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Charvet CJ. Mapping Human Brain Pathways: Challenges and Opportunities in the Integration of Scales. BRAIN, BEHAVIOR AND EVOLUTION 2023; 98:194-209. [PMID: 36972574 PMCID: PMC11310840 DOI: 10.1159/000530317] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 03/16/2023] [Indexed: 03/29/2023]
Abstract
The human brain is composed of a complex web of pathways. Diffusion magnetic resonance (MR) tractography is a neuroimaging technique that relies on the principle of diffusion to reconstruct brain pathways. Its tractography is broadly applicable to a range of problems as it is amenable for study in individuals of any age and from any species. However, it is well known that this technique can generate biologically implausible pathways, especially in regions of the brain where multiple fibers cross. This review highlights potential misconnections in two cortico-cortical association pathways with a focus on the aslant tract and inferior frontal occipital fasciculus. The lack of alternative methods to validate observations from diffusion MR tractography means there is a need to develop new integrative approaches to trace human brain pathways. This review discusses integrative approaches in neuroimaging, anatomical, and transcriptional variation as having much potential to trace the evolution of human brain pathways.
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Affiliation(s)
- Christine J Charvet
- Department of Anatomy, Physiology and Pharmacology, College of Veterinary Medicine, Auburn University, Auburn, Alabama, USA
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2
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Sarwar T, Ramamohanarao K, Zalesky A. A critical review of connectome validation studies. NMR IN BIOMEDICINE 2021; 34:e4605. [PMID: 34516016 DOI: 10.1002/nbm.4605] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Revised: 07/22/2021] [Accepted: 08/01/2021] [Indexed: 06/13/2023]
Abstract
Diffusion MRI tractography is the most widely used macroscale method for mapping connectomes in vivo. However, tractography is prone to various errors and biases, and thus tractography-derived connectomes require careful validation. Here, we critically review studies that have developed or utilized phantoms and tracer maps to validate tractography-derived connectomes, either quantitatively or qualitatively. We identify key factors impacting connectome reconstruction accuracy, including streamline seeding, propagation and filtering methods, and consider the strengths and limitations of state-of-the-art connectome phantoms and associated validation studies. These studies demonstrate the inherent limitations of current fiber orientation models and tractography algorithms and their impact on connectome reconstruction accuracy. Reconstructing connectomes with both high sensitivity and high specificity is challenging, given that some tractography methods can generate an abundance of spurious connections, while others can overlook genuine fiber bundles. We argue that streamline filtering can minimize spurious connections and potentially improve the biological plausibility of connectomes derived from tractography. We find that algorithmic choices such as the tractography seeding methodology, angular threshold, and streamline propagation method can substantially impact connectome reconstruction accuracy. Hence, careful application of tractography is necessary to reconstruct accurate connectomes. Improvements in diffusion MRI acquisition techniques will not necessarily overcome current tractography limitations without accompanying modeling and algorithmic advances.
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Affiliation(s)
- Tabinda Sarwar
- School of Computing Technologies, RMIT University, Melbourne, Victoria, Australia
| | - Kotagiri Ramamohanarao
- Department of Computing and Information Systems, The University of Melbourne, Melbourne, Victoria, Australia
| | - Andrew Zalesky
- Melbourne Neuropsychiatry Centre, The University of Melbourne, Melbourne, Victoria, Australia
- Department of Biomedical Engineering, The University of Melbourne, Melbourne, Victoria, Australia
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3
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Going Beyond Diffusion Tensor Imaging Tractography in Eloquent Glioma Surgery–High-Resolution Fiber Tractography: Q-Ball or Constrained Spherical Deconvolution? World Neurosurg 2020; 134:e596-e609. [DOI: 10.1016/j.wneu.2019.10.138] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2019] [Revised: 10/21/2019] [Accepted: 10/22/2019] [Indexed: 11/22/2022]
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4
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Tournier JD. Diffusion MRI in the brain - Theory and concepts. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2019; 112-113:1-16. [PMID: 31481155 DOI: 10.1016/j.pnmrs.2019.03.001] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Revised: 03/05/2019] [Accepted: 03/07/2019] [Indexed: 06/10/2023]
Abstract
Over the past two decades, diffusion MRI has become an essential tool in neuroimaging investigations. This is due to its sensitivity to the motion of water molecules as they diffuse through the microstructural environment, allowing diffusion MRI to be used as a 'probe' of tissue microstructure. Furthermore, this sensitivity is strongly direction-dependent, notably in brain white matter, due to the alignment of structures that restrict or hinder the motion of water molecules, notably axonal membranes. This provides a means of inferring the orientation of fibres in vivo, and by use of appropriate fibre-tracking algorithms, of delineating the path of white matter tracts in the brain. The ability to perform so-called tractography in humans in vivo non-invasively is unique to diffusion MRI, and is now used in applications such as neurosurgery planning and more broadly within investigations of brain connectomics. This review describes the theory and concepts of diffusion MRI and describes its most important areas of application in the brain, with a strong focus on tractography.
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Affiliation(s)
- J-Donald Tournier
- Department of Biomedical Engineering, School of Biomedical Engineering and Imaging Sciences, King's College London, King's Health Partners, St. Thomas' Hospital, London SE1 7EH, UK; Centre for the Developing Brain, School of Biomedical Engineering and Imaging Sciences, King's College London, King's Health Partners, St. Thomas' Hospital, London SE1 7EH, UK.
