Numerical model for calculation of apparent diffusion coefficients (ADC) in permeable cylinders-comparison with measured ADC in spinal cord white matter

We have implemented a numerical method for calculation of the apparent diffusion coefficient (ADC) in spinal cord injury, which takes into account the distribution of axon diameters and permeability found in spinal cord white matter, as well as relative axonal volume. We propose a procedure for determining the status of axonal integrity from measured ADC values. These methods have been applied to a well characterized rat spinal cord injury model, affording a prediction of the increase in axonal permeability which is presumed to be closely related to functional deficit. ADC values are compared to those calculated from analytical formulas in the literature, and possible factors underlying the ADC behavior are explored. Calculated results indicate both axonal swelling and cell membrane permeability to be important factors contributing to ADC in traumatic spinal cord injury.