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Fractional anisotropy (FA), axial diffusivity (AD) and radial diffusivity (RD) are commonly used as MRI biomarkers of white matter microstructure in diffusion MRI studies of neurodevelopment, brain aging, and neurologic injury/disease. Some of the more frequent practices include performing voxel-wise or region-based analyses of these measures to cross-sectionally compare individuals or groups, longitudinally assess individuals or groups, and/or correlate with demographic, behavioral or clinical variables. However, it is now widely recognized that the majority of cerebral white matter voxels contain multiple fiber populations with different trajectories, which renders these metrics highly sensitive to the relative volume fractions of the various fiber populations, the microstructural integrity of each constituent fiber population, and the interaction between these factors. Many diffusion imaging experts are aware of these limitations and now generally avoid using FA, AD or RD (at least in isolation) to draw strong reverse inferences about white matter microstructure, but based on the continued application and interpretation of these metrics in the broader biomedical/neuroscience literature, it appears that this has perhaps not yet become common knowledge among diffusion imaging end-users. Therefore, this paper will briefly discuss the complex biophysical underpinnings of these measures in the context of crossing fibers, provide some intuitive “thought experiments” to highlight how conventional interpretations can lead to incorrect conclusions, and suggest that future studies refrain from using (over-interpreting) FA, AD and RD values as standalone biomarkers of cerebral white matter microstructure.

We collected MRI diffusion tensor imaging data from 80 younger (20–32 years) and 63 older (60–71 years) healthy adults. Tract-based spatial statistics (TBSS) analysis revealed that white matter integrity, as indicated by decreased fractional anisotropy (FA), was disrupted in numerous structures in older compared to younger adults. These regions displayed five distinct region-specific patterns of age-related differences in other diffusivity properties: (1) increases in both radial and mean diffusivity; (2) increases in radial diffusivity; (3) no differences in parameters other than FA; (4) a decrease in axial and an increase in radial diffusivity; and (5) a decrease in axial and mean diffusivity. These patterns suggest different biological underpinnings of age-related decline in FA, such as demyelination, Wallerian degeneration, gliosis, and severe fiber loss, and may represent stages in a cascade of age-related degeneration in white matter microstructure. This first simultaneous description of age-related differences in FA, mean, axial, and radial diffusivity requires histological and functional validation as well as analyses of intermediate age groups and longitudinal samples.

A spot periodic heating method is a highly accurate, non-contact method for the evaluation of anisotropy and relative thermophysical property distribution. However, accurately evaluating thermal diffusivity is difficult due to the influence of temperature wave reflection from the whole surface of the sample. This study proposes a method to derive thermal diffusivity using a parameter table based on heat transfer equations using the concept of optimum distance between heating-point and measurement point. This method considers finite sample size, sensitivity distribution of infrared ray detector, intensity distribution of heating laser and sample thickness. In these results, the obtained thermal diffusivity of pure copper corresponded well with previous literature values. In conclusion, this method is considered highly effective in evaluating the thermal diffusivity in the horizontal direction.

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot's equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts of the stochastic variations between various training realizations are also investigated. In the inverse case, we also study the effects of noisy measurements. Furthermore, we address the challenge of selecting the hyperparameters of the inverse model and illustrate how this challenge is linked to the hyperparameters selection performed for the forward one.

Local thermal nonequilibrium (LTNE) effects in heterogeneous media can affect subsurface temperature distributions, as well as the capacity of the heat transport model to solve the inverse problem of estimating groundwater fluxes. We present a synthetic coupled flow and heat transport numerical model with five scenarios to analyze the influence of subsurface hydraulic and thermal property variations on heat transport in heterogeneous streambed sediments, while also evaluating the role of LTNE effects in heat transport processes within heterogeneous streambed sediments and their impact on streambed fluxes estimation. Heterogeneous streambed sediments with varying sand‐gravel‐clay fractions are stochastically generated using a Markov Chain model. Synthetic streambed temperature‐time series are produced to estimate effective thermal diffusivity and thermal front velocity using a heat transport model based on homogeneous and local thermal equilibrium assumptions, and these estimates were compared to known values from numerical models of flow fields analogous to losing streams. Results show that neglecting thermal heterogeneity in streambed sediments leads to significant errors in streambed fluxes estimation, where the effective thermal diffusivity can be underestimated by about 40%, while the thermal front velocity can be overestimated by more than two times. In addition to the effects of streambed heterogeneity, LTNE effects further amplify these errors. Furthermore, the influences of streambed heterogeneity on LTNE effects are primarily influenced by flow velocity, with higher clay content reducing Darcian velocity and weakening LTNE effects.

Background Quantitative magnetic resonance imaging (QMRI) techniques of magnetization transfer ratio (MTR) and diffusion tensor imaging (DTI) provide microstructural information about the spinal cord. Objective Compare neurologic grades using the modified Frankel scale with MTR and DTI measurements in dogs with thoracolumbar intervertebral disk herniation (IVDH). Animals Fifty‐one dogs with thoracolumbar IVDH. Methods Prospective cohort study. Quantitative MRI measurements of the spinal cord were obtained at the region of compression. A linear regression generalized estimating equations model was used to compare QMRI measurements between different neurological grades after adjusting for age, weight, duration of clinical signs, and lesion location. Results Grade 5 (.79  ×  10−3 mm2/s [median], .43−.91 [range]) and axial (1.47 × 10−3 mm2/s, .58−1.8) diffusivity were lower compared to grades 2 (1.003, .68−1.36; P = .02 and 1.81 × 10−3 mm2/s, 1.36−2.12; P < .001, respectively) and 3 (1.07 × 10−3 mm2/s, .77−1.5; P = .04 and 1.92 × 10−3 mm2/s, 1.83−2.37;P < .001, respectively). Compared to dogs with acute myelopathy, chronic myelopathy was associated with higher mean (1.02 × 10−3 mm2/s, .77−1.36 vs. .83 × 10−3 mm2/s, .64−1.5; P = .03) and radial diffusivity (.75 × 10−3 mm2/s, .38−1.04 vs. .44 × 10−3 mm2/s, .22−1.01; P = .008) and lower MTR (46.76, 31.8−56.43 vs. 54.4, 45.2−62.27; P = .004) and fractional anisotropy (.58, .4−0.75 vs. .7, .46−.85; P = .02). Fractional anisotropy was lower in dogs with a T2‐weighted intramedullary hyperintensity compared to those without (.7, .45−.85 vs. .54, .4−.8; P = .01). Conclusion and Clinical Relevance Mean diffusivity and AD could serve as surrogates of severity of spinal cord injury and are complementary to the clinical exam in dogs with thoracolumbar IVDH.

This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D0), as well as a low (Dm) and a high (Dd) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity Dd will redistribute particles near the channel wall, while the diffusivity Dm will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity Dd, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity Dm, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.

Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f2-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.

In this paper, we prove the stability of the Couette flow for a 2D Navier–Stokes Boussinesq system without thermal diffusivity for the initial perturbation in Gevrey-1s, (1/3

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