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5
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Jeurissen B, Descoteaux M, Mori S, Leemans A. Diffusion MRI fiber tractography of the brain. NMR IN BIOMEDICINE 2019; 32:e3785. [PMID: 28945294 DOI: 10.1002/nbm.3785] [Citation(s) in RCA: 253] [Impact Index Per Article: 50.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2017] [Revised: 07/10/2017] [Accepted: 07/11/2017] [Indexed: 06/07/2023]
Abstract
The ability of fiber tractography to delineate non-invasively the white matter fiber pathways of the brain raises possibilities for clinical applications and offers enormous potential for neuroscience. In the last decade, fiber tracking has become the method of choice to investigate quantitative MRI parameters in specific bundles of white matter. For neurosurgeons, it is quickly becoming an invaluable tool for the planning of surgery, allowing for visualization and localization of important white matter pathways before and even during surgery. Fiber tracking has also claimed a central role in the field of "connectomics," a technique that builds and studies comprehensive maps of the complex network of connections within the brain, and to which significant resources have been allocated worldwide. Despite its unique abilities and exciting applications, fiber tracking is not without controversy, in particular when it comes to its interpretation. As neuroscientists are eager to study the brain's connectivity, the quantification of tractography-derived "connection strengths" between distant brain regions is becoming increasingly popular. However, this practice is often frowned upon by fiber-tracking experts. In light of this controversy, this paper provides an overview of the key concepts of tractography, the technical considerations at play, and the different types of tractography algorithm, as well as the common misconceptions and mistakes that surround them. We also highlight the ongoing challenges related to fiber tracking. While recent methodological developments have vastly increased the biological accuracy of fiber tractograms, one should be aware that, even with state-of-the-art techniques, many issues that severely bias the resulting structural "connectomes" remain unresolved.
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Affiliation(s)
- Ben Jeurissen
- imec-Vision Lab, Dept. of Physics, University of Antwerp, Belgium
| | - Maxime Descoteaux
- Centre de Recherche CHUS, University of Sherbrooke, Sherbrooke, Canada
- Sherbrooke Connectivity Imaging Lab (SCIL), Computer Science Department, Faculty of Science, University of Sherbrooke, Canada
| | - Susumu Mori
- Russell H. Morgan Department of Radiology and Radiological Science, The Johns Hopkins University School of Medicine, Baltimore, MD, USA
- F.M. Kirby Research Center for Functional Brain Imaging, Kennedy Krieger Institute, Baltimore, MD, USA
| | - Alexander Leemans
- Image Sciences Institute, University Medical Center Utrecht, Utrecht, The Netherlands
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6
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Dell'Acqua F, Tournier J. Modelling white matter with spherical deconvolution: How and why? NMR IN BIOMEDICINE 2019; 32:e3945. [PMID: 30113753 PMCID: PMC6585735 DOI: 10.1002/nbm.3945] [Citation(s) in RCA: 68] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2017] [Revised: 04/18/2018] [Accepted: 04/24/2018] [Indexed: 05/30/2023]
Abstract
Since the realization that diffusion MRI can probe the microstructural organization and orientation of biological tissue in vivo and non-invasively, a multitude of diffusion imaging methods have been developed and applied to study the living human brain. Diffusion tensor imaging was the first model to be widely adopted in clinical and neuroscience research, but it was also clear from the beginning that it suffered from limitations when mapping complex configurations, such as crossing fibres. In this review, we highlight the main steps that have led the field of diffusion imaging to move from the tensor model to the adoption of diffusion and fibre orientation density functions as a more effective way to describe the complexity of white matter organization within each brain voxel. Among several techniques, spherical deconvolution has emerged today as one of the main approaches to model multiple fibre orientations and for tractography applications. Here we illustrate the main concepts and the reasoning behind this technique, as well as the latest developments in the field. The final part of this review provides practical guidelines and recommendations on how to set up processing and acquisition protocols suitable for spherical deconvolution.
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Affiliation(s)
- Flavio Dell'Acqua
- Institute of Psychiatry Psychology and Neuroscience, King's College LondonDepartment of NeuroimagingUK
- Sackler Institute for Translational Neurodevelopment, Institute of Psychiatry Psychology and Neuroscience, King's College LondonDepartment of Forensic and Neurodevelopmental SciencesUK
| | - J.‐Donald Tournier
- King's College LondonDivision of Imaging Sciences and Biomedical EngineeringUK
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7
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Improved fidelity of brain microstructure mapping from single-shell diffusion MRI. Med Image Anal 2015; 26:268-86. [PMID: 26529580 DOI: 10.1016/j.media.2015.10.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2015] [Revised: 07/15/2015] [Accepted: 10/02/2015] [Indexed: 01/29/2023]
Abstract
Diffusion weighted imaging (DWI) is sensitive to alterations in the diffusion of water molecules caused by microstructural barriers. Different microstructural compartments are characterized by differences in DWI signal. Diffusion tensor imaging conflates the signal from these compartments into a single tensor, which poorly represents multiple white matter fascicles and extra-axonal space. Diffusion compartment imaging (DCI) models overcome this limitation by providing parametric representations for the signal contribution of each compartment, thereby improving the fidelity of brain microstructure mapping. However, current approaches fail to identify DCI model parameters from conventional single-shell DWI with the desired accuracy. It has been demonstrated that part of this inaccuracy is due to the ill-posedness of the estimation of DCI model parameters from conventional single-shell acquisitions. In this paper, we propose to regularize the estimation problem for single-shell DWI by learning a prior distribution of DCI model parameters from DWI acquired at multiple b-values in an external population of subjects. We demonstrate that this population-informed prior enables, for the first time, accurate estimation of DCI models from single-shell DWI typically acquired in clinical practice. We validated our approach on synthetic and in vivo data of healthy subjects and patients with autism spectrum disorder. We applied the approach to population studies of brain microstructure in autism and found that introducing a population-informed prior leads to reliable detection of group differences. Our algorithm enables novel investigation from large existing DWI datasets in normal development and in disease and injury.
