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In vivo fiber tractography using DT-MRI data
Magnetic Resonance in Medicine
Abstract
Fiber tract trajectories in coherently organized brain white matter pathways were computed from in vivo diffusion tensor magnetic resonance imaging (DT-MRI) data. First, a continuous diffusion tensor field is constructed from this discrete, noisy, measured DT-MRI data. Then a Frenet equation, describing the evolution of a fiber tract, was solved. This approach was validated using synthesized, noisy DT-MRI data. Corpus callosum and pyramidal tract trajectories were constructed and found to be consistent with known anatomy. The method's reliability, however, degrades where the distribution of fiber tract directions is nonuniform. Moreover, background noise in diffusion-weighted MRIs can cause a computed trajectory to hop from tract to tract. Still, this method can provide quantitative information with which to visualize and study connectivity and continuity of neural pathways in the central and peripheral nervous systems in vivo, and holds promise for elucidating architectural features in other fibrous tissues and ordered media.
... Considering these limitations alongside a growing body of literature indicating the importance of patient-specific surgical targeting to optimize outcomes, current research aims to achieve precise and personalized identification of therapeutic targets that conventional imaging cannot identify. To this end, two primary imaging modalities, diffusion MRI (dMRI) and functional MRI (fMRI), have been tested and implemented in the surgical workflow [1,8,9]. Current research is underway to better understand if dMRI and fMRI can improve clinical outcomes. ...
... Model-based techniques fit data to predefined models, such as the tensor or kurtosis model, providing fiber orientations for tracking. Among all the model-based methods, diffusion tensor imaging (DTI) is the most commonly used in dMRI analyses [8]. In brief, neural tissue comprises gray matter (cell bodies and nuclei) and white matter (axons, myelin, and microtubules), with axonal projections connecting specific brain regions. ...
... DTI methods provide voxel-wise information about the structure (i.e., anisotropy) and trajectory (i.e., direction) of axons in three-dimensional space. Voxel-wise analysis can then be implemented to generate the maps of white matter pathways, a processing known as tractography [8,31]. The anisotropy defines the termination criterion of fiber trajectories. ...
Surgical neuromodulation has witnessed significant progress in recent decades. Notably, deep brain stimulation (DBS), delivered precisely within therapeutic targets, has revolutionized the treatment of medication-refractory movement disorders and is now expanding for refractory psychiatric disorders, refractory epilepsy, and post-stroke motor recovery. In parallel, the advent of incisionless treatment with focused ultrasound ablation (FUSA) can offer patients life-changing symptomatic relief. Recent research has underscored the potential to further optimize DBS and FUSA outcomes by conceptualizing the therapeutic targets as critical nodes embedded within specific brain networks instead of strictly anatomical structures. This paradigm shift was facilitated by integrating two imaging modalities used regularly in brain connectomics research: diffusion MRI (dMRI) and functional MRI (fMRI). These advanced imaging techniques have helped optimize the targeting and programming techniques of surgical neuromodulation, all while holding immense promise for investigations into treating other neurological and psychiatric conditions. This review aims to provide a fundamental background of advanced imaging for clinicians and scientists, exploring the synergy between current and future approaches to neuromodulation as they relate to dMRI and fMRI capabilities. Focused research in this area is required to optimize existing, functional neurosurgical treatments while serving to build an investigative infrastructure to unlock novel targets to alleviate the burden of other neurological and psychiatric disorders.
... Their efforts have often been limited to mere speculation, for the availability of reliable methods to trace connections in the human brain being lacking for decades. Recent developments in magnetic resonance imaging (MRI) have introduced new methods, based on diffusion imaging tractography that can reconstruct white matter trajectories in the living human brain ( Basser et al., 2000 ;Le Bihan, 2003 ). The resultant infl ux of information on human connectional anatomy derived from tractography is likely to fi ll the gap on our anatomical knowledge of human brain connections and reinvigorate models of cognition based on asymmetrical distribution of large-scale networks ( Catani & Mesulam, 2008 ). ...
... Given that within cerebral white matter, water molecules diffuse more freely along myelinated tracts than across them -a property termed anisotropy of diffusion- ( Moseley et al., 1990 ), it is possible to obtain in vivo estimates of white matter fi ber orientation by measuring the principal direction of diffusivity of water ( Basser et al., 1994 ). This has led to the development of diffusion tensor tractography ( Basser et al., 2000 ;Conturo et al., 1999 ;Jones et al., 1999 ;Mori et al., 1999 ;Poupon et al., 2000 ), in which white matter tracts are reconstructed in three dimensions by sequentially piecing together discrete and shortly spaced estimates of fi ber orientation to form continuous trajectories. Although these tracts are " virtual, " the connections being defi ned mathematically and not necessarily implying a true axonal pathway, the technique has been used with some success in the living human brain to study the major projection, association, and commissural tracts ( Basser et al., 2000 ;Catani et al., 2002 ;Lawes et al., 2008 ;Mori et al., 1999 ). ...
... This has led to the development of diffusion tensor tractography ( Basser et al., 2000 ;Conturo et al., 1999 ;Jones et al., 1999 ;Mori et al., 1999 ;Poupon et al., 2000 ), in which white matter tracts are reconstructed in three dimensions by sequentially piecing together discrete and shortly spaced estimates of fi ber orientation to form continuous trajectories. Although these tracts are " virtual, " the connections being defi ned mathematically and not necessarily implying a true axonal pathway, the technique has been used with some success in the living human brain to study the major projection, association, and commissural tracts ( Basser et al., 2000 ;Catani et al., 2002 ;Lawes et al., 2008 ;Mori et al., 1999 ). Diffusion tensor tractography offers the advantage of being completely noninvasive, as previously established methods for tracing fi ber pathways, such as those used in axonal tracer studies, are restricted for use in nonhuman primates only. ...
State-of-the-art research on brain asymmetry, explained from molecular to clinical levels.
Hemispheric asymmetry is one of the basic aspects of perception and cognitive processing. The different functions of the left and right hemispheres of the brain have been studied with renewed interest in recent years, as scholars explore applications to new areas, new measuring techniques, and new theoretical approaches. This volume provides a comprehensive view of the latest research in brain asymmetry, offering not only recent empirical and clinical findings but also a coherent theoretical approach to the subject. In chapters that report on the field at levels from the molecular to the clinical, leading researchers address such topics as the evolution and genetics of brain asymmetry; animal models; findings from structural and functional neuroimaging techniques and research; sex differences and hormonal effects; sleep asymmetry; cognitive asymmetry in visual and auditory perception; and auditory laterality and speech perception, memory, and asymmetry in the context of developmental, neurological, and psychiatric disorders.
Contributors Katrin Amunts, Ulrike Bayer, Alfredo Brancucci, Vince D. Calhoun, Maria Casagrande, Marco Catani, Michael C. Corballis, Patricia E. Cowell, Timothy J. Crow, Tom Eichele, Stephanie Forkel, Patrick J. Gannon, Isabelle George, Onur Güntürkün, Heikki Hämäläinen, Markus Hausmann, Joseph B. Hellige, Kenneth Hugdahl, Masud Husain, Grégoria Kalpouzos, Bruno Laeng, Martina Manns, Chikashi Michimata, Deborah W. Moncrieff, Lars Nyberg, Godfrey Pearlson, Stefan Pollmann, Victoria Singh-Curry, Iris E.C. Sommer, Tao Sun, Nathan Swanson, Fiia Takio, Michel Thiebaut de Schotten, René Westerhausen
... Then, steps are taken following directions extracted from local models of the dMR signal. Stepping in the white matter volume brings the tractography algorithm to a new point, where the process can be repeated until a termination criterion is met [4]. Since its inception, countless algorithms have been proposed, improving how directions are followed [12,16], which termination criterion are used [51] or how the local model is computed [28,45]. ...
... where N is determined like M . This process produces another half-streamline which is concatenated to the first half to produce a complete streamline p N..0..M in the WM [3,4]. ...
... Since its inception, many algorithms have been developed to learn the optimal policy defined in Eq. (4). These can be classified into two broad categories: model-based and model-free. ...
Recently, deep reinforcement learning (RL) has been proposed to learn the tractography procedure and train agents to reconstruct the structure of the white matter without manually curated reference streamlines. While the performances reported were competitive, the proposed framework is complex, and little is still known about the role and impact of its multiple parts. In this work, we thoroughly explore the different components of the proposed framework, such as the choice of the RL algorithm, seeding strategy, the input signal and reward function, and shed light on their impact. Approximately 7,400 models were trained for this work, totalling nearly 41,000 hours of GPU time. Our goal is to guide researchers eager to explore the possibilities of deep RL for tractography by exposing what works and what does not work with the category of approach. As such, we ultimately propose a series of recommendations concerning the choice of RL algorithm, the input to the agents, the reward function and more to help future work using reinforcement learning for tractography. We also release the open source codebase, trained models, and datasets for users and researchers wanting to explore reinforcement learning for tractography.
... Diffusion tractography is a technique that creates three-dimensional reconstructions of the WM pathways while also offering an accurate anatomical picture (Schiavi). Tractography techniques (or fiber tracking), primarily introduced in 1998 (Basser, 1998;Basser et al., 2000), provide the investigators with the in-vivo delineation of WM tract architecture that dramatically improves the topographical specificity. Some assessments have combined diffusion tensor imaging with corticospinal tractography, since it is one of the largest tracts of the brain. ...
... These methods are founded on different properties and ranges from line-propagation and front-evolution to the probabilistic ones. Particularly, despite significant speeds, line-propagation approaches (Basser et al., 2000;Mori et al., 1999) characteristically apply deterministic algorithms (orientation distribution function or fiber orientation distribution) that exclusively recruit the values of voxel's neighbors. However, the propagation of local statistical errors throughout the track could be a remarkable drawback (Daducci et al., 2014). ...
... 10,11 An accurate reconstruction of these contralateral projections requires a superior identification of the crossing fibers in the optic chiasm. Several tractography-based reconstructions in rodents 7-9 applied diffusion tensor imaging 12,13 to correctly identify principal fiber directions of optic tracts. However, the diffusion tensor imaging representation underestimates the known complexity of the optic chiasm. ...
... Throughout the study, we used the Euler's method-based deterministic tractography algorithm 12 implemented in DSI Studio 39 (the winner of the ISMRM 2015 Tractography Challenge 40 ) to ensure intuitive interpretation of streamlines as the most probable neural connections between given regions. For every mouse, we defined: two spherical seeding ROIs (1 mm diameter) fully intersecting with the intraorbital portions of the Optic Nerves † , one primary pass-through spherical ROI (2 mm diameter) covering the whole optic chiasm, and two secondary pass-through spherical ROIs (1 mm diameter) in the Lateral Geniculate Nuclei (LGNs), as illustrated in Figure 1C. ...
Purpose
The accuracy of diffusion MRI tractography reconstruction decreases in the white matter regions with crossing fibers. The optic pathways in rodents provide a challenging structure to test new diffusion tractography approaches because of the small crossing volume within the optic chiasm and the unbalanced 9:1 proportion between the contra‐ and ipsilateral neural projections from the retina to the lateral geniculate nucleus, respectively.
Methods
Common approaches based on Orientation Distribution Function (ODF) peak finding or statistical inference were compared qualitatively and quantitatively to ODF Fingerprinting (ODF‐FP) for reconstruction of crossing fibers within the optic chiasm using in vivo diffusion MRI (n=18$$ n=18 $$ healthy C57BL/6 mice). Manganese‐Enhanced MRI (MEMRI) was obtained after intravitreal injection of manganese chloride and used as a reference standard for the optic pathway anatomy.
Results
ODF‐FP outperformed by over 100% all the tested methods in terms of the ratios between the contra‐ and ipsilateral segments of the reconstructed optic pathways as well as the spatial overlap between tractography and MEMRI.
Conclusion
In this challenging model system, ODF‐Fingerprinting reduced uncertainty of diffusion tractography for complex structural formations of fiber bundles.
... Tractography allows to reconstruct fiber tracts in each individual without image registration and alignment to a common space (such as MNI or Talairach coordinates in TBSS). Accordingly, tractography can be applied even if the location of the tract varies across individuals, which is often the case (Basser, Pajevic, Pierpaoli, Duda, & Aldroubi, 2000;Conturo et al., 1999;Mori & Barker, 1999). ...
... While single tensor deterministic tractography works well for most of the major fiber tracts, crossing and fanning fibers within a voxel make this method problematic because the algorithm calculates only a single tensor that may follow an incorrect tract or even stop (Basser et al., 2000). The multi-tensor tractography and the probabilistic tractography, however, perform better in regions of crossing and fanning fibers, are more accurate, and can identify multiple tracts within a voxel (Lifshits et al., 2009). ...
