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 compar tments, one intravascular (iv) and one extravascular (ev), is solved by Lap lace transformation of two coupled differential equations. By assuming a fu nctional form for the arterial input function (AIF), or by fitting to an ex perimentally determined AIF, this function is introduced into the solution as a boundary condition describing the time dependent input to the capillar y. The solution to the tissue homogeneity model equations in Laplace space are numerically inverted to obtain the concentration of tracer in the ev sp ace as a function of time and in the iv space as a function of both positio n and time. Magn Reson Med 45:42-45, 2001, (C) 2001 Wiley-Liss, Inc.