Haut PDF New ODE Model for Diffusion MRI Signal

New ODE Model for Diffusion MRI Signal

New ODE Model for Diffusion MRI Signal

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A new multi-fiber model for low angular resolution diffusion MRI

A new multi-fiber model for low angular resolution diffusion MRI

3. EXPERIMENTAL VALIDATION 3.1. Experimental setup 3.1.1. Crossing angle resolution of the model The crossing angle resolution (CAR) is the minimum de- tectable angle between two different FOs. We performed its evaluation on the 2-fiber model (M = 2) using synthetic data on a single voxel. We generated the simulated data sets ac- cording to the spherical deconvolution method proposed in [12]. They simulate multiple FOs assuming that the fiber ori- entation distribution function is a sum of equally weighted delta functions. They perform its convolution with the kernel proposed in [13], which models restricted diffusion within a cylindrical fiber of radius ρ = 5µm and length L = 5mm. We chose this method because (i) they implemented it on-line, as part of the fanDTasia toolbox 3 , (ii) this method has been used in more than 20 papers and (iii) the spherical deconvolution in its discrete version is close to multi-compartment models.
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A Unifying Framework for Spatial and Temporal Diffusion in Diffusion MRI

A Unifying Framework for Spatial and Temporal Diffusion in Diffusion MRI

(a) Gamma Distributions (b) Signal Optic Nerve (c) Signal Sciatic Nerve Fig. 1: Signals generated using the Callaghan model. 3.2 Signal fitting and Effect of Regularization In our first experiment we test how many spatial or temporal basis functions we need to fit a 3D+t diffusion signal. We choose to study in the case of restricted diffusion in a cylindrical compartment, since this is a good model for white mat- ter tissue in highly organized areas. We generate the noiseless signal as described in Section 2.3 with the sampling scheme we described in Section 3.1 . We then fit the signal with increasing maximum order for the spatial and temporal basis. We then compute the mean squared error (MSE) of the fitted signal compared to the ground truth. We show a heat map of the results in Figure 2a where we see that the signal fitting in this specific signal model only improves very little after a spatial order of 6 and a temporal order of 5. Using Eq. ( 5 ) this means we fit 300 coefficients to accurately represent the 3D+t signal.
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Diffusion MRI Anisotropy: Modeling, Analysis and Interpretation

Diffusion MRI Anisotropy: Modeling, Analysis and Interpretation

ing GFA [ Cohen-Adad et al. , 2011 ] or PA [ Fick et al. , 2016a ], while large-scale comparisons like those for FA are missing. Moreover, the typical criterium for being a biomarker is that the measure of inter- est should provide a statistically significant difference between healthy and diseased populations. However, care should be taken in prematurely calling a non-specific marker such as diffusion anisotropy a biomarker. As an illustration, in the particular case of Parkinson’s disease, after many studies had claimed that FA could be used as a diagnostic biomarker, a systematic review of these studies actually showed that on its own, it cannot [ Hirata et al. , 2016 ]. It is likely that the non-specificity of diffusion anisotropy will continue to confound its interpretation as a biomarker for pathology. On multi-compartment-based anisotropy: To overcome this lack of specificity, multi-compartment approaches strive to separate the signal contributions of different tissue compartments using biophysical models. However, it is important to realize that these models still describe diffusion anisotropy in some reparameterized way. For example, while NODDI is a multi-compartment model that separates the signal contributions of CSD, intra- and extra-axonal compartments, it can only describe one axon bundle using a Watson distribution with a single ODI, which is a function of concentration parameter κ. Illustrating the Watson ODFs together with the signal- based ODFs in Fig. 7 , we indeed find its similarity to others, in particular DTI. Of course, ODI has a different interpretation than FA, but it is important to see how they are related. Furthermore, µFA describes the per-axon micro-environment and is theoretically insensitive to crossing or dispersed axon configurations.
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Multi-Dimensional Diffusion MRI Sampling Scheme: B-tensor Design and Accurate Signal Reconstruction

Multi-Dimensional Diffusion MRI Sampling Scheme: B-tensor Design and Accurate Signal Reconstruction

We present the first 4D basis and reconstruction algorithm for representing and reconstructing the axisymmetric b-tensor encoded diffusion signal. We study the properties of the signal to inform how many and which b-tensors should be used, thereby providing sampling recommendations. Although preliminary, the high reconstruction accuracy achieved on Magic DIAMOND model is promising for interpolation of b-tensors encoded measurements to enable algorithms for recovering the DTD to achieve higher accuracy and/or reduce the number of measurements.

