The shank length was measured 45

by identifying the medial condyle of the tibia and the medial malleolus by palpation. The length was then divided into nine equidistant portions, and the perimeter length of the shank was measured at each of these nine points. All measurements were made to the nearest millimeter with the subject standing upright (Figure 4.1). The density of the shank was assumed to be the same as that determined by Clauser et al. (1969). The modeling of the shanks produced their inertial parameters (mass, center of mass location, and moments of inertia). As the segments were modeled with a circular cross-section the moments of inertia about a medial-lateral and anterior-posterior axes were equal therefore for each segment two moments of inertia through axes through the center of mass were determined, a transverse and a longitudinal. Segment masses were normalized with respect to whole body mass. Center of mass locations were expressed as a percentage of segment length and measured from the proximal end of the segment. Segmental moments of inertia were normalized by expressing them as radii of gyration,

Where is radius of gyration, L is the length of the segment, I is the moment of inertia, and m is the mass of the segment.

Figure 4.1. The measurements of the leg. 46

4.4 Ultrasound and Gastrocnemius Measurements The gastrocnemius muscle was selected for this experiment given its superficial location. Images of the gastrocnemius muscle were obtained using a ALOKA SSD-1000 ultrasound machine with a 7.5 MHz linear array ultrasound probe of 5 cm. The real-time B-Mode was use to obtain longitudinal images (5 cm by 4 cm) of the gastrocnemius. All ultrasound images were recorded using Scion Image (Scion Corporation, Frederick, MD). The subjects lay in a prone position with their feet hanging at the border of a padded table, this position of the foot was taken as the relaxed position. Using the ultrasound machine, the origin point of both heads of the gastrocnemius were identified, also the insertion point with the Achilles tendon of both heads were identified using the myotendinous junction (Figure 4.2), finally the connective tissue separating the two heads was identified (Figure 4.3) along the muscle. The superficial edges of the calcaneus at the medial and lateral sides were identified by palpation (Figure 4.2), and these points were assumed to be the insertion point of the Achilles tendon. The resting length of the tendon was measured between the calcaneus points and the myotendinous junction. Using the marks (Figure 4.2), the ultrasound probe was placed over the muscle belly along the longitudinal axis of the gastrocnemius, making sure that in the contracted state, the image captured the muscle belly. The tests were run with the probe on one head first and then changed to the other head. The probe was placed in a supporting cup and attached to the leg with self-adhesive wrap (Figure 4.4, and Figure 4.5). Videos of each test were made at 20 Hz using Scion Image (Scion Corporation, Frederick, MD).

LG MG

Division between heads

Figure 4.3. Identification of the separation between the heads of the gastrocnemius (LG is the lateral head, and MG is the medial head) using the ultrasound image.

Figure 4.4. Ultrasound probe positioning on the leg, with subject in the Biodex dynamometer.

Figure 4.5. Ultrasound machine and Biodex dynamometer set-up.

4.5 Biodex Isokinetic Dynamometer Tests The isometric and isokinetic tests were performed in the Biodex Medical System 3 isokinetic dynamometer. Both tests were performed with the knee extended at 0° and with the knee flexed at 90° (Figure 4.6 A and B respectively). The right foot (for one subject the left foot) was strapped to the foot platform, and the ankle center of rotation was aligned with the dynamometer’s center of rotation. This was done using a laser level tool. Flexion of the knee to 90° was verified using a manual goniometer. The ankle maximal voluntary range of motion in the dorsi-flexion and plantar-flexion direction for all subjects was defined before starting each test. The tests were performed with the ultrasound located on both the medial and lateral heads of the gastrocnemius. All subjects started the tests with the knee flexed. Having a clear image of the gastrocnemius with the knee flexed was more difficult than at the extended knee condition, and by starting with the knee flexed it was possible to position the probe to capture good muscle images. In this way it was also ensure a clear image in the extended knee condition. The order of the tests was randomized in order to minimize the possible influence of the effects of fatigue on the muscle. Ankle moment and angle data were collected at 100 Hz.

A B

Figure 4.6. Biodex testing with A) Knee extended at 0° and B) knee flexed at 90°.

4.5.1 Isometric Test Protocol For the isometric test, nine ankle angles were defined including dorsi-flexion and plantar-flexion ankle angles (20°, 10°, 5°, 0°, -5°, -15°, -20°, -25°, and -30°) (Figure 4.7). The test was set to start at an ankle angle of 20° and ended at -30°. At each angle the subjects had to perform three maximal isometric contractions in the plantar-flexion direction for 5 seconds, and each contraction was followed by a 10 seconds rest period. There was a 20 seconds rest period between ankle angles. Given data processing difficulties, data was analyzed for only nine of the 24 subjects that participated in this study for the isometric testing.

Figure 4.7. Illustration of ankle angle definition, where the ankle angle (φANKLE) used was defined as φANKLE = θ - 90°.

4.5.2 Isokinetic Test Protocol For the isokinetic test, three ankle angular velocities were used (20°/second, 75°/second, and 120°/second). The test trials started with the slow velocity and ended with the fastest velocity. The movement started at a dorsi-flexed angle, and the subjects were instructed to plantar-flex as hard as they could and then to dorsi-flex. With increasing angular velocity an increasing number of trials were performed: 20°/second - 3 trial, 75°/second - 4 trials, and 120°/second - 6 trials. There was a 30 seconds rest period between each angular velocity trial.

