A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation

Abstract

Contractions on the descending limb of the total (active + passive) muscle force—length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarcomere—length inhomogeneities. This is however not observed in experiments—vast half-sarcomere—length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sarcomere—length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin—titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force—length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided.

Microstructural analysis of skeletal muscle force generation during aging

“…As muscle fiber has little resistance under compression in the fiber direction, experimental data from skeletal muscle tissue under uniaxial compression along the fiber direction can be used to calibrate the material parameters of the CT material models . Figure A summarizes the experimental data extracted from literature for the uniaxial compressive experiments in the muscle fiber direction, conducted on rat tibialis anterior muscle, porcine, bovine, and ovine muscles, and human forearm muscle .…”

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

“…For example, the normalized active stress can be calculated by the arithmetic mean of the single muscle fiber stresses weighted by their volume fraction in an referential elementary volume, that is, where w MU i is the volume fraction of the i ‐th MU at a specific material point, cf. Heidlauf and Röhrle (Heidlauf & Röhrle, ), Heidlauf et al (Heidlauf et al, ; Heidlauf et al, ). Note that in the work of Heidlauf and co‐workers (Heidlauf et al, ; Heidlauf et al, ; Heidlauf & Röhrle, ) additionally complexity arises from coupling the cellular muscle model to a model of the action potential propagation (cf.…”

“…Both the active stress approach and the active strain approach are valid from a macroscopic and phenomenological point of view, that is, both methods can be fitted in such a way that they reproduce the same macroscopic data. While some authors pointed out that the active stress approach might be beneficial from a mathematical point of view, since it is more straight forward to enforce convexity and thus guarantee the existence of a unique solution of the mathematical problem (Ambrosi & Pezzuto, 2012;Rossi, Ruiz-Baier, Pavarino, & Quarteroni, 2012), the active stress approach is more intuitive and has, for example, proven to be a useful method to study knock-out conditions (Heidlauf, Klotz, Rode, Siebert, & Röhrle, 2017).…”

Simulating electromechanical delay across the scales – relating the behavior of single sarcomers on a sub‐cellular scale and the muscle‐tendon system on the organ scale

“…[4,5]) solves for macroscopic deformations of the tissue while taking into account the chemo-electro-mechanical behavior of embedded computational muscle fibers, i.e. [4,5]) solves for macroscopic deformations of the tissue while taking into account the chemo-electro-mechanical behavior of embedded computational muscle fibers, i.e.…”