Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue (preprint)


This is my first preprint!

Under the supervision of Prof. Bernd Simeon, I used mathematical tools from kinetic theory to work towards a mathematically rigorous link between physiological models of action-myosin contraction in muscle cells and kinetic description of these models.

The key contributions are

  • strict inclusion of constraints in the mean-field limit for coupled muscle models,
  • a general class, called partially kinetic systems, for which the mean-field limit is applicable.

It is important to notice that this is centered around mathematical problems only. There is no new biological insight yet.

This article provides examples and motivation for the theory. (Currently, I am working on a related article which shall present the rigorous analysis and missing proofs.)

Download preprint here