Modeling tissue contrast agent concentration: A solution to the tissue homogeneity model using a simulated arterial input function

The tissue homogeneity model, which describes tissue in terms of two compartments, one intravascular (iv) and one extravascular (ev), is solved by Laplace transformation of two coupled differential equations. By assuming a functional form for the arterial input function (AIF), or by fitting to an experimentally determined AIF, this function is introduced into the solution as a boundary condition describing the time dependent input to the capillary. The solution to the tissue homogeneity model equations in Laplace space are numerically inverted to obtain the concentration of tracer in the ev space as a function of time and in the iv space as a function of both position and time. Magn Reson Med 45:42-45, 2001.