Numerical Simulation Model of Hyperacute/Acute Stage White Matter Infarction

Purpose: Although previous studies have revealed the mechanisms of changes in diffusivity (apparent diffusion coefficient [ADC]) in acute brain infarction, changes in diffusion anisotropy (fractional anisotropy [FA]) in white matter have not been examined. We hypothesized that membrane permeability as well as axonal swelling play important roles, and we therefore constructed a simulation model using random walk simulation to replicate the diffusion of water molecules. Materials and Methods: We implemented a numerical diffusion simulation model of normal and infarcted human brains using C++ language. We constructed this 2-pool model using simple tubes aligned in a single direction. Random walk simulation diffused water. Axon diameters and membrane permeability were then altered in step-wise fashion. To estimate the effects of axonal swelling, axon diameters were changed from 6 to 10 μm. Membrane permeability was altered from 0% to 40%. Finally, both elements were combined to explain increasing FA in the hyperacute stage of white matter infarction. Results: The simulation demonstrated that simple water shift into the intracellular space reduces ADC and increases FA, but not to the extent expected from actual human cases (ADC approximately 50%; FA approximately +20%). Similarly, membrane permeability alone was insufficient to explain this phenomenon. However, a combination of both factors successfully replicated changes in diffusivity indices. Conclusion: Both axonal swelling and reduced membrane permeability appear important in explaining changes in ADC and FA based on eigenvalues in hyperacute-stage white matter infarction.