... Aside from microstructural assessments of muscle, dMRI can be used to model muscle macrostructure through the use of a postprocessing technique called tractography. 5 This technique exploits the principle that diffusion magnitude is greatest in the direction along the main axis of a muscle fiber. Several algorithms have been developed to connect the primary axis of diffusion through all voxels within a dMRI experiment to generate estimations of gross muscle fiber length and pennation angle-key components of muscle architecture-and are referred to as fiber tracts. ...
Skeletal muscle has a classic structure function relationship; both skeletal muscle microstructure and architecture are directly related to force generating capacity. Biopsy, the gold standard for evaluating muscle microstructure, is highly inva-sive, destructive to muscle, and provides only a small amount of information about the entire volume of a muscle. Similarly, muscle fiber lengths and pennation angles, key features of muscle architecture predictive of muscle function, are traditionally studied via cadaveric dissection. Noninvasive techniques such as diffusion magnetic resonance imaging (dMRI) offer quantitative approaches to study skeletal muscle microstructure and architecture. Despite its prevalence in applications for musculoskeletal research, clinical adoption is hindered by a lack of understanding regarding its sensitivity to clinically important biomarkers such as muscle fiber cross-sectional area. This review aims to elucidate how dMRI has been utilized to study skeletal muscle, covering fundamentals of muscle physiology, dMRI acquisition techniques, dMRI modeling, and applications where dMRI has been leveraged to noninvasively study skeletal muscle changes in response to disease, aging, injury, and human performance. Level of Evidence: 5 Technical Efficacy: Stage 2 J. MAGN. RESON. IMAGING 2024.
... For pre-processing, we corrected for subject motion and eddy current induced geometric distortions, as well as for EPI distortions (Leemans et al. 2009). After tensor estimation (Leemans et al. 2009), we performed a whole-brain fiber tractography [47,48]: we used a seed resolution grid of 2 × 2 × 2 mm 3 and the following tracking stop criteria: 0.2 minimum fractional anisotropy (FA), 30° angle threshold, and 2 mm step size (Schlaffke et al. 2017 [11]). To select the white matter pathways of interest (bilateral): ILF, superior and temporal part of the CNG, IFOF, UNC, and FX, we used a region of interest (ROI) approach as described in Catani & Schotten [49]. ...
Cognitive functions, such as learning and memory processes, depend on effective communication between brain regions which is facilitated by white matter tracts (WMT). We investigated the microstructural properties and the contribution of WMT to extinction learning and memory in a predictive learning task. Forty-two healthy participants completed an extinction learning paradigm without a fear component. We examined differences in microstructural properties using diffusion tensor imaging to identify underlying neural connectivity and structural correlates of extinction learning and their potential implications for the renewal effect. Participants with good acquisition performance exhibited higher fractional anisotropy (FA) in WMT including the bilateral inferior longitudinal fasciculus (ILF) and the right temporal part of the cingulum (CNG). This indicates enhanced connectivity and communication between brain regions relevant to learning and memory resulting in better learning performance. Our results suggest that successful acquisition and extinction performance were linked to enhanced structural connectivity. Lower radial diffusivity (RD) in the right ILF and right temporal part of the CNG was observed for participants with good acquisition learning performance. This observation suggests that learning difficulties associated with increased RD may potentially be due to less myelinated axons in relevant WMT. Also, participants with good acquisition performance were more likely to show a renewal effect. The results point towards a potential role of structural integrity in extinction-relevant WMT for acquisition and extinction.
... Однако, опыт применения МР-трактографии в диагностике ХИМ в отечественной литературе практически отсутствует. Вместе с тем, зарубежные авторы сходятся во мнении, что эта методика способна дополнить объем и качество получаемой диагностической информации [1,5]. Следует отметить, что среди зарубежных ученых также нет единого мнения о возможностях количественной МРтрактографии в диагностике и прогнозе развития УКР при ХИМ. ...
A significant decline in the fractional anisotropy in patients with chronic cerebral ischemia with mild cognitive disorders, especially in the white matter of the frontal lobes is proof starting neurodegenerative process in the brain, which can later be transformed into one or another form of dementia. The latter may indicate a need for MR tractography in all patients with cognitive impairment, which in turn will improve the early diagnosis of various forms of dementia.
... However, functional measures do not provide information about the white matter underpinnings of cortical integration. This leaves diffusion-weighted imaging (DWI) tractography [20] as the only tool to non-invasively study the SAF connections and their detailed organisation in humans, where invasive tracer studies are not applicable. ...
The extraordinary number of short association fibres (SAF) connecting neighbouring cortical areas is a prominent feature of the large gyrified human brain. The contribution of SAF to the human connectome is largely unknown because of methodological challenges in mapping them. We present a method to characterise cortico–cortical connectivity mediated by SAF in topologically organised cortical areas. We introduce the ‘structural connective fields’ (sCF) metric which specifically quantifies neuronal signal propagation and integration mediated by SAF. This new metric complements functional connective field metrics integrating across contributions from short- and long-range white matter and intracortical fibres. Applying the method in the human early visual processing stream, we show that SAF preserve cortical functional topology. Retinotopic maps of V2 and V3 could be predicted from retinotopy in V1 and SAF connectivity. The sCF sizes increased along the cortical hierarchy and were smaller than their functional counterparts, in line with the latter being additionally broadened by long-range and intracortical connections. In vivo sCF mapping provides insights into short-range cortico– cortical connectivity in humans comparable to tract tracing studies in animal research and is an essential step towards creating a complete human connectome.
Highlights
Non-invasive mapping of Short Association Fibre (SAF) connectivity via diffusion-weighted MRI-based probabilistic tractography accurately predicted cortical functional neuroanatomy.
The novel structural Connective Fields (sCF) concept provides a quantitative measure of cortico-cortical integration facilitated by SAF, complementing the existing functional Connective Field (CF) concept.
Sub-millimeter resolution diffusion-weighted MRI enables tractography and connective field modeling of SAF, unlocking applications previously restricted to invasive tract tracing in animal studies.
... DTI tractography was performed using a deterministic fibre tracking algorithm (Basser et al., 2000) and anatomically constrained tractography (Smith et al., 2012), built into MRtrix (Tournier et al., 2019). ...
The human rotator cuff consists of four muscles, each with a complex, multipennate architecture. Despite the functional and clinical importance, the architecture of the human rotator cuff has yet to be clearly described in humans in vivo. The purpose of this study was to investigate the intramuscular, intermuscular, and interindividual variations in architecture and moment arms of the human rotator cuff. Muscle volumes, fascicle lengths, physiological cross‐sectional areas (PCSAs), pennation angles, and moment arms of all four rotator cuff muscles were measured from mDixon and diffusion tensor imaging (DTI) scans of the right shoulders of 20 young adults. In accordance with the most detailed dissections available to date, we found substantial intramuscular variation in fascicle length (coefficients of variation (CVs) ranged from 26% to 40%) and pennation angles (CVs ranged from 56% to 62%) in all rotator cuff muscles. We also found substantial intermuscular and interindividual variations in muscle volumes, but relatively consistent mean fascicle lengths, pennation angles, and moment arms (CVs for all ≤17%). Moreover, when expressed as a proportion of total rotator cuff muscle volume, the volumes of individual rotator cuff muscles were highly consistent between individuals and sexes (CVs ≤16%), suggesting that rotator cuff muscle volumes scale uniformly, at least in a younger population without musculoskeletal problems. Together, these data indicate limited interindividual and intermuscular variability in architecture, which may simplify scaling routines for musculoskeletal models. However, the substantial intramuscular variation in architecture questions the validity of previously reported mean architectural parameters to adequately describe rotator cuff function.
... Conversely, at the macro scale, structural brain connectivity points to large, myelinated bundles of fibers of white-matter (and partially grey matter), which can be imagined through the data of DW-MRI with the help of certain specialized computer software, for e.g., tractography. 30,31 As far as functional brain connectivity, which means that connections in stimulation amongst spatially discrete regions-of-brains, whichever in a latent, i.e., resting state or through the exterior (peripheral) stimulations which can be evaluated as the bi variate correlations of their behaviors while applying the data of f-MRI. 26,[32][33][34] Secondly, connectomes are only the connectivity-ofbrain about compound spatial scales. ...
Shaking palsy is a brain disease involving motor and non motor zones affecting circa 1 to 2%of humans>60 years age. To date there has been no invention for curing this chronic disease and to stop its progression. But existing therapeutic procedures can offer symptomatic relief to Parkinson patients. DBS is most successful therapy for the Parkinson`s yet depends on the accuracy of electrode implantation and location within the anatomical subcortical neural-structures.
This study examines the likelihood of net-work-based induced stimuli and the application of connectomic DBS in Parkinson`s.
The subthalamic nucleus is divided into3 sub zones, namely, limbic (anterior), associative (middle) and motor (posterior) as well as diffusion weighted imaging (D W I). The surgical targets are tiny (few millimeters) and good enough to neuroanatomical-structures within the b r a i n. STN (size:12×5×3mm3) and lies nearby internal capsule, medial lemniscus, corticospinal tract, plus red-nucleus. Through sub optimal lead insertion and over stimuli, flow of electrons can spread to these adjoining sucortics, thereby developing dyskinesias ( ). With time, DW-MRI plus f-MRI is used to study the anatomical-structural functional connectivity in advanced idiopathic Parkinson`s. Contrasting conventional lesion based stimulus hypothesis, the novel net stimulus hypothesis advocated that induced stimulus of exact circuits of b r a i n can modulate pathophysiological net-work, reinstate near the tissue region, thus producing stabilization-of human-brain-connectome within Parkinson`s.
The DBS connectomes makes use of circuit based stimulus procedure instead of lesion-based stimulus, has transformed neuromodulation.
Connectomes via DBS can be tailor made for every Parkinson plus enhance the operation. It`s just a sketch for human-brain-connectivity (HMC) transversely compound longitudinal-scales. Yet, it won`t yield cell information plus cotacts with cells at the level of micro scale.
... Frontiers in Neuroscience 02 frontiersin.org (Mori et al., 1999;Basser et al., 2000) involves the algorithmic reconstruction of these WM pathways, generating a multitude of fibers (El Kouby et al., 2005) for each subject. This is followed by the delineation of the obtained fiber trajectories or streamlines into bundles or their association with anatomically well-defined tracts, a process commonly referred to as WM tract segmentation or dissection (Bullock et al., 2019). ...
White matter tract segmentation is a pivotal research area that leverages diffusion-weighted magnetic resonance imaging (dMRI) for the identification and mapping of individual white matter tracts and their trajectories. This study aims to provide a comprehensive systematic literature review on automated methods for white matter tract segmentation in brain dMRI scans. Articles on PubMed, ScienceDirect [NeuroImage, NeuroImage (Clinical), Medical Image Analysis], Scopus and IEEEXplore databases and Conference proceedings of Medical Imaging Computing and Computer Assisted Intervention Society (MICCAI) and International Symposium on Biomedical Imaging (ISBI), were searched in the range from January 2013 until September 2023. This systematic search and review identified 619 articles. Adhering to the specified search criteria using the query, “white matter tract segmentation OR fiber tract identification OR fiber bundle segmentation OR tractography dissection OR white matter parcellation OR tract segmentation,” 59 published studies were selected. Among these, 27% employed direct voxel-based methods, 25% applied streamline-based clustering methods, 20% used streamline-based classification methods, 14% implemented atlas-based methods, and 14% utilized hybrid approaches. The paper delves into the research gaps and challenges associated with each of these categories. Additionally, this review paper illuminates the most frequently utilized public datasets for tract segmentation along with their specific characteristics. Furthermore, it presents evaluation strategies and their key attributes. The review concludes with a detailed discussion of the challenges and future directions in this field.
... FA reflects fiber structure integrity, orientation coherence of the fiber tract, and degree of white matter myelination [22,23], and is commonly reported as a general indicator of white matter microstructure. RD reflects water diffusivity that runs perpendicular to the major axis of the axon and is sensitive to myelin abnormalities [23][24][25]. Integrating the above content, FA and RD were selected as metrics for evaluating white matter microstructure in this study. ...
There is inconsistent evidence for an association of obesity with white matter microstructural alterations. Such inconsistent findings may be related to the cumulative effects of obesity and alcohol dependence. This study aimed to investigate the possible interactions between alcohol dependence and overweight/obesity on white matter microstructure in the human brain. A total of 60 inpatients with alcohol dependence during early abstinence (44 normal weight and 16 overweight/obese) and 65 controls (42 normal weight and 23 overweight/obese) were included. The diffusion tensor imaging (DTI) measures [fractional anisotropy (FA) and radial diffusivity (RD)] of the white matter microstructure were compared between groups. We observed significant interactive effects between alcohol dependence and overweight/obesity on DTI measures in several tracts. The DTI measures were not significantly different between the overweight/obese and normal-weight groups (although widespread trends of increased FA and decreased RD were observed) among controls. However, among the alcohol-dependent patients, the overweight/obese group had widespread reductions in FA and widespread increases in RD, most of which significantly differed from the normal-weight group; among those with overweight/obesity, the alcohol-dependent group had widespread reductions in FA and widespread increases in RD, most of which were significantly different from the control group. This study found significant interactive effects between overweight/obesity and alcohol dependence on white matter microstructure, indicating that these two controllable factors may synergistically impact white matter microstructure and disrupt structural connectivity in the human brain.
