High-fidelity meshes from tissue samples for diffusion MRI simulations

Post mortem mapping of connectional anatomy for the validation of diffusion MRI

Diffusion MRI (dMRI) is a unique tool for the study of brain circuitry, as it allows us to image both the macroscopic trajectories and the microstructural properties of axon bundles in vivo. The Human Connectome Project ushered in an era of impressive advances in dMRI acquisition and analysis. As a result of these efforts, the quality of dMRI data that could be acquired in vivo improved substantially, and large collections of such data became widely available. Despite this progress, the main limitation of dMRI remains: it does not image axons directly, but only provides indirect measurements based on the diffusion of water molecules. Thus, it must be validated by methods that allow direct visualization of axons but that can only be performed in post mortem brain tissue. In this review, we discuss methods for validating the various features of connectional anatomy that are extracted from dMRI, both at the macro-scale (trajectories of axon bundles), and at micro-scale (axonal orientations and other microstructural properties). We present a range of validation tools, including anatomic tracer studies, Klingler's dissection, myelin stains, label-free optical imaging techniques, and others. We provide an overview of the basic principles of each technique, its limitations, and what it has taught us so far about the accuracy of different dMRI acquisition and analysis approaches.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

ConFiG: Contextual Fibre Growth to generate realistic axonal packing for diffusion MRI simulation

This paper presents Contextual Fibre Growth (ConFiG), an approach to generate white matter numerical phantoms by mimicking natural fibre genesis. ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. Signals simulated from ConFiG phantoms match real diffusion MRI data well, showing that ConFiG phantoms can be used to generate realistic diffusion MRI data. This demonstrates the feasibility of ConFiG to generate realistic synthetic diffusion MRI data for developing and validating microstructure modelling approaches.

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We present ConFiG, a biologically motivated numerical phantom generator for white matter.

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ConFiG produces phantoms with state-of-the-art density and realistic microstructure.

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Diffusion MRI simulations in ConFiG phantoms are comparable to real dMRI signals.

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Towards microstructure fingerprinting: Estimation of tissue properties from a dictionary of Monte Carlo diffusion MRI simulations

Many closed-form analytical models have been proposed to relate the diffusion-weighted magnetic resonance imaging (DW-MRI) signal to microstructural features of white matter tissues. These models generally make assumptions about the tissue and the diffusion processes which often depart from the biophysical reality, limiting their reliability and interpretability in practice. Monte Carlo simulations of the random walk of water molecules are widely recognized to provide near groundtruth for DW-MRI signals. However, they have mostly been limited to the validation of simpler models rather than used for the estimation of microstructural properties. This work proposes a general framework which leverages Monte Carlo simulations for the estimation of physically interpretable microstructural parameters, both in single and in crossing fascicles of axons. Monte Carlo simulations of DW-MRI signals, or fingerprints, are pre-computed for a large collection of microstructural configurations. At every voxel, the microstructural parameters are estimated by optimizing a sparse combination of these fingerprints. Extensive synthetic experiments showed that our approach achieves accurate and robust estimates in the presence of noise and uncertainties over fixed or input parameters. In an in vivo rat model of spinal cord injury, our approach provided microstructural parameters that showed better correspondence with histology than five closed-form models of the diffusion signal: MMWMD, NODDI, DIAMOND, WMTI and MAPL. On whole-brain in vivo data from the human connectome project (HCP), our method exhibited spatial distributions of apparent axonal radius and axonal density indices in keeping with ex vivo studies. This work paves the way for microstructure fingerprinting with Monte Carlo simulations used directly at the modeling stage and not only as a validation tool.

Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook

Phantoms, both numerical (software) and physical (hardware), can serve as a gold standard for the validation of MRI methods probing the brain microstructure. This review aims to provide guidelines on how to build, implement, or choose the right phantom for a particular application, along with an overview of the current state-of-the-art of phantoms dedicated to study brain microstructure with MRI. For physical phantoms, we discuss the essential requirements and relevant characteristics of both the (NMR visible) liquid and (NMR invisible) phantom materials that induce relevant microstructural features detectable via MRI, based on diffusion, intra-voxel incoherent motion, magnetization transfer or magnetic susceptibility weighted contrast. In particular, for diffusion MRI, many useful phantoms have been proposed, ranging from simple liquids to advanced biomimetic phantoms consisting of hollow or plain microfibers and capillaries. For numerical phantoms, the focus is on Monte Carlo simulations of random walk, for which the basic principles, along with useful criteria to check and potential pitfalls are reviewed, in addition to a literature overview highlighting recent advances. While many phantoms exist already, the current review aims to stimulate further research in the field and to address remaining needs.

Efficient GPU-based Monte-Carlo simulation of diffusion in real astrocytes reconstructed from confocal microscopy

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.

Novel insights into in-vivo diffusion tensor cardiovascular magnetic resonance using computational modeling and a histology-based virtual microstructure

Purpose

To develop histology‐informed simulations of diffusion tensor cardiovascular magnetic resonance (DT‐CMR) for typical in‐vivo pulse sequences and determine their sensitivity to changes in extra‐cellular space (ECS) and other microstructural parameters.

Methods

We synthesised the DT‐CMR signal from Monte Carlo random walk simulations. The virtual tissue was based on porcine histology. The cells were thickened and then shrunk to modify ECS. We also created idealised geometries using cuboids in regular arrangement, matching the extra‐cellular volume fraction (ECV) of 16–40%. The simulated voxel size was 2.8 × 2.8 × 8.0 mm³ for pulse sequences covering short and long diffusion times: Stejskal–Tanner pulsed‐gradient spin echo, second‐order motion‐compensated spin echo, and stimulated echo acquisition mode (STEAM), with clinically available gradient strengths.

Results

The primary diffusion tensor eigenvalue increases linearly with ECV at a similar rate for all simulated geometries. Mean diffusivity (MD) varies linearly, too, but is higher for the substrates with more uniformly distributed ECS. Fractional anisotropy (FA) for the histology‐based geometry is higher than the idealised geometry with low sensitivity to ECV, except for the long mixing time of the STEAM sequence. Varying the intra‐cellular diffusivity (D_IC) results in large changes of MD and FA. Varying extra‐cellular diffusivity or using stronger gradients has minor effects on FA. Uncertainties of the primary eigenvector orientation are reduced using STEAM.

Conclusions

We found that the distribution of ECS has a measurable impact on DT‐CMR parameters. The observed sensitivity of MD and FA to ECV and D_IC has potentially interesting applications for interpreting in‐vivo DT‐CMR parameters.

Relationships between tissue microstructure and the diffusion tensor in simulated skeletal muscle

PURPOSE

To establish a series of relationships defining how muscle microstructure and diffusion tensor imaging (DTI) are related.

METHODS

The relationship among key microstructural features of skeletal muscle (fiber size, fibrosis, edema, and permeability) and the diffusion tensor were systematically simulated over physiologically relevant dimensions individually, and in combination, using a numerical simulation application. Stepwise multiple regression was used to identify which microstructural features of muscle significantly predict the diffusion tensor using single-echo and multi-echo DTI pulse sequences. Simulations were also performed in models with histology-informed geometry to investigate the relationship between fiber size and the diffusion tensor in models with real muscle geometry.

RESULTS

Fiber size is the strongest predictor of λ2, λ3, mean diffusivity, and fractional anisotropy in skeletal muscle, accounting for approximately 40% of the variance in the diffusion model when calculated with single-echo DTI. This increased to approximately 70% when diffusion measures were calculated from the short T2 component of the multi-echo DTI sequence. This nonlinear relationship begins to plateau in fibers with greater than 60-μm diameter.

CONCLUSIONS

As the normal fiber size of a human muscle fiber is 40 to 60 μm, this suggests that DTI is a sensitive tool to monitor muscle atrophy, but may be limited in measurements of muscle with larger fibers. Magn Reson Med 80:317-329, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Design and validation of diffusion MRI models of white matter

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the "biological accuracy" of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open questions and converge towards consensus.

Assessing the validity of the approximation of diffusion-weighted-MRI signals from crossing fascicles by sums of signals from single fascicles

PURPOSE

To assess the validity of the superposition approximation for crossing fascicles, i.e., the assumption that the total diffusion-weighted MRI signal is the sum of the signals arising from each fascicle independently, even when the fascicles intermingle in a voxel.

METHODS

Monte Carlo simulations were used to study the impact of the approximation on the diffusion-weighted MRI signal and to assess whether this approximate model allows microstructural features of interwoven fascicles to be accurately estimated, despite signal differences.

RESULTS

Small normalized signal differences were observed, typically 10-3-10-2. The use of the approximation had little impact on the estimation of the crossing angle, the axonal density index, and the radius index in clinically realistic scenarios wherein the acquisition noise was the predominant source of errors. In the absence of noise, large systematic errors due to the superposition approximation only persisted for the radius index, mainly driven by a low sensitivity of diffusion-weighted MRI signals to small radii in general.

