arXiv subjects

Valerij G. Kiselev

Publications and source records attributed to Valerij G. Kiselev.

15 recordsLinked to original sources

arXiv2026

What Does FEXI Measure in Neurons?

Exchange between tissue compartments is crucial for interpretation of diffusion MRI measurements in brain gray matter. However, reported values of exchange time are broadly dispersed, about two orders of magnitude. We analyze the measurement technique called Filtered Exchange Imaging (FEXI) using numerical solution of Bloch--Torrey equation in digitalized neurons downloaded from NeuroMorpho.org. The FEXI outcome, which is the recovery of diffusion coefficient in cells with impermeable membrane is multiexponential, with the time constants defined by the eigenvalues of Laplace operator. Fitting the commonly used exponential recovery function results in a strong dependence of the apparent exchange time on the involved mixing time interval and the adjustment or fixation of the equilibrium diffusivity. To obtain an estimate of membrane permeability, we reinterpret previously published data on preexchange lifetime in neuronal cell culture. It results in 0.005 micrometer/ms. The corresponding exchange time is approximately 140 ms. We conclude that essentially shorter exchange times are due to fast geometric exchange inside the ramified cells.

physics.bio-ph↗

arXiv2024

The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources

Magnetic susceptibility imaging may provide valuable information about chemical composition and microstructural organization of tissue. However, its estimation from the MRI signal phase is particularly difficult as it is sensitive to magnetic tissue properties ranging from the molecular to macroscopic scale. The MRI Larmor frequency shift measured in white matter (WM) tissue depends on the myelinated axons and other magnetizable sources such as iron-filled ferritin. We have previously derived the Larmor frequency shift arising from a dense media of cylinders with scalar susceptibility and arbitrary orientation dispersion. Here we extend our model to include microscopic WM susceptibility anisotropy as well as spherical inclusions with scalar susceptibility to represent subcellular structures, biologically stored iron etc. We validate our analytical results with computer simulations and investigate the feasibility of estimating susceptibility using simple iterative linear least squares without regularization or preconditioning. This is done in a digital brain phantom synthesized from diffusion MRI (dMRI) measurements of an ex vivo mouse brain at ultra-high field.

physics.med-ph↗

arXiv2023

Incorporating the effect of white matter microstructure in the estimation of magnetic susceptibility in ex-vivo mouse brain

Accurate estimation of microscopic magnetic field variations induced in biological tissue can be valuable for mapping tissue composition in health and disease. Here, we present an extension to Quantitative susceptibility mapping (QSM) to account for local white matter (WM) magnetic microstructure by using our previously presented model for solid cylinders with arbitrary orientations to describe axons in terms of concentric cylinders. Through computer simulations, we find that our model improves susceptibility estimation compared to QSM, and Susceptibility Tensor Imaging (STI) are substantially biased by the unaccounted-for structural anisotropy due to the mesoscopic frequency contribution, indicating the observed STI tensor might not represent susceptibility anisotropy as expected. Experiments in mouse brains acquired at ultrahigh field shows the mesoscopic contribution due to WM microstructure to be substantial. This in turn changed estimated susceptibility values up to 25% root-mean-squared-difference in WM compared to standard QSM. Our work underscores how microstructural field effects impact susceptibility estimates, and should not be neglected when imaging anisotropic tissue such as brain WM.

physics.med-ph↗

arXiv2022

To mask or not to mask? Investigating the impact of accounting for spatial frequency distributions and susceptibility sources on QSM quality

Estimating magnetic susceptibility using MRI depends on inverting a forward relationship between the susceptibility and measured Larmor frequency. However, an often-overlooked constraint in susceptibility fitting is that the Larmor frequency is only measured inside the sample, and after background field removal, susceptibility sources should only reside inside the same sample. Here we test the impact of accounting for such effects in susceptibility fitting and demonstrate that such effects should not be ignored.

physics.med-ph↗

arXiv2022

Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution

We present a theoretical framework for the NMR and MRI measured Larmor frequency in media with magnetized microstructure using the mesoscopic Lorentz sphere and the principle of coarse graining. We obtain an analytical expression for infinite cylinders with arbitrary orientation dispersion and show how it depends on the fiber orientation distribution, measurable using diffusion MRI. Through simulations, we scrutinize the framework including the effect of the shape and size of the Lorentz cavity and validate our result for cylinders.

physics.med-ph↗

arXiv2022

What Does FEXI Measure?

