Abstract
The output (observations) of the tracer kinetic process is usually expressed by a sum of decaying exponemtials : q (t) =pΣi=1 Ai exp (-αit). The compartmental analysis which is widely used in the tracer kinetic study is a method by which the pertinent parameters (Ai and αi) as well as number of compartments (p) are determined. In this study the optimal time scale interval (τ) and sample size (m) in a definite set of observations in radio-isotope (RI) tracer kinetics were obtained to minimize the variances of the parameters (Ai and αi), assuming the observations to be Poisson-distributed. The best unbiased estimators of variances of the parameters were obtained by the Fisher in formation and the Cramér-Rao inequality. Since the expectation value in the jth observation <nj> is represented by <nj> =∫tjtj-1 pΣi=1 Ai exp (-αit) dt in RI study, the information matrix can be defined by Ai, αi, τ and m.
Analysis of the effect of the sample size (m), the time scale interval (τ) and the number of exponentials (p) on the variance of Ai and αi by numerical examples revealed the following results : (1) For a fixed sample size, there is an optimal time scale interval which increases with sample size. (2) For a fixed time scale interval, the variance of each parameter decreases withthe sample size, but it converges to a certain level for a large sample size. (3) The allowable limit on τ as the optimal time scale interval decreases with increase of the number of exponentials.
Application of this method to the dynamic study of cerebral circulation using 133Xe revealed that 15-20 minutes of sampling period was necessary to estimate the pertinent parameters accurately.
