Relative to other approaches that have been recommended, fitting all head data, solving for a time shift, and including an air passage artifact term in the model significantly improved the estimate of gray matter blood flow by the inhalation technique. A robust algorithm, which incorporates these features, has been developed. Formulas which facilitate implementation of this algorithm are reported. An artifact from large scalp arteries was not significant and does not need to be included in the model. (Stroke 1987; 18:495-502) W E report experiments designed to answer the following questions regarding calculation of regional cerebral blood flow (rCBF) by the inhalation method: 1) Does solving for the time shift (At) between the head and expired alveolar time-activity curves decrease the bias in the estimate of rCBF? 2) Do an air passage artifact (APA) and an arterial artifact (AA) exist physiologically? 3) If APA and AA exist, does including them in the model improve the estimate of rCBF? 4) If APA exists and must be accounted for in the model, does fitting all head data with a model containing an APA term improve the estimate of rCBF compared to a delayed-start fit? Studies investigating these questions have led to the development of a robust new rCBF algorithm that has been demonstrated to improve estimates of rCBF compared with approaches that have been employed in the past.
Overview of the Approach for Determination of Regional Gray Matter Flow by Xenon-133 InhalationAssumptions based on the Fick principle and a model containing two tissue compartments and artifact terms lead to the equation for expected head counts, h(tj), at any time, tj, as:where A,, v (t) = time-activity curve for radionuclide in expired alveolar gas sampled from the mouth and measured at time t, At = time subtracted from head times (t,,) so that A llv (t h -At) coincides in time with the Received August 2, 1985; accepted October 14, 1986. arterial input function at t,,, k, = rate constant for jth compartment, Xj = partition coefficient for tracer in jth compartment, Wj = fractional weight of jth compartment, a = constant scaling A,, v (t) to the arterial input function for each tissue compartment, P t = WjlcjO/X-j for J = 1,2, and P, = constant determining artifact magnitude for J = 3,...x.'~7 The first artifact term is APA, multiplied by the linear scaling factor P 3 , and the second artifact is AA, multiplied by the linear scaling factor P 4 . The usual approach to finding k, for the calculation of gray matter flow is to apply least-squares criteria, where the set or a subset of the parameters Q = {k,, k 2 , P,, P 2 , ••• P,, At} is found that minimizes the sum of the squares of the residuals (S) between the measured and expected head curves.where H(t,) = measured head counts at time t,, h(t,) = expected head counts at time t,, and n = number of data points in the measured head curve. Considering both artifacts, Equation 1 contains 7 parameters (k,, k 2 , P,, P 2 , P 3 , P 4 , and At). Two-compartment analysis solving for k,, k 2 , ...