Stochastic modelling of physiologic processes with radiotracers and positron emission tomography

The compartment model, so often used in nuclear medicine and in pharmacokinetics, is formed by a set of linear differential equations of order one with constant coefficients; its validity depends upon the hypothesis that the system described contains a finite number of components, and that each component is homogeneous. These hypotheses exclude the presence of diffusion and of age-dependent processes, or in general of transport of a non-Markovian nature. The fact that frequently the experimental data agree with this model does not necessarily prove the model is appropriate, but only that it is flexible. In addition to the consistency with the experimental data, an obvious conceptual requirement of the model is that its parameters could be interpreted in terms of perceivable physical properties. All this considered, it will be demonstrated that the experimental data can be examined in terms of a model making a minimum number of assumptions and giving the best physical interpretations to the parameters involved. By way of example, a high resolution positron emission tomograph will be used to determine the successive moments describing the blood circulation through different sections of the brain. Whereever the relative moments form a geometric progression, the circulation in that section follows the rules of a perfect compartment; if this is not the case, the analytical method described can be used to describe the behavior of a tracer particle in the part of the organ. (ERB