A thesis submitted for the degree of Doctor of Philosophy Methodological and Anatomical Modifiers of Achilles Tendon Moment Arm Estimates: Implications for Biomechanical Modelling by Florian Fath Centre for Sports Medicine and Human Performance Brunel University London December 2011 This thesis is dedicated to my wife Annick and my son Etienne. Abstract Moment arms are important in many contexts. Various methods have been used to esti- mate moment arms. It has been shown that a moment arm changes as a function of joint angle and contraction state. However, besides the influence of these anatomical factors, results from recent studies suggest that the estimation of moment arm is also dependent on the methods employed. Theoverallgoalofthisthesiswastoexploretheinteractionbetweenthemethodological and anatomical influences on moment arm and their effect on estimates of muscle-tendon forces during biomechanical modelling. The first experiment was a direct comparison between two different moment arm methods that have been previously used for the es- timation of Achilles tendon moment arm. The results of this experiment revealed a sig- nificant difference in Achilles tendon moment arm length dependent on the moment arm method employed. However, besides the differences found, results from both methods were well correlated. Based on these results, methodological differences between these two methods were compared across different joint angles and contraction states in study two. Results of experiment two revealed that Achilles tendon moment arms obtained using both methods change in a similar way as a function of joint angle and contraction state. In the third experiment, results from the first two experiments were used to determine how methodological and anatomical influences on Achilles tendon moment arm would change muscle-tendon forces during the task of submaximal cycling. Results of the third experiment showed the importance of taking the method, ankle angle and contraction state dependence of Achilles tendon moment arm into account when using biomechanical modelling techniques. Together, these findings emphasis the importance of carefully considering methodolog- ical and anatomical modifiers when estimating Achilles tendon moment arm. Acknowledgements ThecompletionofthisPhDthesiswouldnothavepossiblewithoutthesupportofmany people around me. I would like to take this opportunity to express my deepest thanks to mysupervisorsDrThomasKorffandDrAnthonyBlazevichfortheirguidanceandsupport throughout the course of my PhD. I also would like to give special thanks to: my fellow PhD students for all the time we have spent together in the office or in the lab, sharing idea and discussing about data; Dr Charlie Waugh for her immense contribution to the preparation and completion of the first two experiments of this thesis; all participants for their commitment to take part in my experiments; Dr J¨org Schorer for his encouragement to begin this PhD. Finally, I would like to express my deepest thanks to my friends and family for their never-ending support. Without you, I would not be where I am today. Contents I Chapter 1 1 1 General introduction 2 II Chapter 2 5 2 Review of literature 6 2.1 General significance of moment arm measurements . . . . . . . . . . . . . . 6 2.2 Significance of moment arm within the context of biomechanical modelling. 7 2.3 Methodological considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Derivation of the tendon excursion method . . . . . . . . . . . . . . 9 2.3.2 Derivation of the centre of rotation method . . . . . . . . . . . . . . 14 2.4 Anatomical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Achilles tendon moment arm changes as a function of ankle angle . . 19 2.4.2 Achilles tendon moment arm changes as a function of contraction state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Overall summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6 Thesis aims and research hypotheses . . . . . . . . . . . . . . . . . . . . . . 22 III Chapter 3 24 3 Direct comparison of in vivo Achilles tendon moment arms obtained from ten- don excursion and centre of rotation methods 25 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.2 Experimental protocol: MR imaging . . . . . . . . . . . . . . . . . . 28 3.2.3 Experimental protocol: Ultrasonography . . . . . . . . . . . . . . . . 29 3.2.4 Moment arm calculation using the tendon excursion method and determination of torques about the ankle joint . . . . . . . . . . . . 31 III 3.2.5 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 IV Chapter 4 42 4 Interactive effects of joint angle, contraction state and method on estimates of Achilles tendon moment arms 43 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 V Chapter 5 48 5 The impact of Achilles tendon moment arm methods and anatomical modifiers on Achilles tendon forces during an inverse dynamic simulation of submaximal cycling 49 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2.2 Experimental protocol: Kinematic and kinetic analysis of cycling (protocol 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.2.3 Calculation of ankle torque during the cycling tasks . . . . . . . . . 52 5.2.4 Experimentalprotocol: Maximalisometricplantarflexiontorque(pro- tocol 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2.5 Derivation of dependent variables . . . . . . . . . . . . . . . . . . . . 54 5.2.6 Experimental protocol: Achilles tendon moment arm (protocol 3) . . 54 5.2.7 Derivation of Achilles tendon moment arm dependent variables . . . 55 5.2.8 Five methods of deriving Achilles tendon moment arm . . . . . . . . 55 5.2.9 Statistical treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 VI Chapter 6 62 6 General discussion 63 6.1 Summary of findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 IV 6.2 Effect of moment arm method on Achilles tendon moment arm estimates . 64 6.3 Effect of anatomical modifiers on Achilles tendon moment arm and Achilles tendon force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.4 Significance of findings and suggestions for future research . . . . . . . . . . 66 6.5 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 6.6 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 VII References 71 References 72 VIIIAppendices 83 A Appendix 84 A.1 Additional information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.1.1 Influence of knee angle on Achilles tendon moment arm during con- traction state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.1.2 Residual analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 A.1.3 Free-body diagram of the foot segment during cycling . . . . . . . . 