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Fang C, Yang Z, Wassermann D, Li JR. A simulation-driven supervised learning framework to estimate brain microstructure using diffusion MRI. Med Image Anal 2023; 90:102979. [PMID: 37827109 DOI: 10.1016/j.media.2023.102979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2023] [Revised: 09/13/2023] [Accepted: 09/22/2023] [Indexed: 10/14/2023]
Abstract
We propose a framework to train supervised learning models on synthetic data to estimate brain microstructure parameters using diffusion magnetic resonance imaging (dMRI). Although further validation is necessary, the proposed framework aims to seamlessly incorporate realistic simulations into dMRI microstructure estimation. Synthetic data were generated from over 1,000 neuron meshes converted from digital neuronal reconstructions and linked to their neuroanatomical parameters (such as soma volume and neurite length) using an optimized diffusion MRI simulator that produces intracellular dMRI signals from the solution of the Bloch-Torrey partial differential equation. By combining random subsets of simulated neuron signals with a free diffusion compartment signal, we constructed a synthetic dataset containing dMRI signals and 40 tissue microstructure parameters of 1.45 million artificial brain voxels. To implement supervised learning models we chose multilayer perceptrons (MLPs) and trained them on a subset of the synthetic dataset to estimate some microstructure parameters, namely, the volume fractions of soma, neurites, and the free diffusion compartment, as well as the area fractions of soma and neurites. The trained MLPs perform satisfactorily on the synthetic test sets and give promising in-vivo parameter maps on the MGH Connectome Diffusion Microstructure Dataset (CDMD). Most importantly, the estimated volume fractions showed low dependence on the diffusion time, the diffusion time independence of the estimated parameters being a desired property of quantitative microstructure imaging. The synthetic dataset we generated will be valuable for the validation of models that map between the dMRI signals and microstructure parameters. The surface meshes and microstructures parameters of the aforementioned neurons have been made publicly available.
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Affiliation(s)
- Chengran Fang
- INRIA Saclay, Equipe IDEFIX, UMA, ENSTA Paris, 828, Boulevard des Maréchaux, 91762 Palaiseau, France; INRIA Saclay, Equipe MIND, 1 Rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France
| | - Zheyi Yang
- INRIA Saclay, Equipe IDEFIX, UMA, ENSTA Paris, 828, Boulevard des Maréchaux, 91762 Palaiseau, France
| | - Demian Wassermann
- INRIA Saclay, Equipe MIND, 1 Rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France
| | - Jing-Rebecca Li
- INRIA Saclay, Equipe IDEFIX, UMA, ENSTA Paris, 828, Boulevard des Maréchaux, 91762 Palaiseau, France.
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2
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Yang Z, Fang C, Li JR. Incorporating interface permeability into the diffusion MRI signal representation while using impermeable Laplace eigenfunctions. Phys Med Biol 2023; 68:175036. [PMID: 37579758 DOI: 10.1088/1361-6560/acf022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 08/14/2023] [Indexed: 08/16/2023]
Abstract
Objective. The complex-valued transverse magnetization due to diffusion-encoding magnetic field gradients acting on a permeable medium can be modeled by the Bloch-Torrey partial differential equation. The diffusion magnetic resonance imaging (MRI) signal has a representation in the basis of the Laplace eigenfunctions of the medium. However, in order to estimate the permeability coefficient from diffusion MRI data, it is desirable that the forward solution can be calculated efficiently for many values of permeability.Approach. In this paper we propose a new formulation of the permeable diffusion MRI signal representation in the basis of the Laplace eigenfunctions of the same medium where the interfaces are made impermeable.Main results.We proved the theoretical equivalence between our new formulation and the original formulation in the case that the full eigendecomposition is used. We validated our method numerically and showed promising numerical results when a partial eigendecomposition is used. Two diffusion MRI sequences were used to illustrate the numerical validity of our new method.Significance.Our approach means that the same basis (the impermeable set) can be used for all permeability values, which reduces the computational time significantly, enabling the study of the effects of the permeability coefficient on the diffusion MRI signal in the future.