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8
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Jensen JH, Helpern JA. Resolving power for the diffusion orientation distribution function. Magn Reson Med 2015; 76:679-88. [DOI: 10.1002/mrm.25900] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2015] [Revised: 07/05/2015] [Accepted: 07/29/2015] [Indexed: 01/26/2023]
Affiliation(s)
- Jens H. Jensen
- Center for Biomedical Imaging, Medical University of South Carolina; Charleston South Carolina USA
- Department of Radiology and Radiological Science; Medical University of South Carolina; Charleston South Carolina USA
| | - Joseph A. Helpern
- Center for Biomedical Imaging, Medical University of South Carolina; Charleston South Carolina USA
- Department of Radiology and Radiological Science; Medical University of South Carolina; Charleston South Carolina USA
- Department of Neurosciences Sciences; Medical University of South Carolina; Charleston South Carolina USA
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9
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Fan Q, Nummenmaa A, Witzel T, Zanzonico R, Keil B, Cauley S, Polimeni JR, Tisdall D, Van Dijk KRA, Buckner RL, Wedeen VJ, Rosen BR, Wald LL. Investigating the capability to resolve complex white matter structures with high b-value diffusion magnetic resonance imaging on the MGH-USC Connectom scanner. Brain Connect 2015; 4:718-26. [PMID: 25287963 DOI: 10.1089/brain.2014.0305] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
One of the major goals of the NIH Blueprint Human Connectome Project was to map and quantify the white matter connections in the brain using diffusion tractography. Given the prevalence of complex white matter structures, the capability of resolving local white matter geometries with multiple crossings in the diffusion magnetic resonance imaging (dMRI) data is critical. Increasing b-value has been suggested for delineation of the finer details of the orientation distribution function (ODF). Although increased gradient strength and duration increase sensitivity to highly restricted intra-axonal water, gradient strength limitations require longer echo times (TE) to accommodate the increased diffusion encoding times needed to achieve a higher b-value, exponentially lowering the signal-to-noise ratio of the acquisition. To mitigate this effect, the MGH-USC Connectom scanner was built with 300 mT/m gradients, which can significantly reduce the TE of high b-value diffusion imaging. Here we report comparisons performed across b-values based on q-ball ODF metrics to investigate whether high b-value diffusion imaging on the Connectom scanner can improve resolving complex white matter structures. The q-ball ODF features became sharper as the b-value increased, with increased power fraction in higher order spherical harmonic series of the ODF and increased peak heights relative to the overall size of the ODF. Crossing structures were detected in an increasingly larger fraction of white matter voxels and the spatial distribution of two-way and three-way crossing structures was largely consistent with known anatomy. Results indicate that dMRI with high diffusion encoding on the Connectom system is a promising tool to better characterize, and ultimately understand, the underlying structural organization and motifs in the human brain.
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Affiliation(s)
- Qiuyun Fan
- 1 Department of Radiology, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital , Charlestown, Massachusetts
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10
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Tournier JD, Calamante F, Connelly A. Determination of the appropriate b value and number of gradient directions for high-angular-resolution diffusion-weighted imaging. NMR IN BIOMEDICINE 2013; 26:1775-1786. [PMID: 24038308 DOI: 10.1002/nbm.3017] [Citation(s) in RCA: 262] [Impact Index Per Article: 23.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2013] [Revised: 07/22/2013] [Accepted: 08/02/2013] [Indexed: 06/02/2023]
Abstract
High-angular-resolution diffusion-weighted imaging (HARDI) is one of the most common MRI acquisition schemes for use with higher order models of diffusion. However, the optimal b value and number of diffusion-weighted (DW) directions for HARDI are still undetermined, primarily as a result of the large number of available reconstruction methods and corresponding parameters, making it impossible to identify a single criterion by which to assess performance. In this study, we estimate the minimum number of DW directions and optimal b values required for HARDI by focusing on the angular frequency content of the DW signal itself. The spherical harmonic (SH) series provides the spherical analogue of the Fourier series, and can hence be used to examine the angular frequency content of the DW signal. Using high-quality data acquired along 500 directions over a range of b values, we estimate that SH terms above l = 8 are negligible in practice for b values up to 5000 s/mm(2), implying that a minimum of 45 DW directions is sufficient to fully characterise the DW signal. l > 0 SH terms were found to increase as a function of b value, levelling off at b = 3000 s/mm(2), suggesting that this value already provides the highest achievable angular resolution. In practice, it is recommended to acquire more than the minimum of 45 DW directions to avoid issues with imperfections in the uniformity of the DW gradient directions and to meet signal-to-noise requirements of the intended reconstruction method.
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Affiliation(s)
- J-Donald Tournier
- The Florey Institute of Neuroscience and Mental Health, Melbourne, Vic., Australia; Department of Medicine, Austin Health and Northern Health, University of Melbourne, Melbourne, Vic., Australia
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11
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Haldar JP, Leahy RM. Linear transforms for Fourier data on the sphere: application to high angular resolution diffusion MRI of the brain. Neuroimage 2013; 71:233-47. [PMID: 23353603 DOI: 10.1016/j.neuroimage.2013.01.022] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2012] [Revised: 12/15/2012] [Accepted: 01/14/2013] [Indexed: 10/27/2022] Open
Abstract
This paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2-sphere in three-dimensional Fourier space. This family of transforms generalizes the previously-proposed Funk-Radon Transform (FRT), which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data. The new family of transforms is characterized theoretically, and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics. After these general discussions, attention is focused on a particular new transform from this family that we name the Funk-Radon and Cosine Transform (FRACT). Based on theoretical arguments, it is expected that FRACT-based analysis should yield significantly better orientation information (e.g., improved accuracy and higher angular resolution) than FRT-based analysis, while maintaining the strong characterizability and computational efficiency of the FRT. Simulations are used to confirm these theoretical characteristics, and the practical significance of the proposed approach is illustrated with real diffusion weighted MRI brain data. These experiments demonstrate that, in addition to having strong theoretical characteristics, the proposed approach can outperform existing state-of-the-art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors.
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Affiliation(s)
- Justin P Haldar
- Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089-2564, USA.
