A simplified formulation of the gamma variate function

The gamma variate function has been often used to describe the dispersion of a bolus as it passes through a series of compartments. For this reason, it is frequently chosen to fit first-pass data in studies quantifying cardiac output and left-to-right cardiac shunts. Although the gamma variate is an appropriate function to model these situations, it has several undesirable mathematical properties. Changes in the alpha and beta parameters affect not only the rise and fall times of the function, but also change the location and magnitude of the function maximum. This makes it difficult to anticipate how the function will be altered by varying the parameters and often requires an additional renormalization step when the gamma variate is being used to fit a curve. A different but entirely equivalent form of the gamma variate is derived in which these problems are eliminated.