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Affiliation(s)
- Zheyi Yang
- Equipe IDEFIX, INRIA Saclay, UMA, ENSTA PARIS, Palaiseau, France
| | - Chengran Fang
- Equipe IDEFIX, INRIA Saclay, UMA, ENSTA PARIS, Palaiseau, France
| | - Jing-Rebecca Li
- Equipe IDEFIX, INRIA Saclay, UMA, ENSTA PARIS, Palaiseau, France
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3
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Kikuchi J, Yamada S. The exposome paradigm to predict environmental health in terms of systemic homeostasis and resource balance based on NMR data science. RSC Adv 2021; 11:30426-30447. [PMID: 35480260 PMCID: PMC9041152 DOI: 10.1039/d1ra03008f] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2021] [Accepted: 08/31/2021] [Indexed: 12/22/2022] Open
Abstract
The environment, from microbial ecosystems to recycled resources, fluctuates dynamically due to many physical, chemical and biological factors, the profile of which reflects changes in overall state, such as environmental illness caused by a collapse of homeostasis. To evaluate and predict environmental health in terms of systemic homeostasis and resource balance, a comprehensive understanding of these factors requires an approach based on the "exposome paradigm", namely the totality of exposure to all substances. Furthermore, in considering sustainable development to meet global population growth, it is important to gain an understanding of both the circulation of biological resources and waste recycling in human society. From this perspective, natural environment, agriculture, aquaculture, wastewater treatment in industry, biomass degradation and biodegradable materials design are at the forefront of current research. In this respect, nuclear magnetic resonance (NMR) offers tremendous advantages in the analysis of samples of molecular complexity, such as crude bio-extracts, intact cells and tissues, fibres, foods, feeds, fertilizers and environmental samples. Here we outline examples to promote an understanding of recent applications of solution-state, solid-state, time-domain NMR and magnetic resonance imaging (MRI) to the complex evaluation of organisms, materials and the environment. We also describe useful databases and informatics tools, as well as machine learning techniques for NMR analysis, demonstrating that NMR data science can be used to evaluate the exposome in both the natural environment and human society towards a sustainable future.
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Affiliation(s)
- Jun Kikuchi
- Environmental Metabolic Analysis Research Team, RIKEN Center for Sustainable Resource Science 1-7-22 Suehiro-cho, Tsurumi-ku Yokohama 230-0045 Japan
- Graduate School of Bioagricultural Sciences, Nagoya University Furo-cho, Chikusa-ku Nagoya 464-8601 Japan
- Graduate School of Medical Life Science, Yokohama City University 1-7-29 Suehiro-cho, Tsurumi-ku Yokohama 230-0045 Japan
| | - Shunji Yamada
- Environmental Metabolic Analysis Research Team, RIKEN Center for Sustainable Resource Science 1-7-22 Suehiro-cho, Tsurumi-ku Yokohama 230-0045 Japan
- Prediction Science Laboratory, RIKEN Cluster for Pioneering Research 7-1-26 Minatojima-minami-machi, Chuo-ku Kobe 650-0047 Japan
- Data Assimilation Research Team, RIKEN Center for Computational Science 7-1-26 Minatojima-minami-machi, Chuo-ku Kobe 650-0047 Japan
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Ludwig D, Laun FB, Ladd ME, Bachert P, Kuder TA. Apparent exchange rate imaging: On its applicability and the connection to the real exchange rate. Magn Reson Med 2021; 86:677-692. [PMID: 33749019 DOI: 10.1002/mrm.28714] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 01/11/2021] [Accepted: 01/15/2021] [Indexed: 12/15/2022]
Abstract
PURPOSE Water exchange between the intracellular and extracellular space can be measured using apparent exchange rate (AXR) imaging. The aim of this study was to investigate the relationship between the measured AXR and the geometry of diffusion restrictions, membrane permeability, and the real exchange rate, as well as to explore the applicability of AXR for typical human measurement settings. METHODS The AXR measurements and the underlying exchange rates were simulated using the Monte Carlo method with different geometries, size distributions, packing densities, and a broad range of membrane permeabilities. Furthermore, the influence of SNR and sequence parameters was analyzed. RESULTS The estimated AXR values correspond to the simulated values and show the expected proportionality to membrane permeability, except for fast exchange (ie, AXR > 20 - 30 s - 1 ) and small packing densities. Moreover, it was found that the duration of the filter gradient must be shorter than 2 · AX R - 1 . In cell size and permeability distributions, AXR depends on the average surface-to-volume ratio, permeability, and the packing density. Finally, AXR can be reliably determined in the presence of orientation dispersion in axon-like structures with sufficient gradient sampling (ie, 30 gradient directions). CONCLUSION Currently used experimental settings for in vivo human measurements are well suited for determining AXR, with the exception of single-voxel analysis, due to limited SNR. The detection of changes in membrane permeability in diseased tissue is nonetheless challenging because of the AXR dependence on further factors, such as packing density and geometry, which cannot be disentangled without further knowledge of the underlying cell structure.
