An Adiabatic Approximation to the Tissue Homogeneity Model for Water Exchange in the Brain: I. Theoretical Derivation

Abstract

Using the adiabatic approximation, which assumes that the tracer concentration in parenchymal tissue changes slowly relative to that in capillaries, we derived a time-domain, closed-form solution of the tissue homogeneity model. This solution, which is called the adiabatic solution, is similar in form to those of two-compartment models, Owing to its simplicity, the adiabatic solution can be used in CBF experiments in which kinetic data with only limited time resolution or signal-to-noise ratio, or both, are obtained. Using computer simulations, we investigated the accuracy and the precision of the parameters in the adiabatic solution for values that reflect ²H-labeled water (D₂O) clearance from the brain (see Part II). It was determined that of the three model parameters, (1) the vascular volume ( V_i), (2) the product of extraction fraction and blood flow ( EF), and (3) the clearance rate constant ( k_adb), only the last one could be determined accurately, and therefore CBF must be determined from this parameter only. From the error analysis of the adiabatic solution, it was concluded that for the D₂O clearance experiments described in Part II, the coefficient of variation of CBF was approximately 7% in gray matter and 22% in white matter.