Simulation of a Biological System On an Analog Computer

The purpose of this paper is to discuss a method for the construction of a mathematical model of a large biological system. This method, based on Gibbs' free energy hypothesis, uses the format of mathematical programming, while the actual computation is ac complished by the method of steepest descent. The biological system chosen to exemplify the mathe matical method was the respiratory function of the blood in the human lung. This method is based on the postulate that chemical mixtures tend toward a reaction equilibrium which minimizes the potential, or free energy, of the system. We may thus write down the classical Gibbs free energy function for each chemical species, and require that total free energy relative to some standard state be minimized under the conditions of the experiment. The solution of the equilibrium problem consists of a set of mole numbers which minimizes the free energy function, subject to equations for conservation of mass and nonnegativity. The analog computer solution of the respiration model was undertaken not only to give fast, sensitive tests of the mathematical model and its assumptions, but also to obtain a simulation of the time depend ent system. Examples of the mechanization of the equations are presented in this paper, and also results are computed for the static equilibrium of a canoni cal model.