... TBSS is a statistical method used for group-wise analysis of WM microstructure and it is based on the alignment of individual subjects' DTI to a common space (18). On the other hand, tractography is a visualization technique that reconstructs and maps the pathways of WM tracts in the brain based on DTI data (19). In particular, in MDD structural disruptions within WM tissue are reflected by decreased FA mainly localized in the corpus callosum (CC), cingulum and uncinate fasciculus (20). ...
Major Depressive Disorder (MDD) is a severe psychiatric disorder characterized by selective impairments in mood regulation, cognition and behavior. Although it is well-known that antidepressants can effectively treat moderate to severe depression, the biochemical effects of these medications on white matter (WM) integrity are still unclear. Therefore, the aim of the study is to review the main scientific evidence on the differences in WM integrity in responders and non-responders to antidepressant medications. A record search was performed on three datasets (PubMed, Scopus and Web of Science) and ten records matched our inclusion criteria. Overall, the reviewed studies highlighted a good efficacy of antidepressants in MDD treatment. Furthermore, there were differences in WM integrity between responders and non-responders, mainly localized in cingulate cortices, hippocampus and corpus callosum, where the former group showed higher fractional anisotropy and lower axial diffusivity values. Modifications in WM integrity might be partially explained by branching and proliferation as well as neurogenesis of axonal fibers mediated by antidepressants, which in turn may have positively affected brain metabolism and increase the quantity of the serotonergic neurotransmitter within synaptic clefts. However, the reviewed studies suffer from some limitations, including the heterogeneity in treatment duration, antidepressant administration, medical posology, and psychiatric comorbidities. Therefore, future studies are needed to reduce confounding effects of antidepressant medications and to adopt longitudinal and multimodal approaches in order to better characterize the differences in WM integrity between responders and non-responders.
... Specifically, we defined network nodes based on a surface-based multimodal parcellation atlas 42 with 180 cortical areas per hemisphere (Fig. 1a). For network edges, we considered the Pearson correlation coefficient between the time series of all pairs of nodes for the FC 26 and the probabilistic diffusion tractography between nodes for the SC 43 (detailed in the Methods section). Considering that different ranges and properties of SC and FC connections could lead to disproportionate contributions to the following multilayer network analysis, we normalized the FC and SC matrices to a uniform range of 0-1 ( Fig. 1b and 1c). ...
The structural connectome (SC) is tightly coupled to the functional connectome (FC) in the human brain. Most previous related studies have modeled and analyzed SC or FC as isolated brain networks. However, challenges remain in modeling the interdependent structural-functional connectome and elucidating its cognitive implications and molecular underpinnings. Here, we present a multilayer connectome model composed of SC and FC components and further characterize their interacting topological properties. We found that the interdependent connectome is topographically heterogeneous, with the transmodal cortex exhibiting greater modular variability across layers. This spatial topography reflects cortical hierarchy and evolution and shows high test-retest reliability, reproducibility, and heritability. The interdependent connectome contributes to high-order cognitive processes and is associated with multiple neurotransmitter systems and transcriptional signatures of synaptic transmission. Our results provide insights into the nontrivial interdependencies of SC and FC, highlighting their cognitive significance and the molecular mechanisms underlying the connectome of connectomes.
... Diffusion MRI (dMRI) tractography is an advanced imaging method (Basser et al., 2000) that uniquely enables in vivo reconstruction of the 3D streamline trajectory of the RGVP in a non-invasive way. Unlike the widely used T1-weighted (T1w) and T2-weighted (T2w) MRI or other advanced imaging techniques, e.g. ...
The retinogeniculate visual pathway (RGVP) is responsible for carrying visual information from the retina to the lateral geniculate nucleus. Identification and visualization of the RGVP are important in studying the anatomy of the visual system and can inform the treatment of related brain diseases. Diffusion MRI (dMRI) tractography is an advanced imaging method that uniquely enables in vivo mapping of the 3D trajectory of the RGVP. Currently, identification of the RGVP from tractography data relies on expert (manual) selection of tractography streamlines, which is time-consuming, has high clinical and expert labor costs, and is affected by inter-observer variability. In this paper, we present a novel deep learning framework, DeepRGVP, to enable fast and accurate identification of the RGVP from dMRI tractography data. We design a novel microstructure-informed supervised contrastive learning method that leverages both streamline label and tissue microstructure information to determine positive and negative pairs. We propose a simple and successful streamline-level data augmentation method to address highly imbalanced training data, where the number of RGVP streamlines is much lower than that of non-RGVP streamlines. We perform comparisons with several state-of-the-art deep learning methods that were designed for tractography parcellation, and we show superior RGVP identification results using DeepRGVP. In addition, we demonstrate a good generalizability of DeepRGVP to dMRI tractography data from neurosurgical patients with pituitary tumors and we show DeepRGVP can successfully identify RGVPs despite the effect of lesions affecting the RGVPs. Overall, our study shows the high potential of using deep learning to automatically identify the RGVP.
... Accordingly, there has been increasing attention on diffusion-weighted magnetic resonance imaging (MRI)-based fiber tractography (FT) since it non-invasively facilitates maximal tumor resection while preserving neurological function, which improves survival and quality of life [27]. Specifically, diffusion tensor imaging (DTI)-based FT allows identification and visualization of functional sites at the cortical level as well as the trajectory of important fascicles within the white matter [3,22]. Although this approach is userfriendly and already integrated into commonly used navigation systems, it has limited accuracy in the determination of the origin and cortical termination of fibers within the white matter, particularly when diffusion properties are disturbed in afflicted brain tissue. ...
Visual field deficits (VFDs) are common in patients with temporal and occipital lobe lesions. Diffusion tensor fiber tractography (DTI-FT) is widely used for surgery planning to reduce VFDs. Q-ball high-resolution fiber tractography (QBI-HRFT) improves upon DTI. This study aims to evaluate the effectiveness of DTI-FT and QBI-HRFT for surgery planning near the optic radiation (OR) as well as the correlation between VFDs, the nearest distance from the lesion to the OR fiber bundle (nD-LOR), and the lesion volume (LV). This ongoing prospective clinical trial collects clinical and imaging data of patients with lesions in deterrent areas. The present subanalysis included eight patients with gliomas near the OR. Probabilistic HRFT based on QBI-FT and conventional DTI-FT were performed for OR reconstruction based on a standard diffusion-weighted magnetic resonance imaging sequence in clinical use. Quantitative analysis was used to evaluate the lesion volume (LV) and nD-LOR. VFDs were determined based on standardized automated perimetry. We included eight patients (mean age 51.7 years [standard deviation (SD) 9.5]) with lesions near the OR. Among them, five, two, and one patients had temporodorsal, occipital, and temporal lesions, respectively. Four patients had normal vision preoperatively, while four patients had preexisting VFD. QBI-FT analysis indicated that patients with VFD exhibited a significantly smaller median nD-LOR (mean, −4.5; range −7.0; −2.3) than patients without VFD (mean, 7.4; range −4.3; 27.2) ( p = 0.050). There was a trend towards a correlation between tumor volume and nD-LOR when QBI-FT was used (rs = −0.6; p = 0.056). A meticulous classification of the spatial relationship between the lesions and OR according to DTI-FT and QBI-FT was performed. The results indicated that the most prevalent orientations were the FT bundles located laterally and intrinsically in relation to the tumor. Compared with conventional DTI-FT, QBI-FT suggests reliable and more accurate results when correlated to preoperative VFDs and might be preferred for preoperative planning and intraoperative use of nearby lesions, particularly for those with larger volumes. A detailed analysis of localization, surgical approach together with QBI-FT and DTI-FT could reduce postoperative morbidity regarding VFDs. The display of HRFT techniques intraoperatively within the navigation system should be pursued for this issue.
... Tensor-derived maps, including fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were calculated. Anisotropic power (AP) maps [53], which are diffusion-derived maps that contain a good contrast in both grey and white matter, were also computed at this stage. ...
Studies report that the microstructural integrity of the uncinate fasciculus (UF; connecting the anterior temporal lobe to the orbitofrontal cortex) is abnormal in adults with psychopathy and children with conduct problems (CP), especially those with high callous-unemotional (CU) traits. However, it is unknown if these abnormalities are ‘fixed’ or ‘reversible’. Therefore, we tested the hypothesis that a reduction in CP symptoms, following a parenting intervention, would be associated with altered microstructural integrity in the UF. Using diffusion tensor imaging tractography we studied microstructural differences (mean diffusivity (MD) and radial diffusivity (RD)) in the UF of 43 typically developing (TD) and 67 boys with CP before and after a 14-week parenting intervention. We also assessed whether clinical response in CP symptoms or CU traits explained changes in microstructure following the intervention. Prior to intervention, measures of MD and RD in the UF were increased in CP compared to TD boys. Following intervention, we found that the CP group had a significant reduction in RD and MD. Further, these microstructural changes were driven by the group of children whose CU traits improved (but not CP symptoms as hypothesized). No significant microstructural changes were observed in the TD group. Our findings suggest, for the first time, that microstructural abnormalities in the brains of children with CP may be reversible following parenting intervention.
... The CST is often studied using diffusion MRI tractography, the only method that allows in-vivo, non-invasive mapping of the human brain's white matter connections (Basser et al., 2000). CST tractography is clinically used in neurosurgical planning to avoid injury to the CST (Berman et al., 2004;Bucci et al., 2013;Essayed et al., 2017;Farquharson et al., 2013) and to predict motor outcomes after stroke (Nguyen et al., 2022). ...
The corticospinal tract (CST) is a critically important white matter fiber tract in the human brain that enables control of voluntary movements of the body. The CST exhibits a somatotopic organization, which means that the motor neurons that control specific body parts are arranged in order within the CST. Diffusion magnetic resonance imaging (MRI) tractography is increasingly used to study the anatomy of the CST. However, despite many advances in tractography algorithms over the past decade, modern, state‐of‐the‐art methods still face challenges. In this study, we compare the performance of six widely used tractography methods for reconstructing the CST and its somatotopic organization. These methods include constrained spherical deconvolution (CSD) based probabilistic (iFOD1) and deterministic (SD‐Stream) methods, unscented Kalman filter (UKF) tractography methods including multi‐fiber (UKF2T) and single‐fiber (UKF1T) models, the generalized q‐sampling imaging (GQI) based deterministic tractography method, and the TractSeg method. We investigate CST somatotopy by dividing the CST into four subdivisions per hemisphere that originate in the leg, trunk, hand, and face areas of the primary motor cortex. A quantitative and visual comparison is performed using diffusion MRI data ( N = 100 subjects) from the Human Connectome Project. Quantitative evaluations include the reconstruction rate of the eight anatomical subdivisions, the percentage of streamlines in each subdivision, and the coverage of the white matter–gray matter (WM–GM) interface. CST somatotopy is further evaluated by comparing the percentage of streamlines in each subdivision to the cortical volumes for the leg, trunk, hand, and face areas. Overall, UKF2T has the highest reconstruction rate and cortical coverage. It is the only method with a significant positive correlation between the percentage of streamlines in each subdivision and the volume of the corresponding motor cortex. However, our experimental results show that all compared tractography methods are biased toward generating many trunk streamlines (ranging from 35.10% to 71.66% of total streamlines across methods). Furthermore, the coverage of the WM–GM interface in the largest motor area (face) is generally low (under 40%) for all compared tractography methods. Different tractography methods give conflicting results regarding the percentage of streamlines in each subdivision and the volume of the corresponding motor cortex, indicating that there is generally no clear relationship, and that reconstruction of CST somatotopy is still a large challenge. Overall, we conclude that while current tractography methods have made progress toward the well‐known challenge of improving the reconstruction of the lateral projections of the CST, the overall problem of performing a comprehensive CST reconstruction, including clinically important projections in the lateral (hand and face areas) and medial portions (leg area), remains an important challenge for diffusion MRI tractography.
... Diffusion MRI (dMRI) tractography is the only non-invasive method capable of mapping the complex white matter (WM) connections within the brain [2]. Tractography parcellation [42,12,28] classifies the vast numbers of streamlines resulting from whole-brain tractography to enable visualization and quantification of the brain's WM connections. ...