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Multi-compartment modelling of diffusion MRI signal shows TE-based volume fraction bias

Multi-compartment modelling of diffusion MRI signal shows TE-based volume fraction bias

Figure 1 The signal S is defined as the linear combination of the IC, EC and CSF compartments, where the anisotropic components IC and EC are convolved with a Watson distribution W of parameters d and k. The signal shape each compartment Ex depends on the characterising diffusivities and the S0 responses are designed for defining the 3-S0 model. Each parameter in the table was drawn from a normal distribution of mean and standard deviation equal to the ones listed. The S ​ 0 ​ ic ​ and S ​

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Model-free and Analytical EAP Reconstruction via Spherical Polar Fourier Diffusion MRI

Model-free and Analytical EAP Reconstruction via Spherical Polar Fourier Diffusion MRI

values, considering b 0 = 0 and E(0) = 1 for any u ∈ S 2 , which makes our estimation more reasonable and accurate. Otherwise, there is no warranty for the estimated signal ˜ E(0) = 1. Another advantage is that for the single shell HARDI data, considering b = 0 can let us have 2 shells, which will largely improve the results. The second one is how to determine the parameter ζ in basis. The authors in [8] proposed an experience strategy for it, which is dependent on the radial truncation order N. However, we think the parameter should be just dependent on the signal, not on the basis order. Considering E (q) = exp(−4π 2 τq 2 D), b = 4π 2 τq 2 , and a typical diffusion coefficient of D = 0.7 × 10 −3 mm 2 /s, a typical b-value b = 3000s/mm 2 , we set ζ = 1
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Coarse-Grained Spatiotemporal Acquisition Design for Diffusion MRI

Coarse-Grained Spatiotemporal Acquisition Design for Diffusion MRI

In silico data: As first data set, we generated time- dependent diffusion data using our Python-based [9] im- plementation of the two-compartment model with the intra- cellular fraction modeled with a set of Watson dispersed crossing cylinders [10] and the extra-cellular one modeled with a temporal zeppelin [1]. The angles of crossings were controlled by a random variable with a distribution centered at π/2 and a dispersion π/4. Following the study of Zhang et al. [10], we used the concentration parameters of the Watson distribution κ ∈ {0.25, 1, 4, 16}, where κ = 16 means highly concentrated and κ = 0.25 means highly dispersed cylinders. Additionally, we considered two variants of our data set per- turbed with Rician noise having Signal-to-Noise Ratio (SNR) 20 and 10, respectively.
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A Bayes Hilbert Space for Compartment Model Computing in Diffusion MRI

A Bayes Hilbert Space for Compartment Model Computing in Diffusion MRI

However, because of the low spatial resolution in diffusion MRI, it has been shown that the ST model is an average of several diffusion processes arising from multiple populations of tissues in the voxel, ultimately leading to an inaccurate description of the microstructure in most parts of the brain white matter. In addition, even within a single homogeneous tissue population, non-Gaussian dif- fusion has been observed [13]. This has led to the extension of the ST model to mixture models, often called multi-compartment models (MCM), where the voxelwise diffusion signal is modeled as a linear combination of compartmental diffusion signals arising from underlying homogeneous diffusion processes [8]. To the best of our knowledge, the only mathematical framework available for multi- compartment image processing [12] is however limited to multi-tensor images (mixture of single-tensor signals, see [10]) as it relies on log-Euclidean geometry. In this work, we present an alternative to the log-Euclidean space on tensors called the Bayes Hilbert space [3] for processing compartmental diffusion signals instead of tensors. It provides a unified framework that can accommodate an- alytic compartment diffusion signals of any type (Gaussian and non-Gaussian). Section 2 gives a general introduction to Bayes Hilbert spaces with motivation and setup in diffusion MRI. Section 3 describes a simulation study and a tractog- raphy application on real data to compare Euclidean, log-Euclidean and Bayes interpolation. Results commented in Section 4 show that Bayes interpolation fea- tures improved robustness to noise and yields better pyramidal tract reconstruc- tions when combined with MCM-based deterministic tractography to account for streamline atlas priors when diffusion models cannot be locally trusted.
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A new multi-directional fiber model for low angular resolution diffusion imaging