4.6 Muscle Architecture Measurements Muscle architecture parameters were measured on the longitudinal gastrocnemius ultrasound images using Scion Image (Scion Corporation, Frederick, MD). Muscle images were in gray scale, with the brighter areas reflecting connective tissue (collagen). Therefore in these images it was possible to identify the tendinous sheets as well as the line of action of the fascicles (Figure 4.8). All measurements were made by trained operators.

4.6.1 Isometric Data Analysis In the isometric images the measurements identified in Figure 4.8 were made. Thickness was defined as the internal distance between superficial and deep aponeuroses, the thickness of each muscle image was measured at both ends of the image which represented the proximal and distal sides of the imaged portion of the muscle. The final muscle thickness was taken as the mean of these two measurements. Muscle fascicles were approximated by the brightest diagonal lines running between the aponeuroses, the length was measured from the deep aponeurosis to the superficial aponeurosis, and in the case where the superficial insertion of the fascicle was not visible on the image, a straight line was drawn following the line of the superficial aponeurosis, and the fascicle length was estimated by extrapolating the fascicle line over the drawn aponeurosis line. Pennation angle was defined as the angle formed between the fascicle and the aponeurosis, in the case where the fascicle inserting at the superficial aponeurosis was not in the image only the deep pennation angle was measured. Each ankle angle test was divided in six periods: three contractions and three resting periods. For each contraction, the peak moment was identified in the dynamometer data and synchronized with the ultrasound image to find the frames that were going to be measured. For each of these images the thickness, three fascicle lengths and their corresponding pennation angles were measured. Averages of the three parameters for each subject were calculated for each ankle angle.

4.6.2 Isokinetic Data Analysis For the isokinetic test, 24 subjects were analyzed. In the isokinetic images the measurements in Figure 4.8 were all made except for the fascicle length. Muscle thickness and pennation angle were defined as was previously described. Using the dynamometer data, the period of contractions was identified (plantar-flexion), the movement was considered to start at the 0° ankle angle and end at the -30° ankle angle, these points were synchronized with the ultrasound images to find the starting and ending frames to make the measurements. Two contractions periods were analyzed for each angular velocity. Measurements of pennation angle and muscle thickness were made on each frame from the start of the movement at 0° ankle angle to the end of the movement. The pennation angles of three fascicles were measured on each frame. The three fascicles were selected so that there was one close to the distal end, one in the middle, and one at the proximal end of the image, and the same three fascicles were measured during the whole contraction.

To be able to compare between the isometric and isokinetic tests, frames in the isokinetic images for the nine ankle angles defined in the isometric test were identified to

use the pennation angles at these frames, for the three angular velocities. This was done for only nine subjects matching with the subjects analyzed in the isometric test.

4.7 Pennation angle Model and Experimental Data The model described in Chapter 3 was used to calculate the moment-ankle angle relationship of the gastrocnemius during an isometric contraction. The model used experimental values of pennation angle and fascicle length at each ankle angle. The joint angle definitions given in Chapter 3 were changed in the model to match the ankle and knee definitions used in the experiment. The muscle model output was compared with the experimental data from the isometric testing.

4.8 Statistics For pennation angle and peak moment the descriptive statistics were computed. A repeated measures analysis of variance (ANOVA) was used to analyze the isometric test data. The repeated measures ANOVA was used to compare 1) pennation angles between 0° and 90° knee angles and 2) pennation angles between heads. When statistical significant differences were found a Tukey pair-wise comparison test was used. For the comparison between isometric testing and isokinetic testing, a two samples t-test was used to compare the pennation angle means between the isometric and isokinetic tests for all ankle angles for the same head. All tests were consider to be significant if p ≤ 0.05.

4.9 Summary This chapter described the isometric and isokinetic testing protocols during which ultrasound images for both heads of the gastrocnemius muscle at two different knee angles were recorded for nine subjects in the isometric test and 24 subjects in the isokinetic test. The ultrasound images were determined using Scion Image (Scion Corporation, Frederick, MD) and pennation angle, fascicle length, and muscle thickness (distal and proximal) were measured using the images. Finally the experimental pennation angles and fascicle lengths were used in the muscle model and the experimental data was compared with the output of the muscle model.

Chapter 5 – Results

5.1 Overview This chapter contains the results of this study. Section 5.2 presents the examination of the correlation of the shank inertial parameters with the pennation angle for both heads. Section 5.3 presents the examination of the correlation between ankle moment and muscle pennation angle. Section 5.4 presents the results for the ankle moment-ankle angle relationship with knee angle changes, first the model predictions are presented and then the experimental results are presented. Section 5.5 presents the results for the inter-subject variability of pennation angle. Section 5.6 presents the results of the comparison of pennation angle between isokinetic and static conditions. Section 5.7 is a summary of this chapter.

5.2 Anthropometry The inertial parameters of the shank of each subject were calculated to examine if there was a correlation between the inertial parameters of the shank and the pennation angle of both heads of the gastrocnemius (Table 5.1).

