Modelling of muscle moment-angle relations using a mechanistic approach

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Journal of Biomechanics 2006, Vol. 39 (Suppl 1)

6111 Th, 14:30-14:45 (P43) An experimental approach for obtaining joint torque strength parameters for use in a whole body simulation model M.R. Yeadon, M.A. King. School of Sport and Exercise Sciences, Loughborough University, UK When the results of computer simulations of human movement are used as evidence for conclusions regarding the operation of the human musculoskeletal system there is always an inherent assumption of some level of model accuracy. Many studies use muscle parameter values from the literature since it is not possible to obtain model parameters for individual muscles in vivo. This has the drawback that such parameter values are based on samples from different individuals and may not be representative of any individual. As a consequence establishing accuracy levels beyond an order of magnitude is problematic. This paper describes a method of determining subject-specific joint torque parameters experimentally and assessing whether the resulting performance of a whole body simulation model is realistic. The relationship between maximum (tetanic) muscular torque and angular velocity was modelled using two hyperbolic functions defined by four parameters with requirements on continuity and relative slopes at zero angular velocity. Maximal muscle activations are typically suppressed in the eccentric mode and so the relationship between maximum voluntary activation and angular velocity was modelled using a monotonic three parameter function which rose from a minimum level in eccentric mode to full activation in concentric mode. Maximum voluntary joint torque was then expressed as a product of these two functions giving a seven parameter function of angular velocity. Quadratic dependence of joint torque on angle was modelled using an additional two parameters. The nine parameters were then determined using a least squares fit to torque data obtained from eccentric-concentric movements by an individual on an isovelocity dynamometer. The resulting accuracy of torque-driven simulations of whole body movement based upon such parameter values was assessed using performance data on the individual. The strength parameters used were deemed to be appropriate since they permitted close matching of a recorded maximal movement but did not allow optimised solutions much in excess of this. 6887 Th, 14:45-15:00 (P43) Modelling of muscle moment-angle relations using a mechanistic approach C.N. Maganaris. Institute for Biophysical & Clinical Research into Human Movement, Manchester Metropolitan University Cheshire, Stoke-on-Trent, UK A generic model for the prediction of moment-angle characteristics in individual human skeletal muscles is presented. The model's prediction is based on the equation M = V Lo 1 ,~ cosq~ d, where M, V and Lo are the momentgenerating potential of the muscle, the muscle volume and the optimal muscle fibre length, respectively, and ,~, q~ and d are the stress-generating potential of the muscle fibres, their pennation angle and the tendon moment arm length, respectively. The input parameters V, Lo, ,~, q~ and d can be measured or derived mechanistically. This eliminates the common problem of the necessity to estimate one or more of the input parameters in the model by fitting its outcome to experimental results often inappropriate for the function modelled. Comparisons of the model's output against experimentally determined M values for the human gastrocnemius (GS) and tibialis anterior (TA) muscles showed that the model can realistically predict the pattern of moment-angle relations. However, the modelled M was overestimated by -14% for the GS muscle and it was underestimated by -10% for the TA muscle. Limitations in both the model and the experimental procedures may account for the M differences between theory and reality. 6141 Th, 15:00-15:15 (P43) Specific tension of intact and skinned muscle fibres R.T. Jaspers 1, H. Degens 3, P.A. Huijing 1, W.J. van der Laarse 2. llnstituut voor Fundamentele and Klinische Bewegingswetenschappen, Vrije Universiteit Amsterdam, 2Department of Physiology, Vrije Universiteit Medical Center, Amsterdam, The Netherlands, 3Institute for Biophysical and Clinical Research into Human Movement, Manchester Metropolitan University, Cheshire, UK Maximum muscle fibre tension (P0) is an important determinant of maximum muscle power. However, large differences in maximum active tension have been reported. Our aim was to study some critical determinants of P0. Comparing P0's of intact amphibian muscle fibres with those of skinned mammalian muscle fibres, we investigated how P0 differs between fibre types. Intact fast (n = 8) and slow (n = 14) twitch muscle fibres were dissected (Xenopus laevis iliofibularis muscle) and mounted in an experimental chamber containing Ringer's solution (20°C). P0 was calculated from maximal tetanic force (50Hz, 250ms) at optimum length (Isa=2.3~tm) and assuming an elliptical cross-section (using smallest and largest diameters measured with