A new multi-directional fiber model for low angular resolution diffusion imaging

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Exploiting the Phase in Diffusion MRI for Microstructure Recovery: Towards Axonal Tortuosity via Asymmetric Diffusion Processes

Exploiting the Phase in Diffusion MRI for Microstructure Recovery: Towards Axonal Tortuosity via Asymmetric Diffusion Processes

We show that by exploiting the DW signal’s phase it is possible to character- ize axonal tortuosity, which can be linked to elongation/compression phenomena in pathological scenarios. Compressed axons are partially convoluted and show irregular undulation with a non-uniform tortuosity along the longitudinal direc- tion (see fig. 1 right). Hence, we model the compressed axon as a sinusoid with varying tortuosity, inducing asymmetry in its shape. Moreover, as the degree of compression increases, the tortuosity variation rate along the axon also increases. Spins diffusing within these axons undergo an asymmetric diffusion process re- sulting in an informative DW signal’s phase, sensible to increasing tortuosity rates. The amount of diffusion asymmetry thus gives important insights into the underlying degree of compression.
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Diffusion Microscopist Simulator - The Development and Application of a Monte Carlo Simulation System for Diffusion MRI

Diffusion Microscopist Simulator - The Development and Application of a Monte Carlo Simulation System for Diffusion MRI

test the accuracy of the results and to provide criteria for improving the modeling and the methodology. A significant aspect of simulation is that the features (e.g. cell membrane’s shape and prop- erty) are completely under the control of users, so that the role of specific property can be examined by altering its attribute. In dMRI, tissue modeling is the task of intensively research in order to clarify the relationship between MRI signal and tissue microscopic characteris- tics. Budde and Frank provide an excellent example of how simulations and experiments can be complementary tools to study the impact of tissue property [ Budde and Frank ( 2010 )]. They constructed a biophysical model for beading axonal membranes, which was validated by the histological evidence of biological nerve fibres, thus highlighting the significant impact of morphological variations of axons on ADC. In their study, the role of simulation offers the flexibility to adjust the magnitude of morphological variations of the axonal membranes, while the role of dMRI experiment verifies the phenomenon in realistic biological conditions. In the future, DMS will be further applied to investigate different tissue characteristics under healthy and pathological states via cross validation between simulations and experiments. This also reflects the benefit and the need of 3D rendering of histological images for the reconstruction of tissue configuration, as described in the previous section (Chapter 7.2.1 ). Although DMS simulations were mostly applied to simulate the tissues in the CNS system, DMS has the potential to be broadly applied to different MRI research fields such as diffusion in the porous media [ Shemesh et al. ( 2010a )], the acinar tree of lung [ Perez-Sanchez et al.
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The role of diffusion MRI in neuroscience

The role of diffusion MRI in neuroscience

However, the past two decades have been marked by the discovery of large inter- individual variability in brain structure and function (i.e. different phenotype), creating additional challenges in furthering the understanding of the brain and a lack of models to explain its functioning 198-201 . Studies have begun to explore and describe these pathways across large numbers of individuals 24,116,202 . Just as studies have found that individual differences in behaviour correlate with variation in local white matter microstructure, so too have tractography studies found that variation in the ‘strength’ or organization of white matter fibres relate to variations in behaviour. For instance, language areas and their interconnections are predominantly represented in the left hemisphere for most but not all healthy participants 203,204 . However, individuals vary in the degree of lateralisation and people with more symmetric patterns of connection have been shown to perform better at episodic memory tasks 203 . These differences are important consideration for the field of clinical neuroscience. Forkel et al. 205 demonstrated that the phenotype of the structural network supporting language (i.e. arcuate fasciculus) may interact with recovery after a stroke in the left hemisphere. Additionally, Lunven et al. 206 reported that the strength of inter- hemispheric communication is important for the recovery of visuospatial neglect after a stroke in the right hemisphere (see 207,208 for extensive reviews on the role of diffusion MRI in clinical neurosciences). Hence the study of inter-individual variability is a new line of research directly accessible in large scale projects such as the Human Connectome Project (https://www.humanconnectome.org), where high quality diffusion MRI data have been acquired in 1200 subjects and openly shared with the community 209 . Using diffusion weighted imaging tractography to characterise the functional specialisation of brain areas at the individual level may therefore benefit the domain of inter-individual variability, providing a more tailored brain model when doing group comparisons eventually making methods like spatial registration and smoothing obsolete.
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A 4D Basis and Sampling Scheme for the Tensor Encoded Multi-Dimensional Diffusion MRI Signal

