AxonPacking: An Open-Source Software to Simulate Arrangements of Axons in White Matter

Exploiting gradient-echo frequency evolution: Probing white matter microstructure and extracting bulk susceptibility-induced frequency for quantitative susceptibility mapping

PURPOSE

This work is to investigate the microstructure-induced frequency shift in white matter (WM) with crossing fibers and to separate the microstructure-related frequency shift from the bulk susceptibility-induced frequency shift by model fitting the gradient-echo (GRE) frequency evolution for potentially more accurate quantitative susceptibility mapping (QSM).

METHODS

A hollow-cylinder fiber model (HCFM) with two fiber populations was developed to investigate GRE frequency evolutions in WM voxels with microstructural orientation dispersion. The simulated and experimentally measured TE-dependent local frequency shift was then fitted to a simplified frequency evolution model to obtain a microstructure-related frequency difference parameter (∆ f $$ \Delta f $$ ) and a TE-independent bulk susceptibility-induced frequency shift (C f $$ {C}_f $$ ). The obtainedC f $$ {C}_f $$ was then used for QSM reconstruction. Reconstruction performances were evaluated using a numerical head phantom and in vivo data and then compared to other multi-echo combination methods.

RESULTS

GRE frequency evolutions and∆ f $$ \Delta f $$ -based tissue parameters in both parallel and crossing fibers determined from our simulations were comparable to those observed in vivo. The TE-dependent frequency fitting method outperformed other multi-echo combination methods in estimatingC f $$ {C}_f $$ in simulations. The fitted∆ f $$ \Delta f $$ ,C f $$ {C}_f $$ , and QSM could be improved further by navigator-based B0 fluctuation correction.

CONCLUSION

A HCFM with two fiber populations can be used to characterize microstructure-induced frequency shifts in WM regions with crossing fibers. HCFM-based TE-dependent frequency fitting provides tissue contrast related to microstructure (∆ f $$ \Delta f $$ ) and in addition may help improve the quantification accuracy ofC f $$ {C}_f $$ and the corresponding QSM.

NRV: An open framework for in silico evaluation of peripheral nerve electrical stimulation strategies

Electrical stimulation of peripheral nerves has been used in various pathological contexts for rehabilitation purposes or to alleviate the symptoms of neuropathologies, thus improving the overall quality of life of patients. However, the development of novel therapeutic strategies is still a challenging issue requiring extensive in vivo experimental campaigns and technical development. To facilitate the design of new stimulation strategies, we provide a fully open source and self-contained software framework for the in silico evaluation of peripheral nerve electrical stimulation. Our modeling approach, developed in the popular and well-established Python language, uses an object-oriented paradigm to map the physiological and electrical context. The framework is designed to facilitate multi-scale analysis, from single fiber stimulation to whole multifascicular nerves. It also allows the simulation of complex strategies such as multiple electrode combinations and waveforms ranging from conventional biphasic pulses to more complex modulated kHz stimuli. In addition, we provide automated support for stimulation strategy optimization and handle the computational backend transparently to the user. Our framework has been extensively tested and validated with several existing results in the literature.

CACTUS: a computational framework for generating realistic white matter microstructure substrates

Monte-Carlo diffusion simulations are a powerful tool for validating tissue microstructure models by generating synthetic diffusion-weighted magnetic resonance images (DW-MRI) in controlled environments. This is fundamental for understanding the link between micrometre-scale tissue properties and DW-MRI signals measured at the millimetre-scale, optimizing acquisition protocols to target microstructure properties of interest, and exploring the robustness and accuracy of estimation methods. However, accurate simulations require substrates that reflect the main microstructural features of the studied tissue. To address this challenge, we introduce a novel computational workflow, CACTUS (Computational Axonal Configurator for Tailored and Ultradense Substrates), for generating synthetic white matter substrates. Our approach allows constructing substrates with higher packing density than existing methods, up to 95% intra-axonal volume fraction, and larger voxel sizes of up to 500μm3 with rich fibre complexity. CACTUS generates bundles with angular dispersion, bundle crossings, and variations along the fibres of their inner and outer radii and g-ratio. We achieve this by introducing a novel global cost function and a fibre radial growth approach that allows substrates to match predefined targeted characteristics and mirror those reported in histological studies. CACTUS improves the development of complex synthetic substrates, paving the way for future applications in microstructure imaging.