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Affiliation(s)
- Dominik Ludwig
- Department of Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany.,Faculty of Physics and Astronomy, University of Heidelberg, Heidelberg, Germany
| | - Frederik Bernd Laun
- Institute of Radiology, University Hospital Erlangen, Friedrich-Alexander-University Erlangen-Nürnberg, Erlangen, Germany
| | - Mark Edward Ladd
- Department of Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany.,Faculty of Physics and Astronomy, University of Heidelberg, Heidelberg, Germany.,Faculty of Medicine, University of Heidelberg, Heidelberg, Germany
| | - Peter Bachert
- Department of Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany.,Faculty of Physics and Astronomy, University of Heidelberg, Heidelberg, Germany
| | - Tristan Anselm Kuder
- Department of Medical Physics in Radiology, German Cancer Research Center (DKFZ), Heidelberg, Germany
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Lee HH, Fieremans E, Novikov DS. Realistic Microstructure Simulator (RMS): Monte Carlo simulations of diffusion in three-dimensional cell segmentations of microscopy images. J Neurosci Methods 2020; 350:109018. [PMID: 33279478 DOI: 10.1016/j.jneumeth.2020.109018] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Revised: 11/16/2020] [Accepted: 11/29/2020] [Indexed: 12/12/2022]
Abstract
BACKGROUND Monte Carlo simulations of diffusion are commonly used as a model validation tool as they are especially suitable for generating the diffusion MRI signal in complicated tissue microgeometries. NEW METHOD Here we describe the details of implementing Monte Carlo simulations in three-dimensional (3d) voxelized segmentations of cells in microscopy images. Using the concept of the corner reflector, we largely reduce the computational load of simulating diffusion within and exchange between multiple cells. Precision is further achieved by GPU-based parallel computations. RESULTS Our simulation of diffusion in white matter axons segmented from a mouse brain demonstrates its value in validating biophysical models. Furthermore, we provide the theoretical background for implementing a discretized diffusion process, and consider the finite-step effects of the particle-membrane reflection and permeation events, needed for efficient simulation of interactions with irregular boundaries, spatially variable diffusion coefficient, and exchange. COMPARISON WITH EXISTING METHODS To our knowledge, this is the first Monte Carlo pipeline for MR signal simulations in a substrate composed of numerous realistic cells, accounting for their permeable and irregularly-shaped membranes. CONCLUSIONS The proposed RMS pipeline makes it possible to achieve fast and accurate simulations of diffusion in realistic tissue microgeometry, as well as the interplay with other MR contrasts. Presently, RMS focuses on simulations of diffusion, exchange, and T1 and T2 NMR relaxation in static tissues, with a possibility to straightforwardly account for susceptibility-induced T2* effects and flow.
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Affiliation(s)
- Hong-Hsi Lee
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA; Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, USA.
