Monte Carlo Simulations of Water Exchange Through Myelin Wraps: Implications for Diffusion MRI

Diffusion MRI with double diffusion encoding and variable mixing times disentangles water exchange from transient kurtosis

Double diffusion encoding (DDE) makes diffusion MRI sensitive to a wide range of microstructural features, and the acquired data can be analysed using different approaches. Correlation tensor imaging (CTI) uses DDE to resolve three components of the diffusional kurtosis: isotropic, anisotropic, and microscopic kurtosis. The microscopic kurtosis is estimated from the contrast between single diffusion encoding (SDE) and parallel DDE signals at the same b-value. Another approach is multi-Gaussian exchange (MGE), which employs DDE to measure exchange. Sensitivity to exchange is obtained by contrasting SDE and DDE signals at the same b-value. CTI and MGE exploit the same signal contrast to quantify microscopic kurtosis and exchange, and this study investigates the interplay between these two quantities. We perform Monte Carlo simulations in different geometries with varying levels of exchange and study the behaviour of the parameters from CTI and MGE. We conclude that microscopic kurtosis from CTI is sensitive to the exchange rate and that intercompartmental exchange and the transient kurtosis of individual compartments are distinct sources of microscopic kurtosis. In an attempt to disentangle these two sources, we propose a heuristic signal representation referred to as tMGE (MGE incorporating transient kurtosis) that accounts for both effects by exploiting the distinct signatures of exchange and transient kurtosis with varying mixing time: exchange causes a slow dependence of the signal on mixing time while transient kurtosis arguably has a much faster dependence. We find that applying tMGE to data acquired with multiple mixing times for both parallel and orthogonal DDE may enable estimation of the exchange rate as well as isotropic, anisotropic, and transient kurtosis.

Compartmental anisotropy of filtered exchange imaging (FEXI) in human white matter: What is happening in FEXI?

PURPOSE

To investigate the effects of compartmental anisotropy on filtered exchange imaging (FEXI) in white matter (WM).

THEORY AND METHODS

FEXI signals were measured using multiple combinations of diffusion filter and detection directions in five healthy volunteers. Additional filters, including a trace-weighted diffusion filter with trapezoidal gradients, a spherical b-tensor encoded diffusion filter, and a T2 filter, were tested with trace-weighted diffusion detection.

RESULTS

A large range of apparent exchange rates (AXR) and both positive and negative filter efficiencies (σ) were found depending on the mutual orientation of the filter and detection gradients relative to WM fiber orientation. The data demonstrated that the fast-diffusion compartment suppressed by diffusional filtering is not exclusively extra-cellular, but also intra-cellular. While not comprehensive, a simple two-compartment diffusion tensor model with water exchange was able to account qualitatively for the trends in positive and negative filtering efficiencies, while standard model imaging (SMI) without exchange could not. This two-compartment diffusion tensor model also demonstrated smaller AXR variances across subjects. When employing trace-weighted diffusion detection, AXR values were on the order of the R1 (=1/T1) of water at 3T for crossing fibers, while being less than R1 for parallel fibers.

CONCLUSION

Orientation-dependent AXR and σ values were observed when using multi-orientation filter and detection gradients in FEXI, indicating that WM FEXI models need to account for compartmental anisotropy. When using trace-weighted detection, AXR values were on the order of or less than R1, complicating the interpretation of FEXI results in WM in terms of biological exchange properties. These findings may contribute toward better understanding of FEXI results in WM.

Diffusion MRI with free gradient waveforms on a high-performance gradient system: Probing restriction and exchange in the human brain

The dependence of the diffusion MRI signal on the diffusion time carries signatures of restricted diffusion and exchange. Here we seek to highlight these signatures in the human brain by performing experiments using free gradient waveforms designed to be selectively sensitive to the two effects. We examine six healthy volunteers using both strong and ultra-strong gradients (80, 200 and 300 mT/m). In an experiment featuring a large set of 150 gradient waveforms with different sensitivities to restricted diffusion and exchange, our results reveal unique and different time-dependence signatures in grey and white matter. Grey matter was characterised by both restricted diffusion and exchange and white matter predominantly by restricted diffusion. Exchange in grey matter was at least twice as fast as in white matter, across all subjects and all gradient strengths. The cerebellar cortex featured relatively short exchange times (115 ms). Furthermore, we show that gradient waveforms with tailored designs can be used to map exchange in the human brain. We also assessed the feasibility of clinical applications of the method used in this work and found that the exchange-related contrast obtained with a 25-minute protocol at 300 mT/m was preserved in a 4-minute protocol at 300 mT/m and a 10-minute protocol at 80 mT/m. Our work underlines the utility of free waveforms for detecting time dependence signatures due to restricted diffusion and exchange in vivo, which may potentially serve as a tool for studying diseased tissue.