Diffusion MRI tractography parcellation classifies streamlines into anatomical fiber tracts to enable quantification and visualization for clinical and scientific applications. Current tractography parcellation methods rely heavily on registration, but registration inaccuracies can affect parcellation and the computational cost of registration is high for large-scale datasets. Recently, deep-learning-based methods have been proposed for tractography parcellation using various types of representations for streamlines. However, these methods only focus on the information from a single streamline, ignoring geometric relationships between the streamlines in the brain. We propose TractCloud, a registration-free framework that performs whole-brain tractography parcellation directly in individual subject space. We propose a novel, learnable, local-global streamline representation that leverages information from neighboring and whole-brain streamlines to describe the local anatomy and global pose of the brain. We train our framework on a large-scale labeled tractography dataset, which we augment by applying synthetic transforms including rotation, scaling, and translations. We test our framework on five independently acquired datasets across populations and health conditions. TractCloud significantly outperforms several state-of-the-art methods on all testing datasets. TractCloud achieves efficient and consistent whole-brain white matter parcellation across the lifespan (from neonates to elderly subjects, including brain tumor patients) without the need for registration. The robustness and high inference speed of TractCloud make it suitable for large-scale tractography data analysis. Our project page is available at https://tractcloud.github.io/.
... Diffusion MRI (dMRI) tractography is the only non-invasive method capable of mapping the complex white matter (WM) connections within the brain [2]. Tractography parcellation [42,12,28] classifies the vast numbers of streamlines resulting from whole-brain tractography to enable visualization and quantification of the brain's WM connections. ...
... For computing whole-brain tractography, we leveraged the Runge-Kutta (RK2) algorithm, which uses the second order Runge-Kutta method to solve a differential equation to estimate the fiber trajectory more reliably [102]. The main mathematical technique behind RK2 is to equate the tangent vector with the principal eigenvector. ...
Background: Sex differences impact Alzheimer's disease (AD) neuropathology, but cell-to-network level dysfunctions in the prodromal phase are unclear. Alterations in hippocampal excitation-inhibition balance (EIB) have recently been linked to early AD pathology.
Objective: Examine how AD risk factors (age, APOE-ɛ4, amyloid-β) relate to hippocampal EIB in cognitively normal males and females using connectome-level measures.
Methods: Individuals from the OASIS-3 cohort (age 42-95) were studied (N = 437), with a subset aged 65+ undergoing neuropsychological testing (N = 231).
Results: In absence of AD risk factors (APOE-ɛ4/Aβ+), whole-brain EIB decreases with age more significantly in males than females (p = 0.021, β = -0.007). Regression modeling including APOE-ɛ4 allele carriers (Aβ-) yielded a significant positive AGE-by-APOE interaction in the right hippocampus for females only (p = 0.013, β = 0.014), persisting with inclusion of Aβ+ individuals (p = 0.012, β = 0.014). Partial correlation analyses of neuropsychological testing showed significant associations with EIB in females: positive correlations between right hippocampal EIB with categorical fluency and whole-brain EIB with the trail-making test (p < 0.05).
Conclusion: Sex differences in EIB emerge during normal aging and progresses differently with AD risk. Results suggest APOE-ɛ4 disrupts hippocampal balance more than amyloid in females. Increased excitation correlates positively with neuropsychological performance in the female group, suggesting a duality in terms of potential beneficial effects prior to cognitive impairment. This underscores the translational relevance of APOE-ɛ4 related hyperexcitation in females, potentially informing therapeutic targets or early interventions to mitigate AD progression in this vulnerable population.
... Diffusion MRI exploits this relationship and collects measurements of spatially localized diffusion signals along many different directions, called b-vectors, to obtain a 3-dimensional picture of diffusion at each location (voxel) on a regular grid over the brain volume. Smooth local models of diffusion are fit to these measurements, e.g. the diffusion tensor (Basser et al., 1994) or the orientation distribution function (ODF) (Tuch, 2004), and are subsequently used to trace out the large-scale white matter fibers using a process called tractography (Basser et al., 2000). ...
Brain structural networks are often represented as discrete adjacency matrices with elements summarizing the connectivity between pairs of regions of interest (ROIs). These ROIs are typically determined a-priori using a brain atlas. The choice of atlas is often arbitrary and can lead to a loss of important connectivity information at the sub-ROI level. This work introduces an atlas-free framework that overcomes these issues by modeling brain connectivity using smooth random functions. In particular, we assume that the observed pattern of white matter fiber tract endpoints is driven by a latent random function defined over a product manifold domain. To facilitate statistical analysis of these high dimensional functional data objects, we develop a novel algorithm to construct a data-driven reduced-rank function space that offers a desirable trade-off between computational complexity and flexibility. Using real data from the Human Connectome Project, we show that our method outperforms state-of-the-art approaches that use the traditional atlas-based structural connectivity representation on a variety of connectivity analysis tasks. We further demonstrate how our method can be used to detect localized regions and connectivity patterns associated with group differences.
... Diffusion MRI (dMRI) tractography is the only non-invasive method capable of mapping the complex white matter (WM) connections within the brain [2]. Tractography parcellation [42,12,28] classifies the vast numbers of streamlines resulting from whole-brain tractography to enable visualization and quantification of the brain's WM connections. ...
Diffusion MRI tractography parcellation classifies streamlines into anatomical fiber tracts to enable quantification and visualization for clinical and scientific applications. Current tractography parcellation methods rely heavily on registration, but registration inaccuracies can affect parcellation and the computational cost of registration is high for large-scale datasets. Recently, deep-learning-based methods have been proposed for tractography parcellation using various types of representations for streamlines. However, these methods only focus on the information from a single streamline, ignoring geometric relationships between the streamlines in the brain. We propose TractCloud, a registration-free framework that performs whole-brain tractography parcellation directly in individual subject space. We propose a novel, learnable, local-global streamline representation that leverages information from neighboring and whole-brain streamlines to describe the local anatomy and global pose of the brain. We train our framework on a large-scale labeled tractography dataset, which we augment by applying synthetic transforms including rotation, scaling, and translations. We test our framework on five independently acquired datasets across populations and health conditions. TractCloud significantly outperforms several state-of-the-art methods on all testing datasets. TractCloud achieves efficient and consistent whole-brain white matter parcellation across the lifespan (from neonates to elderly subjects, including brain tumor patients) without the need for registration. The robustness and high inference speed of TractCloud make it suitable for large-scale tractography data analysis. Our project page is available at https://tractcloud.github.io/.
... Nodes are defined as different brain sites and edges represent their anatomical interconnections. To this purpose, diffusion tensor imaging (DTI) is a noninvasive technology that allows to infer the diffusion of water molecules through white matter tracts of the brain in the three-dimensional space [29]. The collected data are discretized into non-overlapping gray matter volumes (nodes) and the connection weights (edges) between two nodes are proportional to the anatomical properties of the fiber tracks (e.g. ...
The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying network structure is crucial to understand the brain functioning under both healthy and pathological conditions.
Yet, analyzing brain networks is challenging, in part because their structure represents only one possible realization of a generative stochastic process which is in general unknown. Having a formal way to cope with such intrinsic variability is therefore central for the characterization of brain network properties.
Addressing this issue entails the development of appropriate tools mostly adapted from network science and statistics. Here, we focus on a particular class of maximum entropy models for networks, i.e. exponential random graph models (ERGMs), as a parsimonious approach to identify the local connection mechanisms behind observed global network structure. Efforts are reviewed on the quest for basic organizational properties of human brain networks, as well as on the identification of predictive biomarkers of neurological diseases such as stroke.
We conclude with a discussion on how emerging results and tools from statistical graph modeling, associated with forthcoming improvements in experimental data acquisition, could lead to a finer probabilistic description of complex systems in network neuroscience.
... [21][22][23][24] However, those findings may not be sufficient to determine whether the WM integrity of the cerebello-thalamic tract is actually altered in OCD, as those findings are derived from hypothesis-free whole-brain comparison analysis, making it difficult to distinguish between the cerebello-thalamic tract and adjacent WM fibers, such as the central tegmental tract or medial longitudinal fasciculus. 25,26 Probabilistic tractography is an approach that allows specific tracing of anatomical connections between different brain regions, 27,28 and is relatively appropriate for examining the WM integrity of the entire tract. 29,30 Thus, using probabilistic tractography, structural fingerprints of the cerebello-thalamic tract can be more reliably and reproducibly reconstructed and quantified than existing hypothesisfree whole-brain analysis, in that probabilistic tractography examines changes in the diffusion index of the entire tract rather than measuring regional diffusion index changes, as in hypothesis-free whole-brain analysis. ...
Objective:
The cerebello-thalamic tract is the only efferent white matter (WM) bundle of the cerebellum that connects the cerebellum to the thalamus and has recently attracted much attention in obsessive-compulsive disorder (OCD) with its integral role in higher order cognitive functions commonly impaired in OCD patients. Previous neuroimaging studies have shown that the cerebello-thalamic circuit is functionally impaired in OCD patients. However, the WM integrity of the cerebello-thalamic tract in OCD, which may underly functional abnormalities of the cerebello-thalamic circuit, is not yet sufficiently understood. Therefore, the current study aimed to elucidate whether compromised cerebello-thalamic WM integrity is observed in medication-free OCD patients.
Methods:
In this study, diffusion tensor imaging was acquired from 106 medication-free OCD patients and 105 matched healthy controls (HCs). Probabilistic tractography was then used to reconstruct the cerebello-thalamic tract with accurate anatomical features. Three diffusion indices (fractional anisotropy, FA; mean diffusivity, MD; radial diffusivity, RD) were measured from the reconstructed bilateral cerebello-thalamic tract and then compared between groups.
Results:
We found that patients with OCD showed significantly increased MD and RD in the right cerebello-thalamic tract compared to HCs, and there was no difference in FA between groups.
Conclusion:
Our findings may indicate the underlying structural abnormalities of the dysfunctional cerebello-thalamic circuit in OCD patients. Therefore, our findings are expected to provide novel insights into the pathophysiology of OCD on the cerebello-thalamic WM architecture, extending our knowledge from the existing functional neurobiological model of OCD.
... Diffusion magnetic resonance imaging (dMRI) is the main technique to non-invasively study the white matter (WM) structures of the human brain (Basser et al., 1994). Diffusion MRI provides images which can be used to identify white matter fiber tracts (Basser et al., 2000;Van Essen et al., 2014). Quantitative analysis of brain WM fiber tracts has been used extensively for the characterization of brain architecture in the healthy and diseased populations such as neurodegenerative, neuropsychiatric, and neurodevelopmental diseases (Ciccarelli et al., 2008;Catani et al., 2006;Yamada, 2018). ...
Quantitative analysis of white matter fiber tracts from diffusion Magnetic Resonance Imaging (dMRI) data is of great significance in health and disease. For example, analysis of fiber tracts related to anatomically meaningful fiber bundles is highly demanded in pre-surgical and treatment planning, and the surgery outcome depends on accurate segmentation of the desired tracts. Currently, this process is mainly done through time-consuming manual identification performed by neuro-anatomical experts. However, there is a broad interest in automating the pipeline such that it is fast, accurate, and easy to apply in clinical settings and also eliminates the intra-reader variabilities. Following the advancements in medical image analysis using deep learning techniques, there has been a growing interest in using these techniques for the task of tract identification as well. Recent reports on this application show that deep learning-based tract identification approaches outperform existing state-of-the-art methods. This paper presents a review of current tract identification approaches based on deep neural networks. First, we review the recent deep learning methods for tract identification. Next, we compare them with respect to their performance, training process, and network properties. Finally, we end with a critical discussion of open challenges and possible directions for future works.
... The CST is often studied using diffusion MRI tractography, the only method that allows in-vivo, non-invasive mapping of the human brain's white matter connections (Basser et al., 2000). CST tractography is clinically used in neurosurgical planning to avoid injury to the corticospinal tract (Berman et al., 2004;Bucci et al., 2013;Essayed et al., 2017a; and to predict motor outcomes after stroke (Nguyen et al., 2022). ...
The corticospinal tract (CST) is a critically important white matter fiber tract in the human brain that enables control of voluntary movements of the body. Diffusion MRI tractography is the only method that enables the study of the anatomy and variability of the CST pathway in human health. In this work, we explored the performance of six widely used tractography methods for reconstructing the CST and its somatotopic organization. We perform experiments using diffusion MRI data from the Human Connectome Project. Four quantitative measurements including reconstruction rate, the WM-GM interface coverage, anatomical distribution of streamlines, and correlation with cortical volumes to assess the advantages and limitations of each method. Overall, we conclude that while current tractography methods have made progress toward the well-known challenge of improving the reconstruction of the lateral projections of the CST, the overall problem of performing a comprehensive CST reconstruction, including clinically important projections in the lateral (hand and face area) and medial portions (leg area), remains an important challenge for diffusion MRI tractography.