A 4D Basis and Sampling Scheme for the Tensor Encoded Multi-Dimensional Diffusion MRI Signal

While algorithms have been proposed for recovering the DTD from b-tensor encoded measurements of the diffusion signal [ 7 ]–[ 10 ], only recently some consideration has been given to designing the b-tensor sampling scheme [ 11 ], [ 12 ]. In most cases, b-tensors are empirically chosen, often from uniform sampling of b-tensor parameters [ 9 ], [ 13 ]. Due to the inverse Laplace transform being ill-conditioned, on the order of 1000 samples are required by existing algorithms to recover marginal distributions of the full DTD [ 14 ], [ 15 ]. Such large numbers of samples require long scan times and are unrealistic for use in a clinical setting. Two recent studies [ 11 ], [ 12 ] proposed optimized b-tensor sampling schemes for the estimation of the parameters of a multi-tensor model of white matter. In contrast, in this work we propose a versatile method to design an optimal sampling scheme based on the properties of the signal, irrespective of the choice of a particular biophysical model.
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Multi-Tissue Multi-Compartment Models of Diffusion MRI

Multi-Tissue Multi-Compartment Models of Diffusion MRI

Keywords diffusion MRI, microstructure, multi tissue, single-TE, volume fraction, signal fraction 1 Introduction Diffusion MRI (dMRI) is an imaging technique that allows to inspect the brain tissue microstructure in- vivo non-invasively. One of the most commonly studied microstructural feature is the volume fraction of a tissue in a sample. In particular, the intra-axonal (i.e., intra-cellular - IC), extra-axonal (i.e., extra-cellular - EC) and cerebro-spinal fluid (CSF) volume fractions have been investigated with models like the neurite orientation dispersion and density imaging (NODDI) ( Zhang et al. , 2012 ), ActiveAx ( Alexander et al. , 2010 ), and the multi-compartment microscopic diffusion imaging framework ( Kaden et al. , 2016 ). The differences between these models lie on the representation employed in describing the tissue-specific signal and on the assumptions made on the model parameters. For example, intra-axonal diffusion can be modelled as the diffusion within a stick or a cylinder and some models fix the value of the diffusivity or tortuosity. A unifying aspect that characterizes most of the brain microstructure models is the building-blocks concept behind their formalisation. In other words, models are defined in a multi-compartment (MC) fashion, where the dMRI signal is described as a linear combination of single-tissue models. The resulting models are called MC models and they require the acquisition of multi-shell dMRI data in order to accurately disentangle the contribution of each compartment ( Scherrer and Warfield , 2010 ). Thorough reviews have been dedicated to the design and validation of such models ( Jelescu and Budde , 2017 ), to the sensitivity of MC models to experimental factors and microstructural properties of the described tissues ( Afzali et al. , 2020 ), and to the abstraction of these models that allows to obtain a unified theory ( Fick et al. , 2019 ).
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Numerical investigations of some mathematical models of the diffusion MRI signal

Numerical investigations of some mathematical models of the diffusion MRI signal

4.7. Conclusions and further improvements 4.7 Conclusions and further improvements Our analysis of the parameters estimation problem in the previous sections has re- vealed advantages and limitations of this approach. On the one hand, it seems to be possible to estimate a number of physiologically relevant parameters for “simple” tissues composed of not too elongated constituents. Among these parameters are the volume fractions, the apparent diffusion coefficient in the extra-cellular space, and the residence time which is related to the membrane permeability and surface- to-volume ratio. Clearly, these parameters can only represent averaged properties of the tissue. Nevertheless, a reliable experimental determination of these param- eters has always presented a great challenge. We showed on simplified examples a possibility of solving the parameters estimation problem. Most importantly, we analyzed the stability features of this problem. In particular, we studied the ro- bustness of the estimates against various biological and physical parameters (e.g., permeability, sequence timing, the range and number of b-values), as well as the robustness against noise. The ODE model always provided more accurate and sta- ble estimates than the Kärger model. This study suggests a promising perspective for estimating many important parameters from dMRI signals.
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Numerical study of a macroscopic finite pulse model of the diffusion MRI signal

