Cardiac chemical constant. Part I: Derivation of the characteristic phenomenological equation

A physiochemical parameter is derived and defined as the cardiac chemical equilibrium dissociation constant (KD). KD is based upon a phenomenological model in which the cardiac muscle chemical reaction kinetics describe the interconversion between long and short units (i.e. the individual sarcomere is fully extended or fully contracted). KD is defined as the ratio of the number of units in the long state to the number of units in the short state. The mathematical development proceeds through four stages: derivation of the governing differential equation during cardiac systole; simplification of the differential equation to describe the cardiac model; determination of the upper and lower limits and average value of Nt (the total number of units in a hypothetical mid-wall circumferential fibre): definition and calculation of the cardiac chemical constant (KD). KD is shown to describe a series of equilibrium points throughout cardiac systole. This requires that each mechanical equilibrium state (a series of static, steady-state intervals over time) is also associated with its own specific chemical equilibrium state.