DTI-based upper limit of voxel free water fraction

Abstract

Background: Free water (FW) in neuroimaging is non-flowing extracellular water in the cranium and brain tissue, and includes both cerebral spinal fluid (CSF) and fluid in intercellular space or edema. For a region such as a voxel (spatial unit of measurement in neuroimaging), the FW fraction is defined as the volume fraction of FW within that volume. Quantifying the FW fraction allows estimating contamination by fluid of neuroimaging or magnetic resonance spectroscopy measurements within a voxel. New method: An upper limit to the fraction of FW within a voxel, based on any diffusion tensor imaging (DTI) sequence including a standard single shell at one b-value, can be derived from the standard diffusion tensor by scaling the third eigenvalue of the diffusion tensor. Assuming a two-compartment model, the diffusivity of a voxel is a combination of tissue and FW diffusivity. FW fraction is FW volume divided by voxel volume. Assuming FW diffuses equally in all directions, the diffusivity component is representable by a single, non-tensor diffusivity value. Since the diffusivity of water is known for a given temperature, and brain temperature is relatively constant, the FW diffusivity value can be assumed constant. The third eigenvector of the voxel diffusion tensor is the direction of least diffusivity and since the FW component of diffusivity is equal in all directions, we show that FW diffusivity cannot be lower than the third eigenvalue. Assuming FW contributes proportionally to voxel diffusivity, we show that the third eigenvalue divided by water diffusivity (as a constant based on known water diffusivity at 36.7 °C) forms an upper limit on the FW-fraction (fUL). Results: We calculated fUL for 384 subjects from the IXI dataset. Values mostly ranged from 0.1 to 0.6, and were closely related to radial diffusivity. Comparison with Existing Methods: fUL is easily calculated from any DTI data, but is not a true estimate of FW-fraction. Conclusions: The fUL measure offers a starting point in calculating the true FW-fraction of a voxel, or an easy-to-calculate voxel characteristic.