Table 5.1. Inertial parameters for the shank, where shank mass is expressed in percent of body mass, the moment of inertia is represented by the radius of gyration, and the center of mass is expressed as a percentage of shank length. Mean SD Minimum Maximum Shank Mass (%) 4.36 0.58 3.48 5.88 Center of Mass (%) 41.80 1.22 40.58 46.73 Transverse Radius of 0.28 0.01 0.27 0.29 Gyration (-) Longitudinal Radius of 0.09 0.01 0.08 0.11 Gyration (-)

To examine the correlation between the inertial parameters of the shank and the pennation angle of both gastrocnemius heads the pennation angle from the isokinetic testing at an angular velocity of 20° per second at 0º ankle angle (neutral position of ankle) and at 0º knee angle (position at which the anthropometric measurements were

taken) were used. There were no statistically significant correlation coefficients between pennation angle and the location of the shank center of mass (Table 5.2, Figure 5.1). The correlation coefficients were small and non-significant between pennation angle and longitudinal radius of gyration (Table 5.2). The largest correlation was between the transverse radius of gyration and pennation angle of the medial head of the gastrocnemius (Figure 5.2), but the correlations for both heads were not statistically significant (Table 5.2).

Table 5.2. Correlation between pennation angle and shank inertial parameters. Correlation p-value Center of Mass Medial head 0.08 0.730 Lateral head 0.164 0.450 Radius of Gyration for the Transverse Axis Medial head -0.346 0.115 Lateral head -0.077 0.720 Radius of Gyration for the Longitudinal Axis Medial head 0.122 0.582 Lateral head 0.05 0.799

20 Pennation Angle (degrees) Angle Pennation

10 40.5 41 41.5 42 42.5 43 Center of mass (% of segment length) Figure 5.1. Pennation angle and center of mass for each subject for the lateral head at 0º knee angle.

25 Pennation Angle (degrees) Angle Pennation

15 0.265 0.27 0.275 0.28 0.285 0.29 Radius of Gyration

Figure 5.2. Pennation angle and radius of gyration on the transverse axis presented for each subject for the medial head at 0º knee angle. 57

5.3 Pennation Angle and the Peak Isometric Moment To examine the potential correlation between muscle strength and pennation angle, the pennation angle of both heads of the gastrocnemius were taken from the isometric testing for nine subjects (age: 27.0 ± 6.65 years; height: 1.72 ± 0.11 m; mass: 74.6 ± 17.7 kg). The ankle angle selected for the analysis was 10° given that the majority of the subjects had the greatest moment at this ankle angle. The correlation coefficients were not statistically significant (Table 5.3), however there is a trend for muscles with greater pennation angles to produce greater peak moments (Figures 5.3 and 5.4), except for the lateral head when the knee was flexed at 90° which presented lower peak moments with larger pennation angles (Table 5.3 and Figure 5.4). The medial head presented greater peak moments and smaller pennation angles when the knee was extended compared with the knee flexed (Figure 5.3). The correlation coefficients for the medial head were higher but not statistically significant.

Table 5.3. Correlation between pennation angle and ankle moment at 10° ankle angle for the medial and lateral head of the gastrocnemius at two knee angles. Knee Medial Head Lateral Head angle Correlation p-value Correlation p-value 90° 0.498 0.172 -0.324 0.395 0° 0.302 0.428 0. 078 0.842

Figure 5.3. Moment-pennation angle relationship for the medial head at 90° (blue) and 0° (red) knee angles, solid lines reflect linear trend lines.

Figure 5.4. Moment-pennation angle relationship for the lateral head at 90° (blue) and 0° (red) knee angles, solid lines reflect linear trend lines.

5.4 Peak Isometric Moment–Ankle Angle Relationship with Knee Angle Changes The muscle model and the experimental data were evaluated to examine the effects of changing the knee angle on the ankle moment-ankle angle relationship. For the muscle model the ankle moment was calculated using the mean pennation angle at each ankle angle obtained from the isometric testing. With the muscle model the ankle moment increased with dorsi-flexion when the knee was flexed at 90°. With the knee extended at 0° the ankle moment increased from a plantar-flexion angle to neutral position (0° ankle angle) and then it decreased with dorsi-flexion (Figure 5.5). During plantar-flexion with the knee extended there was a greater moment than with the knee flexed, however at higher dorsi-flexion angles greater moments were reached with the knee flexed compared with the knee extended.

Figure 5.5. Peak moment-ankle angle relationship at 90° (flexed) and 0° (extended) knee angles for the muscle model using the group mean pennation angles.

For the experimental results the group mean isometric plantar-flexion peak moment for both knee angles are presented in Figure 5.6. A repeated measures analysis of

variance was used to examine differences in the moments between knee angles, there was no statistically significant differences between knee angles (p-value = 0.056).

1.4 Knee Extended Knee Flexed

1.2

0.8

0.6 Ankle Moment (Nm/kg) Moment Ankle

0.4

0.2

0 -30 -25 -20 -15 -10 -5 0 5 10 15 20 Ankle Angle (degrees) Figure 5.6. Peak moment-ankle angle relationship at 0° (extended, solid line) and 90° (flexed, dashed line) knee angles for the group mean isometric peak moment with the standard deviation.

