Figure 8.

The Tuch cross-property relationship overestimates the conductivity of brain tissues. (a) Mapping diffusion tensor eigenvalues to conductivity tensor eigenvalues using equation 8. Fitted parameters were varied according to the ranges (mean plus/minus one standard deviation) given in (Tuch et al., 2001). Mean diffusivities in brain parenchyma vary between 0.5 and 1.0 µm²/ms (Yu et al., 2006) (b) A diffusion tensor field was fit to the DW image, and equation 8 was used to calculate the eigenvalues (σ₁, σ₂, and σ₃) of the conductivity tensor field within the brain. The histograms summarize the distribution of σ₁ (red), σ₂ (blue), and σ₃ (green) in the cerebral spinal fluid (CSF, top), grey matter (middle), and white matter (bottom). Examples of measured isotropic conductivities for CSF and grey matter are 1.45 S/m (Baumann et al., 1997) and 0.23 S/m (Gabriel et al., 2009), respectively. 0.61 S/m and 0.067 S/m are examples of longitudinal and transverse conductivities, respectively, that have been measured in white matter (Ranck Jr and BeMent, 1965).