... Indeed, the introduction and fast evolution of neuroimaging techniques (Leemans, 2019), the revisitation of early neuroanatomical discoveries (De Benedictis et al., 2014;Hope et al., 2016;Sarubbo et al., 2016), and the renovation of Klingler's microdissection approach (Agrawal et al., 2011;Klingler, 1935;Martino et al., 2011) led to the production of increasingly more detailed descriptions of the human WM pathways. In particular, the dissemination of diffusion magnetic resonance imaging-based tractography (Basser et al., 2000) enabled the first characterization of the arcuate fascicle in vivo (Catani et al., 2002), leading off a series of innovative studies aimed to achieve the most accurate and comprehensive characterization of the wiring and extension of this bundle. Concurrently with these efforts, the ensuing functional relevance of the AF has become steadily more evident: damages of this bundle, both in terms of altered microstructural features or disconnection, have been implicated in a broad spectrum of syndromes, spanning from psychiatric symptoms (Jiang et al., 2017;Psomiades et al., 2016) to neurological diseases (Nakajima et al., 2018). ...
Background
Two Centuries from today, Karl Friedrich Burdach attributed the nomenclature “arcuate fasciculus” to a white matter (WM) pathway connecting the frontal to the temporal cortices by arching around the Sylvian fissure. Although this label remained essentially unvaried, the concepts related to it and the characterization of the structural properties of this bundle evolved along with the methodological progress of the past years. Concurrently, the functional relevance of the arcuate fasciculus (AF) classically restricted to the linguistic domain has extended to further cognitive abilities. These features make it a relevant structure to consider in a large variety of neurosurgical procedures.
Objective
Herein, we build on our previous review uncovering the connectivity provided by the Superior Longitudinal System, including the AF, and provide a handy representation of the structural organization of the AF by considering the frequency of defined reports in the literature. By adopting the same approach, we implement an account of which functions are mediated by this WM bundle. We highlight how this information can be transferred to the neurosurgical field by presenting four surgical cases of glioma resection requiring the evaluation of the relationship between the AF and the nearby structures, and the safest approaches to adopt.
Conclusions
Our cumulative overview reports the most common wiring patterns and functional implications to be expected when approaching the study of the AF, while still considering seldom descriptions as an account of interindividual variability. Given its extension and the variety of cortical territories it reaches, the AF is a pivotal structure for different cognitive functions, and thorough understanding of its structural wiring and the functions it mediates is necessary for preserving the patient's cognitive abilities during glioma resection.
... Diffusion-weighted MRI enables visualization of brain white matter structures. It can be used to generate tractography data consisting of millions of synthetic fibers or streamlines for a single subject stored in a tractogram that approximate groups of biological axons [1]. Many applications require streamlines to be segmented into individual tracts corresponding to known anatomy. ...
Accurately identifying white matter tracts in medical images is essential for various applications, including surgery planning and tract-specific analysis. Supervised machine learning models have reached state-of-the-art solving this task automatically. However, these models are primarily trained on healthy subjects and struggle with strong anatomical aberrations, e.g. caused by brain tumors. This limitation makes them unsuitable for tasks such as preoperative planning, wherefore time-consuming and challenging manual delineation of the target tract is typically employed. We propose semi-automatic entropy-based active learning for quick and intuitive segmentation of white matter tracts from whole-brain tractography consisting of millions of streamlines. The method is evaluated on 21 openly available healthy subjects from the Human Connectome Project and an internal dataset of ten neurosurgical cases. With only a few annotations, the proposed approach enables segmenting tracts on tumor cases comparable to healthy subjects (dice=0.71), while the performance of automatic methods, like TractSeg dropped substantially (dice=0.34) in comparison to healthy subjects. The method is implemented as a prototype named atTRACTive in the freely available software MITK Diffusion. Manual experiments on tumor data showed higher efficiency due to lower segmentation times compared to traditional ROI-based segmentation.
... The diffusion tensor and fractional anisotropy (FA) of each voxel ( Fig. 3:A-B) and the mean diffusion parameters (FA, diffusivity (MD), and the three eigenvalues λ 1 , λ 2 , and λ 3 ) were calculated for each muscle from the DTI data using previously described procedures (Bolsterlee Raw fibre tracts were reconstructed using MRtrix and deterministic tractography algorithms (Basser et al., 2000) that were similar to those reported by Bolsterlee and colleagues (2018;. The following settings were used in MRtrix: seed image and masking region of interest = muscle label, maximum number of tracts = 2000, step size = 0.5 mm, maximum angle between successive steps = 10 • , minimum FA = 0.1, 1 mm ≤ tract length ≤ 200 mm. ...
Little is known about the skeletal muscle architecture of living humans at birth. In this study, we used magnetic resonance imaging (MRI) to measure the volumes of ten muscle groups in the lower legs of eight human infants aged less than three months. We then combined MRI and diffusion tensor imaging (DTI) to provide detailed, high-resolution reconstructions and measurements of moment arms, fascicle lengths, physiological cross-sectional areas (PCSAs), pennation angles and diffusion parameters of the medial (MG) and lateral gastrocnemius (LG) muscles. On average, the total lower leg muscle volume was 29.2 cm3. The largest muscle was the soleus muscle with a mean volume of 6.5 cm3. Compared to the LG muscles, the MG muscles had, on average, greater volumes (by ∼35%) and greater PCSAs (by ∼63%) but similar ankle-to-knee moment arm ratios (∼0.1 difference), fascicle lengths (∼5.7 mm difference) and pennation angles (∼2.7° difference). The MG data were compared with data previously collected from adults. The MG muscles of adults had, on average, a 63-fold greater volume, a 36-fold greater PCSA, and 1.7-fold greater fascicle length. This study demonstrates the feasibility of using MRI and DTI to reconstruct the three-dimensional architecture of skeletal muscles in living human infants. It is shown that, between infancy and adulthood, MG muscle fascicles grow primarily in cross-section rather than in length.
... Another major feature of DTI is the delineation of white matter fiber bundles as streamlines [50][51][52]. Since water molecules tend to diffuse in the direction of the fiber bundles, quantifying the orientation of the diffusion distribution of water molecules from diffusion MRI data can provide indirect information about how the white matter fiber bundles travel. ...
Neonatal-hypoxic ischemic encephalopathy (HIE) is the leading cause of acquired neonatal brain injury with the risk of developing serious neurologic sequelae and death. An accurate and robust prediction of short- and long-term outcomes may provide clinicians and families with fundamental evidence for their decision-making, the design of treatment strategies, and the discussion of developmental intervention plans after discharge. Diffusion tensor imaging (DTI) is one of the most powerful neuroimaging tools with which to predict the prognosis of neonatal HIE by providing microscopic features that cannot be assessed by conventional MRI. DTI provides various scalar measures that represent the properties of the tissue, such as fractional anisotropy (FA) and mean diffusivity (MD). Since the characteristics of the diffusion of water molecules represented by these measures are affected by the microscopic cellular and extracellular environment, such as the orientation of structural components and cell density, they are often used to study the normal developmental trajectory of the brain and as indicators of various tissue damage, including HIE-related pathologies, such as cytotoxic edema, vascular edema, inflammation, cell death, and Wallerian degeneration. Previous studies have demonstrated widespread alteration in DTI measurements in severe cases of HIE and more localized changes in neonates with mild-to-moderate HIE. In an attempt to establish cutoff values to predict the occurrence of neurological sequelae, MD and FA measured in the corpus callosum (CC), thalamus, basal ganglia, corticospinal tract (CST), and frontal white matter have proven to have an excellent ability to predict severe neurological outcomes. In addition, a recent study has suggested that a data-driven, unbiased approach using machine-learning techniques on features obtained from whole-brain image quantification may accurately predict the prognosis of HIE, including for mild-to-moderate cases. Further efforts are needed to overcome current challenges, such as MRI infrastructure, diffusion modeling methods, and data harmonization for clinical application. In addition, external validation of predictive models is essential for clinical application of DTI to prognostication.
... Frontostriatal connectivity is the initial component of frontrostriatal circuitry, which modulates functions that are abnormal in schizophrenia such as executive functions [1]. Diffusion magnetic resonance imaging (dMRI) tractography [2][3][4][5] allows for an in vivo method to measure the local variation in brain connectivity patterns in human subjects. Here, we have applied dMRI tractography in a novel manner to investigate putative structural connectivity disturbances (brain miswiring) in frontostriatal connections in early psychosis patients. ...
Background
Alterations in brain connectivity may underlie neuropsychiatric conditions such as schizophrenia. We here assessed the degree of convergence of frontostriatal fiber projections in 56 young adult healthy controls (HCs) and 108 matched Early Psychosis-Non-Affective patients (EP-NAs) using our novel fiber cluster analysis of whole brain diffusion magnetic resonance imaging tractography.
Methods
Using whole brain tractography and our fiber clustering methodology on harmonized diffusion magnetic resonance imaging data from the Human Connectome Project for Early Psychosis we identified 17 white matter fiber clusters that connect frontal cortex (FCtx) and caudate (Cd) per hemisphere in each group. To quantify the degree of convergence and, hence, topographical relationship of these fiber clusters, we measured the inter-cluster mean distances between the endpoints of the fiber clusters at the level of the FCtx and of the Cd, respectively.
Results
We found (1) in both groups, bilaterally, a non-linear relationship, yielding convex curves, between FCtx and Cd distances for FCtx-Cd connecting fiber clusters, driven by a cluster projecting from inferior frontal gyrus; however, in the right hemisphere, the convex curve was more flattened in EP-NAs; (2) that cluster pairs in the right (p = 0.03), but not left (p = 0.13), hemisphere were significantly more convergent in HCs vs EP-NAs; (3) in both groups, bilaterally, similar clusters projected significantly convergently to the Cd; and, (4) a significant group by fiber cluster pair interaction for 2 right hemisphere fiber clusters (numbers 5, 11; p = .00023; p = .00023) originating in selective PFC subregions.
Conclusions
In both groups, we found the FCtx-Cd wiring pattern deviated from a strictly topographic relationship and that similar clusters projected significantly more convergently to the Cd. Interestingly, we also found a significantly more convergent pattern of connectivity in HCs in the right hemisphere and that 2 clusters from PFC subregions in the right hemisphere significantly differed in their pattern of connectivity between groups.
In recent years, there has been a growing interest in studying the Superficial White Matter (SWM). The SWM consists of short association fibers connecting near giry of the cortex, with a complex organization due to their close relationship with the cortical folding patterns. Therefore, their segmentation from dMRI tractography datasets requires dedicated methodologies to identify the main fiber bundle shape and deal with spurious fibers. This paper presents an enhanced short fiber bundle segmentation based on a SWM bundle atlas and the filtering of noisy fibers. The method was tuned and evaluated over HCP test-retest probabilistic tractography datasets (44 subjects). We propose four fiber bundle filters to remove spurious fibers. Furthermore, we include the identification of the main fiber fascicle to obtain well-defined fiber bundles. First, we identified four main bundle shapes in the SWM atlas, and performed a filter tuning in a subset of 28 subjects. The filter based on the Convex Hull provided the highest similarity between corresponding test-retest fiber bundles. Subsequently, we applied the best filter in the 16 remaining subjects for all atlas bundles, showing that filtered fiber bundles significantly improve test-retest reproducibility indices when removing between ten and twenty percent of the fibers. Additionally, we applied the bundle segmentation with and without filtering to the ABIDE-II database. The fiber bundle filtering allowed us to obtain a higher number of bundles with significant differences in fractional anisotropy, mean diffusivity, and radial diffusivity of Autism Spectrum Disorder patients relative to controls.
This paper provides comparisons between microstructure and two-dimensional fiber orientations measured optically using polarization-sensitive optical coherence tomography (PS-OCT) and those estimated from ultra-high-field diffusion MRI (dMRI) at 10.5T in the macaque brain. The PS-OCT imaging is done at an in-plane resolution of ~10 microns in and around the thalamus. Whole brain dMRI is acquired at an isotropic resolution of 0.75 mm. We provide comparisons between cross-polarization and optical orientation from PS-OCT with the fractional anisotropy and two-dimensional orientations extracted from dMRI using a diffusion tensor model. The orientations from PS-OCT are also extracted computationally using a structure tensor. Additionally, we demonstrate the utility of mesoscale, PS-OCT imaging in improving the MRI resolution by learning the mapping between these contrasts using a super-resolution Generative Adversarial Network.
