Supplementary Fig. 4.

A two-compartment model $\mathrm{S}\left(\mathrm{TE},\mathrm{b}\right)={\mathrm{\nu }}_1\exp \left(-\mathrm{TE}/\mathrm{T}{2}_1\right)\exp \left(-{\mathrm{bD}}_1\right)+\left(1-{\mathrm{\nu }}_1\right)\exp \left(-\mathrm{TE}/\mathrm{T}{2}_2\right)\exp \left(-{\mathrm{bD}}_2\right)$ - in which the two compartments can have different T2 - represented by $\mathrm{S}\left(\mathrm{TE},\mathrm{b}\right)=\mathrm{S}\left(\mathrm{TE},0\right)({\mathrm{f}}_1\left(\mathrm{TE}\right)\exp \left(-{\mathrm{bD}}_1\right)+\left(1-{\mathrm{f}}_1\right)\exp \left(-{\mathrm{bD}}_2\right))$. Rearranging the equations gives ${\mathrm{f}}_1\left(\mathrm{TE}\right)={\mathrm{\nu }}_1\exp \left(-\mathrm{TE}/\mathrm{T}{2}_1\right)/\left({\mathrm{\nu }}_1\exp \left(-\mathrm{TE}/\mathrm{T}{2}_1\right)+\left(1-{\mathrm{\nu }}_1\right)\exp \left(-\mathrm{TE}/\mathrm{T}{2}_2\right)\right)$. This relationship is plotted for $\mathrm{T}{2}_1=60\text{ms}$ and different values of ${\mathrm{\nu }}_1$ and $\mathrm{T}{2}_2$. When $\mathrm{T}{2}_2>\mathrm{T}{2}_1$, a decrease in ${\mathrm{f}}_1$ with increasing TE can be observed.