Study and parameters identification of a rheological model for excised quiescent cardiac muscle

Numerical method for a model of inhomogeneous muscle fibers

“…As an immediate consequence we have the following useful result. On the other hand, taking the difference between the first equation of (2.1) and (2.6) with (3.1) we see, using (4.1), (2.8), the mean value theorem and the fact that v:At = z: -z;-' + O((At)'), that, for 1 5 i d m, j E Z, 1 5 n 5 N, which, for 1 We shall need to see the actual ones, v: = that, for 1 5 i I m , 1 that the approximate velocities, V: = (Z: -Z:-')/At, are close to [(z: -…”

“…Several models describing the contraction of a muscle have been proposed and analyzed in the last decade (see, e.g., [1][2][3][4][5]). Most of them simulate the cross-bridge dynamics responsible for the contraction of the muscle [6] using a two-state cross-bridge model.…”

A mathematical study of the plasticity effects in muscle contraction

“…Notice that the integral in (2.10) is meaningful thanks to (2.2), (2.3), and (2.8). As the fitting of experimental data in excised quiescent muscle shows [3], the function ~ can be expressed by an exponential law; here we work under the general assumption (2.4). The functions F and G in (2.6) are related to the biochemical reactions function ~ (see (1.1)) in the following way:…”

“…In fact, here we want to provide a mathematical tool, well established from the mathematical point of view (existence, uniqueness, numerical approach), useful in interpretating the experimental data. We are now working on this matter, following the validation work already carried out, in collaboration with the Institute of Human Physiology at the University of Pavia, on previous models (see [3], [8], and [12]). …”

“…In the past a great deal of effort has been directed toward analysis of the material properties of passive muscle (see, e.g., [3], [16], and literature therein) and of the structure of the contractile element (see, e.g., [9], [19], [20], [23], [27], [28], [30], and related literature). Less work seems to have been directed toward material properties of activated muscle.…”