Figure 3: Contrast and goodness of fit for different combinations of restriction and exchange. Panel (a) shows that the proposed model describes that data well in all simulated cases. (b) Exchange rate and cell size estimates are in good agreement with simulation. (c) Changes in exchange rate for a fixed size do not erroneously manifest in our model as a change in size. This demonstrates the independent contributions of restriction and exchange to the signal as captured by our model.

Figure 4: Demonstration of the robustness of the developed theory to ultrahigh b-values and long encoding times. Panel (a) shows a good agreement between model and simulation for all considered b-values. Panels (b) and (c) show that the theory produces stable estimates of size and exchange over the entire range of simulates b-values and encoding times.

Figure 1. Illustration of the inversion-free inference. Although the model is not invertible (each oval in parameter space (left) corresponds to a single point in measurement space (right)) we can still infer the true underlying parameter change by comparing actual change in measurements (black arrow) to the expected change as a result of particular changes in parameters (red and green arrows).

Figure 5. A) Posterior probability maps P(s|y, Δy) of change in the parameters of NODDI for the WMH dataset. The maps show that change in s_ex can explain the differences between WMH and normal tissue in deep white matter. On the other hand, the null model explains the data in periventricular WMHs. The rest of the parameters did not explain differences between NAWM and WMH. B) Parcellation of the WMHs based on the best model that can explain the change. C) Estimated amount of change in s_ex, which shows the amount of change is higher in deep white matter.

Fig 2. Both somas and neurites contribute to mean kurtosis in the cerebral cortex and total kurtosis as well as K_sc,v, K_nc,v are sensitive to diffusion time. Both soma K_sc,v=(1-f_ec)f_isK_sc, (green lines) and neurite K_nc,v=(1-f_ec)(1-f_is)K_nc, (blue lines) contribute to total intracellular kurtosis K across diffusion times and various soma volume fractions. As demonstrated by the vertical purple dashed lines, K_sc,v+K_nc,v=K as expected for 25ms in the case f_ec=0.

Fig 4. Cortical mean kurtosis(MK) is sensitive to diffusion time in in-vivo data. Left: Significant total MK change across relevant diffusion times 16-31ms for both subjects. Right: Bar plot for MK values in ROIs chosen for the frontal, temporal, thalamus also quantitatively shown significant MK drop.

Figure 3: Simulated ihMTR(T_1D) curves with various Δt values for (a, b) WM and GM respectively, using the single-T_1D model. The 2% line represents the detectability threshold, arbitrarily chosen. (c, d) ihMTR(T_1D) simulated for WM and GM, using the bi-T_1D model. The long T_1D component was fixed at 6.0 ms for WM and 5.8 ms for GM, and the short component was varied in the [10 µs; 1 ms] range. (e) Experimental ihMTR templates corresponding to different levels about the bregma.

Figure 4: ihMTR(T_1D) curves corresponding to the subtractions between the non-filtered and the filtered configurations for (a) WM and (b) GM. Only CM-Δt_0.8 was able to isolate a detectable signal within a finite range of T_1D values (100 µs - 1 ms). (c) Experimental subtracted ihMTR maps template at different bregma levels.

Simulated CA flow in the vascular system after bolus injection. The flow patterns exhibit a natural behaviour with a flow from the arterial network roots feeding the whole vasculature, spreading to the capillaries and a washout through the veins. The images were captured at 6, 8, 10, 15, 20, 25, 35, 50, 70 and 100 second respectively (from left to right).

Plasma flow (PF) estimation results using four tracer kinetic models in 11 ROIs. The MS model is systematically underestimating PF, but generate the best estimation among the four models in terms of absolute values. The remaining models are, in general, overestimating PF and generate close to identical values, except for ROI 2. This reveals that the 2-compartment models are over-parameterized and not suited for estimations in our CA flow phantom. The proposed flow model only accounts for blood circulation in the intravascular structures.

Figure 2: Representative axial slices of T₁ (upper row) and MPF (lower row) maps from VFA protocols A to E.

Figure 1: Simulated difference (ΔT₁) between input T₁ (1000 ms) and estimated T₁ by the VFA method as a function of the pulse width for an SPGR sequence without MT effects (orange) or perfect spoiling (yellow), SPGR with MT and realistic spoiling (blue), and SPGR with CSMT pulses with MT and realistic spoiling at reference FA of 30° (purple) and 90° (green). Simulated bias related to protocols A to E are reported. SPGR-CSMT estimations were performed with a pulse duration superior to 1-ms as spectral overlapping was found suitably limited to not disrupt the on-resonance component.

Figure 3: Representative slices of MWF maps resulting from parameter inference using DECAES, MLE, and CVAE. Both CVAE and MLE are able to produce high quality MWF maps for all datasets, despite being trained only on simulated data. In dataset #3, DECAES fails to properly estimate the MWF when using the default refocusing control angle. This can be manually corrected (adjacent), but no such issue occurs for CVAE or MLE which estimate the refocusing control angle directly.

Table 2: Mean absolute error values over inferred $$$\hat{\theta}$$$ for each method. CVAE ($$$n$$$) indicates that $$$\hat{\theta}$$$ is an average over $$$n$$$ samples $$$\hat{\theta}\sim\hat{P}(\theta\,|\,\hat{Y})$$$ from the approximate CVAE posterior $$$\hat{P}$$$.

Figure 4: The trend of the effective MR radius r [μm] along the tract (posterior to anterior or inferior to superior) for each individual measurements (5 subjects and 2 repetitions) are shown in shaded lines. In addition, we show the average (solid) and 95% confidence intervals (dashed).

Figure 2: (top) The distribution of MR axon radii [μm]. (bottom) The average MR axon radii for each individual subject (markers) is shown for all scan scan sessions.

Figure 1: (a-c) show the mean, normalized $$$B_1^+$$$ ($$$nB_1^+$$$ ) map of all 373 subjects in MNI space in axial, sagittal and coronal views. Note that the scale is normalized by the nominal $$$B_1^+$$$ field strength. Images (d-f) show the coefficient of variation (CoV) map in axial, sagittal and coronal views calculated from all 373 subjects.

Figure 2: Mean normalized $$$B_1^+$$$ calculated bilaterally for several regions of interest in MNI space. Frontal regions tend to have smaller $$$B_1^+$$$, while central regions have larger $$$B_1^+$$$. The central mark on each box represents the median and the left and right edges represent the 25th and 75th percentiles, respectively. Maximum and minimum, excluding outliers, are marked by the whiskers with all data points scattered across the boxes.

Figure 1: The relative Wilcoxon rank-sum test statistics that were computed to compare a) SC degree, b) SC degree, and c) SC-FC coupling between impaired vs not-impaired people with MS. Higher relative statistic value indicates that the variable in this region was greater in the impaired people with MS as compared to not-impaired people with MS.

Figure 2: The prediction accuracy of the models that included a) SC degree, b) FC degree, c) concatenation of SC and FC degree, and d) SC-FC coupling in classifying people with MS by impairment level. * indicates significant differences in AUC, corrected p < 0.05.

Figure 2: The synthesized GE spectra at the three different echo times along with the fits for the four different basis sets. The synthesized spectra are given in black, the fit in red and the residual in grey. Perfect fits can be observed with the GE basis, as expected, since these particular spectra were synthesized from the GE basis, while non-perfect fits were obtained with the other three basis sets. Similar results were obtained for the synthesized Philips and Siemens spectra (results not shown).

Figure 1: The synthesized spectra for TE = 30 ms, A, TE = 80 ms, B, and TE = 144 ms, C, across the three different vendor implementations of PRESS with blue depicting the Siemens implementation, red depicting the GE implementation and black depicting the Philips implementation. Spectra have been normalized to account for differences in voxel profile due to different pulses (i.e., different transition widths).

Fig. 2: (Top) Three-plane localization of the volume-of-interest (VOI) in the brain phantom. The VOI size was 10.5cm × 10.5cm × 7.5cm and the field-of-view (FOV) for spectroscopic imaging was 24cm × 24cm × 12cm along the left-to-right (L-R), anterior-to-posterior (A-P) and foot-to-head (F-H) directions, respectively. Sixteen voxels (red square) within the VOI were quantified. (Bottom) Axial NAA maps acquired along the F-H dimension within the FOV. Signal from five slices was measurable within the VOI, which had an extent of 7.5 cm along F-H.

