High resolution measurement of cerebral blood flow using intravascular tracer bolus passages. Part I: Mathematical approach and statistical analysis

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Abstract
The authors review the theoretical basis of determination of cerebral blood flow (CBF) using dynamic measurements of nondiffusible contrast agents, and demonstrate how parametric and nonparametric deconvolution techniques can be modified for the special requirements of CBF determination using dynamic MRI. Using Monte Carlo modeling, the use of simple, analytical residue models is shown to introduce large errors in flow estimates when actual, underlying vascular characteristics are not sufficiently described by the chosen function. The determination of the shape of the residue function on a regional basis is shown to be possible only at high signal‐to‐noise ratio. Comparison of several nonparametric deconvolution techniques showed that a nonparametric deconvolution technique (singular value decomposition) allows estimation of flow relatively independent of underlying vascular structure and volume even at low signal‐to‐noise ratio associated with pixel‐by‐pixel deconvolution.