Typical microscopic images with 2x (left) and 100x (right) magnifications taken from ROI#5 of one of our cases.

<p>Nuclei are colorless; myelin is blue and axons are black in the stained sections.</p

Illustration of the 7 ROIs considered in this study for taking microscopy images.

<p>All ROIs belong to the corpus callosum.</p

The overall look of the proposed model for deriving the diffusion signal.

<p>The unknown parameters are <i>D_in</i>, <i>D_out,||</i>, <i>D_out,⊥</i>, <i>R</i>, <i>v</i>, and <i>h</i>. The direction of axons is estimated using the conventional DTI model.</p

Estimated values of the axonal volume fraction for all cases.

<p>Estimated values of the axonal volume fraction for all cases.</p

Estimated values of the diameter, 2<i>R</i>, and axonal volume fraction, <i>v</i>, for the center part of the corpus callosum in normal cases, estimated by fitting our proposed model to the DWI data.

<p>The results are consistent with the measured values shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095921#pone-0095921-t001" target="_blank">Tables 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095921#pone-0095921-t002" target="_blank">2</a>. The intra-class correlation coefficients within 95% of the confidence interval are 0.970 (<i>p</i> = 0.008) and 0.933 (<i>p</i> = 0.026) for the diameter and volume fraction of the axons, respectively.</p

A typical PGSE sequence. δ is the gradient pulse width and Δ is the diffusion time.

<p>A typical PGSE sequence. δ is the gradient pulse width and Δ is the diffusion time.</p

A typical result of final distribution of the particles shown in a cross section of the structure.

<p>In this experiment, the particles did not pass the boundaries because permeability was set to 0.</p

Illustration of the segmented regions of the corpus callosum fiber tract overlaid on the FA map.

<p>For each subject, the CC is segmented into three regions manually: left, right, and center. Our proposed model is applied to these regions and only the center part is used for validating the model using histological data.</p

Cross sectional view of the distribution of (a) the axons and (b) the spins at <i>t</i> = 0.

<p>The axons are realized as parallel same size cylinders with permeable boundaries. Initial spins are distributed in the center of the voxel such that the ratio of spins inside the central axon is equal to the axonal volume fraction.</p

Measured values of the axon diameter for all cases.

<p>Measured values of the axon diameter for all cases.</p