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Positron emission tomography is a noninvasive research technique used in medicine to measure the three-dimensional distribution of the biologically active substances, marked with a positron emitter in the living body. Positron emission tomography provides information about function of the tissue and not solely about its morphology, and is thus complementary to computer tomography and magnetic resonance imaging. Its basic principle is simultaneous detection of two photons generated by annihilation of the emitted positron in the space around the object studied, using a scintillation camera, or multiwire proportional chambers with photon converters, produced at the Jože Štefan institute. In principle, it is easy to mark different biomolecules with positron emitters, which are mostly isotopes of the basic elements composing organic substances, and to study the corresponding physiological processes. Good knowledge of the compartment theory and of the kinetic models of such processes is essential for quantification of these processes, which is the basis of positron emission tomography diagnosis. For measuring blood flow through tissues, as well as the rate of glucose utilization and permeability of the blood-Brain barrier, we currently use alcans, 2–deoxy–D–glucose and 3–deoxy–D–glucose marked with ¹⁸F. starting with basic measurements on animals, we shall try to find new tracers and to develop the corresponding quantification models.