Filter-exchange imaging (FEXI) has already been utilized in several biomedical studies for evaluating the permeability of cell membranes. The method relies on suppressing the extracellular signal using strong diffusion weighting (the mobility filter causing a reduction in the overall diffusivity) and monitoring the subsequent diffusivity recovery. Using Monte Carlo (MC) simulations, we demonstrate that FEXI is not uniquely sensitive to the transcytolemmal exchange but also to the geometry of involved compartments: Complicated geometry offers locations where spins remain unaffected by the mobility filter; moving to other locations afterward, such spins contribute to the diffusivity recovery without actually permeating any membrane. This exchange mechanism challenges the interpretation of FEXI in complex media such as brain gray matter and opens large room for investigation towards crystallizing the genuine membrane permeation and characterizing the compartment geometry.

physics.med-ph↗

arXiv2020

Microstructure with Diffusion MRI: What Scale We Are Sensitive to?

Diffusion-weighted MRI is the forerunner of the rapidly developed microstructural MRI aimed at in vivo evaluation of the cellular tissue architecture. This brief review focuses on the spatiotemporal scales of the microstructure that are accessible using different diffusion MRI techniques and the need to weight the measurability against the interpretability of results. Diffusion phenomena and models are first classified in two-dimensional space (the q-t-plane) of the measurement with narrow gradient pulses. Three-dimensional parameter space of the Stejskal--Tanner diffusion weighting adds more phenomena to this collection. Modern measurement techniques with larger number of parameters are briefly discussed under the overarching idea of diffusion weighting matching the geometry of the targeted cell species.

physics.med-ph↗

arXiv2018

Observation of magnetic structural universality using transverse NMR relaxation

Transverse NMR relaxation from spins diffusing through a random magnetic medium is sensitive to its structure on a mesoscopic scale. In particular, this results in the time-dependent relaxation rate. We show analytically and numerically that this rate approaches the long-time limit in a power-law fashion, with the exponent reflecting the disorder class of mesoscopic magnetic structure. The spectral line shape acquires a corresponding non-analytic power law singularity at zero frequency. We experimentally detect a change in the dynamical exponent as a result of the transition into a maximally random jammed state characterized by hyperuniform correlations.

cond-mat.soft↗

arXiv2018

A Unique Analytical Solution of the White Matter Standard Model using Linear and Planar Encodings

Diffusion-weighted magnetic resonance imaging in brain white matter probes tissue microstructure and allows for the estimation of compartmental diffusion parameters. Recently, it became apparent that traditional single-direction diffusion encodings are not fully sufficient to resolve the white matter compartmental diffusivities. Multiple diffusion encodings have been suggested to make the problem less ambiguous, however, it still remained unclear whether such protocols would completely solve the problem. Here, we constructively prove that a combination of linear and planar diffusion encodings is enough to determine the parameters of the three compartment white matter model.

physics.bio-ph↗

arXiv2018

Larmor Frequency Depends on Structural Anisotropy in Magnetically Heterogeneous Media

Purpose: To investigate the effect of anisotropic magnetic microstructure on the measurable Larmor frequency offset in media with heterogeneous magnetic susceptibility. Specific objectives were (i) validation of recently developed theory for the case of fast diffusion and (ii) investigation of the transition between the regimes of fast and slow diffusion. Methods: Monte Carlo simulations in synthetic media. Results: Simulations demonstrate a perfect agreement with the previously developed theory for fast diffusion. Beyond this regime, the frequency offset shows a pronounced dependence on the medium microarchitecture and the diffusivity of NMR-reporting spins in relation to the magnitude of the susceptibility-induced magnetic field. Conclusion: While the effect of myelin in brain white matter is commonly treated assuming efficient diffusion narrowing, this regime does not hold for larger cells or higher magnetic susceptibility. In such a case, the effect essentially deviates from the prediction based on the assumption of diffusion narrowing.

