Theoretical effects of radioligand diffusional gradients and microscopic neuroreceptor distribution in in vivo kinetic studies

A simplified one-dimensional model system was used to test the possibility that physically realistic parameters would lead to the prediction of microscopic heterogeneity of radioligand distribution in the brain and that microscopic heterogeneity of radioligand and neuroreceptor distribution could influence the macroscopically observedin vivo kinetics. The model was represented mathematically by a partial differential equation which is similar to the heat diffusion equation, but with special boundary conditions. The equation was solved analytically under the condition of negligible receptor occupancy by inversion of the Laplace transform and in the more general case of arbitrary receptor occupancy by cubic spline approximation. In simulations with physically reasonable values for rate constants and parameters, we find that significant radioligand gradients can occur. Thus, the level of radioligand in the immediate vicinity of the receptor may be substantially different from the average level in a macroscopically measured region of interest.