87 A.2 Ethical approval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 A.3 Participants health questionnaire . . . . . . . . . . . . . . . . . . . . . . . . 92 A.4 Consent form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 A.5 Conference abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.6 Peer-reviewed publication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 V List of Tables 2.1 Summary of Achilles tendon moment arm reported at rest over a full range (cid:176) (cid:176) of motion (20 dorsiflexion to 30 plantarflexion) . . . . . . . . . . . . . . . 17 3.1 Pearson’s product moment correlations between Achilles tendon moment arm obtained from COR and TE methods at a neutral ankle angle, as well as CV for interexperimental set-ups. . . . . . . . . . . . . . . . . . . . . . . 35 4.1 Pearson’s product moment correlations between Achilles tendon moment arm obtained from the COR and the TE methods at four different ankle angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.1 Descriptive kinematic results during submaximal cycling at two resistances (mean ± SD). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 The impact of five Achilles tendon moment arm modifications on the max- imal resulting Achilles tendon force and the Achilles tendon force profiles (RAD) during submaximal cycling. . . . . . . . . . . . . . . . . . . . . . . . 58 VI List of Figures 2.1 Schematicillustrationofthecentreofrotationmethod(COR)usingReuleaux’ (cid:176) geometrical method. To determine the moment arm at 0 (ankle is perpen- (cid:176) dicular to the tibia), scans at ±15 were used to determine the COR of the ankle joint. The tibia was assumed to be constant throughout the rotation (cid:176) and the talus was the rotating segment. The moment arm at 0 was defined as the perpendicular distance from the COR of the ankle joint to the line of force, represented by the Achilles tendon. . . . . . . . . . . . . . . . . . . 15 3.1 Schematic illustration of the relationship between ankle rotation and move- ment of the muscle-tendon junction (MTJ) of the gastrocnemius medialis and the Achilles tendon. The ankle was rotated from a dorsiflexed posi- (cid:176) (cid:176) tion of a minimum of -15 to a plantarflexed position of a minimum of +30 (cid:176) (plantar) andvice versa (dorsi) at10 ·s−1 (five consecutive rotationsresult- ing in three plantar- and two dorsiflexion rotations). The MTJ shortened or lengthened according to the ankle rotation. . . . . . . . . . . . . . . . . . 30 3.2 Schematicillustrationofthetendonexcursionmethod. Achillestendonmo- ment arm was calculated as the first derivative of the ratio of the change in muscle-tendonlengthrepresentedbythedisplacementofthemuscle-tendon junction (MTJ) of the gastrocnemius medialis and the Achilles tendon (∆ MTJ) to the change in ankle angle (∆ angle). The derivative was calcu- (cid:176) lated for 0 (ankle is perpendicular to the tibia) over five linear intervals (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (±1 , ±2 , ±5 , ±10 , ±15 numbered as 1 to 5, respectively, in the figure). In addition, a second- and third-order polynomial was fitted to the ratio of thechangeinmuscle-tendonlengthtothechangeinangleanddifferentiated (cid:176) at 0 (numbered 6 and 7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 VII 3.3 Comparison of Achilles tendon moment arm results between the center of rotation (COR; MR imaging) and the tendon excursion (TE; ultrasound imaging) methods as the mean of three consecutive plantarflexion rotations for the neutral ankle angle. The moment arm calculated using the COR (cid:176) method was determined over a ±15 angular interval using a geometrical approach. The moment arm for the TE method was calculated over five (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) different angular differentiation intervals (±15 , ±10 , ±5 , ±2 , ±1 ) and two polynomial fitting procedures (2nd- and 3rd-order polynomials) as the ratio of tendon to ankle displacement. COR: centre of rotation method; ± (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) (cid:176) 15 , ± 10 , ± 5 , ± 2 , ± 1 : angular intervals for differentiation; 2 poly: (cid:176) 2nd -order polynomial fit; 3 poly: 3rd -order polynomial fit. * indicates a significant difference between the COR and the TE methods (p ≺ .01) . . . 34 3.4 Highest correlation between Achilles tendon moment arms calculated using the centre of rotation method (COR) using MR imaging and the tendon excursion method (TE) using ultrasonography. For the COR method, the (cid:176) moment arm was determined over a ±15 angular interval using a geomet- rical approach. For the TE method, tendon displacement of the muscle- tendon junction of the gastrocnemius medialis and the Achilles tendon was (cid:176) (cid:176) differentiated over an angular interval of ±10 (i.e. 20 range) for three consecutive plantarflexion rotations. . . . . . . . . . . . . . . . . . . . . . . 36 3.5 Loading and unloading curves of torques about the ankle joint measured during passive rotations. The ankle joint was rotated from a plantarflexed (cid:176) (cid:176) (cid:176) position of 30 to a dorsiflexed position of 15 three times at 10 ·s−1 and two times vice versa. * indicates a significantly smaller torque about the ankle joint during plantar- compared to dorsiflexion rotations (p ≺ .01, two-tailed, Bonferroni corrected). . . . . . . . . . . . . . . . . . . . . . . . 37 4.1 Achilles tendon moment arm measurements (mean ± SD) at four different ankle angles obtained from the tendon excursion method at rest (TE ) rest and from the centre of rotations method at both rest (COR ) and during rest (cid:176) a maximum isometric contraction (COR ). 0 ankle angle refers to the MVC foot being perpendicular to the tibia. . . . . . . . . . . . . . . . . . . . . . . 46 A.1 Graph showing the relationship between knee angle and the percentage increase in Achilles tendon moment arm from rest to a maximal voluntary contraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 A.2 Plot of the residual between a filtered and an unfiltered torque signal which changes as a function of the 4th-order Butterworth filter cutoff frequencies (until 500 Hz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 VIII