In DT-MRI, a linearly varying pulsed magnetic field gradient is applied to the tissue. Two
pulses in the same direction but opposite magnitude are applied. A reduction in signal happens
due to the movement of the protons during this time interval, and it can be related to the amount
of water diffusion through the following equation
A = e-b*D (2-1)
where A is the signal attenuation, D is the diffusion coefficient and b is a factor that
characterizes the gradient's shape, amplitude and timing.18 In anisotropic diffusion, the
coefficient D is a symmetric rank-2 tensor. This tensor characterizes water molecule mobility
along three axes that correspond to the MR machine's axes. Therefore, in order to properly
obtain the diffusion tensor one needs to take into account the tissue's local coordinates.
Measuring Tissue Electrical Conductivity
When characterizing electrical properties of tissue, capacitive and resistive elements need
to be specified. These two parameters vary with frequency 19 but at the frequencies of present
interest in the current study the effects of frequency dependence were disregarded. A more
detailed explanation of this assumption will be given in the following paragraph.
Electrical conductivity, G, (equal to 1/r where r is electrical ressistivity), and
permittivity, e, are needed to describe the electrical properties of tissue. These properties are
commonly measured using the four-electrode technique.20 When using this technique, for an
alternating current of frequency,f the ratio of voltage, V, and current, I, is proportional to
specific impedance, Z. This is a complex quantity and can be written as
= Z (2-2)
I
where