Oral Presentations microscope). P0 of fast twitch fibres was higher than that of slow twitch fibres (363±54 vs. 255±37 kPa, respectively, mean±SD). As dissection of single mammalian muscle fibres is more difficult; we used skinned muscle fibre segments obtained from different muscles to determine the P0 of slow and fast twitch rat muscle fibres. Muscle fibre segments were mounted in relaxing solution (12°C) and activated by submerging them in similar solution also containing 10 -4.5 M Ca 2+. Assuming elliptical cross-sections, P0's of type I, Ila and lib were 183±59 (n = 14), 180±73 (n =5) and 155±34 (n = 14) kPa, respectively. In contrast to Xenopus muscle fibres, no significant difference in fibre type could be shown. Note that the common assumption of circular cross-sections would yield more than 25% lower estimates of P0. As Q10 for Xenopus P0 is 1.2, the calculated P0 of intact Xenopus fibres at 12°C is 15-100% higher than that of skinned rat muscle fibres. This difference is explained partially by the decline in tetanic force shown after skinning of Rana fibres, which varies from 20% for the smaller muscle fibres up to 40% for the largest muscle fibres (J Physiol 410: 171-185, 1989). We conclude that estimates of isolated muscle fibre P0 depend strongly on fibre type and species related differences, as well as the methods applied. Extrapolation to in vivo conditions should account for effects of myofascial force transmission. 6318 Th, 15:15-15:30 (P43) All you need is work: Muscle function predicted from fiber kinematics A.J. van den Bogert 1, C.N. Maganaris 2, M.F. Bobbert 3. 1Cleveland Clinic Foundation, Cleveland, USA, 2Manchester Metropolitan University, Manchester, United Kingdom, 3 Vrije Universiteit Amsterdam, The Netherlands The basic force generating properties of muscle tissue are well known. In order to predict gross motor performance, these must be combined with a model of musculoskeletal architecture, which typically includes morphological parameters such as physiological cross sectional area, optimal fiber length, pennation angle, and muscle moment arms. In many cases, these models have not correctly predicted how maximal isometric joint moments vary with joint angle. One solution to this problem is to adjust model parameters by fitting the model to measured isometric joint moments. A more purist approach, but hardly practical, is to increase model complexity by including better representations of three-dimensional fiber arrangement and force transmission within muscle. Here we present an alternative approach based on the simple concept that the musculosketal architecture represents a transmission mechanism with a kinematic relationship between muscle fiber length and joint angle. Recent work using ultrasound imaging has produced measurements of this relationship for several major muscle groups. Using such data, the sliding filament model can be applied to predict muscle stress, which is then directly converted into joint moment via the principle of virtual work. Apart from fiber kinematics, the only required muscle-specific parameters are the volume of contractile tissue and the optimal fiber length. Classical architecture parameters such as pennation angle and moment arm are not required. We applied this method to predict the isometric function of the triceps surae muscle group. Ultrasound data on fiber length changes of medial gastrocnemius, lateral gastrocnemius, and soleus were obtained from the literature [1] and combined with known muscle volumes to predict maximal isometric plantarflexion moments as a function of ankle angle. Model predictions were in agreement with typical human performance data. In contrast, the classical modeling method has greatly underestimated the width of the isometric moment-angle relationship for plantarflexion. References [1] Maganaris CN, Baltzopoulos V, Sargeant AJ. In vivo measurements of the triceps surae complex architecture in man: implications for muscle function. J Physio11998; 512(Pt 2): 603~14.

2.8. Tendons and Ligaments 2.8.1. Mechanics of Normal Tissue 7878 Mo, 08:15-08:30 (P5) Tibial tunnel placement in anatomic ACL reconstruction W. Petersen, T. Zantop. Department of Trauma-, Hand-, and Reconstructive Surgery, Wilhelms University Muenster, Germany Background: The ACL can be anatomically divided into two bundles: the anteromedial (AM) and the posterolateral (PL) bundles, named for the orientation of their tibial insertions [1]. Biomechanical studies revealed that single bundle ACL reconstruction techniques were successful in limiting anterior tibial translation in response to an anterior tibial load but were insufficient to control a combined rotatory load of internal and valgus torque [2]. These results motivated surgeon replacing the anteromedial bundle and the posterolateral bundle of the ACL [3]. The research question of this study is if there is need for