With the knee flexed the muscle model and experimental data presented a similar ankle moment-ankle angle relationship where the ankle moment increased with dorsi- flexion, however the model presented greater ankle moments than the experimental data with the knee flexed (Figure 5.7). With the knee extended the muscle model and the experimental data presented a different ankle moment-ankle angle relationship, where the model predicted an increase of ankle moment from plantar-flexion to neutral position and a decrease of ankle moment from this point to dorsi-flexion, and the experimental data presented only an increase in ankle moment from plantar-flexion to dorsi-flexion and related to these differences the moments predicted by the model are greater in the plantarflexed angles and lower for dorsiflexed angles compared with the experimental data (Figure 5.8). 61

Figure 5.7. Peak moment-ankle angle relationship for the knee flexed comparing the muscle model with the mean experimental results.

Figure 5.8. Peak moment-ankle angle relationship for the knee extended comparing the muscle model with the mean experimental results.

5.5 Inter-subject Pennation Angle Variability The pennation angles of both heads of the gastrocnemius were measured at each of the nine ankle angles for the isometric testing to examine the variability between subjects (Figures 5.9 and 5.10).

Figure 5.9. Pennation angle-ankle angle relationship of both gastrocnemius heads for the group mean and standard deviation for the isometric testing at 0° knee angle.

There were no statistically significant differences in pennation angles between heads with knee extended (p-value = 0.999) or knee flexed (p-value = 0.966).

To illustrate the inter-subject variability the pennation angles for each subject were plotted for one condition (Figure 5.11). Table 5.4 shows the group coefficients of variation.

Figure 5.10. Pennation angle-ankle angle relationship of both gastrocnemius heads for the group mean and standard deviation for the isometric testing at 90° knee angle.

Table 5.4. Group coefficients of variation expressed as percentages for each gastrocnemius head at two knee angles for nine ankle angles. Ankle angle Medial head Lateral Head Knee at 90° Knee at 0° Knee at 90° Knee at 0° -30° 30.3 34.3 29.2 26.3 -25° 27.9 27.8 32.7 23.6 -20° 25.5 27.4 27.1 21.4 -15° 29.6 27.2 24.9 18.8 -5° 27.9 26.3 30.7 29.2 0° 25.9 22.0 31.4 25.5 5° 23.6 25.9 27.7 26.1 10° 28.4 27.9 22.9 23.8 20° 22.2 24.9 25.9 31.2

Figure 5.11. Pennation angle-ankle angle relationship for every subject (dotted lines) and the group mean (solid line) for the medial head at 0° knee angle.

There was variability in pennation angle between subjects at each ankle angle for both gastrocnemius heads at both knee angles (Figure 5.11 and Table 5.4). The behavior of the muscle for each subject varied with knee angle, and also the relationship of pennation angle with ankle angle of both heads was different, however there were no subjects with great variability from the group as all subject values were within two standard deviations of the mean.

The smallest pennation angle for the medial head of the gastrocnemius were from females (subject 8: 1.55 m height and 56.3 kg mass for knee extended, and subject 13: 1.57 m height and 58.5 kg mass for knee flexed), and for the lateral head were from a male subject (subject 17: 1.79 m height and 68.9 kg mass). Largest pennation angles for the medial head with knee extended was from a male (subject 1: 1.89 m height and 115.6 kg mass), and for knee flexed was from a male subject (subject 2: 1.64 m height and 66.2 kg mass), and for the lateral head at both knee angles were from a male (subject 3: 1.75 m height and 73.2 kg mass) (Table 5.5).

Table 5.5. Largest and smallest pennation angles for both gastrocnemius heads at two knee angles for nine ankle angles. Ankle angle Medial head Lateral head Knee at 90° Knee at 0° Knee at 90° Knee at 0° Largest Smallest Largest Smallest Largest Smallest Largest Smallest

(°) (°) (°) (°) (°) (°) (°) (°) -30° 42.2 19.1 56.9 24.3 35.4 18.1 32.8 19.9 -25° 39.1 22.0 47.5 29.4 31.5 15.5 34.8 23.7 -20° 40.1 21.6 46.2 29.1 34.3 18.6 32.9 23.0 -15° 38.2 18.5 45.6 25.0 32.9 16.9 30.1 19.8 -5° 39.6 23.2 40.7 25.9 31.9 15.8 34.9 19.7 0° 38.5 20.9 36.2 21.5 27.7 18.1 33.1 18.3 5° 31.7 22.8 34.9 19.7 30.8 17.8 28.8 17.5 10° 23.8 18.2 33.3 17.7 28.4 18.2 27.9 17.2 20° 25.7 17.9 29.3 18.4 26.5 20.1 26.7 15.6

5.6 Pennation Angle for Static Condition Compared with Isokinetic Conditions To compare between static and dynamic conditions, the pennation angles at each ankle angle were used for the static condition, and pennation angles for the dynamic condition were found at each of the nine ankle angles defined for the static condition for each of the angular velocities for both knee angles (Table 5.6 and Figure 5.12).

At 90° knee angle there were statistically significant differences between the static and dynamics conditions for the medial head at 0° ankle angle for all angular velocities, at -5°, -15 °, -20°, and -30° ankle angles for 75° per second and 120° per second, and at -25° ankle angles for 120° per second. For the lateral head there were statistically significant differences at -15° and -20° ankle angles for 20° per second. At 0° knee angle there were statistically significant differences between the static and dynamic conditions for the medial head at all ankle angles for all angular velocities. For the lateral head there were statistically significant differences at 0°, -5°, and -15° ankle angles for 75° per second and 120° per second, and at -25° ankle angle for 20° per second. In 66

general both heads at the static condition had greater pennation angles than the dynamic condition at both knee angles, however for the later head at -15° and -20° ankle angles at 20° per second with knee flexed and at -25° ankle angle at 20° per second with the knee extended the pennation angles for the dynamic condition were greater.

