A two element model incorporating two 4-state sarcomeres in series. This model is based on the 4 state model of a cardiac sarcomere originally developed by Landesberg and Sideman (Am J Physiol 267:H779-H795, 1994) and has been further developed to describe two sarcomeres.

Description

This model describes two sarcomere elements joined in series between two attachment points a fixed length apart. Each sarcomere element consists of a contractile sarcomere in parallel with a Voigt body. The Voigt body is defined as a linear spring and viscous dashpot connected in parallel. A diagram of the system is shown to the right. The contractile sarcomere force generation is governed by the response of a 4 state model of troponin in the sarcomere to an input calcium transient. This 4 state model has been previously developed by Landesberg and Sideman (Amer J Physiol Heart Circ Physiol 267:H779-H795, 1994.)
Note that the convention used by Landesberg and Sideman for positive velocity is when the sarcomere is contracting. Therefore we applied this convention to force generation and acceleration also.

Equations

ODE's governing four state sarcomere representation in element 1:

ODE's governing four state sarcomere representation in element 2:

ODE governing the strain in element 1:

Algebraic expressions to determine remaining stresses, strains, velocities, etc.: