Indirect measurement of regional axon diameter in excised mouse spinal cord with q-space imaging: simulation and experimental studies

Abstract

Q-space imaging (QSI), a diffusion MRI technique, can provide quantitative tissue architecture information at cellular dimensions not amenable by conventional diffusion MRI. By exploiting regularities in molecular diffusion barriers, QSI can estimate the average barrier spacing such as the mean axon diameter in white matter (WM). In this work, we performed ex vivo QSI on cervical spinal cord sections from healthy C57BL/6 mice at 400 MHz using a custom-designed uniaxial 50T/m gradient probe delivering a 0.6 microm displacement resolution capable of measuring axon diameters on the scale of 1 microm. After generating QSI-derived axon diameter maps, diameters were calculated using histology from seven WM tracts (dorsal corticospinal, gracilis, cuneatus, rubrospinal, spinothalamic, reticulospinal, and vestibulospinal tracts) each with different axon diameters. We found QSI-derived diameters from regions drawn in the seven WM tracts (1.1 to 2.1 microm) to be highly correlated (r(2)=0.95) with those calculated from histology (0.8 to 1.8 microm). The QSI-derived values overestimated those obtained by histology by approximately 20%, which is likely due to the presence of extra-cellular signal. Finally, simulations on images of synthetic circular axons and axons from histology suggest that QSI-derived diameters are informative despite diameter and axon shape variation and the presence of intra-cellular and extra-cellular signal. QSI may be able to quantify nondestructively changes in WM axon architecture due to pathology or injury at the cellular level.

Figure 1

Synthetic circular axon images generated with a Gaussian distribution of diameters (mean and standard deviation are µ and σ respectively): a) σ/µ = 0.0, b) σ/µ = 0.1, c) σ/µ = 0.25, d) σ/µ = 0.5. The white rings signify myelin. The mean axon diameter (excluding myelin) was held constant at 14.48 µm. Synthetic ellipsoidal axon images generated with different ratios (R) of major axis over minor axis lengths e) R = 1.25, f) R = 1.5, g) R = 2.0. The mean axon diameter (excluding myelin) was held constant at ~25 µm.

Figure 2

Top Image: Optical image of C6/C7 mouse cord section showing WM tract locations: A) dorsal corticospinal (dCST), B) gracilis (FG), C) cuneatus (FC), D) rubrospinal (RST), E) spinothalamic (STT), F) reticulospinal (ReST), G) vestibulospinal (VST). The spinal cord is approximately 3 mm wide. Middle Images: Optical images of WM tracts from mouse spinal cord C6/C7 section. Each image is 700 × 700 with a pixel resolution of 0.1 × 0.1 µm. Bottom Images: Segmented down-sampled images of WM tracts from mouse spinal cord C6/C7 section. Each image is 256 × 256 with a pixel resolution of 0.27 × 0.27 µm.

Figure 3

Sample diffusion-weighted stimulated echo magnitude images (Δ/δ = 10/0.4 ms) at two different q-values: 0 and 0.12 µm⁻¹. The white bar represents a length of 1 mm. Note the fluid surrounding the spinal cord, which exhibits free diffusion, is attenuated to background intensity in b).

Figure 4

Sample q-space echo attenuation plots and displacement profiles for seven WM tract ROIs, alongside with sample FWHM, zero-displacement probability (ZDP), and kurtosis maps under experimental parameters with a) high displacement resolution (q_max = 0.82 µm⁻¹) and fulfilling the narrow gradient pulse condition (Δ/δ = 10/0.4 ms), b) high displacement resolution (q_max = 0.82 µm⁻¹) and failing to fulfill the narrow gradient pulse condition (Δ/δ = 10/5 ms), and c) low displacement resolution (q_max = 0.21 µm⁻¹) and failing to fulfill the narrow gradient pulse condition (Δ/δ = 10/5 ms). The fourth case of low displacement resolution (q_max = 0.21 µm⁻¹) and fulfilling the narrow gradient pulse condition (Δ/δ = 10/0.4 ms) was excluded to its similarity with c).

Figure 5

Results of our investigation into how much axon diameter variation occurred through a 1 mm slice. a) Calculated mean axon diameters from seven 20-pixel ROIs of WM tracts from six equally spaced sections spanning 1 mm. Section positions 1 and 6 define the edges of the slice. b) WM tract average axon diameters calculated from all 5 specimens, the WM tract average axon diameters calculated from all six sections in one specimen, the WM tract average axon diameters calculated from one section from the same specimen, and the measured FHWM of the displacement profile (DP) from the same specimen. Each asterisk represents the p-value of a paired t-test comparison with the next similar colored bar to the right.

Figure 6

Summary plots of q-space experiments showing mean axon diameter calculated from histology, FHWM, zero-displacement probability (ZDP), and kurtosis values for each WM tract averaged over all five specimens under experimental conditions fulfilling and not fulfilling the SPGA and with and without q-space truncation (to simulate low displacement profile resolution). Each asterisk represents the p-value of a paired t-test comparison with the next similar colored bar to the right.

Figure 7

Summary of simulation results for synthetic circular axons of varying diameter mean and standard deviation ratios (µ and σ respectively). a) Echo attenuation for signal from ICS only. b) Echo attenuation for signal from ECS only. c) Displacement profile for signal from ICS only. d) Displacement profile for signal from ECS only. Mean axon diameter, FWHM, zero displacement probability, and kurtosis for e) signal from ICS only and f) signal from ECS only.

Figure 8

Summary of simulation results for synthetic ellipsoidal axons of varying diameter major and minor axis ratios (R). a) q-space echo attenuations and b) displacement profiles for synthetic c) Mean axon diameter, FWHM, zero displacement probability, and kurtosis.

Figure 9

Summary plots of q-space simulations based on histologic images showing mean axon diameter calculated from histology, FHWM, zero-displacement probability (ZDP), and kurtosis values for each WM tract averaged over all five specimens under simulation conditions of ICS weighted signal and ECS weighted signal. Each asterisk represents the p-value of a paired t-test comparison with the next similar colored bar to the right.