| | - Els Fieremans
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA; Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, USA
| | - Dmitry S Novikov
- Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, USA; Center for Advanced Imaging Innovation and Research (CAI2R), New York University School of Medicine, New York, NY, USA
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Fang C, Nguyen VD, Wassermann D, Li JR. Diffusion MRI simulation of realistic neurons with SpinDoctor and the Neuron Module. Neuroimage 2020; 222:117198. [PMID: 32730957 DOI: 10.1016/j.neuroimage.2020.117198] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Revised: 06/30/2020] [Accepted: 07/22/2020] [Indexed: 02/08/2023] Open
Abstract
The diffusion MRI signal arising from neurons can be numerically simulated by solving the Bloch-Torrey partial differential equation. In this paper we present the Neuron Module that we implemented within the Matlab-based diffusion MRI simulation toolbox SpinDoctor. SpinDoctor uses finite element discretization and adaptive time integration to solve the Bloch-Torrey partial differential equation for general diffusion-encoding sequences, at multiple b-values and in multiple diffusion directions. In order to facilitate the diffusion MRI simulation of realistic neurons by the research community, we constructed finite element meshes for a group of 36 pyramidal neurons and a group of 29 spindle neurons whose morphological descriptions were found in the publicly available neuron repository NeuroMorpho.Org. These finite elements meshes range from having 15,163 nodes to 622,553 nodes. We also broke the neurons into the soma and dendrite branches and created finite elements meshes for these cell components. Through the Neuron Module, these neuron and cell components finite element meshes can be seamlessly coupled with the functionalities of SpinDoctor to provide the diffusion MRI signal attributable to spins inside neurons. We make these meshes and the source code of the Neuron Module available to the public as an open-source package. To illustrate some potential uses of the Neuron Module, we show numerical examples of the simulated diffusion MRI signals in multiple diffusion directions from whole neurons as well as from the soma and dendrite branches, and include a comparison of the high b-value behavior between dendrite branches and whole neurons. In addition, we demonstrate that the neuron meshes can be used to perform Monte-Carlo diffusion MRI simulations as well. We show that at equivalent accuracy, if only one gradient direction needs to be simulated, SpinDoctor is faster than a GPU implementation of Monte-Carlo, but if many gradient directions need to be simulated, there is a break-even point when the GPU implementation of Monte-Carlo becomes faster than SpinDoctor. Furthermore, we numerically compute the eigenfunctions and the eigenvalues of the Bloch-Torrey and the Laplace operators on the neuron geometries using a finite elements discretization, in order to give guidance in the choice of the space and time discretization parameters for both finite elements and Monte-Carlo approaches. Finally, we perform a statistical study on the set of 65 neurons to test some candidate biomakers that can potentially indicate the soma size. This preliminary study exemplifies the possible research that can be conducted using the Neuron Module.
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Affiliation(s)
- Chengran Fang
- INRIA Saclay, Equipe DEFI, CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France; INRIA Saclay, Equipe Parietal, 1 Rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France
| | - Van-Dang Nguyen
- Department of Computational Science and Technology, KTH Royal Institute of Technology, Sweden
| | - Demian Wassermann
- INRIA Saclay, Equipe Parietal, 1 Rue Honoré d'Estienne d'Orves, 91120 Palaiseau, France
| | - Jing-Rebecca Li
- INRIA Saclay, Equipe DEFI, CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France.
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7
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Li JR, Tran TN, Nguyen VD. Practical computation of the diffusion MRI signal of realistic neurons based on Laplace eigenfunctions. NMR IN BIOMEDICINE 2020; 33:e4353. [PMID: 32725935 DOI: 10.1002/nbm.4353] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 05/14/2020] [Accepted: 05/26/2020] [Indexed: 06/11/2023]
Abstract
The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold-standard reference model for the diffusion MRI signal arising from different tissue micro-structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion-encoding sequences and b-values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB-based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch-Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b-values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch-Torrey operator and compute the Bloch-Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI.
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Affiliation(s)
- Jing-Rebecca Li
- INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique, Palaiseau, France
| | - Try Nguyen Tran
- INRIA Saclay-Equipe DEFI, CMAP, Ecole Polytechnique, Palaiseau, France
| | - Van-Dang Nguyen
- Division of Computational Science and Technology, KTH Royal Institute of Technology, Sweden
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8
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Li JR, Nguyen VD, Tran TN, Valdman J, Trang CB, Nguyen KV, Vu DTS, Tran HA, Tran HTA, Nguyen TMP. SpinDoctor: A MATLAB toolbox for diffusion MRI simulation. Neuroimage 2019; 202:116120. [DOI: 10.1016/j.neuroimage.2019.116120] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2019] [Revised: 08/21/2019] [Accepted: 08/22/2019] [Indexed: 12/15/2022] Open
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Karunanithy G, Wheeler RJ, Tear LR, Farrer NJ, Faulkner S, Baldwin AJ. INDIANA: An in-cell diffusion method to characterize the size, abundance and permeability of cells. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 302:1-13. [PMID: 30904779 PMCID: PMC7611012 DOI: 10.1016/j.jmr.2018.12.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2018] [Revised: 11/30/2018] [Accepted: 12/03/2018] [Indexed: 05/13/2023]
Abstract
NMR and MRI diffusion experiments contain information describing the shape, size, abundance, and membrane permeability of cells although extracting this information can be challenging. Here we present the INDIANA (IN-cell DIffusion ANAlysis) method to simultaneously and non-invasively measure cell abundance, effective radius, permeability and intrinsic relaxation rates and diffusion coefficients within the inter- and intra-cellular populations. The method couples an experimental dataset comprising stimulated-echo diffusion measurements, varying both the gradient strength and the diffusion delay, together with software to fit a model based on the Kärger equations to robustly extract the relevant parameters. A detailed error analysis is presented by comparing the results from fitting simulated data from Monte Carlo simulations, establishing its effectiveness. We note that for parameters typical of mammalian cells the approach is particularly effective, and the shape of the underlying cells does not unduly affect the results. Finally, we demonstrate the performance of the experiment on systems of suspended yeast and mammalian cells. The extracted parameters describing cell abundance, size, permeability and relaxation are independently validated.
