Number of exponential terms describing the solution of an N-compartmental mammillary model: vanishing exponentials.

The solution for a linear mammillary model is always described by a summation of m + 1 negative exponential terms with constant coefficients. m + 1 less than or equal to N, where N is the number of compartments in the model. m is equal to the number of distinct values for the peripheral Ej values. Use is made of matrix notation and the theorems of Browne concerning the eigenvalues of a matrix. The consequences of vanishing exponentials are derived, and in particular the apparent volume of distribution frequently calculated from experimental data is shown not to be unique.