Table 5.6. Pennation angles for static and dynamic conditions at each ankle angle for both gastrocnemius heads at two knee angles. Lateral Head Knee Angular velocity Ankle angle (°) angle (°) (°/second) 0 -5 -15 -20 -25 -30 0 21.56 22.96 23.10 24.38 25.03 26.86 20 21.97 24.19 27.65 27.20 26.22 29.68 90 75 19.96 22.44 24.93 27.20 27.45 30.15 120 20.42 21.49 25.25 25.95 27.13 30.63 0 23.25 24.90 26.41 26.92 27.38 28.98 20 22.09 25.29 24.84 26.43 30.03 24.38 0 75 20.22 21.29 23.82 25.73 26.65 26.98 120 20.59 22.42 23.57 24.42 25.98 25.66 Medial Head 0 30.03 29.16 30.47 32.39 34.01 37.38 20 27.43 26.45 29.28 32.25 33.81 39.01 90 75 22.90 24.36 26.67 28.41 30.91 27.85 120 24.63 24.76 26.55 27.31 28.41 26.43 0 29.06 31.33 33.75 35.17 35.18 35.62 20 25.06 26.31 30.08 30.57 26.77 30.20 0 75 21.55 22.67 26.87 26.52 29.84 29.42 120 19.74 22.04 24.10 25.47 25.84 29.52

Figure 5.12. Pennation angle-ankle angle relationship of the medial head for the static and dynamic conditions at 0° knee angle.

5.7 Summary The results in this study indicated that there was no evidence of a correlation between shank inertial parameters and pennation angle. There was no significant evidence of greater moments related with larger pennation angles at an ankle angle of 10° in the dorsiflexed position. The muscle model predicted a decreased in ankle moment with plantar-flexion only with the knee flexed, but with the knee extended the model predicted an increase in ankle moment from plantar-flexion to neutral position (0°) and a decrease with dorsi-flexion which differ with the experimental data. There was small variability in pennation angle between the subjects participating in this study. There are statistically significant differences in pennation angle between static and dynamic conditions, where in general static conditions presented greater pennation angles compared with dynamic conditions.

Chapter 6 - Discussion

6.1 Overview This chapter will discuss the findings of the study. In section 6.2 the results of the study are summarized. In section 6.3 these results are discussed and compared with other studies. In section 6.4 the limitation of the study are presented. Section 6.5 presents suggestions for future research, and finally this chapter ends with section 6.6 where the conclusions of the study are presented.

6.2 General Findings in the Study The first aim of this study was to investigate the relationship of pennation angle with the segmental inertial parameters. We found no statistically significant correlation between the segment inertial parameters and the pennation angles of both gastrocnemius heads (p-values > 0.05). The second aim of this study was to investigate the relationship between muscle pennation and muscle strength. In general, normalized peak moment was reached at an ankle angle of 10° dorsi-flexion by each subject. For the medial head of the gastrocnemius at this ankle angle, larger pennation angles tended to be associated with higher normalized moments, however there was no statistically significant correlation. Changing the knee angle did not change the trend for the medial head. For the lateral head at the same ankle angle, changing the knee angle produced a change in the trend. With the knee extended it behaved as the medial head also without statistically significant correlation, and with the knee flexed larger pennation angles were associated with lower normalized moments nevertheless there was no statistically significant correlation. The third aim of this study was to investigate the influence of knee angle changes on the ankle moment-ankle angle relationship. For the isometric testing the normalized ankle moment increased with dorsi-flexion with the knee fully extended at 0° and with the knee flexed at 90°, and there were no statistically significant differences between the peak moments at each ankle angle for both knee angles (p-value > 0.05). With the muscle model using the group mean pennation angle a similar ankle moment-ankle angle 69

relationship was found with the knee flexed but the moments predicted by the model were higher compared with the experimental data. The ankle moment-ankle angle relationship predicted by the model with the knee extended was different from the experimental data. The model presented an increase in ankle moment from plantar- flexion to neutral ankle angle (0°) with higher moments compared with the experimental data, and from neutral position to 20° dorsi-flexion there was an ankle moment decrease at which point the experimental data had higher moments than the model. The fourth aim of this study was to study the inter-subject variability in pennation angles. Pennation angle for both heads of the gastrocnemius increased with plantar- flexion with knee extended and knee flexed as it has been reported before (Maganaris et al., 1998, Kawakami et al., 1998). There were no statistically significant differences between heads for pennation angles. Coefficients of variation indicated the variability of pennation angle between the subjects participating in this study. Finally, the fifth aim of this study was to compare pennation angles between static and dynamic conditions. In general there were statistically significant differences in pennation angle between the static condition and the isokinetic condition for both gastrocnemius heads at both knee angles with the static condition presenting larger pennation angles. There were a few exceptions for the lateral head at both knee angles at the slowest angular velocity (20° per second). The lateral and medial heads did not behave the same way for the tested contractions, where in some cases the differences with the static condition at each ankle angle were different between heads. Changes of pennation angles with contraction have been reported before (Maganaris et al., 1998, Kawakami et al., 1998), as well as differences of pennation angle between gastrocnemius heads (Huijing, 1985), and the ankle moment-ankle angle relationship for the triceps surae (Sale et al., 1982) and the effects of knee and ankle angle changes on this relationship (Sale et al., 1982, Li et al., 2002, and Gallucci and Challis 2002). This study presented changes of pennation angle with different ankle angles, and significant differences in pennation angles between static and isokinetic conditions. The muscle model and experimental data presented similar results for the flexed knee condition but not for the extended knee condition. 70

