Abstract
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.
In order to analyze the simulated data, we derived a rigorous steady-state solution, including both a statement of necessary and sufficient conditions for the validity of the steady-state approximation as well as a demonstration of the proper technique for assessing the consistency of the derived parameter with the requirements of the approximation. The radioligand heterogeneity leads to significant errors in the parameters estimated in the steady-state kinetic analysis. In particular, the pseudo first-order rate constant for radioligand-neuroreceptor association, which is often used as a measure of the total amount of neuroreceptor, is underestimated. The first-order rate constant for radioligand-neuroreceptor dissociation is also underestimated. These effects can partially account for the experimentally-observed discrepancy betweenin vivo andin vitro estimates of these kinetic parameters.
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Zeebèrg, B.R., Reid, R.C., Murphy, K.A. et al. Theoretical effects of radioligand diffusional gradients and microscopic neuroreceptor distribution inin vivo kinetic studies. Bltn Mathcal Biology 50, 423–444 (1988). https://doi.org/10.1007/BF02458845
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DOI: https://doi.org/10.1007/BF02458845