Effects of signal to noise and parametric limitations on fitting biexponential magnetic resonance (MR) inversion-recovery curves using a constrained nonlinear least-squares algorithm

Ischemic stoke is a local reduction in brain tissue perfusion due to an obstruction (such as a blood clot) of the inflowing arterial blood. Using diffusion-weighted magnetic resonance imaging (DWI), it is possible to visualize the brain tissue affected in the acute (early) stages of ischemic stroke. Due to metabolic changes and disruptions in osmotic equilibrium, water moves from the extracellular to the intracellular compartment, which results in cytotoxic edema (cell swelling) and marked changes in the apparent diffusion coefficient (ADC) of brain tissue water. The mechanisms responsible for these ADC changes are not well understood but are thought to involve changes in the separation of restricting barriers and in the relative contributions from the intra- and extracellular compartments. Yeast cells have been investigated as a model system to provide some insight into intra- and extracellular ADC characteristics. Inversion-recovery MR data were fitted to a biexponential equation using a constrained nonlinear least squares algorithm. An ideal fit by the algorithm is not guaranteed since the goodness of fit is sensitive to the relative fractional compartmental contributions and the relaxation time constants of each compartment. Test data sets were created to determine the effects of signal to noise and system parameters on the goodness of fit. It was determined that the best fit was obtained for systems with equal compartmental contributions, relaxation time constants that differed by more than a factor of 3, and a high signal-to-noise ratio. The test data sets will be used to determine the optimal conditions for the yeast cell preparations and, eventually, the design of in vivo stroke experiments. Knowledge of the ADC characteristics in ischemic stroke can guide future research in therapy design and treatment approach.