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12
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Angular smoothing and radial regularization of ODF fields: Application on deterministic crossing fiber tractography. Phys Med 2013; 29:17-32. [DOI: 10.1016/j.ejmp.2011.10.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/24/2011] [Revised: 08/31/2011] [Accepted: 10/06/2011] [Indexed: 11/18/2022] Open
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13
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Scherrer B, Warfield SK. Parametric representation of multiple white matter fascicles from cube and sphere diffusion MRI. PLoS One 2012; 7:e48232. [PMID: 23189128 PMCID: PMC3506641 DOI: 10.1371/journal.pone.0048232] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2011] [Accepted: 09/28/2012] [Indexed: 12/13/2022] Open
Abstract
The characterization of the complex diffusion signal arising from the brain remains an open problem. Many representations focus on characterizing the global shape of the diffusion profile at each voxel and are limited to the assessment of connectivity. In contrast, Multiple Fascicle Models (MFM) seek to represent the contribution from each white matter fascicle and may be useful in the investigation of both white matter connectivity and diffusion properties of each individual fascicle. However, the most appropriate representation of multiple fascicles remains unclear. In particular, a multiple tensor representation of multiple fascicles has frequently been reported to be numerically challenging and unstable. We provide here the first analytical demonstration that when using a diffusion MRI acquisition with only one non-zero b-value, such as in conventional single-shell HARDI acquisition, a co-linearity in model parameters makes the precise model estimation impossible. Motivated by this theoretical result, we propose the novel CUSP (CUbe and SPhere) optimal acquisition scheme to achieve multiple non-zero b-values. It combines the gradients of a single-shell HARDI with gradients in its enclosing cube, in which varying b-values can be acquired by modulation of the gradient strength, without modifying the minimum echo time. Compared to a multi-shell HARDI acquisition, our scheme has significantly increased signal-to-noise ratio. We propose a novel estimation algorithm that enables efficient, robust and accurate estimation of the parameters of a multi-tensor model. In conjunction with a CUSP acquisition, it enables full estimation of the multi-tensor model. We present an evaluation of CUSP-MFM on both synthetic phantoms and invivo data. We report qualitative and quantitative experimental evaluations which demonstrate the ability of CUSP-MFM to characterize multiple fascicles from short duration acquisitions. CUSP-MFM enables rapid and effective investigation of multiple white matter fascicles, in both normal development and in disease and injury, in research and clinical practice.
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Affiliation(s)
- Benoit Scherrer
- Computational Radiology Laboratory, Department of Radiology Children's Hospital, Boston, Massachusetts, United States of America.
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14
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Functional MRI and diffusion tensor imaging of brain reorganization after experimental stroke. Transl Stroke Res 2012; 3:36-43. [PMID: 22408692 PMCID: PMC3284658 DOI: 10.1007/s12975-011-0143-8] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2011] [Revised: 12/23/2011] [Accepted: 12/27/2011] [Indexed: 11/27/2022]
Abstract
The potential of the adult brain to reorganize after ischemic injury is critical for functional recovery and provides a significant target for therapeutic strategies to promote brain repair. Despite the accumulating evidence of brain plasticity, the interaction and significance of morphological and physiological modifications in post-stroke brain tissue remain mostly unclear. Neuroimaging techniques such as functional MRI (fMRI) and diffusion tensor imaging (DTI) enable in vivo assessment of the spatial and temporal pattern of functional and structural changes inside and outside ischemic lesion areas. This can contribute to the elucidation of critical aspects in post-stroke brain remodeling. Task/stimulus-related fMRI, resting-state fMRI, or pharmacological MRI enables direct or indirect measurement of neuronal activation, functional connectivity, or neurotransmitter system responses, respectively. DTI allows estimation of the structural integrity and connectivity of white matter tracts. Together, these MRI methods provide an unprecedented means to (a) measure longitudinal changes in tissue structure and function close by and remote from ischemic lesion areas, (b) evaluate the organizational profile of neural networks after stroke, and (c) identify degenerative and restorative processes that affect post-stroke functional outcome. Besides, the availability of MRI in clinical institutions as well as research laboratories provides an optimal basis for translational research on stroke recovery. This review gives an overview of the current status and perspectives of fMRI and DTI applications to study brain reorganization in experimental stroke models.
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15
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Raffelt D, Tournier JD, Crozier S, Connelly A, Salvado O. Reorientation of fiber orientation distributions using apodized point spread functions. Magn Reson Med 2011; 67:844-55. [PMID: 22183751 DOI: 10.1002/mrm.23058] [Citation(s) in RCA: 76] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2010] [Revised: 05/19/2011] [Accepted: 05/25/2011] [Indexed: 11/06/2022]
Abstract
Using high angular resolution diffusion-weighted images, spherical deconvolution enables multiple white matter fiber populations to be resolved within a single voxel by computing the fiber orientation distribution (FOD). Higher order information provided by FODs could improve several methods for investigating population differences in white matter, including image registration, voxel-based analysis, atlas-based segmentation and labeling, and group average fiber tractography. All of these methods require spatial normalization of FODs. In this article, a novel method to reorient the FOD is presented, which is an important step required for FOD spatial normalization. The proposed method was assessed using both qualitative and quantitative experiments, with numerical simulations and in vivo human data. Results demonstrate that the proposed method improves FOD reorientation accuracy, removes undesired artefacts, and decreases computation time compared to a previous approach. The utility of the proposed method is illustrated by nonlinear FOD spatial normalization of 10 human subjects. Accurate reorientation and normalization of FODs is a critical step toward investigating white matter tissue in the context of multiple fiber orientations.
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Affiliation(s)
- David Raffelt
- CSIRO Preventative Health National Research Flagship ICTC, The Australian e-Health Research Centre, Royal Brisbane and Women's Hospital, Herston, Queensland, Australia.