6.3 Discussion of the Results No previous research has examined the potential relationship between inertial parameters and pennation angle of humans. In a study made on the forelimbs of monkeys Cheng and Scott (2000) measured pennation angle and inertial parameters however they did not examine potential statistical relationships. In similar studies the inertial parameters were calculated and the pennation angle of the muscles under study were measured but were used to calculate other muscle parameters (Veeger et al., 1997). Here we found that there was no statistically significant correlation between pennation angle and shank center of mass or radius of gyration. Values of pennation angles for the gastrocnemius in the literature can be found around 37 ± 2.3 to 52.9 ± 2.6° for the medial head and 32 ± 2.9 to 41.3 ± 2.7° for the lateral head from ankle angle of 15° to -30° of isometric contraction for six male subjects with the knee flexed using a similar procedure as was used in this study (Maganaris et al., 1998). We found that with the knee flexed pennation angles went from 25.0 ± 4.7 to 36.3 ± 11.0° for the medial head and 21.0 ± 3.4 to 25.9 ± 5.4° for the lateral head. These values are smaller than those found by Maganaris et al. (1998) however, they only analyzed male subjects and the present study had subjects of both genders which might be the cause of the mean low values of pennation angle. Chow et al. (2000) reported that males had greater pennation angles than females. In the present study, with the knee flexed the pennation angles for male subjects ranged from 27.9 ± 2.1 to 39.2 ± 8.7° for the medial head and from 21.8 ± 3.2 to 25.2 ± 5.9° for the lateral head, while for female subjects from 20.5 ± 3.7 to 23.34 ± 1.9° for the medial head and from 19.1 ± 0.42 to 28.3 ± 2.8° for the lateral head. The male pennation angle values were still small compared with those found by Maganaris et al. (1998), however including the females subject data lowered the mean values for the medial head, but not for the lateral head. This suggests that while gender may be a factor influencing the differences between the results of this study and other studies, there are other factors which must contribute to the differences. There were no statistically significant correlations between pennation angle and maximal moment for an ankle angle of 10° dorsi-flexion. This was not expected since it

has been presented that larger muscles present greater moments than small muscles within a healthy population (Holzbaur et al., 2007) and larger muscles have greater pennation angles (Kawakami et al., 2006). Sample size could have been an influencing factor in not finding a statistically significant correlation since the statistical power was low for both knee angles (power = 0.41 at 90° and power = 0.20 at 0°). It was surprising to find that there were no statistically significant differences in ankle moments for the two knee angles. The gastrocnemius is a bi-articular muscle and it was expected that by flexing the knee it would change its potential force contribution by shortening the fibers, and this would produce lower moments at the ankle. The effects of knee changes on the function of the gastrocnemius has been studied before, and studies found that by changing the knee angle and ankle angle there are differences (e.g., Li et al., 2002). For the knee moment it has been found that with the knee extended there are greater moments (Li et al., 2002), and for the ankle greater moments are produced with the knee extended (Sale et al., 1982). A factor that might have contributed to this lack of difference is that the tests were always started with knee flexed and fatigue might have been a factor in part explaining the lack of increase in the moments with the knee extended. For the model the results with the knee flexed were similar to those found by Sale et al. (1982) and agree with the experimental results however the moments were greater in the model output. However, it is important to underline that the moments found in this study in the experimental data and with the muscle model are lower that those found in the literature. The results for the model with the knee extended were not similar to the experimental data however an increase from plantar-flexion to neutral position was the same, once in dorsi-flexion a decrease was not expected, for example Sale et al. (1982) found that peak moments were found at dorsi-flexed positions. The model showed that including pennation angle is good for predictions with the knee flexed but not for the knee extended however care must be taken because moments for the model where higher than the experimental data. The differences found between experimental data and the model could be attributed to a difference between model component and its behavior in vivo. The most likely model component which accounts for this discrepancy in the 72

