The use of radiopharmaceuticals and the imaging of their biodistribution and kinetics with modern instrumentation are key components to successful developments in PET. Clever design and synthesis of sensitive and specific radiopharmaceuticals is the necessary first step. Each tracer must be targeted to measure a physiological parameter of interest such as blood flow, metabolism, receptor content, etc., in one or more organs or regions. State-of-the-art PET instrumentation produces high-quality 3-dimensional images after injection of tracer into a patient, normal volunteer, or research animal. With an appropriate reconstruction algorithm and with proper corrections for the physical effects such as attenuation and scatter, quantitatively accurate measurements of regional radioactivity concentration can be obtained. These images of tracer distribution can be usefully applied to answer clinical and scientific questions.

With the additional use of tracer kinetic modeling techniques, however, there is the potential for a substantial improvement in the kind and quality of information that can be extracted from these biological data. The purpose of a mathematical model is to define the relationship between the measurable data and the physiological parameters that affect the uptake and metabolism of the tracer.

In this chapter, the concepts of mathematical modeling as applied to PET are presented. Many of these concepts can be applied to radioactivity measurements from small animals made by tissue sampling or quantitative autoradiography. The primary focus in this chapter will be on methods applicable to data that can be acquired with PET imaging technology. The advantages and disadvantages of various modeling approaches are presented. Then, classes of models are introduced, followed by a detailed description of compartment modeling and of the process of model development and application. Finally, the factors to be considered in choosing and using various model-based methods are presented.

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