Simple model of the smooth muscle isotonic contraction as a dynamical system

Abstract eng:
The paper discusses a mathematical model of the isotonic smooth muscle contraction considering the influence of the excitation processes on the sarcolemma and inside the muscle cell. The discussed model is based on the approach published in Rosenberg and Svobodov´ (2010) where the muscle fibre model containing the term corresponding a to the state of ATP hydrolysis was proposed. ATP hydrolysis is the main source of muscle energy. This term is considered in the study to be proportional to the intracellular Ca2+ concentration, its sigmoidal function respectively. A lot of models of the intracellular Ca2+ concentration time evolution have been published. The model introduced in Keener and Sneyd (1998) was chosen. The model has the form of the dynamical system with 6 DOFs. Its basic dynamical analysis was done. The results from the numerical simulation are consistant with the published experimental results. The periodic solution of the model corresponds in some specific cases to the myogenic vascular response known in medicin. The advantage of the discussed approach is the natural integration of the active and passive components of the muscle tissue into the model. The model facilitates also the integration of the other sophicticated muscle cell models.

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