Monte Carlo simulation of water diffusion through cardiac tissue models

Monte Carlo diffusion simulations are commonly used to establish a reliable ground truth of tissue microstructure, including for the validation of diffusion-weighted MRI. However, selecting simulation parameters is challenging and affects validity and reproducibility. We conducted experiments to investigate critical conditions in Monte Carlo simulations, such as tissue representation complexity, simulated molecules, update duration, and compartment size. Results show significant changes in microstructure characteristics when parameters are altered, emphasizing the importance of careful control for a reliable ground truth.

A Method for In-Vivo Mapping of Axonal Diameter Distributions in the Human Brain Using Diffusion-Based Axonal Spectrum Imaging (AxSI)

In this paper we demonstrate a generalized and simplified pipeline called axonal spectrum imaging (AxSI) for in-vivo estimation of axonal characteristics in the human brain. Whole-brain estimation of the axon diameter, in-vivo and non-invasively, across all fiber systems will allow exploring uncharted aspects of brain structure and function relations with emphasis on connectivity and connectome analysis. While axon diameter mapping is important in and of itself, its correlation with conduction velocity will allow, for the first time, the explorations of information transfer mechanisms within the brain. We demonstrate various well-known aspects of axonal morphometry (e.g., the corpus callosum axon diameter variation) as well as other aspects that are less explored (e.g., axon diameter-based separation of the superior longitudinal fasciculus into segments). Moreover, we have created an MNI based mean axon diameter map over the entire brain for a large cohort of subjects providing the reference basis for future studies exploring relation between axon properties, its connectome representation, and other functional and behavioral aspects of the brain.

Metabolic activity diffusion imaging (MADI): I. Metabolic, cytometric modeling and simulations

Evidence mounts that the steady-state cellular water efflux (unidirectional) first-order rate constant (k_io [s^-1 ]) magnitude reflects the ongoing, cellular metabolic rate of the cytolemmal Na⁺ , K⁺ -ATPase (NKA), ^c MR_NKA (pmol [ATP consumed by NKA]/s/cell), perhaps biology's most vital enzyme. Optimal ¹ H₂ O MR k_io determinations require paramagnetic contrast agents (CAs) in model systems. However, results suggest that the homeostatic metabolic k_io biomarker magnitude in vivo is often too large to be reached with allowable or possible CA living tissue distributions. Thus, we seek a noninvasive (CA-free) method to determine k_io in vivo. Because membrane water permeability has long been considered important in tissue water diffusion, we turn to the well-known diffusion-weighted MRI (DWI) modality. To analyze the diffusion tensor magnitude, we use a parsimoniously primitive model featuring Monte Carlo simulations of water diffusion in virtual ensembles comprising water-filled and -immersed randomly sized/shaped contracted Voronoi cells. We find this requires two additional, cytometric properties: the mean cell volume (V [pL]) and the cell number density (ρ [cells/μL]), important biomarkers in their own right. We call this approach metabolic activity diffusion imaging (MADI). We simulate water molecule displacements and transverse MR signal decays covering the entirety of b-space from pure water (ρ = V = 0; k_io undefined; diffusion coefficient, D₀ ) to zero diffusion. The MADI model confirms that, in compartmented spaces with semipermeable boundaries, diffusion cannot be described as Gaussian: the nanoscopic D (D_n ) is diffusion time-dependent, a manifestation of the "diffusion dispersion". When the "well-mixed" (steady-state) condition is reached, diffusion becomes limited, mainly by the probabilities of (1) encountering (ρ, V), and (2) permeating (k_io ) cytoplasmic membranes, and less so by D_n magnitudes. Importantly, for spaces with large area/volume (A/V; claustrophobia) ratios, this can happen in less than a millisecond. The model matches literature experimental data well, with implications for DWI interpretations.

Altered White Matter Microstructure in Herpes Zoster and Postherpetic Neuralgia Determined by Automated Fiber Quantification

This study aimed to explore changes in the white matter microstructure in herpes zoster (HZ) and postherpetic neuralgia (PHN) patients and to estimate the correlation of these changes with clinical data. Diffusion tensor imaging (DTI) data were collected from 33 HZ patients, 32 PHN patients, and 35 well-matched healthy controls (HCs). Subsequently, these data were analyzed by automated fiber quantification (AFQ) to accurately locate alterations in the white matter microstructure. Compared with HCs, HZ and PHN patients both showed a wide range of changes in the diffusion properties of fiber tracts. HZ patients exhibited changes primarily in the left superior longitudinal fasciculus (SLF), whereas PHN patients predominantly exhibited changes in the left inferior fronto-occipital fasciculus. The bilateral SLF and the left corticospinal tract were altered in the PHN patients compared with HZ patients. In addition, PHN patients showed a trend toward more expansive white matter alterations compared with those observed in HZ patients; additionally, in PHN patients, changes in the left cingulum cingulate were significantly correlated with changes in emotion and the duration of disease. These findings may help to elucidate the transformation from HZ to PHN and provide new ideas regarding the reasons for intractable neuropathic pain in PHN.