cond-mat.soft↗

arXiv2018

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along the three major avenues. The first avenue focusses on the transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that studying the transient effects has the potential to quantify the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, the degree of neuronal beading, and compartment sizes. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple non-exchanging anisotropic Gaussian components. Here the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on the future directions which can open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

physics.bio-ph↗

arXiv2018

Larmor Frequency in Heterogeneous Media

The Larmor frequency shift is found in porous media consisting of NMR-reporting fluid filling a connected pore within an NMR-invisible matrix for the case of fast diffusion in the fluid. The matrix material has a distinct location-independent anisotropic magnetic susceptibility tensor that induces a heterogeneous microscopic magnetic field when exposed to the strong main field of an NMR device. Aside from the connectivity of the pore, the matrix geometry is arbitrary.

cond-mat.soft↗

arXiv2017

Intra-axonal Diffusivity in Brain White Matter

Biophysical modeling is the mediator of evaluating the cellular structure of biological tissues using diffusion-weighted MRI. It is however the bottleneck of microstructural MRI. Beyond the complexity of diffusion, the current development is hindered by the fact that biophysical models heavily rely on diffusion-specific properties of diverse cellular compartments that are still unknown and must be measured in vivo. Obtaining such parameters by straightforward fitting is hindered by the degenerated landscape of the likelihood functions, in particular, the signal obtained for multiple diffusion directions and moderate diffusion weighting strength is not enough to estimate these parameters: different parameter constellations explain the signal equally well. The aim of this study is to measure the central parameter of white matter models, namely the intra-axonal water diffusivity in the normal human brain. Proper estimation of this parameter is complicated due to (i) the presence of both intra- and extra-axonal water compartments and (ii) the orientation dispersion of axons. Our measurement involves an efficient suppression of extra-axonal space and all cellular processes oriented outside a narrow cone around the principal fiber direction. This is achieved using a planar water mobility filter -- a strong diffusion weighting that suppresses signal from all molecules that are mobile in the plane transverse to the fiber bundle. Following the planar filter, the diffusivity in the remaining compartment is measured using linear and isotropic weighting. We find the specifically averaged intra-axonal diffusivity $D_0 = 2.25\pm 0.03{\,\rm μm^2/ms}$ for the timing of the applied gradients. Extrapolation to the infinite diffusion time gives $D_\infty \approx 2.0{\,\rm μm^2/ms}$. This result imposes a strong limitation on the parameter selection for biophysical modeling of diffusion-weighted MRI.

physics.bio-ph↗

arXiv2011

Surface-to-volume ratio with oscillating gradients

Restrictions to diffusion result in the dispersion of the bulk diffusion coefficient. We derive the exact universal high-frequency behavior of the diffusion coefficient in terms of the surface-to-volume ratio of the restrictions. This frequency dependence can be applied to quantify structure of complex samples with NMR using oscillating field gradients and static-gradient CPMG. We also demonstrate the inter-relations between different equivalent diffusion metrics, and describe how to calculate the effect of restrictions for arbitrary gradient waveforms.

cond-mat.soft↗

arXiv2003

Transverse NMR relaxation as a probe of mesoscopic structure

Transverse NMR relaxation in a macroscopic sample is shown to be extremely sensitive to the structure of mesoscopic magnetic susceptibility variations. Such a sensitivity is proposed as a novel kind of contrast in the NMR measurements. For suspensions of arbitrary shaped paramagnetic objects, the transverse relaxation is found in the case of a small dephasing effect of an individual object. Strong relaxation rate dependence on the objects' shape agrees with experiments on whole blood. Demonstrated structure sensitivity is a generic effect that arises in NMR relaxation in porous media, biological systems, as well as in kinetics of diffusion limited reactions.

cond-mat.soft↗