Development of Mathematical Models

The primary factor affecting the form of a model is the nature of the tracer itself. Usually, a priori information can be used to predict all of the relevant metabolic paths of the tracer in tissue, i.e., a complete model. However, technical and statistical limitations of the available data will prevent the use of such a comprehensive model, which includes all steps in the physiological uptake, metabolism, and clearance of a tracer.

Figure 6.1 shows the process of development and application of a model in PET [69, 70]. This section presents the steps starting with a complete model, then generating an identifiable model, and ultimately a practical model. An identifiable model is one which can be applied to regional kinetic data and used to extract estimates of model parameters. Such a model is a simplified version of a comprehensive description of the interactions of a radiotracer in tissue. However, this model may not be workable if its parameter estimates are too variable or inaccurate. A useful model may be derived by further simplification of the identifiable model. The useful model provides reproducible and accurate estimates of model parameters. Validation studies are necessary to demonstrate these characteristics.

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