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Affiliation(s)
- Gogulan Karunanithy
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Richard J Wheeler
- Peter Medawar Building for Pathogen Research, Nuffield Department of Medicine, University of Oxford, Oxford OX1 3SY, United Kingdom
| | - Louise R Tear
- Chemistry Research Laboratory, University of Oxford, 12 Mansfield Road, Oxford OX1 3TA, United Kingdom
| | - Nicola J Farrer
- Chemistry Research Laboratory, University of Oxford, 12 Mansfield Road, Oxford OX1 3TA, United Kingdom
| | - Stephen Faulkner
- Chemistry Research Laboratory, University of Oxford, 12 Mansfield Road, Oxford OX1 3TA, United Kingdom
| | - Andrew J Baldwin
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.
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Nguyen KV, Hernández-Garzón E, Valette J. Efficient GPU-based Monte-Carlo simulation of diffusion in real astrocytes reconstructed from confocal microscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 296:188-199. [PMID: 30296779 DOI: 10.1016/j.jmr.2018.09.013] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Revised: 09/14/2018] [Accepted: 09/27/2018] [Indexed: 06/08/2023]
Abstract
The primary goal of this work is to develop an efficient Monte-Carlo simulation of diffusion-weighted signal in complex cellular structures, such as astrocytes, directly derived from confocal microscopy. In this study, we first use an octree structure for spatial decomposition of surface meshes. Octree structure and radius-search algorithm help to quickly identify the faces that particles can possibly encounter during the next time step, thus speeding up the Monte-Carlo simulation. Furthermore, we propose to use a three-dimensional binary marker to describe the complex cellular structure and optimize the particle trajectory simulation. Finally, a GPU-based version of these two approaches is implemented for more efficient modeling. It is shown that the GPU-based binary marker approach yields unparalleled performance, opening up new possibilities to better understand intracellular diffusion, validate diffusion models, and create dictionaries of intracellular diffusion signatures.
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Affiliation(s)
- Khieu-Van Nguyen
- Molecular Imaging Research Center (MIRCen), Commissariat l'Energie Atomique, Fontenay-aux-Roses, France.
| | - Edwin Hernández-Garzón
- Molecular Imaging Research Center (MIRCen), Commissariat l'Energie Atomique, Fontenay-aux-Roses, France
| | - Julien Valette
- Molecular Imaging Research Center (MIRCen), Commissariat l'Energie Atomique, Fontenay-aux-Roses, France
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Edwards LJ. Simulation of coherence selection by pulsed field gradients in liquid-state NMR using an auxiliary matrix formalism. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 240:95-101. [PMID: 24577118 DOI: 10.1016/j.jmr.2014.01.011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2013] [Revised: 01/20/2014] [Accepted: 01/22/2014] [Indexed: 06/03/2023]
Abstract
An algorithm for simulating coherence selection due to a pulse sequence element consisting of two pulsed field gradients separated by a short collection of pulses and delays is introduced. This algorithm involves computation of the matrix exponential of an auxiliary matrix twice the size of the system Liouvillian, a dimensional increase smaller than is required with other known computational methods. Approximations valid for most simulations of liquid-state NMR spectra are involved in the derivation. Diffusion is omitted, but could be treated in an approximate way as a damping over the pulse sequence element. Several NMR pulse sequences using gradients for coherence selection have been implemented, making use of the functionality of Spinach (http://spindynamics.org/Spinach.php). Example simulations testing these implementations are presented, and the extent to which the formal dimensional reduction can lead to a speedup in simulation time discussed. It is found that the previously known methods can be made competitive with the auxiliary matrix method by making use of their embarrassingly parallel nature. Cases where the relative dimensional reduction of the auxiliary matrix method is very large, or where efficient parallelization of the simulation independent of the nature of the algorithm used exists, are found to lead to situations beneficial for the auxiliary matrix algorithm in this comparison.
