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Accuracy of axon diameter estimation using diffusion MRI in fiber space

Mohammad Ashtarayeh¹, Tobias Streubel^1,2, Francisco Javier Fritz¹, Joao Periquito³, Andreas Pohlmann³, Thoralf Niendorf³, Henriette Rusch⁴, Markus Morawski⁴, Carsten Jäger², Stefan Geyer², Bibek Dhital⁵, Muhamed Barakovic^6,7, Simona Schiavi ⁸, Alessandro Daducci⁸, and Siawoosh Mohammadi^1,2
¹Department of Systems Neurosciences, University Medical Center Hamburg-Eppendorf, Hamburg, Germany, ²Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, ³Berlin Ultrahigh Field Facility (B.U.F.F.), Max-Delbrueck-Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany, ⁴Paul Flechsig Institute of Brain Research, University of Leipzig, Leipzig, Germany, ⁵Department of Radiology, University Medical Center Freiburg, Freiburg, Germany, ⁶Signal Processing Lab (LTS5), Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland, ⁷Translational Imaging in Neurology (ThINk) Basel, Department of Medicine and Biomedical Engineering, University Hospital Basel and University of Basel, Basel, Switzerland, ⁸Department of computer science, University of Verona, Verona, Italy

Synopsis

We investigated the effect of different diffusion MRI acquisition protocols (incl. varying gradient-strength and signal-to-noise ratio) on the accuracy of axon diameter index (ADI) estimation in fiber space for human specimens. We used the Bland-Altman plot to estimate the error in the MRI-based ADI measurement. We found that gradient strengths above 900mT/m and b-values larger than b=50k s/mm² provided accurate estimation of ADI (error smaller than 0.13 µm). The error for the best protocol was about 0.04 µm, allowing to distinguish white matter tracts with varying effective axon diameters (e.g. corpus callosum, genu, 1.5 µm and posterior body, 1.93 µm).

Introduction

A variety of biophysical models^{1, 2, 3} have been proposed to estimate axon diameter index (ADI) using diffusion MRI. Recently, one of these models¹ was extended to estimate ADI in fiber space⁴. As compared to the standard approach of estimating ADI in voxel space^{1, 2, 5}, the fiber space approach considers different configurations of fibers within a voxel and preliminary results showed that it provides better agreement with histology⁶. Previous studies^{7, 8} assessing the influence of protocol parameters on the accuracy of ADI estimation worked in voxel space using non-human specimens. Here, we investigate how diffusion MRI protocol parameters affect the accuracy of ADI estimates in fiber space for human specimens.

