Modelling of red and white muscle fibres in force generation

Abstract

Abstract. Force development mechanisms in white and red muscle fibres are investigated. Both types of fibres play different roles in muscular force generation, expressed in force onset velocity and duration. The purpose of the work is to find the key parameters in the model imitating differences in onset velocity for both types of muscle fibre cells, which further would allow to model the propagation of excitation wave. The model allowed to estimate the effect of differences in capacitances of cell membranes of red and white muscle cells to depolarization velocity. With the model we were able to determine the conditions of appearance of low amplitude oscillations interrupting the force generation. Investigation of different behaviour of red and white muscle fibres is needed to understand reaction mechanisms of living objects to sudden external situation changes, such as obstacles or attacks. Similar ability to have two types of force production -slow sustained, and fast of short duration -is often required for robotic devices Keywords: red and white muscle fibres, muscular force generation, modelling. IntroductionRed and white muscle fibres are characteristic for cross-striated muscles taking part in force generation in different movements and other muscular activities. White muscular fibres have a typical fast action needed to develop large force in a short time interval, whereas red muscular fibres are typically slow motion fibres able to generate force for a long duration, e.g., to hold a given position of a body [1]. Existence of two different patterns of motion control -long duration with low energy consumption and very fast action with large energy consumption is a relevant feature for robotic devices providing efficient capability to react on sudden obstacles or another need for change of the trajectory of different moving parts of such devices.In order to model excitation activity, we based on Hodgkin-Huxley type equations [2; 3], describing the excitation process in a single cell membrane. Sum of ionic currents flowing across the cell membrane, including external current representing external excitation, is described as follows:-C dV/dt = m 3 h g Na (V -V Na ) + g K n