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16
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Kaden E, Kruggel F. A reproducing kernel hilbert space approach for q-ball imaging. IEEE TRANSACTIONS ON MEDICAL IMAGING 2011; 30:1877-1886. [PMID: 21609878 DOI: 10.1109/tmi.2011.2157517] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Diffusion magnetic resonance (MR) imaging has enabled us to reveal the white matter geometry in the living human brain. The Q-ball technique is widely used nowadays to recover the orientational heterogeneity of the intra-voxel fiber architecture. This article proposes to employ the Funk-Radon transform in a Hilbert space with a reproducing kernel derived from the spherical Laplace-Beltrami operator, thus generalizing previous approaches that assume a bandlimited diffusion signal. The function estimation problem is solved within a Tikhonov regularization framework, while a Gaussian process model allows for the selection of the smoothing parameter and the specification of confidence bands. Shortcomings of Q-ball imaging are discussed.
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Affiliation(s)
- Enrico Kaden
- Department of Computer Science, University of Leipzig,Germany.
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17
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Yeh FC, Tseng WYI. NTU-90: a high angular resolution brain atlas constructed by q-space diffeomorphic reconstruction. Neuroimage 2011; 58:91-9. [PMID: 21704171 DOI: 10.1016/j.neuroimage.2011.06.021] [Citation(s) in RCA: 332] [Impact Index Per Article: 25.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2011] [Revised: 05/24/2011] [Accepted: 06/09/2011] [Indexed: 10/18/2022] Open
Abstract
We present a high angular resolution brain atlas constructed by averaging 90 diffusion spectrum imaging (DSI) datasets in the ICBM-152 space. The spatial normalization of the diffusion information was conducted by a novel q-space diffeomorphic reconstruction method, which reconstructed the spin distribution function (SDF) in the ICBM-152 space from the diffusion MR signals. The performance of this method was examined by a simulation study modeling nonlinear transformation. The result showed that the reconstructed SDFs can resolve crossing fibers and that the accumulated quantitative anisotropy can reveal the relative ratio of the fiber populations. In the in vivo study, the SDF of the constructed atlas was shown to resolve crossing fiber orientations. Further, fiber tracking showed that the atlas can be used to present the pathways of fiber bundles, and the termination locations of the fibers can provide anatomical localization of the connected cortical regions. This high angular resolution brain atlas may facilitate future connectome research on the complex structure of the human brain.
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Affiliation(s)
- Fang-Cheng Yeh
- Department of Biomedical Engineering, Carnegie Mellon University, PA, USA
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18
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Symmetric diffeomorphic registration of fibre orientation distributions. Neuroimage 2011; 56:1171-80. [PMID: 21316463 DOI: 10.1016/j.neuroimage.2011.02.014] [Citation(s) in RCA: 168] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2010] [Revised: 02/01/2011] [Accepted: 02/02/2011] [Indexed: 11/23/2022] Open
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19
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Tournier JD, Mori S, Leemans A. Diffusion tensor imaging and beyond. Magn Reson Med 2011; 65:1532-56. [PMID: 21469191 DOI: 10.1002/mrm.22924] [Citation(s) in RCA: 637] [Impact Index Per Article: 49.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2010] [Accepted: 02/18/2011] [Indexed: 12/13/2022]
Affiliation(s)
- Jacques-Donald Tournier
- Brain Research Institute, Florey Neuroscience Institutes, Neurosciences Building, Austin Health, Heidelberg West, Victoria, Australia
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20
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Lienhard S, Malcolm JG, Westin CF, Rathi Y. A full bi-tensor neural tractography algorithm using the unscented Kalman filter. EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2011; 2011:77. [PMID: 24348546 PMCID: PMC3860596 DOI: 10.1186/1687-6180-2011-77] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We describe a technique that uses tractography to visualize neural pathways in human brains by extending an existing framework that uses overlapping Gaussian tensors to model the signal. At each point on the fiber, an unscented Kalman filter is used to find the most consistent direction as a mixture of previous estimates and of the local model. In our previous framework, the diffusion ellipsoid had a cylindrical shape, i.e., the diffusion tensor's second and third eigenvalues were identical. In this paper, we extend the tensor representation so that the diffusion tensor is represented by an arbitrary ellipsoid. Experiments on synthetic data show a reduction in the angular error at fiber crossings and branchings. Tests on in vivo data demonstrate the ability to trace fibers in areas containing crossings or branchings, and the tests also confirm the superiority of using a full tensor representation over the simplified model.
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Affiliation(s)
- Stefan Lienhard
- Computer Vision Laboratory, ETH Zürich, 8092 Zürich, Switzerland
| | - James G. Malcolm
- Psychiatry Neuroimaging Laboratory, Harvard Medical School, Boston, MA, USA
| | | | - Yogesh Rathi
- Psychiatry Neuroimaging Laboratory, Harvard Medical School, Boston, MA, USA
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21
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Abstract
We describe a technique that uses tractography to drive the local fiber model estimation. Existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by those previous. To do this we perform tractography within a filter framework and use a discrete mixture of Gaussian tensors to model the signal. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Using two- and three-fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.
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Affiliation(s)
- James G Malcolm
- Psychiatry Neuroimaging Laboratory, Brigham and Womens Hospital, Harvard Medical School, Boston, MA 02215, USA
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22
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Lazar M. Mapping brain anatomical connectivity using white matter tractography. NMR IN BIOMEDICINE 2010; 23:821-35. [PMID: 20886567 PMCID: PMC4503207 DOI: 10.1002/nbm.1579] [Citation(s) in RCA: 74] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Integration of the neural processes in the human brain is realized through interconnections that exist between different neural centers. These interconnections take place through white matter pathways. White matter tractography is currently the only available technique for the reconstruction of the anatomical connectivity in the human brain noninvasively and in vivo. The trajectory and terminations of white matter pathways are estimated from local orientations of nerve bundles. These orientations are obtained using measurements of water diffusion in the brain. In this article, the techniques for estimating fiber directions from diffusion measurements in the human brain are reviewed. Methods of white matter tractography are described, together with the current limitations of the technique, including sensitivity to image noise and partial voluming. The applications of white matter tractography to the topographical characterization of the white matter connections and the segmentation of specific white matter pathways, and corresponding functional units of gray matter, are discussed. In this context, the potential impact of white matter tractography in mapping the functional systems and subsystems in the human brain, and their interrelations, is described. Finally, the applications of white matter tractography to the study of brain disorders, including fiber tract localization in brains affected by tumors and the identification of impaired connectivity routes in neurologic and neuropsychiatric diseases, are discussed.