Numerical study of a macroscopic finite pulse model of the diffusion MRI signal

acteristic time to traverse the correlation length of the cell packing. These statements are quite difficult to interpret and verify, for example, even when considering a reasonable geometrical model of brain tissue such as a voxel-sized domain containing densely packed dendrite trees and cylindrical axons with some orientation distribution and spherical cells modeling soma and glia cells. Hence we consider numerical simulations on voxel-sized (three dimensional) domains that contain densely packed, randomly placed and oriented cells of spherical and cylindrical geometries (and tree structures) to verify the above statemetns an extremely useful future direction. We illustrate this by showing preliminary results of applying the FPK model to a two dimensional voxel-sized non-periodic domain in Section 5. In this paper, we study the FPK model for periodic domains because the macroscopic model parameters can be defined rigorously for periodic domains, and we are able to show the convergence of the FPK model to the microscopic model in the homogenization parameter ε in a clear way. We hope that these results can then guide us improving and generalizing macroscopic models to brain tissue dMRI.
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Homogenized and analytical models for the diffusion MRI signal

Homogenized and analytical models for the diffusion MRI signal

moi toutes les joies et les douleurs de ce parcours (votre soutenance va arriver bientôt, courage !) ; Kevish, même si tu viens d’arriver, tu t’es déjà fait une belle place dans la meilleure équipe de foot (allez l’A.S. Saint Hessienne) ; Hang Tuan et Van Dang pour m’avoir introduit l’IRMD et le modèle FPK ; Tobias pour ses photos de l’équipe de foot ; Federico perché non so come avrei fatto i primi mesi senza il tuo supporto; Irene for showing me that you have always a reason to be in a good mood; Shixu for showing me that there exist people who have never seen a musical; and finally Jake who is a very good friend (I am sorry I have no better words to describe you but I have really enjoyed the time we spent together and I am really glad that I had the opportunity to meet you!). Even if she is not really a member of DeFI group, I would like to thank Prof. Fioralba Cakoni for bringing always a good spirit when she is around. Au sein de l’INRIA je tiens aussi à remercier vivement Valérie Berthou pour toute l’aide qu’elle m’a apportée avant mon arrivée en France puis pendant mes trois ans ici !
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Multi Tissue Modelling of Diffusion MRI Signal Reveals Volume Fraction Bias

Multi Tissue Modelling of Diffusion MRI Signal Reveals Volume Fraction Bias

Index Terms— Diffusion MRI, White Matter, Microstruc- ture, Generalized Multi Tissue Modelling 1. INTRODUCTION Diffusion MRI (dMRI) is able to probe brain tissue mi- crostructure in-vivo non-invasively. Two of the most com- monly studied microstructural features are the intra-axonal and cerebro-spinal fluid (CSF) volume fractions and sev- eral microstructural models have been proposed to retrieve them [1, 2, 3]. These models differ in the type of signal model used to represent a given tissue type (e.g. diffusion within a stick or cylinder for modeling the intra-axonal diffusion)
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Diffusion MRI Simulation with the Virtual Imaging Platform

Diffusion MRI Simulation with the Virtual Imaging Platform

Perspectives The simulated noise-free and non-artifact images can be used for evaluating diffusion image processing algorithms, such as denoising, k-space reconstruction, and motion correction. In addition, the simulation can help optimize the imaging parameters for high-b value imaging and q-space imaging. Furthermore, in vivo cardiac fiber models can be constructed based on PLI data and motion information from MRI cine sequences and as a result in vivo DW images can be simulated. As detailed in [12], load-balancing among computing resources is close to optimal for the simulation phase. However, there is still room for improving performance, especially in the merging phase: (i) the merging phase could be improved by using multiple parallel mergers as done in [13], (ii) the influence of the checkpointing frequency on the merging phase could be studied, (iii) the placement of partial simulation results on different storage locations could be investigated to reduce the cost of the merging phase. These could reduce the amount of manual intervention by grid experts which, to date, is still required to conduct such experiments.
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