arXiv subjects

Javier A. Almonacid

Publications and source records attributed to Javier A. Almonacid.

3 recordsLinked to original sources

arXiv2025

On the dynamical stability of skeletal muscle

There has been debate for over 70-years about whether active skeletal muscle is dynamically stable at lengths greater than its optimal length. The stability of computational muscle models is a critical issue, as it directly affects our ability to simulate muscle deformation across different operating lengths, especially at lengths where muscles are known to remain functional despite model-predicted instabilities. In this study, we revisit the question of dynamical stability of ODE-based models of skeletal muscle. In particular, we investigate whether activation-independent tissue properties can provide stability to contractions along the dip region of the total force-length curve. First, using a combination of analytical tools (eigenvalue analysis and non-dimensionalization) and numerical simulations, we confirm that traditional Hill-type muscle models can display divergent dynamics in this region. Then, we propose a stabilized version of a 1D Hill-type muscle model that incorporates the 3D nature of skeletal muscle deformation. This results in a completely convex force-length relationship that can bring robustness to numerical simulations, while preserving the computational efficiency of 1D models. Our findings suggest that activation-independent intrinsic mechanical properties of muscle are sufficient to stabilize contractions even in the dip region, offering new insight into how muscles maintain functional integrity during active stretch.

physics.med-ph↗

arXiv2023

Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study

The propagation of internal gravity waves in stratified media, such as those found in ocean basins and lakes, leads to the development of geometrical patterns called "attractors". These structures accumulate much of the wave energy and make the fluid flow highly singular. In more analytical terms, the cause of this phenomenon has been attributed to the presence of a continuous spectrum in some nonlocal zeroth-order pseudo-differential operators. In this work, we analyze the generation of these attractors from a numerical analysis perspective. First, we propose a high-order pseudo-spectral method to solve the evolution problem (whose long-term behaviour is known to be not square-integrable). Then, we use similar tools to discretize the corresponding eigenvalue problem. Since the eigenvalues are embedded in a continuous spectrum, we compute them using viscous approximations. Finally, we explore the effect that the embedded eigenmodes have on the long-term evolution of the system.

math.SP↗

arXiv2022

A three-dimensional model of skeletal muscle tissues

Skeletal muscles are living tissues that can undergo large deformations in short periods of time and that can be activated to produce force. In this paper we use the principles of continuum mechanics to propose a dynamic, fully non-linear, and three-dimensional model to describe the deformation of these tissues. We model muscles as a fibre-reinforced composite and transversely isotropic material. We introduce a flexible computational framework to approximate the deformations of skeletal muscle to provide new insights into the underlying mechanics of these tissues. The model parameters and mechanical properties are obtained through experimental data and can be specified locally. A semi-implicit in time, conforming finite element in space scheme is used to approximate the solutions to the governing nonlinear dynamic model. We provide a series of numerical experiments demonstrating the application of this framework to relevant problems in biomechanics, and also discuss questions around model validation.

math.NA↗