Types of Models

There are a wide variety of approaches to extract meaningful physiological data from PET tissue radioactivity measurements. All modeling approaches share some basic assumptions, in particular the principle of conservation of mass. A number of sources provide a comprehensive presentation of modeling alternatives [13-18]. Some approaches are termed stochastic or non-compart-mental, and require minimal assumptions concerning the underlying physiology of the tracer's uptake and metabolism [19]. These methods permit the measurement of certain physiological parameters, such as mean transit time and volume of distribution, without an explicit description of all of the specific pools or compartments that a tracer molecule may enter.

Alternatively, there are distributed models that try to achieve a precise description of the fate of the radiotracer. These models not only specify the possible physical locations and biochemical forms of the tracer, but also include the concentration gradients that exist within different physiological domains. In particular, distributed models for capillary-tissue exchange of tracer have been extensively developed [20-26]. Since this is the first step in the uptake of any tracer into tissue, a precise model for delivery of tracer at the capillary is important. Distributed models are also used to account for processes, such as diffusion, where concentration gradients are present [27].

A class of models whose complexity lies between stochastic and distributed is the compartmental models. These models define some of the details of the underlying physiology, but do not include concentration gradients present in distributed models. The development and application of these models is the principal focus of this chapter. The most common application of compartmental modeling is the mathematical description of the distribution of a tracer throughout the body [28, 29]. Here, different body organs or groups of organs are assigned to individual compartments, and the model defines the kinetics into and out of each compartment. This type of model is useful when the primary measurable data is the time-concentration curve of the tracer in blood and urine. If there are many measurements with good accuracy, fairly complex models with many compartments and parameters can be used.

In PET, compartmental modeling is applied in a different manner. Here, scanners provide one or more measurements of radioactivity levels in a specific organ, region, or even pixel. If the tracer enters and leaves the organ via the blood, the tracer kinetics in other body regions need not be considered to evaluate the physiological traits of the organ of interest. In this way, each region or pixel can be analyzed independently. Generally, there must be some knowledge of the time-course of blood radio activity. Since each region can be evaluated separately, the models can be relatively simple, and can therefore be usefully applied to determine regional physiological parameters from PET data.

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