Simultaneous estimation of blood flow distribution and instrumentation noise from dynamic H/sub 2//sup 15/O PET study with stochastic block model

In order to model reasonably and flexibly the blood flow or perfusion in skeletal muscles with PET using H₂ ¹⁵O as tracer or radiopharmaceutical we introduce a new stochastic two-block - two-rate constants model with two new measurement equations. The stochastic two-block - two rate constants model utilizes the probability theory to describe the inherent variation of the muscle tissue with similarly distributed random rate constants realized uniquely for each volume element in tissue separately. The new measurement equations include both the uncertainty caused by the positron emission (Poisson noise) and the instrumentation or measurement noise (Gaussian) allowing an easy characterization of the radioactive decay and the deviation of the instrumentation noise. Applying maximum likelihood estimation procedure to the density function results in the volume-element-wise rate constant estimates providing the information about regional perfusion. In addition, we can calculate the estimator variation of the rate constant estimates and remove it resulting in the pure tissue heterogeneity, i.e. the variation of the volume-element-wise rate constants, the regional perfusion. We tested our model and methods by executing simulation runs. The simulations showed that we are able to estimate the unknown parameter values and their deviations the better the higher the time and spatial resolutions are. This is an expected phenomenon due to the consistency property of the maximum likelihood estimator