Stiffness-distortion sarcomere model for muscle simulation

• Published in: Journal of applied physiology (1985) Vol. 87; no. 5; pp. 1861 - 1876
• Main Authors: Razumova, Maria V, Bukatina, Anna E, Campbell, Kenneth B
• Format: Journal Article
• Language: English
• Published: United States Am Physiological Soc 01.11.1999; American Physiological Society
• Subjects: Algorithms; Anatomy & physiology; Biomechanical Phenomena; Electric Stimulation; Electrophysiology; Linear Models; Mathematical models; Models, Biological; Muscle, Skeletal - anatomy & histology; Muscle, Skeletal - physiology; Muscle, Skeletal - ultrastructure; Muscular system; Sarcomeres - physiology; Sarcomeres - ultrastructure
• ISSN: 8750-7587; 1522-1601
• DOI: 10.1152/jappl.1999.87.5.1861

Departments of 1  Veterinary and Comparative Anatomy, Pharmacology and Physiology and 2  Biological Systems Engineering, Washington State University, Pullman, Washington 99164; 3  Department of Physics, Division of Biophysics, Moscow State University, Moscow; and 4  Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, Puschino, Russia A relatively simple method is presented for incorporating cross-bridge mechanisms into a muscle model. The method is based on representing force in a half sarcomere as the product of the stiffness of all parallel cross bridges and their average distortion. Differential equations for sarcomeric stiffness are derived from a three-state kinetic scheme for the cross-bridge cycle. Differential equations for average distortion are derived from a distortional balance that accounts for distortion entering and leaving due to cross-bridge cycling and for distortion imposed by shearing motion between thick and thin filaments. The distortion equations are unique and enable sarcomere mechanodynamics to be described by only a few ordinary differential equations. Model predictions of small-amplitude step and sinusoidal responses agreed well with previously described experimental results and allowed unique interpretations to be made of various response components. Similarly good results were obtained for model reproductions of force-velocity and large-amplitude step and ramp responses. The model allowed reasonable predictions of contractile behavior by taking into account what is understood to be basic muscle contractile mechanisms. mathematical model; muscle mechanics; muscle cross bridge; muscle contraction