# Katsnelson, Nikitina, Chemla, Solovyova, Coirault, Lecarpentier, Markhasin, 2004

#### Model Status

This model has been checked and it runs in both COR and PCEnv to recreate the published results. Units are consistent throughout. In this particular version of the model, time is expressed in milliseconds and all calcium variables and parameters have been normalized to the total concentration of TnC (parameter A_tot).

With default setting the model produce isometric contraction (parameter isotonic=0). To switch from isomentric mode to isotonic mode isotonic parameter should be set 1. Then set parameter F_afterload to the value less then the maximum force calculated at isometric mode. Make sure that the model is run in isometric mode first and see the value of the maximum of isometric force. If F_afterload is not less than this value, model performs isometric mode instead of isotonic.

#### Model Structure

Abstract: We have previously proposed and validated a mathematical model of myocardium contraction-relaxation cycle based on current knowledge of regulatory role of Ca2+ and cross-bridge kinetics in cardiac cell. That model did not include viscous elements. Here we propose a modification of the model, in which two viscous elements are added, one in parallel to the contractile element, and one more in parallel to the series elastic element. The modified model allowed us to simulate and explain some subtle experimental data on relaxation velocity in isotonic twitches and on a mismatch between the time course of sarcomere shortening/lengthening and the time course of active force generation in isometric twitches. Model results were compared with experimental data obtained from 28 rat LV papillary muscles contracting and relaxing against various loads. Additional model analysis suggested contribution of viscosity to main inotropic and lusitropic characteristics of myocardium performance.

Schematic diagram of the Katsnelson et al model - an updated rheological scheme of the heart muscle including contractile element CE, two passive elastic elements PE (parallel one) and SE (series one) and two viscous elements VS1 and VS2. The effect of calcium and the calcium binding ligand (B) in facilitating actin-myosin binding is also highlighted. |

The original paper reference is cited below:

Influence of viscosity on myocardium mechanical activity: a mathematical model, Leonid B. Katsnelson, Larissa V. Nikitina, Denis Chemla, Olga Solovyova, Catherine Coirault, Yves Lecarpentier and Vladimir S. Markhasin, 2004,
*Journal of Theoretical Biology*, 230, 385-485. PubMed ID: 15302547