OBJECTIVE
The free-water correction algorithm (Freewater Estimator Using Interpolated Initialization [FERNET]) can be applied to standard diffusion tensor imaging (DTI) tractography to improve visualization of subcortical bundles in the peritumoral area of highly edematous brain tumors. Interest in its use for presurgical planning in purely infiltrative gliomas without peritumoral edema has never been evaluated. Using subcortical maps obtained with direct electrostimulation (DES) in awake surgery as a reference standard, the authors sought to 1) assess the accuracy of preoperative DTI-based tractography with FERNET in a series of nonedematous glioma patients, and 2) determine its potential usefulness in presurgical planning.
METHODS
Based on DES-induced functional disturbances and tumor topography, the authors retrospectively reconstructed the putatively stimulated bundles and the peritumoral tracts of interest (various associative and projection pathways) of 12 patients. The tractography data obtained with and without FERNET were compared.
RESULTS
The authors identified 21 putative tracts from 24 stimulation sites and reconstituted 49 tracts of interest. The number of streamlines of the putative tracts crossing the DES area was 26.8% higher (96.04 vs 75.75, p = 0.016) and their volume 20.4% higher (13.99 cm ³ vs 11.62 cm ³ , p < 0.0001) with FERNET than with standard DTI. Additionally, the volume of the tracts of interest was 22.1% higher (9.69 cm ³ vs 7.93 cm ³ , p < 0.0001).
CONCLUSIONS
Free-water correction significantly increased the anatomical plausibility of the stimulated fascicles and the volume of tracts of interest in the peritumoral area of purely infiltrative nonedematous gliomas. Because of the functional importance of the peritumoral zone, applying FERNET to DTI could have potential implications on surgical planning and the safety of glioma resection.
The changes in the necrotic core and the penumbra following induction of focal ischemia have been the focus of attention for some time. However, evidence shows, that ischemic injury is not confined to the primarily affected structures and may influence the remote areas as well. Yet many studies fail to probe into the structures beyond the penumbra, and possibly do not even find any significant results due to their short-term design, as secondary damage occurs later. This slower reaction can be perceived as a therapeutic opportunity, in contrast to the ischemic core defined as irreversibly damaged tissue, where the window for salvation is comparatively short. The pathologies in remote structures occur relatively frequently and are clearly linked to the post-stroke neurological outcome. In order to develop efficient therapies, a deeper understanding of what exactly happens in the exo-focal regions is necessary. The mechanisms of glia contribution to the ischemic damage in core/penumbra are relatively well described and include impaired ion homeostasis, excessive cell swelling, glutamate excitotoxic mechanism, release of pro-inflammatory cytokines and phagocytosis or damage propagation via astrocytic syncytia. However, little is known about glia involvement in post-ischemic processes in remote areas. In this literature review, we discuss the definitions of the terms “ischemic core”, “penumbra” and “remote areas.” Furthermore, we present evidence showing the array of structural and functional changes in the more remote regions from the primary site of focal ischemia, with a special focus on glia and the extracellular matrix. The collected information is compared with the processes commonly occurring in the ischemic core or in the penumbra. Moreover, the possible causes of this phenomenon and the approaches for investigation are described, and finally, we evaluate the efficacy of therapies, which have been studied for their anti-ischemic effect in remote areas in recent years.
Myelinated axons form long-range connections that enable rapid communication between distant brain regions, but how genetics governs the strength and organization of these connections remains unclear. We perform genome-wide association studies of 206 structural connectivity measures derived from diffusion magnetic resonance imaging tractography of 26,333 UK Biobank participants, each representing the density of myelinated connections within or between a pair of cortical networks, subcortical structures or cortical hemispheres. We identify 30 independent genome-wide significant variants after Bonferroni correction for the number of measures studied (126 variants at nominal genome-wide significance) implicating genes involved in myelination (SEMA3A), neurite elongation and guidance (NUAK1, STRN, DPYSL2, EPHA3, SEMA3A, HGF, SHTN1), neural cell proliferation and differentiation (GMNC, CELF4, HGF), neuronal migration (CCDC88C), cytoskeletal organization (CTTNBP2, MAPT, DAAM1, MYO16, PLEC), and brain metal transport (SLC39A8). These variants have four broad patterns of spatial association with structural connectivity: some have disproportionately strong associations with corticothalamic connectivity, interhemispheric connectivity, or both, while others are more spatially diffuse. Structural connectivity measures are highly polygenic, with a median of 9.1 percent of common variants estimated to have non-zero effects on each measure, and exhibited signatures of negative selection. Structural connectivity measures have significant genetic correlations with a variety of neuropsychiatric and cognitive traits, indicating that connectivity-altering variants tend to influence brain health and cognitive function. Heritability is enriched in regions with increased chromatin accessibility in adult oligodendrocytes (as well as microglia, inhibitory neurons and astrocytes) and multiple fetal cell types, suggesting that genetic control of structural connectivity is partially mediated by effects on myelination and early brain development. Our results indicate pervasive, pleiotropic, and spatially structured genetic control of white-matter structural connectivity via diverse neurodevelopmental pathways, and support the relevance of this genetic control to healthy brain function.
Glial tumors represent the leading etiology of primary brain tumors. Their particularities lie in (i) their location in a highly functional organ that is difficult to access surgically, including for biopsy, and (ii) their rapid, anisotropic mode of extension, notably via the fiber bundles of the white matter, which further limits the possibilities of resection. The use of mathematical tools enables the development of numerical models representative of the oncotype, genotype, evolution, and therapeutic response of lesions. The significant development of digital technologies linked to high-resolution NMR exploration, coupled with the possibilities offered by AI, means that we can envisage the creation of digital twins of tumors and their host organs, thus reducing the use of physical sampling.
Using neuroanatomical investigations in the macaque, Deepak Pandya and his colleagues have established the framework for auditory cortex organization, with subdivisions into core and belt areas. This has aided subsequent neurophysiological and imaging studies in monkeys and humans, and a nomenclature building on Pandya's work has also been adopted by the Human Connectome Project. The foundational work by Pandya and his colleagues is highlighted here in the context of subsequent and ongoing studies on the functional anatomy and physiology of auditory cortex in primates, including humans, and their relevance for understanding cognitive aspects of speech and language.
Parcellation of anatomically segregated cortical and subcortical brain regions is required in diffusion MRI (dMRI) analysis for region-specific quantification and better anatomical specificity of tractography. Most current dMRI parcellation approaches compute the parcellation from anatomical MRI (T1- or T2-weighted) data, using tools such as FreeSurfer or CAT12, and then register it to the diffusion space. However, the registration is challenging due to image distortions and low resolution of dMRI data, often resulting in mislabeling in the derived brain parcellation. Furthermore, these approaches are not applicable when anatomical MRI data is unavailable. As an alternative we developed the Deep Diffusion Parcellation (DDParcel), a deep learning method for fast and accurate parcellation of brain anatomical regions directly from dMRI data. The input to DDParcel are dMRI parameter maps and the output are labels for 101 anatomical regions corresponding to the FreeSurfer Desikan-Killiany (DK) parcellation. A multi-level fusion network leverages complementary information in the different input maps, at three network levels: input, intermediate layer, and output. DDParcel learns the registration of diffusion features to anatomical MRI from the high-quality Human Connectome Project data. Then, to predict brain parcellation for a new subject, the DDParcel network no longer requires anatomical MRI data but only the dMRI data. Comparing DDParcel’s parcellation with T1w-based parcellation shows higher test-retest reproducibility and a higher regional homogeneity, while requiring much less computational time. Generalizability is demonstrated on a range of populations and dMRI acquisition protocols. Utility of DDParcel’s parcellation is demonstrated on tractography analysis for fiber tract identification.
Preterm-born neonates are prone to impaired neurodevelopment that may be associated with disrupted whole-brain structural connectivity. The present study aimed to investigate the longitudinal developmental pattern of the structural network from preterm birth to term-equivalent age (TEA), and identify how prematurity influences the network topological organization and properties of local brain regions. Multi-shell diffusion-weighted MRI of 28 preterm-born scanned a short time after birth (PB-AB) and at TEA (PB-TEA), and 28 matched term-born (TB) neonates in the Developing Human Connectome Project (dHCP) were used to construct structural networks through constrained spherical deconvolution tractography. Structural network development from preterm birth to TEA showed reduced shortest path length, clustering coefficient, and modularity, and more "connector" hubs linking disparate communities. Furthermore, compared with TB newborns, premature birth significantly altered the nodal properties (i.e., clustering coefficient, within-module degree, and participation coefficient) in the limbic/paralimbic, default-mode, and subcortical systems but not global topology at TEA, and we were able to distinguish the PB from TB neonates at TEA based on the nodal properties with 96.43% accuracy. Our findings demonstrated a topological reorganization of the structural network occurs during the perinatal period that may prioritize the optimization of global network organization to form a more efficient architecture; and local topology was more vulnerable to premature birth-related factors than global organization of the structural network, which may underlie the impaired cognition and behavior in PB infants.
Background and purpose:
Improving the accuracy of brain tumour radiotherapy (RT) treatment planning is important to optimise patient outcomes. This systematic review investigates primary studies providing clinical evidence for the integration of quantitative magnetic resonance imaging (qMRI) biomarkers and MRI radiomics to optimise brain tumour RT planning.
Materials and methods:
PubMed, Scopus, Embase and Web of Science databases were searched for all years until June 21, 2022. The search identified original articles demonstrating clinical evidence for the use of qMRI biomarkers and MRI radiomics for the optimization of brain cancer RT planning. Relevant information was extracted and tabulated, including qMRI metrics and techniques, impact on RT plan optimization and changes in target and normal tissue contouring and dose distribution.
Results:
Nineteen articles met the inclusion criteria. Studies were grouped according to the qMRI biomarkers into: 1) diffusion-weighted imaging (DWI) and perfusion-weighted imaging (PWI; five studies); 2) diffusion tensor imaging (DTI; seven studies); and 3) MR spectroscopic imaging (MRSI; seven studies). No relevant MRI-based radiomics studies were identified. Integration of DTI maps offers the potential for improved organs at risk (OAR) sparing. MRSI metabolic maps are a promising technique for improving delineation accuracy in terms of heterogeneity and infiltration, with OAR sparing. No firm conclusions could be drawn regarding the integration of DWI metrics and PWI maps.
Conclusions:
Integration of qMRI metrics into RT planning offers the potential to improve delineation and OAR sparing. Clinical trials and consensus guidelines are required to demonstrate the clinical benefits of such approaches.
The conductivity, in general, of the brain tissues is a characteristic key of functional cerebral changes. White matter electric conductivity appears to be extremely anisotropic, so a tensor (matrix) is needed to describe it. Traditional methods of imaging brain electrical properties fail to capture it and required the interpolation of the diffusion matrix. The electrochemical model is suitable for analysis, while, on the other hand, the volume fraction model is suitable for studying the effect of white matter structural changes in relation to electrical conductivity. It adopts a relevant algorithm, based upon a linear conductivity-to-diffusivity relationship and a volume constraint, respectively. It incorporates the effects of the partial volume of the cerebrospinal fluid and the structure of the neuronal fiber crossing, which was not achieved by the existing algorithms, accomplishing a more accurate estimation of the anisotropic conductivity of the white matter. Diffusion matrix imaging is a powerful noninvasive method for characterizing neuronal tissue in the human brain. The ultimate goal is to study and draw appropriate conclusions, regarding the molecule diffusion in the brain under normal physiological conditions and the changes that occur in development, diseases, and aging. The ability to measure the electrical conductivity of brain tissues in a noninvasive way also helps in characterizing endogenous currents by measuring the associated electromagnetic fields.
Ethic code: IR.KAUMS.MEDNT.REC.1401.015
Structural brain organization in infancy is associated with later cognitive, behavioral, and educational outcomes. Due to practical limitations, such as poor in-utero imaging, there is a lack of understanding of the early emergence of topological organization. We combine the developing Human Connectome Project’s large infant dataset with generative network modeling to simulate the emergence of network organization over early development. Preterm infants had reduced connectivity, shorter connection lengths and lower network efficiency compared to term-born infants. The models were able to recapitulate the organizational differences between term and preterm networks and revealed that preterm infant networks are better simulated under tighter wiring constraints than term infants. Tighter constraints for preterm models resulted in shorter connection lengths while preserving vital, long-range rich club connections. These simulations suggest that preterm birth is associated with a renegotiation of the cost/value wiring trade-off that may drive the emergence of different network organization.
