arXiv subjects

Sune Nørhøj Jespersen

Publications and source records attributed to Sune Nørhøj Jespersen.

13 recordsLinked to original sources

arXiv2026

Beyond directions: Symmetry-aware rotation sets for triaxial diffusion encoding by geometric filter optimization

Purpose: To improve the accuracy of diffusion-weighted powder average signals for diffusion encoding with arbitrary b-tensors. Methods: We identify an intrinsic dihedral ($D_2$) symmetry of diffusion signals for arbitrary diffusion encoding, which defines their natural signal space (a quotient of 3D rotations). Based on this, we propose a method to generate optimal rotation sets that are applied to the diffusion-encoding gradient waveform to yield powder averages with maximal accuracy. The method, termed ``Geometric Filter Optimization'' (GFO), amounts to designing a sampling filter that is approximately flat over the relevant part of the associated frequency space. We characterize the filter properties and benchmark performance in terms of the accuracy and precision of powder averages and higher-order rotational invariants, including comparison with spherical designs and electrostatic-repulsion-based designs defined on the same space. Results: We found that GFO leads to marked improvements in precision and accuracy in powder averaging over diffusion encoding b-tensors, including axisymmetric and triaxial configurations. For higher-order rotational invariants, the performance was more nuanced, with GFO, electrostatic repulsion, and spherical designs exhibiting different trade-offs in bias and precision depending on $b$ and $N$. Conclusion: A fundamental $D_2$-symmetry of tensor-valued diffusion encoding was shown to constrain its rotational structure and guide the design of optimal rotation sets. This yielded GFO, which provides an efficient recipe for obtaining orientations for powder averaging of signals with axisymmetric and triaxial diffusion encoding. It places no additional demands on gradient system performance and can be used to shorten scan time.

physics.med-ph↗

arXiv2026

Predicting Mesoscopic Larmor Frequency Shifts in Ex Vivo Porcine Optic Nerve

Larmor frequency shifts in white matter (WM) vary with fiber orientation due to anisotropic microstructure. Since clinical voxels are significantly larger than these microscopic frequency variations, the measured signal represents a bulk average of local shifts. Accurate estimation of magnetic susceptibility therefore requires accounting for these underlying frequency distributions that exist below the imaging resolution. We evaluated whether Microstructure-informed Quantitative Susceptibility Mapping (μQSM) can predict orientation-dependent sub-voxel frequency shifts from orientationally dispersed hollow cylinders and spherical inclusions. Diffusion-weighted and multi-gradient-echo images were acquired from ex vivo pig optic nerves at multiple orientations relative to the main magnetic field using a 3T Siemens Connectom scanner. We also analyzed de-ironed optic nerves to try and separate the effects of myelin and iron on susceptibility. The estimated sub-voxel frequency shifts closely matched μQSM predictions, consistent with mesoscopic field perturbations generated by uniformly magnetized axons. De-ironing had minimal effect on the frequency shifts, indicating negligible iron contribution. μQSM accurately reproduces the orientation dependence of Larmor frequency shifts in optic nerve WM, providing new insight into their microstructural origin and supporting improved estimation of tissue magnetic susceptibility in Quantitative Susceptibility Mapping.

physics.med-ph↗

arXiv2026

Axonal microstructure and compartmentalization impact the orientation and time dependence of mesoscopic transverse relaxation

In biological tissue, MR transverse relaxation stems from mechanisms spanning multiple scales, from molecular dipole-dipole interactions to mesoscopic field variations driven by tissue microstructure. While mesoscopic relaxation reflects cellular organization, its dynamics in white matter, specifically its dependence on axonal orientation and echo time, remain less investigated. This study employs theoretical frameworks and Monte-Carlo simulations using 3D EM-based white matter (WM) geometries to investigate how compartmentalization and realistic morphology drive these effects. Specifically, we simulate intra-axonal relaxation driven by magnetic fields induced by realistic axonal myelin sheaths and intra-axonal spheres as a model of iron-containing mitochondria. Our results confirm that orientation dependence of mesoscopic relaxation in WM is detectable and agrees with experimental observations. The time-dependence aligns with 1-dimensional short-range structural disorder, but at clinical echo times, this signature may be masked by dominant molecular relaxation. This work moves beyond idealized models to aid the development of more specific biophysical models of mesoscopic relaxation to achieve better biomarkers for neurodegenerative disease.

physics.med-ph↗

arXiv2024

Predicting Mesoscopic Larmor Frequency Shifts in White Matter with Diffusion MRI -- A Monte-Carlo Study in axonal phantoms

This study aims to validate if MRI can measure anisotropic mesoscopic Larmor frequency shifts from white matter axonal microstructure relative to the B0 direction and if dMRI can estimate this anisotropy. Recent models describe how mesoscopic Larmor frequency shifts depend on induced magnetic fields by axons, described by an orientation distribution function. Using Monte-Carlo simulations of MRI signals in mesoscopic white matter axon substrates, we show MRI can estimate this mesoscopic frequency shift and dMRI can estimate its orientation dependence.

physics.med-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↗

arXiv2021

Evidence for microscopic kurtosis in neural tissue revealed by Correlation Tensor MRI

