The influence of tissue heterogeneity on results of fitting nonlinear model equations to regional tracer uptake curves: with an application to compartmental models used in positron emission tomography

Abstract

An analytical method based on Taylor expansions was developed to analyze errors caused by tissue heterogeneity in dynamic positron emission tomography (PET) measurements. Some general rules concerning the effect of parameter variances and covariances were derived. The method was further applied to various compartmental models currently used for measurement of blood flow, capillary permeability, glucose metabolism, and tracer binding. Blood flow and capillary permeability are shown to be generally underestimated in heterogenous tissue, the underestimation being more severe for slowly decaying, constant or increasing input functions rather than for bolus input, and increasing with measurement time. Typical errors caused by the heterogeneity due to insufficient separation between gray and white matter by a PET scanner with full width at half-maximum (FWHM) = 5 to 10 mm resolution range between -0.9 and -6% in dynamic CBF measurements with intravenous (i.v.) bolus injection of 15O-water or inhalation of 18F-fluoromethane and total measurement times of 6 or 10 min, respectively. Binding or metabolic rates determined with tracers that are essentially trapped in tissue (e.g., FDG for measurement of cerebral glucose metabolism) are only slightly overestimated (0.5-3.0%) at typical measurement times and are essentially independent of the shape of the input function. The error increases considerably if tracer accumulation is very slow, however, or if short measurement times [<5/(k2 + k3)] are used. Some rate constants are also subject to larger errors.