In rafaelsommer1/myelinmap: Q-Space Myelin Map functions

Q-Space Imaging

Complete rationale and methodological explanations can be found in the technique validation paper:

Normalized signal decay (ADC) formula:

$$ln(S_{g}/S_{o}) = -\gamma^2g^2\delta^2(\Delta-\delta/3)D = -bD$$

Given:

$\delta =$ Duration of MPG

$\Delta =$ Time separation of MPG

$g =$ Strength of MPG (amplitude)

$\gamma =$ Magnetogyric ratio

$D =$ Self-diffusion coefficient

This stands for Stejskal‐Tanner equation, assuming mono exponential signal attenuation and single water population

Relation between difusion echo measurements and displacement probabilities:

$$ E_{\Delta}(q) = \int \overline{P}_{s}(R,\Delta)exp(i2\piqR)dR $$

Given:

$q = \sqrt{\frac{b}{\Delta - \frac{\delta}{3}}}$

$E_{\Delta}(q)$ stands for the echo decay curve as a function of $q$

$R =$ the displacement

$\overline{P}_{s}(R,\Delta)$ The probability of displacement

rafaelsommer1/myelinmap documentation built on Aug. 25, 2020, 5:19 p.m.