Generalization of a physiological model of input function for PET data analysis

Introduction

Tracer kinetic modeling has been widely used to analyze and/or interpret tissue time-series data obtained with dynamic PET studies quantitatively in terms of physiological or pharmacological parameters. Estimation of these parameters requires a mathematical model (which describes the kinetics of radiotracer in the tissue) and an input function (IF) to the model (usually obtained through frequent peripheral blood sampling or by imaging blood pool). However, measurement noise in tissue and in plasma or blood (the IF) can hamper reliable estimation of parameters. Considerable work has been done on PET imaging to improve the accuracy of tissue data. Correction of errors associated with IF, however, received much less attention. Direct use of measured (noisy) IF in kinetic modeling can lead to statistical uncertainties in the estimated parameters. Fitting blood data by mathematical functions has been found useful in reducing statistical fluctuations but abrupt changes in the input function and differed in administration protocols can cause ill-conditioned fitting. A physiologically reasonable model should be more appropriate for this task. The focus of this work is to generalize an IF model of single-bolus injection of radiotracer so that the case of constant tracer infusion of a finite duration can also be accommodated.

Methods

A 4-compartment model, parameterized by a sum of 4-exponentials (with a pair of repeated eigenvalues), which consists of 7 parameters (6 for the model plus a time delay) can reasonably describe the kinetics of blood circulatory system upon a single-bolus injection [Int J Biomed Comput 1993; 32: 95–110]. For constant tracer infusion over a finite duration T, the above parameterization is found inadequate to fit the blood data. In this study, a generalization is proposed in which the constant tracer infusion is modeled as a unit rectangular pulse (with a duration equals T) convolved with the response function of the single-bolus IF model. Since numerical calculation of convolution integral in the generalized IF model can introduce computation errors, we make use of the superposition and time-shift properties of linear systems for which a simple subtraction of the analytically-integrated model response function from its delayed (for time T) version can be computed instead. When T=0, the generalized model is reduced to the single-bolus IF model.

Results

Dynamic FDG-PET studies were performed on 12 patients few months after surgical removal of the brain tumor. FDG was administered using an automated infusion pump which delivers the tracer at a flow rate of 100mL/hr over 3 min. Dynamic images and blood data were acquired continuously over 60 min. Assuming counting statistics noise, blood data was fitted to the 8-parameter generalized IF model. For comparisons, data was also fitted to a sum of n-exponentials (n=1,2,3). It was found that the generalized IF model provided reliable and reproducible fits to the blood data, whereas fitting by sum of exponentials failed in majority cases.

Conclusions

The model presented here provides an efficient means to reduce noise and interpolation of blood data. Its application to PET data analysis is warranted.