A non-parametric bayesian method to smooth PET time-activity-curves

Positron Emission Tomography (PET) is an imaging technique in which a radionuclide is introduced into a molecule of potential biological relevance (to form what is called a tracer) and administered to a patient. The regional evolution of the uptake of the tracer over time is called a TimeActivity-Curve (TAC) and is used to derive some clinical measures that give information about the process under study. One of these measures is the Distribution Volume (DV ) which can be estimated by several methods, notably the Graphical Analysis Method (GA). It has been shown that using GA method on noisy TAC leads to a systematic underestimation of the Distribution Volume (Hsu et al., 1997; Slifstein and Laruelle, 1999). We propose a method that allows to smooth the Time-Activity-Curves in a non-parametric way by using Bayesian P-splines. This method may be used in all the cases, whatever the compartmental model that might underly the observed data. Simulations have shown that this method gives an unbiased estimation of the true TAC, whatever the level of noise. We show that smoothing TAC with the non-parametric method before computing the Distribution Volume allows to reduce considerably the bias. Logan et al. (2001) proposes to smooth data before computing the Distribution Volume by using the Generalized Linear Least Squares (GLLS) method if a one-tissue compartment model is considered and by applying the GLLS to the data in two parts for a two-tissues compartment model : one set of parameters is estimated from times 0 to T1 and a second set from T1 to the end time where T1 has to be chosen from data. This method provides good results but, if we are not sure about the compartmental model suitable for the data or, if we want to avoid the choice of T1, using the Bayesian nonparameteric model is a good alternative.