moments with the knee extended is the muscle kinematics, specifically the model of the muscle length and moment arm. These aspects of muscle kinematics were calculated from equations derived from cadaver studies (Grieve et al., 1978); it is feasible that a representation of muscle kinematics based on measurements made on the subjects, for example using ultrasound (Lee et al., 2008), could have improve the estimation of the moments produce by the model. It has been suggested that pennation needs to be accounted for when pennation angles are greater than 20° (Zajac, 1989). We found that in general subjects have pennation angles greater than 20° when we consider ankle angles from the neutral position (0°) to total plantar-flexion however some subjects did present smaller pennation angle. Coefficients of variation were found between 18.8% and as high as 34.3%. In the literature there is not a defined scale for coefficients of variation on which to base if the variation in this study was low or high. It has been proposed that coefficients of variation are consider low when they are less than 30% (Lande, 1977). Base on this it is difficult to say if there is evidence of great variability in the pennation angles of the population participating in this study. The pennation angles can be considered in light of their functional importance, that is the cosine of the angle reflect the portion of the muscle force transmitted to the muscle’s tendon. If we compute the coefficient of variations of the cosine of the pennation angles we obtained coefficients of variation between 3.08% and 17.5% which are smaller than the coefficients of variation of pennation angle. It is feasible that different (more diverse) populations might produce greater variability, for example if the population had included the highly trained and sedentary elderly individuals. It was expected that for the static condition there would be greater pennation angles compared with the isokinetic condition. It has been found before that with increasing joint angular velocity for a given joint angle the fascicle length increases (Reeves and Narici, 2003, Ichinose et al., 2000) since an increase in contraction velocity decreases the muscle force leading to less stretch of the tendon resulting in longer fascicles with smaller pennation angles compared with an isometric contraction which generates greater pennation angles since the muscle is allowed to shorten more in this 73

condition. As was also found by Reeves and Narici (2003) for the tibialis anterior, in this study we found that pennation angles were statistically significantly different between static and dynamic conditions in general for all cases for the gastrocnemius heads, however it seems that the lateral head behaves a little different from what was expected. It is important to underline that these differences were maintained with ankle angles changes. This is the first study that has examined the pennation angle differences between static and dynamic conditions for the gastrocnemius muscle.

6.4 Limitations in the Study A major limitation of this study was the ultrasound operation, image capturing, and image measurement since it takes experience with the equipment to obtain quality images. Also, as the muscles contracted the contact of the probe with the leg can be lost producing unclear images. Another limitation of this study was the lack of randomization in the tests. For the isometric testing the ankle angle was fixed to go from dorsi-flexion to plantar-flexion for all subjects, the possibility of muscle fatigue at higher plantar-flexion angles exists. This was done given the lack of experience with the equipment since the idea of having different testing protocols with a varying ankle angle order was only thought after half of the subjects were tested. Also the tests were always started with the knee flexed, presenting the possibility that the muscle was fatigued when performing the tests with the extended knee. The muscles were tested with the knee initially flexed because it was easiest to locate a suitable portion of the muscle to image with the leg in this position; then the same location was used for the knee extended position; alternative procedures took excessive amount of subject time. Muscle fatigue influences on pennation angle changes have not been evaluated, so we do not know to what extent this could have affected the results. When examining the potential relationship between the shank inertial parameters and the pennation angles of the heads of the gastrocnemius this analysis did not take into account the contribution of the other muscles contributing to the triceps surae, for example the soleus. It may be that the soleus in some way changes the theoretical

relationship between the limb inertial parameters and the pennation of the heads of the gastrocnemius. Unfortunately it is not easy to measure the architectural features of the soleus using ultrasound given that the soleus lies deeper than the gastrocnemius and to be able to visualize it a higher frequency probe would be need, or a different probe position on the leg could be used which would have prevented the simultaneous analysis of the gastrocnemius.

6.5 Future Research The introduction of ultrasound for visualizing muscle in vivo has opened the possibility of acquiring data for more research into muscle function. Together with the dynamometer, these tools permit the expansion of research on muscle function. Azizi et al. (2007) proposed that differences in changes in pennation angle depending on contraction level are an adaptation of the muscle and help the muscles to be effective under different loading conditions. As was presented in this thesis there are significant differences between contraction types and this relationship merits more attention. Some research has been done on the relationship between pennation angle changes and fascicle length changes during different contractions (e.g., Lichtwark et al., 2007) and after strength training (Blazevich et al., 2007), however there is more to understand in this area such as the changes with whole muscle contraction and muscle- tendon complex length changes. There is little research on dynamic pennation angle changes given equipment restraints however new technology, such as portable ultrasound equipment, can be used to extend knowledge regarding dynamic pennation angle changes in different type of movements and involving more complex movements. The muscle model here presented similarities with the experimental data however the implementation of a better model that includes the architecture of the soleus would potentially improve the model predictions.

6.6 Conclusions This study has presented new data on the pennation angle of the gastrocnemius muscle, including the pennation angle of both heads of this muscle. No significant correlations were found between pennation angles and the segmental inertial parameters of the shank, or between pennation angle and ankle moment. The model presented similarities with the experimental data with the knee flexed but not with the knee extended. The predicted ankle moments were higher compared with the experimental data with knee extended, but with the knee flexed at plantar-flexion the model predicted higher moments but at dorsi-flexion the experimental data presented higher moments. Moments in this study were low compared with other studies. Pennation angles in static and dynamic contractions presented significant differences where in general larger pennation angles were found for the static conditions for all ankle angles, but the lateral head in some cases presented bigger pennation angles in the dynamic condition than in the static condition. This study has helped in the understanding of in vivo pennation angle changes and is the first study to examine pennation angles and segmental inertial parameters, and to compare pennation angle between static and dynamic conditions for different ankle angles within the normal ankle range of motion.