Neurite Exchange Imaging (NEXI): A minimal model of diffusion in gray matter with inter-compartment water exchange

Biophysical models of diffusion in white matter have been center-stage over the past two decades and are essentially based on what is now commonly referred to as the "Standard Model" (SM) of non-exchanging anisotropic compartments with Gaussian diffusion. In this work, we focus on diffusion MRI in gray matter, which requires rethinking basic microstructure modeling blocks. In particular, at least three contributions beyond the SM need to be considered for gray matter: water exchange across the cell membrane - between neurites and the extracellular space; non-Gaussian diffusion along neuronal and glial processes - resulting from structural disorder; and signal contribution from soma. For the first contribution, we propose Neurite Exchange Imaging (NEXI) as an extension of the SM of diffusion, which builds on the anisotropic Kärger model of two exchanging compartments. Using datasets acquired at multiple diffusion weightings (b) and diffusion times (t) in the rat brain in vivo, we investigate the suitability of NEXI to describe the diffusion signal in the gray matter, compared to the other two possible contributions. Our results for the diffusion time window 20-45 ms show minimal diffusivity time-dependence and more pronounced kurtosis decay with time, which is well fit by the exchange model. Moreover, we observe lower signal for longer diffusion times at high b. In light of these observations, we identify exchange as the mechanism that best explains these signal signatures in both low-b and high-b regime, and thereby propose NEXI as the minimal model for gray matter microstructure mapping. We finally highlight multi-b multi-t acquisition protocols as being best suited to estimate NEXI model parameters reliably. Using this approach, we estimate the inter-compartment water exchange time to be 15 - 60 ms in the rat cortex and hippocampus in vivo, which is of the same order or shorter than the diffusion time in typical diffusion MRI acquisitions. This suggests water exchange as an essential component for interpreting diffusion MRI measurements in gray matter.

The direction-dependence of apparent water exchange rate in human white matter

Transmembrane water exchange is a potential biomarker in the diagnosis and understanding of cancers, brain disorders, and other diseases. Filter-exchange imaging (FEXI), a special case of diffusion exchange spectroscopy adapted for clinical applications, has the potential to reveal different physiological water exchange processes. However, it is still controversial whether modulating the diffusion encoding gradient direction can affect the apparent exchange rate (AXR) measurements of FEXI in white matter (WM) where water diffusion shows strong anisotropy. In this study, we explored the diffusion-encoding direction dependence of FEXI in human brain white matter by performing FEXI with 20 diffusion-encoding directions on a clinical 3T scanner in-vivo. The results show that the AXR values measured when the gradients are perpendicular to the fiber orientation (0.77 ± 0.13 s ^- 1, mean ± standard deviation of all the subjects) are significantly larger than the AXR estimates when the gradients are parallel to the fiber orientation (0.33 ± 0.14 s ^- 1, p < 0.001) in WM voxels with coherently-orientated fibers. In addition, no significant correlation is found between AXRs measured along these two directions, indicating that they are measuring different water exchange processes. What's more, only the perpendicular AXR rather than the parallel AXR shows dependence on axonal diameter, indicating that the perpendicular AXR might reflect transmembrane water exchange between intra-axonal and extra-cellular spaces. Further finite difference (FD) simulations having three water compartments (intra-axonal, intra-glial, and extra-cellular spaces) to mimic WM micro-environments also suggest that the perpendicular AXR is more sensitive to the axonal water transmembrane exchange than parallel AXR. Taken together, our results show that AXR measured along different directions could be utilized to probe different water exchange processes in WM.

Measuring compartmental T2-orientational dependence in human brain white matter using a tiltable RF coil and diffusion-T2 correlation MRI

