Adequacy of compartmental model for positron emission tomography examinations

The objective of this work is the determination of the most adequate compartmental model for the study of physiological dynamics based on positron emission tomography exams. We propose the use of Akaike's information criterion for the optimal model selection, and Levenberg-Marquardt algorithm with sensitivity equations for the task of estimating the characteristic parameters of the differential equations describing the models. We have considered three compartmental structures represented, respectively, by two compartments and two characteristic constants, three compartments and four characteristic constants and four compartments and six characteristics constants. The data considered in this work were synthesized taking into account key features of a real tomography exam, such as type and level of noise and morphology of the input function of the system. Applying the proposed methodology with three noise levels (low, medium and high), we obtained agreement of the best model with strong and considerable degrees (with Kappa indexes equal to 0.95, 0.93 and 0.63, respectively). It was observed that, with high noise level and more complex models (four compartments), the classification is deteriorated due to lack of data for the decision. Programs have been developed and a graphical interface that can be used in research, development, simulation and parameter identification of compartmental models, supporting analysis of clinical diagnostics and scientific practices. (author)