Methods

Sample: Two human optic chiasms (OC) and subregions (genu, posterior body and splenium) of two corpus callosum (CC) samples (figure 1) were obtained at autopsy with prior informed consent (20-24 hrs postmortem) and approved by the responsible authorities. Following the local standard brain bank procedures, two CC and one OC samples were immersion-fixed with 3 % paraformaldehyde + 1% glutaraldehyde (CCPG, OCPG) and one OC was fixed with 4 % paraformaldehyde (OCP).
MRI: Ex vivo diffusion MRI was performed on a small bore 9.4T MR system (Bruker Biospin, Ettlingen, Germany) using two protocols (table 1):
1. Seven diffusion shells using a standard gradient coil and a 4 TX/ 4 RX RF-coil (protocol_1a) or cryogenically-cooled TX/RX RF-coil (protocol_1b), to enhance SNR. These protocols were presented together as protocol_1.
2. Twelve diffusion shells using a gradient insert coil and a 4 TX/ 4 RX RF-coil (protocol_2a). We generated extra datasets, protocol_2b and 2c, by sub-selecting the first four and seven diffusion shells.
Tractography: To generate fibers, we utilized the iFOD2 algorithm of MRtrix⁹. We analyzed the entire subregions of the CC but restricted the analysis of the OC to the ipsilateral bundles¹⁰ (figure 1), with the aim of comparing them to the histological analysis^{11, 12}.
Microstructure analysis: Cylinder-Zeppelin-Ball model¹³ was used in COMMIT⁴ to describe the intra-axonal compartment with cylinders at varying radius, corresponding to ensemble-averaged axon diameters for each fiber. For each protocol, the lowest sensitive diameter of cylinder (resolution limit) was calculated as explained in¹⁴. The extra-axonal compartment was modeled with zeppelins having d_||=0.6 µm²/ms for OCP or 0.5 µm²/ms for OCPG, CCPG and three d_⊥= [0.24, 0.36, 0.48] µm²/ms. The isotropic diffusion was modeled by balls with d_iso= 2 µm²/ms.
Effective axon diameter: The mean of ADIs in MRI has been reported to be unequal to the arithmetic mean in histology^15,16. We calculated the effective mean proposed in¹⁵ $$$r_{eff}=\sqrt[4]{<r^6>/<r^2>}$$$ from the histological axon diameter distribution and used it as the gold standard to assess the accuracy of the MRI-based ADI estimation for each protocol.
Bland-Altman plots¹⁷: In this representation the difference Δ_ADI = ADI_MRI - ADI_Hist of the data is plotted against the mean m_ADI= (ADI_MRI + ADI_Hist)/2 . If there is no obvious relation between the difference and the mean in the Bland-Altman plot, error introduced when replacing the electron microscopy-based axon diameter by the corresponding MRI-based ADI can be estimated by the standard deviation of the difference std (Δ_ADI).

Results and Discussion

The theoretical resolution limit¹⁴ of MRI-based ADI estimation was the smallest for protocol_2a (1 µm) and the largest for protocol_2c (1.73 µm) (figure 2). The mean ADI in the CC subregions followed the well-known¹² low-high-low trend for all protocols (figure 3a). However, the mean ADI estimated from protocols with larger gradients (protocol_2a and 2b) resembled closely the corresponding histological axon diameters. This was particularly apparent for the genu where the frequency of small-diameter axons is larger (figure 3b). The error of the Bland-Altman plot between MRI-based ADI and effective mean from gold standard varied between protocols (figure 4), it was the smallest for protocol_2a (0.04 µm), intermittent for protocol _2b (0.13 µm), and the largest for protocol_1 and 2c (0.36 µm). The relevance of better SNR vs. higher gradient strength and b-value, could be measured when comparing the OC sample in protocols 1b and 2b. ADI measured with protocol_1b with higher SNR but lower maximal b-value and gradient strength had a larger difference to histology ( Δ_ADI = 0.18 µm, figure 4a) than when using protocol 2b ( Δ_ADI= 0.12 µm , figure 4c).

Conclusion

Our results show that the error in fiber space with protocols_2a and b, is small enough to distinguish between white matter tracts with varying effective axon diameters (e.g. between genu, 1.5 µm and posterior body, 1.93 µm). On the opposite, these fiber pathways would be indistinguishable for MRI-based ADI using protocol_1 and 2c. The small error for protocols_2a and b could be due to the larger gradient strength which increases the resolution limit^7,14 or due to the suppression of the signal from the extra-axonal space³. To the best of our knowledge, this is the first study that puts an error margin on the MRI-based ADI and thus allows to assess its ability in distinguishing of ADIs of different fiber pathways. However, the presented preliminary results need further validation because they may be affected by the low number of samples and unkown inter-subject varibility (i.e. histological literature values were compared with MRI-based ADI from our samples).

Acknowledgements

Acknowledgments: This work was supported by the German Research Foundation (DFG Priority Program 2041 "Computational Connectomics”, [AL 1156/2-1;GE 2967/1-1; MO 2397/5-1; MO 2249/3–1], by the Emmy Noether Stipend: MO 2397/4-1) and by the BMBF (01EW1711A and B) in the framework of ERA-NET NEURON and the Forschungszentrums Medizintechnik Hamburg (fmthh; grant 01fmthh2017). The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 616905

References

1. Alexander, D.C. et al. Orientationally invariant indices of axon diameter and density from diﬀusion MRI. NeuroImage, 52(4):1374–1389, 2010.

