Spectral Analysis

In compartmental model fitting, the number of compartments and their interconnection are defined a priori. This implies that the physiological or biochemical pathways are somewhat known. Yet, a priori knowledge about the behavior of novel anticancer drugs may not be available. Further, the compartmental modeling approach assumes well-mixed, homogeneous tracer distribution within the tissue or the ROI. This may not be true for tumor which normally has high degree of heterogeneity. Spectral analysis does not rely on tracer assumptions and the number of compartments and their connectivity; it is particularly useful for tracer kinetics studies.

Spectral analysis [87] fits the model defined in equation (2.22) with a predefined set of basis functions, eijt <g> Cp(t), where ¡j can take on a discrete set of values so that a large number (100 or more) of basis functions are generated. The fitting to tissue data is accomplished by nonnegative least squares (NNLS) algorithm with a constraint ai > 0 [88]. Typically, a linear combination of only two or three basis functions from the complete set of basis functions are identified which can best describe the observed tissue data. From the fitted basis functions, the impulse response function and other physiological parameters can be estimated. Spectral analysis can also be applied to projection data directly, but it may not produce results equivalent to those obtained from reconstructed images because the NNLS fitting may not be linear [89].

Since spectral analysis does not require any a priori definition of the numerical identifiable components present in the PET data, it is more flexible than compartmental model fitting. However, the assumption on the nonnegativity coefficients of exponentials may not be valid in a generic compartmental model as negative coefficients of exponentials are also possible if the input and output are not taken from the same compartment [90]. Furthermore, repeated eigenvalues may be inherent in the data and the impulse response function of the underlying system could have different formats [91].

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