The anisotropy of brain white matter microstructure manifests itself in orientational-dependence of various MRI contrasts, and can result in significant quantification biases if ignored. Understanding the origins of this orientation-dependence could enhance the interpretation of MRI signal changes in development, ageing and disease and ultimately improve clinical diagnosis. Using a novel experimental setup, this work studies the contributions of the intra- and extra-axonal water to the orientation-dependence of one of the most clinically-studied parameters, apparent transverse relaxation T2. Specifically, a tiltable receive coil is interfaced with an ultra-strong gradient MRI scanner to acquire multidimensional MRI data with an unprecedented range of acquisition parameters. Using this setup, compartmental T2 can be disentangled based on differences in diffusional-anisotropy, and its orientation-dependence further elucidated by re-orienting the head with respect to the main magnetic field B→0. A dependence of (compartmental) T2 on the fibre orientation w.r.t. B→0 was observed, and further quantified using characteristic representations for susceptibility- and magic angle effects. Across white matter, anisotropy effects were dominated by the extra-axonal water signal, while the intra-axonal water signal decay varied less with fibre-orientation. Moreover, the results suggest that the stronger extra-axonal T2 orientation-dependence is dominated by magnetic susceptibility effects (presumably from the myelin sheath) while the weaker intra-axonal T2 orientation-dependence may be driven by a combination of microstructural effects. Even though the current design of the tiltable coil only offers a modest range of angles, the results demonstrate an overall effect of tilt and serve as a proof-of-concept motivating further hardware development to facilitate experiments that explore orientational anisotropy. These observations have the potential to lead to white matter microstructural models with increased compartmental sensitivity to disease, and can have direct consequences for longitudinal and group-wise T2- and diffusion-MRI data analysis, where the effect of head-orientation in the scanner is commonly ignored.

Time dependence in diffusion MRI predicts tissue outcome in ischemic stroke patients

Purpose:

Reperfusion therapy enables effective treatment of ischemic stroke presenting within 4–6 hours. However, tissue progression from ischemia to infarction is variable, and some patients benefit from treatment up until 24 hours. Improved imaging techniques are needed to identify these patients. Here, it was hypothesized that time dependence in diffusion MRI may predict tissue outcome in ischemic stroke.

Methods:

Diffusion MRI data were acquired with multiple diffusion times in five non-reperfused patients at 2, 9, and 100 days after stroke onset. Maps of “rate of kurtosis change” (k), mean kurtosis, ADC, and fractional anisotropy were derived. The ADC maps defined lesions, normal-appearing tissue, and the lesion tissue that would either be infarcted or remain viable by day 100. Diffusion parameters were compared (1) between lesions and normal-appearing tissue, and (2) between lesion tissue that would be infarcted or remain viable.

Results:

Positive values of k were observed within stroke lesions on day 2 (P = .001) and on day 9 (P = .023), indicating diffusional exchange. On day 100, high ADC values indicated infarction of 50 ± 20% of the lesion volumes. Tissue infarction was predicted by high k values both on day 2 (P = .026) and on day 9 (P = .046), by low mean kurtosis values on day 2 (P = .043), and by low fractional anisotropy values on day 9 (P = .029), but not by low ADC values.

Conclusions:

Diffusion time dependence predicted tissue outcome in ischemic stroke more accurately than the ADC, and may be useful for predicting reperfusion benefit.

Machine learning based white matter models with permeability: An experimental study in cuprizone treated in-vivo mouse model of axonal demyelination

The intra-axonal water exchange time (τ_i), a parameter associated with axonal permeability, could be an important biomarker for understanding and treating demyelinating pathologies such as Multiple Sclerosis. Diffusion-Weighted MRI (DW-MRI) is sensitive to changes in permeability; however, the parameter has so far remained elusive due to the lack of general biophysical models that incorporate it. Machine learning based computational models can potentially be used to estimate such parameters. Recently, for the first time, a theoretical framework using a random forest (RF) regressor suggests that this is a promising new approach for permeability estimation. In this study, we adopt such an approach and for the first time experimentally investigate it for demyelinating pathologies through direct comparison with histology. We construct a computational model using Monte Carlo simulations and an RF regressor in order to learn a mapping between features derived from DW-MRI signals and ground truth microstructure parameters. We test our model in simulations, and find strong correlations between the predicted and ground truth parameters (intra-axonal volume fraction f: R² =0.99, τ_i: R² =0.84, intrinsic diffusivity d: R² =0.99). We then apply the model in-vivo, on a controlled cuprizone (CPZ) mouse model of demyelination, comparing the results from two cohorts of mice, CPZ (N=8) and healthy age-matched wild-type (WT, N=8). We find that the RF model estimates sensible microstructure parameters for both groups, matching values found in literature. Furthermore, we perform histology for both groups using electron microscopy (EM), measuring the thickness of the myelin sheath as a surrogate for exchange time. Histology results show that our RF model estimates are very strongly correlated with the EM measurements (ρ = 0.98 for f, ρ = 0.82 for τ_i). Finally, we find a statistically significant decrease in τ_i in all three regions of the corpus callosum (splenium/genu/body) of the CPZ cohort (<τ_i>=310ms/330ms/350ms) compared to the WT group (<τ_i>=370ms/370ms/380ms). This is in line with our expectations that τ_i is lower in regions where the myelin sheath is damaged, as axonal membranes become more permeable. Overall, these results demonstrate, for the first time experimentally and in vivo, that a computational model learned from simulations can reliably estimate microstructure parameters, including the axonal permeability .

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

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.