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Affiliation(s)
- Mariana Lazar
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY 10016, USA.
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23
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Rathi Y, Malcolm JG, Michailovich O, Westin CF, Shenton ME, Bouix S. Tensor kernels for simultaneous fiber model estimation and tractography. Magn Reson Med 2010; 64:138-48. [PMID: 20572129 PMCID: PMC3043656 DOI: 10.1002/mrm.22292] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2009] [Accepted: 10/21/2009] [Indexed: 11/12/2022]
Abstract
This paper proposes a novel framework for joint orientation distribution function estimation and tractography based on a new class of tensor kernels. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. In this work, fiber tracking is formulated as recursive estimation: at each step of tracing the fiber, the current estimate of the orientation distribution function is guided by the previous. To do this, second-and higher-order tensor-based kernels are employed. A weighted mixture of these tensor kernels is used for representing crossing and branching fiber structures. While tracing a fiber, the parameters of the mixture model are estimated based on the orientation distribution function at that location and a smoothness term that penalizes deviation from the previous estimate along the fiber direction. This ensures smooth estimation along the direction of propagation of the fiber. In synthetic experiments, using a mixture of two and three components it is shown that this approach improves the angular resolution at crossings. In vivo experiments using two and three components examine the corpus callosum and corticospinal tract and confirm the ability to trace through regions known to contain such crossing and branching.
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Affiliation(s)
- Yogesh Rathi
- Psychiatry Neuroimaging Laboratory, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts 02215, USA.
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24
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Abstract
We describe a technique to simultaneously estimate a weighted, positive-definite multi-tensor fiber model and perform tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a weighted mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Further, we modify the Kalman filter to enforce model constraints, i.e. positive eigenvalues and convex weights. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach significantly improves the angular resolution at crossings and branchings while consistently estimating the mixture weights. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization.
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Affiliation(s)
- James G Malcolm
- Psychiatry Neuroimaging Laboratory, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA
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25
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The effect of finite diffusion gradient pulse duration on fibre orientation estimation in diffusion MRI. Neuroimage 2010; 51:743-51. [DOI: 10.1016/j.neuroimage.2010.02.041] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2009] [Revised: 01/19/2010] [Accepted: 02/13/2010] [Indexed: 11/19/2022] Open
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26
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Malcolm JG, Michailovich O, Bouix S, Westin CF, Shenton ME, Rathi Y. A filtered approach to neural tractography using the Watson directional function. Med Image Anal 2010; 14:58-69. [PMID: 19914856 PMCID: PMC3967593 DOI: 10.1016/j.media.2009.10.003] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2009] [Revised: 10/09/2009] [Accepted: 10/12/2009] [Indexed: 11/26/2022]
Abstract
We propose a technique to simultaneously estimate the local fiber orientations and perform multi-fiber tractography. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the measured signal or estimated fiber orientation. Further, to overcome noise, many algorithms use a filter as a post-processing step to obtain a smooth trajectory. We formulate fiber tracking as causal estimation: at each step of tracing the fiber, the current estimate of the signal is guided by the previous. To do this, we model the signal as a discrete mixture of Watson directional functions and perform tractography within a filtering framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the signal and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides an accurate estimate of the local structure at each point along the fiber. We choose the Watson function since it provides a compact representation of the signal parameterized by the principal diffusion direction and a scaling parameter describing anisotropy, and also allows analytic reconstruction of the oriented diffusion function from those parameters. Using a mixture of two and three components (corresponding to two-fiber and three-fiber models) we demonstrate in synthetic experiments that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments examine the corpus callosum and internal capsule and confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization.
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Affiliation(s)
- James G Malcolm
- Psychiatry Neuroimaging Laboratory, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02215, USA.
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27
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Leergaard TB, White NS, de Crespigny A, Bolstad I, D'Arceuil H, Bjaalie JG, Dale AM. Quantitative histological validation of diffusion MRI fiber orientation distributions in the rat brain. PLoS One 2010; 5:e8595. [PMID: 20062822 PMCID: PMC2802592 DOI: 10.1371/journal.pone.0008595] [Citation(s) in RCA: 152] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2009] [Accepted: 11/27/2009] [Indexed: 11/19/2022] Open
Abstract
Diffusion MRI (dMRI) is widely used to measure microstructural features of brain white matter, but commonly used dMRI measures have limited capacity to resolve the orientation structure of complex fiber architectures. While several promising new approaches have been proposed, direct quantitative validation of these methods against relevant histological architectures remains missing. In this study, we quantitatively compare neuronal fiber orientation distributions (FODs) derived from ex vivo dMRI data against histological measurements of rat brain myeloarchitecture using manual recordings of individual myelin stained fiber orientations. We show that accurate FOD estimates can be obtained from dMRI data, even in regions with complex architectures of crossing fibers with an intrinsic orientation error of approximately 5-6 degrees in these regions. The reported findings have implications for both clinical and research studies based on dMRI FOD measures, and provide an important biological benchmark for improved FOD reconstruction and fiber tracking methods.