The structural network of the brain, or structural connectome, can be represented by fiber bundles generated by a variety of tractography methods. While such methods give qualitative insights into brain structure, there is controversy over whether they can provide quantitative information, especially at the population level. In order to enable population-level statistical analysis of the structural connectome, we propose representing a connectome as a Riemannian metric, which is a point on an infinite-dimensional manifold. We equip this manifold with the Ebin metric, a natural metric structure for this space, to get a Riemannian manifold along with its associated geometric properties. We then use this Riemannian framework to apply object-oriented statistical analysis to define an atlas as the Fréchet mean of a population of Riemannian metrics. This formulation ties into the existing framework for diffeomorphic construction of image atlases, allowing us to construct a multimodal atlas by simultaneously integrating complementary white matter structure details from DWMRI and cortical details from T1-weighted MRI. We illustrate our framework with 2D data examples of connectome registration and atlas formation. Finally, we build an example 3D multimodal atlas using T1 images and connectomes derived from diffusion tensors estimated from a subset of subjects from the Human Connectome Project.
Purpose divergence (converging or diverging fiber pattern), (b) non-zero curl (circulating, open or closed fiber pattern), or (c) periodic or uniform fiber directional pattern. Fig 1 shows a fiber tract trajectory, r(s), calculated from such a test map in which all three Euler angles of D(x): φ (x), ϕ(x), and θ(x), varied continuously through the image volume. To propose a methodology to calculate continuous fiber-tract trajectories from measured diffusion tensor MRI data, and a rationale for determining fiber tract continuity. Introduction In normal and pathological tissues, fiber tract trajectories would provide valuable new microstructural information. In aging and development it would provide a means to follow changes in fiber-architecture. DT-MRI (1) is now the first noninvasive imaging modality capable of generating such fiber-tract trajectories. This is because in each voxel, the fiber tract direction is parallel to the eigenvector, ε 1 , associated with the largest eigenvalue, λ 1 , of the local diffusion tensor, D (1). However, ε 1 measured by DT-MRI are inherently discrete, noisy, voxel-averaged estimates of the "true" direction vectors (2). To date, it has not been feasible to reconstruct continuous fiber tract trajectories from the measured ε 1 . However, a new, efficient D-field processing methodology that we just developed, generates a continuous diffusion tensor field, D(x), from measured DT-MRI data (3) from which a continuous ε 1 -field map can be calculated. Then, the method below can be used to calculate fiber tract trajectories, and assess fiber tract continuity. Fig 1. Computed 3-d fiber tract trajectory from synthetic D(x) image.
A model of electromagnetic stimulation predicts the transmembrane potential distribution along a myelinated nerve axon and the volume of stimulated tissue within a limb. Threshold stimulus strength is shown to be inversely proportional to the square of the axon diameter. It is inversely proportional to pulse duration for short pulses and independent of pulse duration for long ones. These results are also predicted by dimensional analysis. Two dimensionless numbers, Sem, the ratio of the induced transmembrane potential to the axon's threshold potential, and Tc/T, the ratio of the pulse duration to the membrane time constant, summarise the dependence of threshold stimulus strength on pulse duration and axon diameter.
Diffusion tensor magnetic resonance imaging (MRI) is a possible new means of elucidating the anatomic structure of the myocardium. It enjoys several advantages over traditional histological approaches, including the ability to rapidly measure fiber organization in isolated, perfused, arrested hearts, thereby avoiding fixation and sectioning of artifacts. However, quantitative validation of this MRI method has been lacking. Here, fiber orientations estimated in the same locations in the same heart using both diffusion tensor MRI and histology are compared in a total of two perfused rabbit hearts. Fiber orientations were statistically similar for both methods and differed on average by 12 degrees at any single location. This is similar to the 10 degrees uncertainty in fiber orientation achieved with histology. In addition, imaging studies performed in a total of seven hearts support a level of organization beyond the myofiber, the recently described laminar organization of the ventricular myocardium.
The relationship between brain structure and complex behavior is governed by large-scale neurocognitive networks. The availability of a noninvasive technique that can visualize the neuronal projections connecting the functional centers should therefore provide new keys to the understanding of brain function. By using high-resolution three-dimensional diffusion magnetic resonance imaging and a newly designed tracking approach, we show that neuronal pathways in the rat brain can be probed in situ. The results are validated through comparison with known anatomical locations of such fibers.
. We construct atomic spaces S # L 2 (R n , T 1 1 ) that are appropriate for the representation and processing of discrete tensor field data. We give conditions for these spaces to be well defined, atomic subspaces of the Wiener amalgam space W (C, L 2 (R n , T 1 1 )) which is locally continuous and globally L 2 . We show that the sampling or discretization operator R from S to l 2 (Z n , T 1 1 ) is a bounded linear operator. We introduce the dilated spaces S# = D# S parametrized by the coarseness #, and show that the discretization operator is also bounded with a bounded inverse for any # # Z n . This allows us to represent discrete tensor field data in terms of continuous tensor fields in S# , and to obtain continous representations with fast filtering algorithms. . 1. Introduction Modern imaging systems, (e.g., Magnetic resonance image scanner) acquire discrete sets of data and store them as arrays of numbers. In many new imaging modalities, the acquired images are ...
The relationship between brain structure and complex behavior is governed by large-scale neurocognitive networks. The availability of a noninvasive technique that can visualize the neuronal projections connecting the functional centers should therefore provide new keys to the understanding of brain function. By using high-resolution three-dimensional diffusion magnetic resonance imaging and a newly designed tracking approach, we show that neuronal pathways in the rat brain can be probed in situ. The results are validated through comparison with known anatomical locations of such fibers. Ann Neurol 1999;45:265–269
General analytical expressions are presented for the b matrix used in diffusion NMR imaging and spectroscopy. These expressions are evaluated in the case of a two-dimensional Fourier-transform spin-echo imaging sequence and show the effect of "cross terms" between gradient pulses. The diagonal and off-diagonal components of the b matrix are calculated for the anisotropic diffusion tenser. The proposed analysis allows diffusion coefficients and tensors to be determined accurately and with greater efficiency.
The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both, however, is that the noise distributions are nearly Gaus-sian for SNR larger than two.
A technique for assessing in vivo fiber connectivity in the human brain is presented. The method utilizes a novel connectivity algorithm that operates in three spatial dimensions and uses estimates of fiber tract orientation and tissue anisotropy, obtained from diffusion tensor magnetic resonance imaging, to establish the pathways of fiber tracts. Sample in vivo connectivity images from healthy human brain are presented that demonstrate connections in the white matter tracts. White matter connectivity information is potentially of interest in the study of a range of neurological, psychiatric, and developmental disorders and shows promise for following the natural history of disease. Magn Reson Med 42:37–41, 1999. © 1999 Wiley-Liss, Inc.
Magnetic resonance diffusion imaging is potentially an important tool for the noninvasive characterization of normal and pathological tissue. The technique, however, is prone to a number of artifacts that can severely affect its ability to provide clinically useful information. In this study, the problem of eddy current-induced geometric distortions that occur in diffusion images acquired with echo planar sequences was addressed. These geometric distortions produce artifacts in computed maps of diffusion parameters and are caused by misalignments in the individual diffusion-weighted images that comprise the diffusion data set. A new approach is presented to characterize and calibrate the eddy current effects, enabling the eddy current distortions to be corrected in sets of Interleaved (or snapshot) echo planar diffusion images. Correction is achieved by acquiring one-dimensional field maps in the read and phase encode direction for each slice and each diffusion step. The method is then demonstrated through the correction of distortions in diffusion images of the human brain. It is shown that by using the eddy current correction scheme outlined, the eddy current-induced artifacts in the diffusion-weighted images are almost completely eliminated. In addition, there is a significant improvement in the quality of the resulting diffusion tensor maps.
This work helps elucidate how background noise introduces statistical artifacts in the distribution of the sorted eigenvalues and eigenvectors in diffusion tensor MRI (DT-MRI) data. Although it was known that sorting eigenvalues (principal diffusivities) by magnitude introduces a bias in their sample mean within a homogeneous region of interest (ROI), here it is shown that magnitude sorting also introduces a significant bias in the variance of the sample mean eigenvalues. New methods are presented to calculate the mean and variance of the eigenvectors of the diffusion tensor, based on a dyadic tensor representation of eigenvalue–eigenvector pairs. Based on their use it is shown that sorting eigenvalues by magnitude also introduces a bias in the mean and the variance of the sample eigenvectors (principal directions). This required the development of new methods to calculate the mean and variance of the eigenvectors of the diffusion tensor, based on a dyadic tensor representation of eigenvalue–eigenvector pairs. Moreover, a new approach is proposed to order these pairs within an ROI. To do this, a correspondence between each principal axis of the diffusion ellipsoid, an eigenvalue–eigenvector pair, and a dyadic tensor constructed from it is exploited. A measure of overlap between principal axes of diffusion ellipsoids in different voxels is defined that employs projections between these dyadic tensors. The optimal eigenvalue assignment within an ROI maximizes this overlap. Bias in the estimate of the mean and of the variance of the eigenvalues and of their corresponding eigenvectors is reduced in DT-MRI experiments and in Monte Carlo simulations of such experiments. Improvement is most significant in isotropic regions, but some is also observed in anisotropic regions. This statistical framework should enhance our ability to characterize microstructure and architecture of healthy tissue, and help to assess its changes in development, disease, and degeneration. Mitigating these artifacts should also improve the characterization of diffusion anisotropy and the elucidation of fiber-tract trajectories in the brain and in other fibrous tissues. Magn Reson Med 44:41–50, 2000. Published 2000 Wiley-Liss, Inc.
Development of efficient imaging techniques to trace neuro nal connections would be very useful. Manganese ion (Mn2+) is an excellent T1 contrast agent for magnetic resonance imaging (MRI). Four reports utilizing radioactive Mn2+ in fish and rat brain indicate that Mn2+ may be useful for tracing neuronal connections. Therefore, the purpose of this work was to determine if Mn2+ can be used as an in vivo MRI neuronal tract tracer. The results indicate that topical admin istration of MnCI2 solution to the naris of mice as well as to the retinal ganglion cells via intravitreal injection leads to en hancement of contrast along the respective pathways. There fore, application of Mn2+ to neurons allows the use of MRI to visualize neuronal connections.
A single-shot echo-planar diffusion imaging sequence (IVIM-EPI: intra-voxel incoherent motion echo-planar imaging) is presented, which is immune from the motion artifacts which may seriously impair images obtained using other diffusion imaging sequences. For a static water phantom, the measured value of diffusion constant (D = 2.30 × 10−9 m2 s−1 at T = 298 K) shows excellent agreement with that obtained using a multipulse spin-echo technique and with literature values. Single-shot diffusion imaging can now be used reliably to make dynamic time-course studies with excellent time resolution.
Lagrangian statistical quantities are of fundamental physical importance in our understanding of turbulence, but are very difficult to measure and hence infrequently reported in the literature. A particle-tracking algorithm is developed to extract accurate Lagrangian statistics from numerically calculated velocity fields. Lagrangian time-series are obtained from the method of direct numerical simulation, which supplies the Eulerian' velocity field on a three-dimensional grid network. The accuracy of the Lagrangian time series depends; primarily; on the accuracy of the interpolation scheme used to calculate fluid-particle velocities. Interpolation schemes based on Taylor series and on cubic splines have been implemented and tested. Errors in computed particle displacements are quantified for simple, frozen velocity fields. The algorithm is applied to stationary homogeneous isotropic turbulence with the energy maintained by artificial forcing. It is demonstrated that with adequate spatial resolution, accurate estimates of Lagrangian statistics such as velocity autocorrelations, structure functions, and frequency spectra can be obtained either with a third-order Taylor series interpolation scheme or with a cubic spline scheme. Cubic splines give higher interpolation accuracy, but they are more difficult to implement in codes that rely on secondary storage.
Power spectrum or magnitude images are frequently presented in magnetic resonance imaging. In such images, measurement of signal intensity at low signal levels is compounded with the noise. This report describes how to extract true intensity measurements in the presence of noise.
A method is described for the correction of geometric distortions occurring in echo planar images. The geometric distortions are caused in large part by static magnetic field inhomogeneities, leading to pixel shifts, particularly in the phase encode direction. By characterizing the field inhomogeneities from a field map, the image can be unwarped so that accurate alignment to conventionally collected images can be made. The algorithm to perform the unwarping is described, and results from echo planar images collected at 1.5 and 4 Tesla are shown.
Patient motion can seriously degrade the quality of diffusion-weighted MR images obtained using standard 2DFT imaging procedures. The main source of error arises from an MR signal phase-shift error which is proportional to the magnitude of the motion. A modified pulse sequence is proposed which uses the phase information from an additional spin echo to correct for patient motion. Application of this technique is demonstrated for a human brain study, which greatly improves the quantification of diffusion values from regions of brain tissue.
