A Mathematical Model for the Estimation of Heart Volumes from Indicator Dilution Curves

The estimation of ventricular volumes by indicator dilution methods is subject to errors resulting from incomplete mixing and nonuniform sampling. A mathematical model is proposed which theoretically permits calculation of these errors. The model allows for nonuniform distribution of indicator in the ventricle and for nonuniform representation of the end-diastolic volume (EDV) in the systolic ejectate. It is assumed that the concentration of indicator and the flow at a given cross section of the aorta are uniform but not necessarily the same at a different cross section, or at different times during the cardiac cycle. In respect to the validity of the popular formula, EDV = SV/l-K (K = average residual fraction), it was shown that the conditions traditionally believed to be satisfying for accurate measurements of EDV are neither sufficient nor necessary. Less restrictive alternative conditions sufficient for accurate measurements are proposed.