Impact of the acquisition protocol on the sensitivity to demyelination and axonal loss of clinically feasible DWI techniques: a simulation study

OBJECTIVE

To evaluate: (a) the specific effect that the demyelination and axonal loss have on the DW signal, and (b) the impact of the sequence parameters on the sensitivity to damage of two clinically feasible DWI techniques, i.e. DKI and NODDI.

METHODS

We performed a Monte Carlo simulation of water diffusion inside a novel synthetic model of white matter in the presence of axonal loss and demyelination, with three compartments with permeable boundaries between them. We compared DKI and NODDI in their ability to detect and assess the damage, using several acquisition protocols. We used the F test statistic as an index of the sensitivity for each DWI parameter to axonal loss and demyelination, respectively.

RESULTS

DKI parameters significantly changed with increasing axonal loss, but, in most cases, not with demyelination; all the NODDI parameters showed sensitivity to both the damage processes (at p < 0.01). However, the acquisition protocol strongly affected the sensitivity to damage of both the DKI and NODDI parameters and, especially for NODDI, the parameter absolute values also.

DISCUSSION

This work is expected to impact future choices for investigating white matter microstructure in focusing on specific stages of the disease, and for selecting the appropriate experimental framework to obtain optimal data quality given the purpose of the experiment.

Monte Carlo Simulator for Diffusion-weighted Imaging Sequences

We developed a Monte Carlo simulator for diffusion-weighted imaging sequences which displays the motion of water molecules and computes the dynamic phase dispersion due to the applied motion probing gradients. This simulator can be used to validate the analytical equations of diffusion models and understand their limitations due to their approximations. Here, we introduce the software and some specific use cases. The software can be downloaded from the following website: https://www.nirs.qst.go.jp/amr_diag.

Decoding the microstructural properties of white matter using realistic models

Multi-echo gradient echo (ME-GRE) magnetic resonance signal evolution in white matter has a strong dependence on the orientation of myelinated axons with respect to the main static field. Although analytical solutions have been able to predict some of the white matter (WM) signal behaviour of the hollow cylinder model, it has been shown that realistic models of WM offer a better description of the signal behaviour observed. In this work, we present a pipeline to (i) generate realistic 2D WM models with their microstructure based on real axon morphology with adjustable fiber volume fraction (FVF) and g-ratio. We (ii) simulate their interaction with the static magnetic field to be able to simulate their MR signal. For the first time, we (iii) demonstrate that realistic 2D WM models can be used to simulate a MR signal that provides a good approximation of the signal obtained from a real 3D WM model derived from electron microscopy. We then (iv) demonstrate in silico that 2D WM models can be used to predict microstructural parameters in a robust way if ME-GRE multi-orientation data is available and the main fiber orientation in each pixel is known using DTI. A deep learning network was trained and characterized in its ability to recover the desired microstructural parameters such as FVF, g-ratio, free and bound water transverse relaxation and magnetic susceptibility. Finally, the network was trained to recover these micro-structural parameters from an ex vivo dataset acquired in 9 orientations with respect to the magnetic field and 12 echo times. We demonstrate that this is an overdetermined problem and that as few as 3 orientations can already provide comparable results for some of the decoded metrics.

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.

Scan-rescan of axcaliber, macromolecular tissue volume, and g-ratio in the spinal cord

PURPOSE

Recent MRI techniques have been introduced that can extract microstructural information in the white matter, such as the density or macromolecular content. Translating quantitative MRI to the clinic raises many challenges in terms of acquisition strategy, modeling of the MRI signal, artifact corrections, and metric extraction (template registration and partial volume effects). In this work, we investigated the scan-rescan repeatability of several quantitative MRI techniques in the human spinal cord.

METHODS

AxCaliber metrics, macromolecular tissue volume, and the fiber g-ratio were estimated in the spinal cord of eight healthy subjects, scanned and rescanned the same day in two different sessions.

RESULTS

Scan-rescan repeatability deviation was 3% for all metrics, in average in the white matter of all subjects. Intraclass correlation coefficient was up to 0.9. A three-way analysis of variance showed significant effects of white matter pathway, laterality, and subject.

CONCLUSION

The present study suggests that quantitative MRI gives stable measurements of white matter microstructure in the spinal cord of healthy subjects. Our findings remain to be evaluated in diseased populations. Magn Reson Med 79:2759-2765, 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.