Purpose: The impact of microscopic diffusional kurtosis ($μK$) - arising from restricted diffusion and/or structural disorder - remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, Correlation Tensor MRI (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori assumptions. Here, we aimed to investigate $μK$ in in vivo rat brains and assess its impact on state-of-the-art methods ignoring $μK$. Methods: CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of CTI estimates from the improved protocol is assessed in simulations. The in vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of $μK$, anisotropic kurtosis, and isotropic kurtosis. Results: The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust $μK$ estimation, alongside Kaniso and Kiso metrics. Our CTI experiments revealed positive $μK$ both in white and grey matter of the rat brain in vivo; $μK$ is the dominant kurtosis source in healthy grey matter tissue. The non-negligible $μK$ substantially biases prior state-of-the-art analyses of Kiso and Kaniso. Conclusion: Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. $μK$ is non-negligible in vivo in healthy white and grey matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future experiments.

physics.bio-ph↗

arXiv2020

Correlation Tensor Magnetic Resonance Imaging

Diffusional Kurtosis Imaging (DKI) is a sensitive biomarker for microstructure in health and disease. However, DKI is not specific to any microstructural property since it may emerge from several different sources. Q-space trajectory encoding has been proposed for decoupling isotropic from anisotropic kurtosis. Still, this method assume that the system is comprised of multiple Gaussian diffusion components. Here, we develop a more general framework for resolving the underlying kurtosis sources. We introduce Correlation Tensor MRI (CTI) - an approach harnessing the versatility of double diffusion encoding (DDE) and capable of explicitly decoupling isotropic and anisotropic kurtosis components from intra-compartmental kurtosis effects arising from restricted diffusion. Additionally, CTI provides an index that is potentially sensitive to intra-compartmental kurtosis. The theoretical foundations of CTI, as well as the first proof-of-concept CTI ex vivo experiments in mouse brains at a field of 16.4T, are presented. We find that anisotropic and isotropic kurtosis can decouple microscopic anisotropy from substantial partial volume effects between tissue and free water. Our intra-compartmental kurtosis index exhibited positive values in both white and grey matter tissues. Simulations in different microenvironments show, however, that our current CTI protocol for estimating intra-compartmental kurtosis is limited by higher-order terms that were not considered in this study. CTI measurements were then extended to in vivo settings and used to map healthy rat brains at 9.4T. These in vivo CTI results were consistent with our ex vivo findings. Although future studies are still required to mitigate the higher-order effects on the intra-compartmental kurtosis index, results show that CTI's more general estimates of anisotropic and isotropic kurtosis contributions are already ripe for future studies.

physics.med-ph↗

arXiv2019

Diffusion Kurtosis Imaging maps neural damage in the EAE model of multiple sclerosis

Diffusion kurtosis imaging (DKI), is an imaging modality that yields novel disease biomarkers and in combination with nervous tissue modeling, provides access to microstructural parameters. Recently, DKI and subsequent estimation of microstructural model parameters has been used for assessment of tissue changes in neurodegenerative diseases and their animal models. In this study, mouse spinal cords from the experimental autoimmune encephalomyelitis (EAE) model of multiple sclerosis (MS) were investigated for the first time using DKI in combination with biophysical modeling to study the relationship between microstructural metrics and degree of animal dysfunction. Thirteen spinal cords were extracted from animals of variable disability and scanned in a high-field MRI scanner along with five control specimen. Diffusion weighted data were acquired together with high resolution T2* images. Diffusion data were fit to estimate diffusion and kurtosis tensors and white matter modeling parameters, which were all used for subsequent statistical analysis using a linear mixed effects model. T2* images were used to delineate focal demyelination/inflammation. Our results unveil a strong relationship between disability and measured microstructural parameters in normal appearing white matter and gray matter. The changes we found in biophysical modeling parameters and in particular in extra-axonal axial diffusivity were clearly different from previous studies employing other animal models of MS. In conclusion, our data suggest that DKI and microstructural modeling can provide a unique contrast capable of detecting EAE-specific changes correlating with clinical disability. These findings could close the gap between MRI findings and clinical presentation in patients and deepen our understanding of EAE and the MS mechanisms.

q-bio.QM↗

arXiv2019

Diffusion time dependence of microstructural parameters in fixed spinal cord

Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust as the clinical acquisitions typically probe a regime in which the associated 4th order cumulant expansion is adequate; however, its parameters are not microstructurally specific a priori. Given an appropriate biophysical model, its parameters may be connected to DKI parameters, but it was previously shown that at the DKI level, it still does not provide sufficient information to uniquely determine all model parameters. Earlier work has shown that by neglecting axonal dispersion, this parameter degeneracy reduces to the question of whether intra-axonal diffusivity is larger than or smaller than extra-axonal diffusivity. Here we develop a model of diffusion in spinal cord white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over an unprecedented diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings to predictions from effective medium theory.

physics.med-ph↗

arXiv2019

Effects of nongaussian diffusion on "isotropic diffusion measurements'': an ex-vivo microimaging and simulation study

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often not strictly fulfilled. The effects of nongaussian diffusion on single shot isotropic diffusion sequences were first considered in detail by de Swiet and Mitra in 1996. They showed theoretically that anisotropic compartments lead to anisotropic time dependence of the diffusion tensors, which causes the measured isotropic diffusivity to depend on gradient frame orientation. Here we show how such deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity. Second, we consider additional contributions to the apparent variance in isotropic diffusivity arising due to intracompartmental kurtosis. These will likewise depend on gradient frame orientation. We illustrate the potential importance of these confounds with analytical expressions, numerical simulations in simple model geometries, and microimaging experiments in fixed spinal cord using isotropic diffusion encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.

physics.bio-ph↗