Gen Physiol. Biophys. (1990). 9, 219 -244 219 Heart Muscle: Mathematical Modelling of the Mechanical Activity and Modelling of Mechanochemical Uncoupling L. B. KATSNELSON, V. YA. IZÁKOV and V. S. MARKHASIN Laboratory of Biophysics, Institute of Industrial Hygiene and Occupational Diseases, Sverdlovsk 620014, USSR Abstract. A mechanical model of heart muscle is proposed which includes rheological equations and equations for Ca-troponin interaction, for the depen- dences of the number of myosin cross-bridges on the length of sarcomere and on the speed of motion. The main assumption of the model is the dependence of the troponin affinity to calcium ions on the number of myosin cross-bridges attached. The model successfully imitates isometric and isotonic contractions, the "length-force" relationships, load-dependent relaxation, and the group of mechanical phenomena known as mechanochemical uncoupling. Key words: Myocardial tension — Muscle mechanics — Modelling of muscle — Troponin-Ca relationship Introduction Several models are available at present which describe different aspects of the mechanical activity of skeletal and cardiac muscles (Fung 1970; Morel 1985; Simmons and Jewell 1973). Depending on the specific objective, these models describe the time course of single isometric and isotonic contractions, the dependence of the speed of shortening on the load, the relation between length and force, etc. A common disadvantage of all these models is that they reproduce but a limited number of phenomena in the mechanical activity of muscle. Thus, while simulating successfully the dynamics of the isometric contractions, the models fail to describe isotonic contractions or responses to rapid changes in the length or load. The models based on the mechanochemical cycle of myosin cross-bridges are very complex and require application of partial differential equations (Hill