Abstract
Muscle models are an important tool in the development of new rehabilitation and diagnostic techniques. Many models have been proposed in the past, but little work has been done on comparing the performance of models. In this paper, seven models that describe the isometric force response to pulse train inputs are investigated. Five of the models are from the literature while two new models are also presented. Models are compared in terms of their ability to fit to isometric force data, using Akaike’s and Bayesian information criteria and by examining the ability of each model to describe the underlying behaviour in response to individual pulses. Experimental data were collected by stimulating the locust extensor tibia muscle and measuring the force generated at the tibia. Parameters in each model were estimated by minimising the error between the modelled and actual force response for a set of training data. A separate set of test data, which included physiological kick-type data, was used to assess the models. It was found that a linear model performed the worst whereas a new model was found to perform the best. The parameter sensitivity of this new model was investigated using a one-at-a-time approach, and it found that the force response is not particularly sensitive to changes in any parameter.
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References
Alexander RM (2003) Modelling approaches in biomechanics. Philos Trans R Soc Lond B Biol Sci 358: 1429–1435
Baratta R, Solomonow M (1990) The dynamic response model of nine different skeletal muscles. IEEE Trans Biomed Eng 37(3): 243–251
Bawa P, Mannard A, Stein RB (1976) Effects of elastic loads on the contractions of cat muscles. Biol Cybern 22(3): 129–137
Bobet J, Gossen ER, Stein RB (2005) A comparison of models of force production during stimulated isometric ankle dorsiflexion in humans. IEEE Trans Neural Syst Rehabil Eng 13(4): 444–451
Bobet J, Stein RB (1998) A simple model of force generation by skeletal muscle during dynamic isometric contractions. IEEE Trans Biomed Eng 45(8): 1010–1016
Bobet J, Stein RB, Oguztoreli MN (1993) A linear time—varying model of force generation in skeletal muscle. IEEE Trans Biomed Eng 40(10): 1000–1006
Burnham KP, Anderson DR (1998) Model selection and multimodel inference a practical information—theoretical approach, 2nd edn. Springer, New York
Burrows M, Horridge GA (1974) The organization of inputs to motoneurons of the locust metathoracic leg. Philos Trans R Soc Lond B Biol Sci 269: 49–94
Burrows M, Morris G (2001) The kinematics and neural control of high-speed kicking movements in the locust. J Exp Biol 204: 3471–3481
Christophy M, Senan NAF, Lotz LC, O’Reilly OM (2011) A musculoskeletal model for the lumbar spine. Biomech Model Mechanobiol (in Press)
Ding J, Wexler AS, Binder-Macleod SA (2002) A mathematical model that predicts the force-frequency relationship of human skeletal muscle. Muscle Nerve 26(4): 477–485
Ebashi S (1980) The croonian lecture, 1979: regulation of muscle contraction. Proc R Soc Lond B Biol Sci 207: 259–286
Freeman CT, Hughes A-M, Burridge JH, Chappell PH, Lewin PL, Rogers E (2009) A model of the upper extremity using fes for stroke rehabilitation. J Biomech Eng 131(3): 031011
Ghigliazza R, Holmes P (2005) Towards a neuromechanical model for insect locomotion: hybrid dynamical systems. Regul Chaotic Dyn 10(2): 193–225
Hamby DM (1994) A reveiw of techniques for parameter sensitivity analysis of environmental models. Environ Monitor Assess 32: 135–154
Hatze H (1977) A myocybernetic control model of skeletal muscle. Biol Cybern 25(2): 103–119
Heitler WJ (1988) The role of the fast extensor motor activity in the locust kick reconsidered. J Exp Biol 136: 289–309
Heitler WJ, Burrows M (1977) The locust jump. I. the motor programme. J Exp Biol 66: 203–219
Hoyle G (1955) Neuromuscular mechanisms of a locust skeletal muscle. Proc R Soc Lond B Biol Sci 143: 343–367
Hoyle G (1978) Distributions of nerve and muscle fibre types in locust jumping muscle. J Exp Biol 73: 205–233
Huxley HE (1985) The crossbridge mechanism of muscular-contraction and its implications. J Exp Biol 115: 17–30
Law LAF, Shields RK (2005) Mathematical models use varying parameter strategies to represent paralyzed muscle force properties: a sensitivity analysis. J NeuroEng Rehabil 2(12): 18
Mannard A, Stein RB (1973) Determination of the frequency response of isometric soleus muscle in the cat using random nerve stimulation. J Physiol 229: 275–296
MathWorks T (2001) Curve fitting toolbox user’s guide. The MathWorks, Inc, Natick
Meijer K, Rosenthal M, Full RJ (2001) Muscle-like actuators? A comparison between three electroactive polymers. Smart Struct Mater 2001 Electroact Polym Actuators Devices 4329: 7–15
Parmiggiani F, Stein RB (1981) Nonlinear summation of contractions in cat muscles. ii. later facilitation and stiffness changes. J Gen Physiol 78: 295–311
Repperger DA, Phillips CA, Neidhard-Doll A, Reynolds DB, Berlin J (2006) Actuator design using biomimicry methods and a pneumatic muscle system. Control Eng Pract 14: 999–1009
Riener R, Quintern J (1997) A physiologically based model of muscle activation verified by electrical stimulation. Bioelectrochem Bioenerg 43: 257–264
Rosen J, Brand M, Fuchs M, Arcan M (2001) A myosignal-based powered exoskeleton system. Syst Man Cybern Part A Syst Hum IEEE Trans 31(3): 210–222
Stein RB, Parmiggiani F (1981) Nonlinear summation of contractions in cat muscles. i. early depression. J Gen Physiol 78(3): 277–293
Theophilidis G, Burns MD (1983) The innervation of the mesothoracic flexor tibiae muscle of the locust. J Exp Biol 105: 373–388
Valero-Cuevas FJ, Hoffmann H, Kurse MU, Kutch JJ, Theodorou EA (2009) Computational models for neuromuscular function. IEEE Rev Biomed Eng 2: 110–135
Wagner H, Boström K, Rinke B (2011) Predicting isometric force from muscular activation using a physiologically inspired model. Biomech Model Mechanobiol (in Press)
Wilson E (2011) Force response of locust skeletal muscle. Ph. D. thesis, Southampton University
Wilson E, Rustighi E, Mace BR, Newland PL (2010) Isometric force generated by locust skeletal muscle: responses to single stimuli. Biol Cybern 6(102): 503–511
Wilson E, Rustighi E, Mace BR, Newland PL (2011) Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle. Biol Cybern (in Press)
Winters JM (1995) How detailed should muscle models be to understand multijoint movement coordination. Hum Mov Sci 14: 401–442
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Wilson, E., Rustighi, E., Newland, P.L. et al. A comparison of models of the isometric force of locust skeletal muscle in response to pulse train inputs. Biomech Model Mechanobiol 11, 519–532 (2012). https://doi.org/10.1007/s10237-011-0330-2
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DOI: https://doi.org/10.1007/s10237-011-0330-2