The diagonal and off-diagonal elements of the effective self-diffusion tensor, Deff, are related to the echo intensity in an NMR spin-echo experiment. This relationship is used to design experiments from which Deff is estimated. This estimate is validated using isotropic and anisotropic media, i.e., water and skeletal muscle. It is shown that significant errors are made in diffusion NMR spectroscopy and imaging of anisotropic skeletal muscle when off-diagonal elements of Deff are ignored, most notably the loss of information needed to determine fiber orientation. Estimation of Deff provides the theoretical basis for a new MRI modality, diffusion tensor imaging, which provides information about tissue microstructure and its physiologic state not contained in scalar quantities such as T1, T2, proton density, or the scalar apparent diffusion constant.
This paper describes a new NMR imaging modality--MR diffusion tensor imaging. It consists of estimating an effective diffusion tensor, Deff, within a voxel, and then displaying useful quantities derived from it. We show how the phenomenon of anisotropic diffusion of water (or metabolites) in anisotropic tissues, measured noninvasively by these NMR methods, is exploited to determine fiber tract orientation and mean particle displacements. Once Deff is estimated from a series of NMR pulsed-gradient, spin-echo experiments, a tissue's three orthotropic axes can be determined. They coincide with the eigenvectors of Deff, while the effective diffusivities along these orthotropic directions are the eigenvalues of Deff. Diffusion ellipsoids, constructed in each voxel from Deff, depict both these orthotropic axes and the mean diffusion distances in these directions. Moreover, the three scalar invariants of Deff, which are independent of the tissue's orientation in the laboratory frame of reference, reveal useful information about molecular mobility reflective of local microstructure and anatomy. Inherently tensors (like Deff) describing transport processes in anisotropic media contain new information within a macroscopic voxel that scalars (such as the apparent diffusivity, proton density, T1, and T2) do not.
Pulsed field gradient nuclear magnetic resonance methods combined with nuclear magnetic resonance imaging were used to determine the water diffusion anisotropy in perfused rat hearts at 37 degrees C. It was found that the observed diffusion coefficient D(app) (apparent diffusion coefficient) depends on the orientation of the applied gradient g. When g is parallel to the epicardial surface, the observed diffusivity is D(app) parallel = 1.8 +/- 0.4 x 10(-9) m2.s-1, whereas when g is perpendicular to it, diffusivity is D(app) perpendicular = 2.5 +/- 0.5 x 10(-9) m2.s-1. To better characterize this directional dependence, images of the second-order diffusion tensor D of the myocardium were obtained. These data demonstrate several essential features of cardiac myoarchitecture, including the helicity of fiber orientation with respect to the ventricular axis and the variation of fiber pitch angle with transmural depth. Diffusion anisotropy may be quantified in a coordinate-independent manner by the eigenvalues of the diffusion tensor. In the myocardial midwall, these eigenvalues were E1 = 3.29 +/- 0.57, E2 = 2.01 +/- 0.42, and E3 = 0.77 +/- 0.58 x 10(-9) m2.s-1 (mean +/- SD). These data suggest that myocardial water diffusion is essentially unrestricted parallel to the myofibers. They further show that failure to measure the complete diffusion tensor may lead to substantial underestimates of diffusion anisotropy in the myocardium.
To interpret the activity of living human brains, their neuroanatomy must be known in detail. New techniques to do this are urgently needed, since most of the methods now used on monkeys cannot be used on humans.
The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both,however, is that the noise distributions are nearly Gaussian for SNR larger than two.
Quantitative-diffusion-tensor MRI consists of deriving and displaying parameters that resemble histological or physiological stains, i.e., that characterize intrinsic features of tissue microstructure and microdynamics. Specifically, these parameters are objective, and insensitive to the choice of laboratory coordinate system. Here, these two properties are used to derive intravoxel measures of diffusion isotropy and the degree of diffusion anisotropy, as well as intervoxel measures of structural similarity, and fiber-tract organization from the effective diffusion tensor, D, which is estimated in each voxel. First, D is decomposed into its isotropic and anisotropic parts, [D] I and D - [D] I, respectively (where [D] = Trace(D)/3 is the mean diffusivity, and I is the identity tensor). Then, the tensor (dot) product operator is used to generate a family of new rotationally and translationally invariant quantities. Finally, maps of these quantitative parameters are produced from high-resolution diffusion tensor images (in which D is estimated in each voxel from a series of 2D-FT spin-echo diffusion-weighted images) in living cat brain. Due to the high inherent sensitivity of these parameters to changes in tissue architecture (i.e., macromolecular, cellular, tissue, and organ structure) and in its physiologic state, their potential applications include monitoring structural changes in development, aging, and disease.
To assess intrinsic properties of water diffusion in normal human brain by using quantitative parameters derived from the diffusion tensor, D, which are insensitive to patient orientation.
Maps of the principal diffusivities of D, of Trace(D), and of diffusion anisotropy indices were calculated in eight healthy adults from 31 multisection, interleaved echo-planar diffusion-weighted images acquired in about 25 minutes.
No statistically significant differences in Trace(D) (approximately 2,100 x 10(-6) mm2/sec) were found within normal brain parenchyma, except in the cortex, where Trace(D) was higher. Diffusion anisotropy varied widely among different white matter regions, reflecting differences in fiber-tract architecture. In the corpus callosum and pyramidal tracts, the ratio of parallel to perpendicular diffusivities was approximately threefold higher than previously reported, and diffusion appeared cylindrically symmetric. However, in other white matter regions, particularly in the centrum semiovale, diffusion anisotropy was low, and cylindrical symmetry was not observed. Maps of parameters derived from D were also used to segment tissues based on their diffusion properties.
A quantitative characterization of water diffusion in anisotropic, heterogeneously oriented tissues is clinically feasible. This should improve the neuroradiologic assessment of a variety of gray and white matter disorders.
Indices of diffusion anisotropy calculated from diffusion coefficients acquired in two or three perpendicular directions are rotationally variant. In living monkey brain, these indices severely underestimate the degree of diffusion anisotropy. New indices calculated from the entire diffusion tensor are rotationally invariant (RI). They show that anisotropy is highly variable in different white matter regions depending on the degree of coherence of fiber tract directions. In structures with a regular, parallel fiber arrangement, water diffusivity in the direction parallel to the fibers (Dparallel approximately 1400-1800 x 10(-6) mm2/s) is almost 10 times higher than the average diffusivity in directions perpendicular to them (D + D)/2 [corrected] approximately 150-300 x 10(-6) mm2/s), and is almost three times higher than previously reported. In structures where the fiber pattern is less coherent (e.g., where fiber bundles merge), diffusion anisotropy is significantly reduced. However, RI anisotropy indices are still susceptible to noise contamination. Monte Carlo simulations show that these indices are statistically biased, particularly those requiring sorting of the eigenvalues of the diffusion tensor based on their magnitude. A new intervoxel anisotropy index is proposed that locally averages inner products between diffusion tensors in neighboring voxels. This "lattice" RI index has an acceptably low error variance and is less susceptible to bias than any other RI anisotropy index proposed to date.
In diffusion tensor imaging (DTI) an effective diffusion tensor in each voxel is measured by using a set of diffusion-weighted images (DWIs) in which diffusion gradients are applied in a multiplicity of oblique directions. However, to estimate the diffusion tensor accurately, one must account for the effects of all imaging and diffusion gradient pulses on each signal echo, which are embodied in the b matrix. For DTI to be practical clinically, one must also acquire DWIs rapidly and free of motion artifacts, which is now possible with diffusion-weighted echo-planar imaging (DW-EPI). An analytical expression for the b matrix of a general DW-EPI pulse sequence is presented and then validated experimentally by measuring the diffusion tensor in an isotropic phantom whose diffusivity is already known. The b matrix is written in a convenient tabular form as a sum of individual pair-wise contributions arising from gradient pulses applied along parallel and perpendicular directions. While the contributions from readout and phase-encode gradient pulse trains are predicted to have a negligible effect on the echo, the contributions from other imaging and diffusion gradient pulses applied in both parallel and orthogonal directions are shown to be significant in our sequence. In general, one must understand and account for the multiplicity of interactions between gradient pulses and the echo signal to ensure that diffusion tensor imaging is quantitative.
Functional properties of the myocardium are mediated by the tissue structure. Consequently, proper physiological studies and modeling necessitate a precise knowledge of the fiber orientation. Magnetic resonance (MR) diffusion tensor imaging techniques have been used as a nondestructive means to characterize tissue fiber structure; however, the descriptions so far have been mostly qualitative. This study presents a direct, quantitative comparison of high-resolution MR fiber mapping and histology measurements in a block of excised canine myocardium. Results show an excellent correspondence of the measured fiber angles not only on a point-by-point basis (average difference of -2.30 +/- 0.98 degrees, n = 239) but also in the transmural rotation of the helix angles (average correlation coefficient of 0.942 +/- 0.008 with average false-positive probability of 0.004 +/- 0.001, n = 24). These data strongly support the hypothesis that the eigenvector of the largest MR diffusion tensor eigenvalue coincides with the orientation of the local myocardial fibers and underscore the potential of MR imaging as a noninvasive, three-dimensional modality to characterize tissue fiber architecture.
A technique for assessing in vivo fiber connectivity in the human brain is presented. The method utilizes a novel connectivity algorithm that operates in three spatial dimensions and uses estimates of fiber tract orientation and tissue anisotropy, obtained from diffusion tensor magnetic resonance imaging, to establish the pathways of fiber tracts. Sample in vivo connectivity images from healthy human brain are presented that demonstrate connections in the white matter tracts. White matter connectivity information is potentially of interest in the study of a range of neurological, psychiatric, and developmental disorders and shows promise for following the natural history of disease.
We used diffusion tensor imaging to assess diffusion anisotropy in the pyramidal tract in ten young, and ten elderly subjects (five males and five females in each group). The purpose of this study was to define normative values for anisotropy at different anatomic levels of the brainstem as well as to assess differences due to age, gender, and laterality. In all subjects, anisotropy was highest in the cerebral peduncle, lowest in the caudal pons, and intermediate in the medulla. In the pons and medulla the regional variability was high, with significant differences in anisotropy even between contiguous slices. Multifactorial ANOVA (performed using the average value of anisotropy within each region of interest) revealed that elderly subjects had significantly lower values than young subjects in the cerebral peduncle, with no differences in the pons and medulla. No significant differences in anisotropy due to gender and side were found. The differences in anisotropy at different levels of the brainstem reflect differences in the local architecture of white matter fibers. Anisotropy is high in the cerebral peduncle because fibers have a highly ordered arrangement, while in the pons and medulla, anisotropy is lower because the local fiber architecture is less coherent due to the presence of other fibers and nuclei. The biologic meaning of the intergroup differences in anisotropy is discussed in light of the structure and architecture of the tissue under investigation. We also consider potential sources of artifacts, such as noise and motion, partial volume contamination, anatomic mismatching, and the use of inappropriate statistical tests. We conclude that the age-related decrease in anisotropy in the cerebral peduncle is not artifactual but rather reflects subtle structural changes of the aging white matter. Our study however shows that caution must be exercised in interpreting diffusion anisotropy data.
This work helps elucidate how background noise introduces statistical artifacts in the distribution of the sorted eigenvalues and eigenvectors in diffusion tensor MRI (DT-MRI) data. Although it was known that sorting eigenvalues (principal diffusivities) by magnitude introduces a bias in their sample mean within a homogeneous region of interest (ROI), here it is shown that magnitude sorting also introduces a significant bias in the variance of the sample mean eigenvalues. New methods are presented to calculate the mean and variance of the eigenvectors of the diffusion tensor, based on a dyadic tensor representation of eigenvalue-eigenvector pairs. Based on their use it is shown that sorting eigenvalues by magnitude also introduces a bias in the mean and the variance of the sample eigenvectors (principal directions). This required the development of new methods to calculate the mean and variance of the eigenvectors of the diffusion tensor, based on a dyadic tensor representation of eigenvalue-eigenvector pairs. Moreover, a new approach is proposed to order these pairs within an ROI. To do this, a correspondence between each principal axis of the diffusion ellipsoid, an eigenvalue-eigenvector pair, and a dyadic tensor constructed from it is exploited. A measure of overlap between principal axes of diffusion ellipsoids in different voxels is defined that employs projections between these dyadic tensors. The optimal eigenvalue assignment within an ROI maximizes this overlap. Bias in the estimate of the mean and of the variance of the eigenvalues and of their corresponding eigenvectors is reduced in DT-MRI experiments and in Monte Carlo simulations of such experiments. Improvement is most significant in isotropic regions, but some is also observed in anisotropic regions. This statistical framework should enhance our ability to characterize microstructure and architecture of healthy tissue, and help to assess its changes in development, disease, and degeneration. Mitigating these artifacts should also improve the characterization of diffusion anisotropy and the elucidation of fiber-tract trajectories in the brain and in other fibrous tissues. Magn Reson Med 44:41-50, 2000. Published 2000 Wiley-Liss, Inc.
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