The impact of realistic axonal shape on axon diameter estimation using diffusion MRI
To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder’s inner diameter. However, the shape of a real axon varies along the axon direction, which couples the l...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-12-01
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| Series: | NeuroImage |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S105381192030714X |
| _version_ | 1819008274011258880 |
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| author | Hong-Hsi Lee Sune N. Jespersen Els Fieremans Dmitry S. Novikov |
| author_facet | Hong-Hsi Lee Sune N. Jespersen Els Fieremans Dmitry S. Novikov |
| author_sort | Hong-Hsi Lee |
| collection | DOAJ |
| description | To study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder’s inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3-dimensional diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D⊥(t)and kurtosis K⊥(t),to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D⊥(t)is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K⊥|t→∞deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations. |
| first_indexed | 2024-12-21T00:37:52Z |
| format | Article |
| id | doaj.art-ad2fd7f1b6ef473fa267dbd1812c2449 |
| institution | Directory Open Access Journal |
| issn | 1095-9572 |
| language | English |
| last_indexed | 2024-12-21T00:37:52Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | NeuroImage |
| spelling | doaj.art-ad2fd7f1b6ef473fa267dbd1812c24492022-12-21T19:21:45ZengElsevierNeuroImage1095-95722020-12-01223117228The impact of realistic axonal shape on axon diameter estimation using diffusion MRIHong-Hsi Lee0Sune N. Jespersen1Els Fieremans2Dmitry S. Novikov3Corresponding author at: Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA.; Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA; Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, USACFIN/MINDLab, Department of Clinical Medicine, Aarhus University, Aarhus, Denmark; Department of Physics and Astronomy, Aarhus University, Aarhus, DenmarkCenter for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA; Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, USACenter for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA; Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, USATo study axonal microstructure with diffusion MRI, axons are typically modeled as straight impermeable cylinders, whereby the transverse diffusion MRI signal can be made sensitive to the cylinder’s inner diameter. However, the shape of a real axon varies along the axon direction, which couples the longitudinal and transverse diffusion of the overall axon direction. Here we develop a theory of the intra-axonal diffusion MRI signal based on coarse-graining of the axonal shape by 3-dimensional diffusion. We demonstrate how the estimate of the inner diameter is confounded by the diameter variations (beading), and by the local variations in direction (undulations) along the axon. We analytically relate diffusion MRI metrics, such as time-dependent radial diffusivity D⊥(t)and kurtosis K⊥(t),to the axonal shape, and validate our theory using Monte Carlo simulations in synthetic undulating axons with randomly positioned beads, and in realistic axons reconstructed from electron microscopy images of mouse brain white matter. We show that (i) In the narrow pulse limit, the inner diameter from D⊥(t)is overestimated by about twofold due to a combination of axon caliber variations and undulations (each contributing a comparable effect size); (ii) The narrow-pulse kurtosis K⊥|t→∞deviates from that in an ideal cylinder due to caliber variations; we also numerically calculate the fourth-order cumulant for an ideal cylinder in the wide pulse limit, which is relevant for inner diameter overestimation; (iii) In the wide pulse limit, the axon diameter overestimation is mainly due to undulations at low diffusion weightings b; and (iv) The effect of undulations can be considerably reduced by directional averaging of high-b signals, with the apparent inner diameter given by a combination of the axon caliber (dominated by the thickest axons), caliber variations, and the residual contribution of undulations.http://www.sciencedirect.com/science/article/pii/S105381192030714XMonte Carlo simulationDiffusion MRIAxonal diameter mappingCaliber variationAxonal undulationDiffusion coarse-graining |
| spellingShingle | Hong-Hsi Lee Sune N. Jespersen Els Fieremans Dmitry S. Novikov The impact of realistic axonal shape on axon diameter estimation using diffusion MRI NeuroImage Monte Carlo simulation Diffusion MRI Axonal diameter mapping Caliber variation Axonal undulation Diffusion coarse-graining |
| title | The impact of realistic axonal shape on axon diameter estimation using diffusion MRI |
| title_full | The impact of realistic axonal shape on axon diameter estimation using diffusion MRI |
| title_fullStr | The impact of realistic axonal shape on axon diameter estimation using diffusion MRI |
| title_full_unstemmed | The impact of realistic axonal shape on axon diameter estimation using diffusion MRI |
| title_short | The impact of realistic axonal shape on axon diameter estimation using diffusion MRI |
| title_sort | impact of realistic axonal shape on axon diameter estimation using diffusion mri |
| topic | Monte Carlo simulation Diffusion MRI Axonal diameter mapping Caliber variation Axonal undulation Diffusion coarse-graining |
| url | http://www.sciencedirect.com/science/article/pii/S105381192030714X |
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