2. Assaf, Y. et al. AxCaliber: a method for measuring axon diameter distribution from diffusion MRI. Magn Reson Med, 59:1347–1354, 2008.

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4. Daducci, A. et al. COMMIT: Convex optimization modeling for microstructure informed tractography. IEEE transciption on medical imaging, 34(1): 246-257, 2015.

5. Daducci, A. et al. Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diﬀusion MRI data. Neuroimage, 105:32–44, 2015.

6. Ashtarayeh, M. et al. Estimation of Axon diameter index estimation in fixed human optic chiasm: voxel or streamline space ?. OHBM 2019.

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8. Sepehrband, F. et al. Towards higher sensitivity and stability of axon diameter estimation with diffusionweighted MRI, NMRM Biomed, 29(3): 293-308, 2016.

9. Tournier, J-D. et al. MRtrix3: A fast, flexible and open software framework for medical image processing and visualization. NeuroImage, 202, 2019.

10. Glen, J. et al. Segregated hemispheric pathways through the optic chiasm distinguish primates from rodents. Neuroscience, 157 (3), 2008.

11. Jonas, JB. et al. Histomorphometry of the Human Optic Nerve. Investigative Ophthalmology & Visual Science,31,1990.

12. Aboitiz, F. et al. Fiber composition of the human, corpus callosum, Biol Res 25:51-61, 1992.

13. Panagiotaki, E. et al. Compartment models of the diﬀusion MR signal in brain white matter: A taxonomy and comparison. NeuroImage, 59(3):2241–2254, 2012.

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15. Benjamini, Dan. et al. White matter microstructure from non parametric axon diameter distribution mapping. NeuroImage,135: 333-344,2016.

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Figures

Table 1: Protocols details: Segmented EPI (4 segments), with 60 diffusion gradient directions for a given b-value. The higher SNR of protocol_1b compared to protocol_1a is due to the use of cryogenically-cooled coil. CC and OC stand for corpus callosum and optic chiasm as explained in the methods section.

Fig. 1: Photograph and schematic drawing¹⁸ of the optic chiasm and corpus callosum samples with their different anatomical regions of interest.

Fig. 2: Illustration of the theoretical resolution limit¹⁴ for different protocols on histological axon diameter distribution of optic chiasm¹¹. Resolution limits of protocol_2a and 2b are 1 and 1.3 µm (dashed green and red lines). Dashed and solid magenta lines represent resolution limits for protocol_1a and 1b. Protocol_2c has the highest resolution limit (dashed blue line). The SNR of the highest shell was used to calculate the resolution limit.

Fig. 3 (a): Mean and standard error of mean (SEM) for the estimated axon diameter index (ADI) across four protocols within subregions in corpus callosum, such as: genu (CC1), posterior body (CC4), splenium (CC5). A similar trend as in histology is seen across all protocols. (b): Relative difference between estimated mean ADI and histology for the protocols. The relative difference for protocols with lower gradients (protocol_1a and 2c) is larger than protocols with higher gradients (protocol_2a and 2b), particularly for CC1 where the frequency of small-diameter axons is larger.

Fig. 4: Assessing the accuracy of MRI-based axon diameter index (ADI) estimation by comparison with the histological gold standard for different protocols (a-d). Depicted are Bland-Altman (BA) plots¹⁷ (right) and scatter plots (left) of estimated ADI from MRI against the effective axon diameters¹⁶ from histology reported in previous studies^11,
12. ROIs are composed of three regions in the corpus callosum: genu (CC1), posterior body (CC4), splenium (CC5) and one region in the optic chiasm (OC).

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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