An analytical solution set for a four-compartment mixed mammillary/catenary model

The purpose of this study was to extract the intercompartmental rate consta nts analytically from the coefficients and exponents of the exponential sum fittest to tracer data points for a unique four-compartment mixed mammilla ry/catenary (extended mammillary, radial) model, with losses solely from th e central (blood) compartment. This model is useful in estimating myocardia l and skeletal blood flow. Using Laplace transforms, the transfer functions of the exponential sum and the differential equations describing the model were obtained and the corresponding coefficients equated sequentially, whi ch yielded the intercompartmental rate constants. Three solution sees of ra te constants were found for the model, each of which satisfies both transfe r functions. A program written in BASIC is provided, which requires only th e coefficients and exponents of the exponential terms as input; the output is the three sets of rate constants. An example is given as an aid in debug ging. Only one solution set of the three was physiologically realizable in the example, but the bounds defining these limits are not known. The advant ages and limitations of the method are discussed. The method is suitable fo r initializing a non-linear least-squares fitting program for the rate cons tants. The appropriate physiological solution set for this model yields fra ctional and total myocardial or skeletal blood flow in a subject in the ste ady state. ((C) 1999 Lippincott Williams & Wilkins).