Model of Kinetic Behavior of Deoxyglucose in Heterogeneous Tissues in Brain: A Reinterpretation of the Significance of Parameters Fitted to Homogeneous Tissue Models

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Abstract
Effects of tissue heterogeneity on regional CMRglc (rCMRglc) calculated by use of the deoxyglucose (DG) method at 45 min following the pulse of DG were evaluated in simulation studies. A theoretical model was developed to describe the kinetics of DG uptake and metabolism in heterogeneous brain tissues. Rate constants were fitted to simulation data for mixed tissue and rCMRglc computed on the basis of this tissue heterogeneity model. The results were compared with those obtained by use of the original model of the DG method for homogeneous tissue, both without (3K model) and with (4K model) a term to describe an apparent loss of deoxyglucose-6-phosphate (DG-6-P). As a direct consequence of tissue heterogeneity, the effective rate constant for phosphorylation of DG, k*3, declined with time. To compensate for the time-changing k*3, estimates of the dephosphorylation rate constant, k*4, were artifactually high when the 4K model was used, even though no dephosphorylation of DG-6-P actually occurred. The present study demonstrates that the finding of a significant k*4, at least within 45 min following a pulse of DG, may not represent dephosphorylation at all, but rather the consequence of measuring radioactivity in a heterogeneous tissue and applying a model designed for a homogeneous tissue. Furthermore, the high estimates of k*4 resulted in significant overestimation of rCMRglc. When rCMRglc was computed with the conventional single-scan or autoradiographic method at 45 min after a pulse of DG, the 3K and tissue heterogeneity models yielded values that were within 5% of the true weighted average value for the heterogeneous tissue as a whole. We conclude that the effects of tissue heterogeneity alone can give the appearance of product loss, even when none occurs, and that the use of the 4K model with the assumption of product loss in the 45-min experimental period recommended for the DG method may lead to overestimation of the rates of glucose utilization.

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