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Affiliation(s)
- Trygve B. Leergaard
- Centre for Molecular Biology and Neuroscience, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway
| | - Nathan S. White
- Department of Cognitive Sciences, University of California San Diego, San Diego, California, United States of America
| | - Alex de Crespigny
- A.A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts, United States of America
| | - Ingeborg Bolstad
- Centre for Molecular Biology and Neuroscience, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway
| | - Helen D'Arceuil
- A.A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts, United States of America
| | - Jan G. Bjaalie
- Centre for Molecular Biology and Neuroscience, Institute of Basic Medical Sciences, University of Oslo, Oslo, Norway
| | - Anders M. Dale
- Departments of Neurosciences and Radiology, University of California San Diego, San Diego, California, United States of America
- * E-mail:
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28
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UMEZAWA E, YOSHIKAWA M, OHNO K, YOSHIKAWA E, YAMAGUCHI K. Multi-shelled q-ball Imaging: Moment-based Orientation Distribution Function. Magn Reson Med Sci 2010; 9:119-29. [DOI: 10.2463/mrms.9.119] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
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29
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Rathi Y, Michailovich O, Shenton ME, Bouix S. Directional functions for orientation distribution estimation. Med Image Anal 2009; 13:432-44. [PMID: 19269242 DOI: 10.1016/j.media.2009.01.004] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2008] [Revised: 01/17/2009] [Accepted: 01/27/2009] [Indexed: 11/16/2022]
Abstract
Computing the orientation distribution function (ODF) from high angular resolution diffusion imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation. Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a "hybrid" framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between two ODF's.
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Affiliation(s)
- Yogesh Rathi
- Psychiatry Neuroimaging Laboratory, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
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30
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Lazar M, Jensen JH, Xuan L, Helpern JA. Estimation of the orientation distribution function from diffusional kurtosis imaging. Magn Reson Med 2009; 60:774-81. [PMID: 18816827 DOI: 10.1002/mrm.21725] [Citation(s) in RCA: 90] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
The Orientation Distribution Function (ODF) is used to describe the directionality of multimodal diffusion in regions with complex fiber architecture present in brain and other biological tissues. In this study, an approximation for the ODF of water diffusion from diffusional kurtosis imaging (DKI) is presented. DKI requires only a relatively limited number of diffusion measurements and, for the brain, b values no higher than 2500 s/mm(2). The DKI-based ODF approximation is decomposed into two components representing the Gaussian and non-Gaussian (NG) diffusion contributions, respectively. Simulations of multiple fiber configurations show that both the total and the NG-ODF are able to resolve the orientations of the component fibers, with the NG-ODF being the most sensitive to profiling the fibers' directions. Orientation maps obtained for in vivo brain imaging data demonstrate multiple fiber components in brain regions with complex anatomy. The results appear to be in agreement with known white matter architecture.
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Affiliation(s)
- Mariana Lazar
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, New York 10016-3240, USA.
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31
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Malcolm JG, Shenton ME, Rathi Y. Neural tractography using an unscented Kalman filter. INFORMATION PROCESSING IN MEDICAL IMAGING : PROCEEDINGS OF THE ... CONFERENCE 2009; 21:126-38. [PMID: 19694258 PMCID: PMC2768602 DOI: 10.1007/978-3-642-02498-6_11] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
We describe a technique to simultaneously estimate a local neural fiber model and trace out its path. Existing techniques estimate the local fiber orientation at each voxel independently so there is no running knowledge of confidence in the estimated fiber model. We formulate fiber tracking as recursive estimation: at each step of tracing the fiber, the current estimate is guided by the previous. To do this we model the signal as a mixture of Gaussian tensors and perform tractography within a filter framework. Starting from a seed point, each fiber is traced to its termination using an unscented Kalman filter to simultaneously fit the local model and propagate in the most consistent direction. Despite the presence of noise and uncertainty, this provides a causal estimate of the local structure at each point along the fiber. Synthetic experiments demonstrate that this approach reduces signal reconstruction error and significantly improves the angular resolution at crossings and branchings. In vivo experiments confirm the ability to trace out fibers in areas known to contain such crossing and branching while providing inherent path regularization.
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Affiliation(s)
- James G Malcolm
- Psychiatry Neuroimaging Laboratory, Harvard Medical School, Boston, MA, USA.
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32
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Barmpoutis A, Jian B, Vemuri BC. Adaptive kernels for multi-fiber reconstruction. INFORMATION PROCESSING IN MEDICAL IMAGING : PROCEEDINGS OF THE ... CONFERENCE 2009; 21:338-49. [PMID: 19694275 PMCID: PMC2760004 DOI: 10.1007/978-3-642-02498-6_28] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
In this paper we present a novel method for multi-fiber reconstruction given a diffusion-weighted MRI dataset. There are several existing methods that employ various spherical deconvolution kernels for achieving this task. However the kernels in all of the existing methods rely on certain assumptions regarding the properties of the underlying fibers, which introduce inaccuracies and unnatural limitations in them. Our model is a non trivial generalization of the spherical deconvolution model, which unlike the existing methods does not make use of a fix-shaped kernel. Instead, the shape of the kernel is estimated simultaneously with the rest of the unknown parameters by employing a general adaptive model that can theoretically approximate any spherical deconvolution kernel. The performance of our model is demonstrated using simulated and real diffusion-weighed MR datasets and compared quantitatively with several existing techniques in literature. The results obtained indicate that our model has superior performance that is close to the theoretic limit of the best possible achievable result.
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33
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Bloy L, Verma R. On computing the underlying fiber directions from the diffusion orientation distribution function. MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION : MICCAI ... INTERNATIONAL CONFERENCE ON MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION 2008; 11:1-8. [PMID: 18979725 DOI: 10.1007/978-3-540-85988-8_1] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Abstract
In this work, a novel method for determining the principal directions (maxima) of the diffusion orientation distribution function (ODF) is proposed. We represent the ODF as a symmetric high-order Cartesian tensor restricted to the unit sphere and show that the extrema of the ODF are solutions to a system of polynomial equations whose coefficients are polynomial functions of the tensor elements. In addition to demonstrating the ability of our methods to identify the principal directions in real data, we show that this method correctly identifies the principal directions under a range of noise levels. We also propose the use of the principal curvatures of the graph of the ODF function as a measure of the degree of diffusion anisotropy in that direction. We present simulated results illustrating the relationship between the mean principal curvature, measured at the maxima, and the fractional anisotropy of the underlying diffusion tensor.
