Validation of Bayesian analysis of compartmental kinetic models in medical imaging.
BACKGROUND
Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated.


METHODS
The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach.


CONCLUSIONS
Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001).


CONCLUSIONS
The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities.
Massachusetts General Hospital and Harvard Medical School, Radiology Department, 55 Fruit Street, Boston, MA 02114, USA. Electronic address: sarkadiu@gmail.com.
Arkadiusz
A
Sitek
Massachusetts General Hospital and Harvard Medical School, Radiology Department, 55 Fruit Street, Boston, MA 02114, USA.
Quanzheng
Q
Li
Massachusetts General Hospital and Harvard Medical School, Radiology Department, 55 Fruit Street, Boston, MA 02114, USA.
Georges
G
El Fakhri
Massachusetts General Hospital and Harvard Medical School, Radiology Department, 55 Fruit Street, Boston, MA 02114, USA.
Nathaniel M
NM
Alpert
D001499:Bayes Theorem; D055592:Biophysical Phenomena; D003198:Computer Simulation; D003952:Diagnostic Imaging / Q000706:statistics & numerical data*; D019788:Fluorodeoxyglucose F18 / Q000493:pharmacokinetics; D006801:Humans; D007700:Kinetics; D016018:Least-Squares Analysis; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D049268:Positron-Emission Tomography / Q000706:statistics & numerical data; D019275:Radiopharmaceuticals / Q000493:pharmacokinetics
D019275:Radiopharmaceuticals; D019788:Fluorodeoxyglucose F18
Bayesian inference; Dynamic nuclear imaging; Kinetic analysis
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