Physical model of a heterogeneous medium as applied to nuclear medicine

Abstract

In nuclear medicine, a patient is administered a radiolabeled pharmaceutical which is distributed in various organs of a patient body. The patient body with distributed emitting radiopharmaceutical is a heterogeneous medium. In this work, the problem of reconstructing the image of the human brain using single-photon emission tomography (SPET) is considered. To obtain the image, the statistical MAP-ENT algorithm is applied. To develop this algorithm, it is necessary to formulate a priori information about the object to be reconstructed. The distribution of radiopharmaceuticals in the patient’s body is a spatially inhomogeneous distribution of non-interacting radiopharmaceutical particles. This distribution is described using the Boltzmann model of a non-equilibrium isolated system. For such a system, one can write the entropy functional, which determines the a priori model. The algorithm was tested using the Hoffman mathematical model, which simulates the distribution of a radiopharmaceutical in the human brain. In numerical experiments, the properties of the MAP-ENT algorithm were studied under conditions close to clinical practice. The results have shown the prospects of the MAP-ENT algorithm.