Introduction
Invasive PET experiments provide valuable tracer kinetic information, but also contain several sources of error and uncertainty. Potential errors in metabolite measurements are often overlooked but can degrade the accuracy of the final quantification of distribution volume and binding potential. Improper or insufficient quantification of the amount of intact tracer can occur for several reasons, including loss of blood samples and insufficient sample volume. Moreover, HPLC-analysis requires isolation of protein-reduced plasma from the samples. Accidental losses during these work-up procedures may occur and the quantification of HPLC data can be noisy due to insufficient separation of intact tracer from metabolites. Finally, increased uncertainties in the quantification are encountered for the samples drawn at later time points of the study due to low count rates. To manage situations where lost or inaccurate (noisy) metabolite samples occur, we hypothesized that the inclusion of population information via model parameter priors and MAP-Bayesian statistics could be used to stabilize the quantification of metabolite kinetics. To evaluate whether this method is applicable to PET metabolite data, we have undertaken a study simulating loss of data using [18F]FDPN data as an example.
Methods
Thirteen healthy male volunteers (39.1 ± 9.5 years) participating in ongoing clinical research studies with [18F]FDPN were included here. Details of the data acquisition are similar to those reported elsewhere (Spilker et al., Neuroimage 2004). Samples for metabolite quantification were taken at 5, 15, 30, 60 and 90 minutes p.i. To simulate loss of metabolite samples, single or multiple points were eliminated from the sequence and either a bi- or mono- exponential function was fit to the data under three conditions: 1) using only available data; 2) using available data and parameter priors with MAP-Bayesian statistics; 3) using an average curve from the population. To generate the parameter priors, the bi-exponential model (A*exp(-at) + B*exp(-bt)) was fit to each individual's full dataset and subsequently each parameter's mean and standard deviation (SD) were calculated. Prior information (mean and SD) was imposed on only the two exponents of the function; not on the coefficients in front of the exponentials.
Results
The results indicated that the inclusion of prior information via Bayesian statistics performed best when there was a severe loss of data. In these situations, the loss of data required a model order reduction from a bi-exponential function to a mono-exponential function under condition 1, while condition 2 was able to maintain the bi-exponential form and better approximated the true data. When only a single data point was lost, conditions 1 and 2 performed similarly; while in all cases condition 2 resulted in a better approximation of the true metabolite kinetics compared to condition 3.
Conclusion
Parameter priors and Bayesian statistics can be useful in modeling noisy and sparse datasets. This method may help stabilize analysis procedures in these situations, thereby increasing our confidence in the final outcome parameters such as distribution volume and binding potential in ligand PET experiments.