Empirical estimators of gamma fits to tracer-dilution curves and their technical basis and practical scope

A gamma fit facilitates smoothing and extrapolation of distorted tracer-dilution curves in blood flow studies. Theoretically based empirical estimators were developed as simple alternatives to direct regression approaches from simulated gamma distributions with a wide range of shape asymmetry. Key curve features of peak height p, full width w at half peak height, rising and falling limb inflection tangents and asymmetry of the peak time with respect to the p/2 height occurrences were related to the parameters of the distribution by multiple linear regression after suitable transformations. The product pw was simply related to the total area A under the curve, pw/A being 0.93 +/- 0.01 in 70 cardiac output determinations from ten surgical patients. Shape and scale parameters were closely related to the standard deviation, inflection point properties and w for the curves. Mensuration devices suitable for cardiac output computers were developed that calculated total areas from incomplete portions under gamma curves and by-passed the need for parameter estimation. There was limited point in estimating the distribution parameters just to derive particle transit times, because of the ad hoc nature of the fitting form, which did not allow for the back-dispersion by Brownian motion of tracer molecules diluting in blood flow. Nonetheless, the accuracy of area prediction using a gamma fit was adequate for most clinical purposes and comparable to that via the random walk function, giving good insight to established results and computing procedures.