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Affiliation(s)
- Luke J Edwards
- Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford OX1 3QG, UK.
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12
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Yeh CH, Schmitt B, Le Bihan D, Li-Schlittgen JR, Lin CP, Poupon C. Diffusion microscopist simulator: a general Monte Carlo simulation system for diffusion magnetic resonance imaging. PLoS One 2013; 8:e76626. [PMID: 24130783 PMCID: PMC3794953 DOI: 10.1371/journal.pone.0076626] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2013] [Accepted: 08/23/2013] [Indexed: 11/18/2022] Open
Abstract
This article describes the development and application of an integrated, generalized, and efficient Monte Carlo simulation system for diffusion magnetic resonance imaging (dMRI), named Diffusion Microscopist Simulator (DMS). DMS comprises a random walk Monte Carlo simulator and an MR image synthesizer. The former has the capacity to perform large-scale simulations of Brownian dynamics in the virtual environments of neural tissues at various levels of complexity, and the latter is flexible enough to synthesize dMRI datasets from a variety of simulated MRI pulse sequences. The aims of DMS are to give insights into the link between the fundamental diffusion process in biological tissues and the features observed in dMRI, as well as to provide appropriate ground-truth information for the development, optimization, and validation of dMRI acquisition schemes for different applications. The validity, efficiency, and potential applications of DMS are evaluated through four benchmark experiments, including the simulated dMRI of white matter fibers, the multiple scattering diffusion imaging, the biophysical modeling of polar cell membranes, and the high angular resolution diffusion imaging and fiber tractography of complex fiber configurations. We expect that this novel software tool would be substantially advantageous to clarify the interrelationship between dMRI and the microscopic characteristics of brain tissues, and to advance the biophysical modeling and the dMRI methodologies.
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Affiliation(s)
- Chun-Hung Yeh
- Institute of Neuroscience, National Yang-Ming University, Taipei, Taiwan
- NeuroSpin, Commissariat à l’énergie atomique et aux énergies alternatives (CEA Saclay), Gif-sur-Yvette, France
- Institut de Federatif de Recherche 49, Gif-sur-Yvette, France
| | - Benoît Schmitt
- NeuroSpin, Commissariat à l’énergie atomique et aux énergies alternatives (CEA Saclay), Gif-sur-Yvette, France
- Institut de Federatif de Recherche 49, Gif-sur-Yvette, France
| | - Denis Le Bihan
- NeuroSpin, Commissariat à l’énergie atomique et aux énergies alternatives (CEA Saclay), Gif-sur-Yvette, France
- Institut de Federatif de Recherche 49, Gif-sur-Yvette, France
| | - Jing-Rebecca Li-Schlittgen
- Détermination de Formes et Identification (Equipe DEFI), Institut national de recherche en informatique et en automatique (INRIA Saclay), Palaiseau, France
| | - Ching-Po Lin
- Institute of Neuroscience, National Yang-Ming University, Taipei, Taiwan
| | - Cyril Poupon
- NeuroSpin, Commissariat à l’énergie atomique et aux énergies alternatives (CEA Saclay), Gif-sur-Yvette, France
- Institut de Federatif de Recherche 49, Gif-sur-Yvette, France
- * E-mail:
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13
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Waudby CA, Mantle MD, Cabrita LD, Gladden LF, Dobson CM, Christodoulou J. Rapid Distinction of Intracellular and Extracellular Proteins Using NMR Diffusion Measurements. J Am Chem Soc 2012; 134:11312-5. [DOI: 10.1021/ja304912c] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Christopher A. Waudby
- Institute of Structural and
Molecular Biology, University College London and Birkbeck College, Gower Street, London WC1E 6BT, U.K
| | - Mick D. Mantle
- Department of Chemical Engineering
and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K
| | - Lisa D. Cabrita
- Institute of Structural and
Molecular Biology, University College London and Birkbeck College, Gower Street, London WC1E 6BT, U.K
| | - Lynn F. Gladden
- Department of Chemical Engineering
and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, U.K
| | - Christopher M. Dobson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge
CB2 1EW, U.K
| | - John Christodoulou
- Institute of Structural and
Molecular Biology, University College London and Birkbeck College, Gower Street, London WC1E 6BT, U.K
| |
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