Robust experiment design for estimating myocardial adrenergic receptor concentration using PET

Myocardial beta adrenergic receptor (beta-AR) concentration can substantially decrease in congestive heart failure and significantly increase in chronic volume overload, such as in severe aortic valve regurgitation. Positron emission tomography (PET) with an appropriate ligand-receptor model can be used for noninvasive estimation of myocardial beta-AR concentration in vivo. An optimal design of the experiment protocol, however, is needed for sufficiently precise estimates of beta-AR concentration in a heterogeneous population. Standard methods of optimal design do not account for a heterogeneous population with a wide range of beta-AR concentrations and other physiological parameters and consequently are inadequate. To address this, we have developed a methodology to design a robust two-injection protocol that provides reliable estimates of myocardial beta-AR concentration in normal and pathologic states. A two-injection protocol of the high affinity beta-AR antagonist [18F]-(S)-fluorocarazolol was designed based on a computer-generated (or synthetic) population incorporating a wide range of beta-AR concentrations. Timing and dosage of the ligand injections were optimally designed with minimax criterion to provide the least bad beta-AR estimates for the worst case in the synthetic population. This robust experiment design for PET was applied to experiments with pigs before and after beta-AR upregulation by chemical sympathectomy. Estimates of beta-AR concentration were found by minimizing the difference between the model-predicted and experimental PET data. With this robust protocol, estimates of beta-AR concentration showed high precision in both normal and pathologic states. The increase in beta-AR concentration after sympathectomy predicted noninvasively with PET is consistent with the increase shown by in vitro assays in pig myocardium. A robust experiment protocol was designed for PET that yields reliable estimates of beta-AR concentration in a population with normal and pathologic states. This methodology is applicable in general to optimal estimation of parameters in heterogeneous populations.