Mechanics of Feline Soleus: II. Design and Validation of a Mathematical Model

Overview

Journal J Muscle Res Cell Motil

Specialties Cell Biology
Physiology

Date 1996 Apr 1

PMID 8793724

Citations 26

Authors

I E Brown

S H Scott

G E Loeb

Affiliations

Soon will be listed here.

Abstract

We have developed a mathematical model to describe force production in cat soleus during steady-state activation over a range of fascicle lengths and velocities. The model was based primarily upon a three element design by Zajac but also considered the many different features present in other previously described models. We compared quantitatively the usefulness of these features and putative relationships to account for a set of force and length data from cat soleus wholemuscle described in a companion paper. Among the novel features that proved useful were the inclusion of a short-length passive force resisting compression, a new normalisation constant for connective-tissue lengths to replace the potentially troublesome slack length, and a new length dependent term for lengthening velocities in the force-velocity relationship. Each feature of this model was chosen to provide the most accurate description of the data possible without adding unneeded complexity. Previously described functions were compared with novel functions to determine the best description of the experimental data for each of the elements in the model.

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References

Sugi H . Tension changes during and after stretch in frog muscle fibres. J Physiol. 1972; 225(1):237-53. PMC: 1331100. DOI: 10.1113/jphysiol.1972.sp009935. View

Durfee W, Palmer K . Estimation of force-activation, force-length, and force-velocity properties in isolated, electrically stimulated muscle. IEEE Trans Biomed Eng. 1994; 41(3):205-16. DOI: 10.1109/10.284939. View

Gordon A, HUXLEY A, Julian F . The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J Physiol. 1966; 184(1):170-92. PMC: 1357553. DOI: 10.1113/jphysiol.1966.sp007909. View

Woittiez R, Huijing P, Rozendal R . Influence of muscle architecture on the length-force diagram. A model and its verification. Pflugers Arch. 1983; 397(1):73-4. DOI: 10.1007/BF00585173. View

Loeb G . Motoneurone task groups: coping with kinematic heterogeneity. J Exp Biol. 1985; 115:137-46. DOI: 10.1242/jeb.115.1.137. View

Huxley H . The structural basis of muscular contraction. Proc R Soc Lond B Biol Sci. 1971; 178(1051):131-49. DOI: 10.1098/rspb.1971.0057. View

MASHIMA H, Akazawa K, Kushima H, Fujii K . The force-load-velocity relation and the viscous-like force in the frog skeletal muscle. Jpn J Physiol. 1972; 22(1):103-20. DOI: 10.2170/jjphysiol.22.103. View

Baratta R, Solomonow M, Best R, DAmbrosia R . Isotonic length/force models of nine different skeletal muscles. Med Biol Eng Comput. 1993; 31(5):449-58. DOI: 10.1007/BF02441979. View

Pollack G . The cross-bridge theory. Physiol Rev. 1983; 63(3):1049-113. DOI: 10.1152/physrev.1983.63.3.1049. View

10.

Magid A, Ting-Beall H, Carvell M, Kontis T, Lucaveche C . Connecting filaments, core filaments, and side-struts: a proposal to add three new load-bearing structures to the sliding filament model. Adv Exp Med Biol. 1984; 170:307-28. DOI: 10.1007/978-1-4684-4703-3_26. View

11.

Joyce G, RACK P, WESTBURY D . The mechanical properties of cat soleus muscle during controlled lengthening and shortening movements. J Physiol. 1969; 204(2):461-74. PMC: 1351564. DOI: 10.1113/jphysiol.1969.sp008924. View

12.

Walmsley B, HODGSON J, Burke R . Forces produced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats. J Neurophysiol. 1978; 41(5):1203-16. DOI: 10.1152/jn.1978.41.5.1203. View

13.

Hatze H . A myocybernetic control model of skeletal muscle. Biol Cybern. 1977; 25(2):103-19. DOI: 10.1007/BF00337268. View

14.

Scott S, Loeb G . Mechanical properties of aponeurosis and tendon of the cat soleus muscle during whole-muscle isometric contractions. J Morphol. 1995; 224(1):73-86. DOI: 10.1002/jmor.1052240109. View

15.

Otten E . A myocybernetic model of the jaw system of the rat. J Neurosci Methods. 1987; 21(2-4):287-302. DOI: 10.1016/0165-0270(87)90123-3. View

16.

Allen J, Moss R . Factors influencing the ascending limb of the sarcomere length-tension relationship in rabbit skinned muscle fibres. J Physiol. 1987; 390:119-36. PMC: 1192169. DOI: 10.1113/jphysiol.1987.sp016689. View

17.

Scott S, Brown I, Loeb G . Mechanics of feline soleus: I. Effect of fascicle length and velocity on force output. J Muscle Res Cell Motil. 1996; 17(2):207-19. DOI: 10.1007/BF00124243. View

18.

Scott S, Winter D . A comparison of three muscle pennation assumptions and their effect on isometric and isotonic force. J Biomech. 1991; 24(2):163-7. DOI: 10.1016/0021-9290(91)90361-p. View

19.

Chanaud C, Pratt C, Loeb G . Functionally complex muscles of the cat hindlimb. II. Mechanical and architectural heterogenity within the biceps femoris. Exp Brain Res. 1991; 85(2):257-70. DOI: 10.1007/BF00229405. View

20.

Seo J, Krause P, McMahon T . Negative developed tension in rapidly shortening whole frog muscles. J Muscle Res Cell Motil. 1994; 15(1):59-68. DOI: 10.1007/BF00123833. View