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Appendix – Informed Consent

Informed Consent Form for Biomedical Research The Pennsylvania State University

Title of Project: Characterization of the function of muscle pennation angle in the human gastrocnemius

Principal investigator: John H. Challis Biomechanics Laboratory 29 Recreation Building The Pennsylvania State University University Park, PA 16802

email [email protected] Phone (814) 863-3675 Fax (814) 863-4755

Other investigator: Laura X. Mendez

1. Purpose: The purpose of this study is to characterize the properties of the internal structure of the human gastrocnemius muscle in order to better understand this muscle’s function in human movement. The gastrocnemius is one of the large muscles located in your calf and is important for both walking and running. Approximately 25 participants will be recruited for this study.

2. Procedures to be followed: This experiment is divided into three main sections; baseline data, medial gastrocnemius strength test, and lateral gastrocnemius strength test. Each strength test will consist of both a static (isometric) test and a dynamic (isokinetic) strength test.

The first step will be to collect baseline data for this study. Prior to data collection, you will be given an informed consent form which will describe the data collection procedures. Your height and weight will be measured using a standard scale found in a physician’s office. Next, you will be placed in a custom, padded table to be able to locate the borders of your calf muscle using an ultrasound machine. To complete this process, I will need to place a small amount of gel on your leg and then position the ultrasound probe over your gastrocnemius muscle. Then, the length of your lower leg will be measured using a standard tape measure. Nine to ten marks will be place on your lower leg using a non-permanent marker to equally divide the length of your leg. These marks will be used to measure the circumference of your calf at each interval.

After these initial measurements are completed, you will then be asked to ride a stationary bicycle for a minimum of 5 minutes at your preferred intensity. Then you will be asked to perform a maximum voluntary contraction of your right calf muscles using the Biodex dynamometer in a prone position. The Biodex is an isokinetic strength testing device which will measure your static strength. After this initial strength measurement, you will be asked to perform three static strength tests repetitions on the Biodex with your right ankle positioned at 9 different

ankle angles in a prone position (See Figure 1). There will be a rest period of about 10 seconds between repetitions and a 30 second rest period between ankle angles. During the strength test, an ultrasound probe will be placed over your medial gastrocnemius muscle using hypoallergenic adhesive tape to gather data relative to your muscle fiber organization. The ultrasound machine produces sound waves and is used in medical facilities to identify different tissues. Then you will be asked to kneel on a padded table (See Figure 2) and repeat the ankle angle tests with the ultrasound. After the static strength tests are completed, you will then be asked to perform a series of ankle dynamic motions against the Biodex dynamometer at three set speeds in a prone position. The dynamometer will limit the speed of your motion but also will not stop you from moving. As described above, the ultrasound probe will be attached to your leg over the medial gastrocnemius. Upon completion of these tests, you will be asked to perform the same motions against the Biodex dynamometer while kneeling on a padded table. Finally, the static and dynamic tests described above will be repeated with the ultrasound probe positioned over the lateral gastrocnemius muscle.

3. Discomforts and risks: There is little or no risk to you associated with these testing procedures. Pilot data gathered using this procedure indicate some discomfort with a participant’s leg being extended or discomfort associated with kneeling for extended periods. If you experience these types of discomfort, you can request a break to alleviate any symptoms.

4. Benefits: There are no benefits for you with this study. The benefits to society are a better understanding of muscle function that will add to the growing knowledge in this field of study.

5. Duration/time of the procedures and study: You will only participate in one session. In this session you will be participating approximately 2 hours.

6. Statement of confidentiality: Your participation in this research is confidential. The data will be stored and secured at the Biomechanics Laboratory of the Department of Kinesiology at The Pennsylvania State University in a password protected file. In the event of any publication or presentation resulting from the research, no personally identifiable information will be shared. Your identification data will be linked to a code and only the principal investigator and the co- investigator will have access to your identification data. The list with the codes linking your data with the experimental data will be destroyed once the study ends. The Pennsylvania State University’s Office for Research Protections, the Institutional Review Board, and the Office for Human Research Protections in the Department of Health and Human Services may review records related to this research study.

7. Right to ask questions: Please contact Laura Mendez at [email protected] or at (267) 772-7527 with questions, complaints or concerns about the research. You can also call this number if you feel this study has harmed you. If you have any questions, concerns, problems about your rights as a research participant or would like to offer input, please contact The Pennsylvania State University’s Office for Research Protections (ORP) at (814) 865-1775 or at [email protected]. The ORP cannot answer questions about research procedures. Questions about research procedures can be answered by the research team.

8. Voluntary participation: Your decision to be in this research is voluntary. You can stop at any time. You do not have to answer any questions you do not want to answer. Refusal to take part in or withdrawing from this study will involve no penalty or loss of benefits you would 83

receive otherwise. If you are taking a class with the principal investigator your grades will not be affected if you decide to stop or withdraw at any point from this study. Your relationship with the principal investigator or the co-investigator will not be affected either.

9. Injury Clause: In the unlikely event that you become injured as a result of your participation in this study, medical care is available. It is the policy of this institution to provide neither financial compensation nor free medical treatment for research-related injury. By signing this document, you are not waiving any rights that you have against The Pennsylvania State University for injury resulting from negligence of the University or its investigators.

You must be 18 years of age or older to be able to participate in this study. If you decide to take part in this study and you have read and understand the information outlined above, and you do not have any question, please sign with your name and indicate the date below.

You will be given a copy of this signed and dated consent form for you to keep in your records.

______Participant Signature Date

______Person Obtaining Consent Date