Wu, J. Z.; Herzog, W.; Cole, G. K. Modeling dynamic contraction of muscle using the cross-bridge theory. (English) Zbl 0880.92005 Math. Biosci. 139, No. 1, 69-78 (1997). Summary: During normal, voluntary movements, skeletal muscles typically contract in a highly dynamic manner; the length of the muscle and the speed of contraction change continuously. We present an approach to predict the accurate behavior of muscles for such dynamic contractions using Huxley’s cross-bridge model. A numerical procedure is proposed to solve, without any assumptions, the partial differential equation that governs the attachment distribution function in Huxley’s cross-bridge model. The predicted attachment distribution functions, and the corresponding force responses for shortening and stretching, were compared with those obtained using G.I. Zahalak’s [ibid. 55, 89-114 (1981; Zbl 0475.92010)] analytical solution and those obtained using the so-called “distribution moment model” in transient and steady-state contractions. Compared to the distribution moment model, the solutions obtained using our model are exact rather than approximate. The solutions obtained using the analytical approach and the present approach were virtually identical; however, in terms of CPU times, the present approach was 250-300 times faster than Zahalak’s. From the results of this study, we concluded that proposed solution is an exact and efficient way for solving the partial differential equation governing the cross-bridge model. Cited in 2 Documents MSC: 92C10 Biomechanics 92C30 Physiology (general) 65Z05 Applications to the sciences 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:actin-myosin bonding reaction Software:IMSL Numerical Libraries PDF BibTeX XML Cite \textit{J. Z. Wu} et al., Math. Biosci. 139, No. 1, 69--78 (1997; Zbl 0880.92005) Full Text: DOI References: [1] Huxley, A.F., Muscle structure and theories of contraction, Prog. biophy. biophy. chem, 7, 255-318, (1957) [2] Huxley, A.F.; Simmons, R.M., Proposed mechanism of force generation in striated muscle, Nature, 233, 533-538, (1971) [3] Zahalak, G.I., A distribution-moment approximation for kinetic theories of muscular contraction, Math. biosci., 55, 89-114, (1981) · Zbl 0475.92010 [4] Rouhand, E.; Zahalak, G.I., The variation of isometric energy rates with muscle length: A distribution-moment model analysis, J. biomech. eng., 114, 542-546, (1992) [5] Zahalak, G.I., A comparison of the mechanical behaviour of the cat soleus muscle with a distribution-moment model, J. biomech. eng., 108, 131-140, (1986) [6] Zahalak, G.I.; Ma, S.P., Muscular activation and contraction: constitutive relations based directly on cross-bridge kinetics, J. biomech. eng., 112, 52-62, (1990) [7] Cole, G.K.; Bogert, A.J.; Herzog, W.; Gerritsen, K.G.M., Modeling of force production in skeletal muscle undergoing stretch, J. biomech., 29, 1091-1104, (1996) [8] IMSL, User’s manual of IMSL mathematical library, (1980), IMSL Publisher Houston [9] Rice, J.R., Numerical methods, software, and analysis, (1983), McGraw-Hill New York [10] Fatunla, S.O., Numerical methods for initial value problems in ordinary differential equations, (1988), Academic Press Boston · Zbl 0659.65071 [11] McMahon, T.A., Muscles, reflexes, and locomotion. chapter 4: the sliding movement of A. F. Huxley’s 1957 model, (1984), Princeton Univ. Press Princeton This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.