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Affiliation(s)
- Luke Bloy
- Department of Bioengineering, University of Pennsylvania, USA.
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34
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Schultz T, Seidel HP. Estimating crossing fibers: a tensor decomposition approach. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 2008; 14:1635-1642. [PMID: 18989020 DOI: 10.1109/tvcg.2008.128] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
Diffusion weighted magnetic resonance imaging is a unique tool for non-invasive investigation of major nerve fiber tracts. Since the popular diffusion tensor (DT-MRI) model is limited to voxels with a single fiber direction, a number of high angular resolution techniques have been proposed to provide information about more diverse fiber distributions. Two such approaches are Q-Ball imaging and spherical deconvolution, which produce orientation distribution functions (ODFs) on the sphere. For analysis and visualization, the maxima of these functions have been used as principal directions, even though the results are known to be biased in case of crossing fiber tracts. In this paper, we present a more reliable technique for extracting discrete orientations from continuous ODFs, which is based on decomposing their higher-order tensor representation into an isotropic component, several rank-1 terms, and a small residual. Comparing to ground truth in synthetic data shows that the novel method reduces bias and reliably reconstructs crossing fibers which are not resolved as individual maxima in the ODF. We present results on both Q-Ball and spherical deconvolution data and demonstrate that the estimated directions allow for plausible fiber tracking in a real data set.
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35
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Clarke RA, Scifo P, Rizzo G, Dell'Acqua F, Scotti G, Fazio F. Noise correction on Rician distributed data for fibre orientation estimators. IEEE TRANSACTIONS ON MEDICAL IMAGING 2008; 27:1242-1251. [PMID: 18753042 DOI: 10.1109/tmi.2008.920615] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
New complex tissue microstructure estimators have been presented recently in order to elucidate white matter fibre orientations. Since these algorithms are based on the diffusion-weighted signal profile, the estimations are affected by noise artefacts. The proven robustness of these methods cannot counteract distortions since the statistical Rician behavior has not been taken into account. In this study, two techniques to counteract the noise distortions are presented to improve the fibre orientation estimations. Simulations and in vivo experiments show an improvement in the angular resolution and convergence of the results. One of these strategies represents a good compromise between computational cost and result improvements.
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Affiliation(s)
- Rafael Alonso Clarke
- Department of Nuclear Medicine, San Raffaele Scientific Institute, 20132 Milan, Italy
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36
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Tournier JD, Yeh CH, Calamante F, Cho KH, Connelly A, Lin CP. Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data. Neuroimage 2008; 42:617-25. [PMID: 18583153 DOI: 10.1016/j.neuroimage.2008.05.002] [Citation(s) in RCA: 412] [Impact Index Per Article: 25.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2007] [Revised: 04/24/2008] [Accepted: 05/01/2008] [Indexed: 11/17/2022] Open
Abstract
Diffusion-weighted imaging can potentially be used to infer the connectivity of the human brain in vivo using fibre-tracking techniques, and is therefore of great interest to neuroscientists and clinicians. A key requirement for fibre tracking is the accurate estimation of white matter fibre orientations within each imaging voxel. The diffusion tensor model, which is widely used for this purpose, has been shown to be inadequate in crossing fibre regions. A number of approaches have recently been proposed to address this issue, based on high angular resolution diffusion-weighted imaging (HARDI) data. In this study, an experimental model of crossing fibres, consisting of water-filled plastic capillaries, is used to thoroughly assess three such techniques: constrained spherical deconvolution (CSD), super-resolved CSD (super-CSD) and Q-ball imaging (QBI). HARDI data were acquired over a range of crossing angles and b-values, from which fibre orientations were computed using each technique. All techniques were capable of resolving the two fibre populations down to a crossing angle of 45 degrees , and down to 30 degrees for super-CSD. A bias was observed in the fibre orientations estimated by QBI for crossing angles other than 90 degrees, consistent with previous simulation results. Finally, for a 45 degrees crossing, the minimum b-value required to resolve the fibre orientations was 4000 s/mm(2) for QBI, 2000 s/mm(2) for CSD, and 1000 s/mm(2) for super-CSD. The quality of estimation of fibre orientations may profoundly affect fibre tracking attempts, and the results presented provide important additional information regarding performance characteristics of well-known methods.
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37
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Tournier JD, Calamante F, Connelly A. Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution. Neuroimage 2007; 35:1459-72. [PMID: 17379540 DOI: 10.1016/j.neuroimage.2007.02.016] [Citation(s) in RCA: 1378] [Impact Index Per Article: 81.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2006] [Revised: 12/13/2006] [Accepted: 02/10/2007] [Indexed: 10/23/2022] Open
Abstract
Diffusion-weighted (DW) MR images contain information about the orientation of brain white matter fibres that potentially can be used to study human brain connectivity in vivo using tractography techniques. Currently, the diffusion tensor model is widely used to extract fibre directions from DW-MRI data, but fails in regions containing multiple fibre orientations. The spherical deconvolution technique has recently been proposed to address this limitation. It provides an estimate of the fibre orientation distribution (FOD) by assuming the DW signal measured from any fibre bundle is adequately described by a single response function. However, the deconvolution is ill-conditioned and susceptible to noise contamination. This tends to introduce artefactual negative regions in the FOD, which are clearly physically impossible. In this study, the introduction of a constraint on such negative regions is proposed to improve the conditioning of the spherical deconvolution. This approach is shown to provide FOD estimates that are robust to noise whilst preserving angular resolution. The approach also permits the use of super-resolution, whereby more FOD parameters are estimated than were actually measured, improving the angular resolution of the results. The method provides much better defined fibre orientation estimates, and allows orientations to be resolved that are separated by smaller angles than previously possible. This should allow tractography algorithms to be designed that are able to track reliably through crossing fibre regions.
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