Which Linear Compartmental Systems Can Be Analyzed by Spectral Analysis of PET Output Data Summed over All Compartments?

Abstract

General linear time-invariant compartmental systems were examined to determine which systems meet the conditions necessary for application of the spectral analysis technique to the sum of the concentrations in all compartments. Spectral analysis can be used to characterize the reversible and irreversible components of the system and to estimate the minimum number of compartments, but it applies only to systems in which the measured data can be expressed as a positively weighted sum of convolution integrals of the input function with an exponential function that has real-valued nonpositive decay constants. The conditions are met by compartmental systems that are strongly connected, have exchange of material with the environment confined to a single compartment, and do not contain cycles, i.e., there is no possibility for material to pass from one compartment through two or more compartments back to the initial compartment. Certain noncyclic systems with traps, systems with cycles that obey a specified loop condition, and noninterconnected collections of such systems also meet the conditions. Dynamic positron emission tomographic data obtained after injection of a radiotracer, the kinetics of which can be described by any model in the class of models identified here, can be appropriately analyzed with the spectral analysis technique.