CONCLUSION

The use of the superposition approximation rather than a model of interwoven fascicles does not adversely impact the estimation of microstructural features of interwoven fascicles in most current clinical settings. Magn Reson Med 79:2332-2345, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Fiber estimation and tractography in diffusion MRI: development of simulated brain images and comparison of multi-fiber analysis methods at clinical b-values

Advances in diffusion-weighted magnetic resonance imaging (DW-MRI) have led to many alternative diffusion sampling strategies and analysis methodologies. A common objective among methods is estimation of white matter fiber orientations within each voxel, as doing so permits in-vivo fiber-tracking and the ability to study brain connectivity and networks. Knowledge of how DW-MRI sampling schemes affect fiber estimation accuracy, tractography and the ability to recover complex white-matter pathways, differences between results due to choice of analysis method, and which method(s) perform optimally for specific data sets, all remain important problems, especially as tractography-based studies become common. In this work, we begin to address these concerns by developing sets of simulated diffusion-weighted brain images which we then use to quantitatively evaluate the performance of six DW-MRI analysis methods in terms of estimated fiber orientation accuracy, false-positive (spurious) and false-negative (missing) fiber rates, and fiber-tracking. The analysis methods studied are: 1) a two-compartment "ball and stick" model (BSM) (Behrens et al., 2003); 2) a non-negativity constrained spherical deconvolution (CSD) approach (Tournier et al., 2007); 3) analytical q-ball imaging (QBI) (Descoteaux et al., 2007); 4) q-ball imaging with Funk-Radon and Cosine Transform (FRACT) (Haldar and Leahy, 2013); 5) q-ball imaging within constant solid angle (CSA) (Aganj et al., 2010); and 6) a generalized Fourier transform approach known as generalized q-sampling imaging (GQI) (Yeh et al., 2010). We investigate these methods using 20, 30, 40, 60, 90 and 120 evenly distributed q-space samples of a single shell, and focus on a signal-to-noise ratio (SNR = 18) and diffusion-weighting (b = 1000 s/mm(2)) common to clinical studies. We found that the BSM and CSD methods consistently yielded the least fiber orientation error and simultaneously greatest detection rate of fibers. Fiber detection rate was found to be the most distinguishing characteristic between the methods, and a significant factor for complete recovery of tractography through complex white-matter pathways. For example, while all methods recovered similar tractography of prominent white matter pathways of limited fiber crossing, CSD (which had the highest fiber detection rate, especially for voxels containing three fibers) recovered the greatest number of fibers and largest fraction of correct tractography for complex three-fiber crossing regions. The synthetic data sets, ground-truth, and tools for quantitative evaluation are publically available on the NITRC website as the project "Simulated DW-MRI Brain Data Sets for Quantitative Evaluation of Estimated Fiber Orientations" at http://www.nitrc.org/projects/sim_dwi_brain.

Diffusion microscopist simulator: a general Monte Carlo simulation system for diffusion magnetic resonance imaging

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.

The future developments in gastrointestinal radiology

The last decade has witnessed great advances in abdominal imaging with technological developments and diagnostic improvements in CT, MRI and positron emission tomography-CT. Over the next decade, gastrointestinal imaging is set to rapidly evolve. Fluoroscopic techniques will be left behind and we will develop beyond simply anatomical imaging, embracing increasingly functional and quantitative techniques. Dose reduction and radiation-free modalities will take centre stage as imaging goes mobile, allowing clinicians at the bedside and remote subspecialty radiologists to review radiology from electronic devices. The authors discuss some of the key trends set to define the next decade in gastrointestinal radiology.

A finite difference method with periodic boundary conditions for simulations of diffusion-weighted magnetic resonance experiments in tissue

A new finite difference (FD) method for calculating the time evolution of complex transverse magnetization in diffusion-weighted magnetic resonance imaging and spectroscopy experiments is described that incorporates periodic boundary conditions. The new FD method relaxes restrictions on the allowable time step size employed in modeling which can significantly reduce computation time for simulations of large physical extent and allow for more complex, physiologically relevant, geometries to be simulated.

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR

The matrix formalism is a general framework for evaluating the diffusion NMR signal from restricted spins under generalised gradient waveforms. The original publications demonstrate the method for waveforms that vary only in magnitude and have fixed orientation. In this work, we extend the method to allow for variations in the direction of the gradient. This extension is necessary, for example to incorporate the effects of crusher gradients or imaging gradients in diffusion MRI, to characterise signal anisotropy in double pulsed field gradient (dPFG) experiments, or to optimise the gradient waveform for microstructure sensitivity. In particular, we show for primitive geometries (planes, cylinders and spheres), how to express the matrix operators at each time point of the gradient waveform as a linear combination of one or two fundamental matrices. Thus we obtain an efficient implementation with both the storage and CPU demands similar to the fixed-orientation case. Comparison with Monte Carlo simulations validates the implementation on three different sequences: dPFG, helical waveforms and the stimulated echo (STEAM) sequence.