Fig. 3: Multi-voxel contour plots of COSY spectra from the central slice of the brain phantom. Sixteen voxels within a 4 x 4 region (red square) inside the volume-of-interest (VOI) were quantified using peak integration to compute metabolite ratios for the reproducibility analysis.

(A) Distribution of the GABA+/tCr. Boxplot, smoothed distribution, and mean +- SD for all MM3co models (color-coded) and knot spacings. The coefficient of variation (SD/mean x 100) is depicted in the second row. (B) Summary of the CV analysis with the five key findings.

A) Co-edited MM3co model implementations – Overview of the six model implementations based on the 3 ppm co-edited MM basis function MM3co (B) Combinations of modeling strategies – Overview of the possible combinations of fit range, spline knot spacing ,and MM3co model.

Figure 4: The true CRLBs (red) and estimated CRLBs (black) divided by the standard deviations calculated through MC simulations for the estimated amplitudes for the 18 metabolites and the macromolecules signal across 5 different noise factors (NF = 1 to 16) in the case where the model properly characterizes the data. The circles, squares and stars represent Gb = 3 Hz², 8 Hz², and 20 Hz², respectively. The breakdown SNR is reached when the true CRLB divided by standard deviation (red) is greater than 1. Similar results were obtained for the other four estimated parameters.

Figure 5: The true CRLBs (red) and estimated CRLBs (black) divided by the standard deviations calculated through MC simulations for the estimated amplitudes for the 18 metabolites and the macromolecules signal across 5 different noise factors (NF 1 to 16) in the case where the model does not properly characterize the data. The circles, squares and stars represent Gb = 3 Hz², 8 Hz², and 20 Hz², respectively. The breakdown SNR is reached when the true CRLB/SD (red) is consistently greater than 1. Similar results were obtained for the other four estimated parameters.

Table 1: The standard deviation and CRLB for the 18 measured metabolites and macromolecules (MM) across the three different pipelines. Note that for no preprocessing the CRLB is an excellent proxy for standard deviation for all metabolites, while there is an artificial reduction of CRLBs for the two preprocessing steps. Furthermore, the exponential line broadening results in a reduction in precision on most metabolites. Note that these CRLBs are in the same units of standard deviation (i.e., au), it is not relative CRLBs (%) as is typically presented in MRS.

Figure 4: The effect cutting/zero-filling, A, and exponential linebroadening, B, has on the autocorrelation function of a simulated white Gaussian noise spectrum. In both cases as the effect of the processing steps is increased the autocorrelation of the noise spectrum deviates further from its assumed shape of $$$\delta(f)$$$. Cut/zero-fill factor = 2/4/8 means that the entire time domain signal except for the first half/quarter/eighth has been artificially set to zero.

ComBat Harmonization: Box plots illustrating the means and significance with * or p-values (A) before harmonization and (B) after harmonization in all 4 sites, for (i) tNAA (ii) tCr (iii) Glx; (C) Visualization of Site effects that are removed by ComBat.

(A) Voxel placement of PCG within the brain (B) LCModel output showing the processed spectrum in one subject at SITE 1. The selected scan passed all the manual QA measures and had an FWHM of 8 after pre-processing, the lowest in our dataset.

SNR maps for area-under-the-curve (AUC) lactate images (obtained by summing images over all 20 time points) after applying k_PL error mask. Both denoising methods (c, d) recover more voxels than the artificially noise-added data (b) and are comparable to the originally acquired data (a). The GLHOSVD-denoised SNR map better agrees with the originally acquired data.

Representative slices of (a) acquired, (b) noise-added lactate signal. (c) and (d) show the denoised images after applying TD and GLHOSVD to the noise-added images from (b).

Figure 1: The factor graph of the proposed nonlinear AMP framework for T₂* mapping, the circle represents the variable node, and the black square represents the factor node.

Figure 3: Sampling rate = 10%. The recovered T₂* map, proton density and their corresponding relative error images using different approaches.

Figure 2. The parameter maps obtained all methods with SR=16.47$$$\%$$$, 25.00$$$\%$$$ and 33.15$$$\%$$$.

Figure 1. The reconstruction results of all comparison methods at TSL=1ms and TSL= 80ms with SR= 25.00$$$\%$$$.

Figure 2. Discrimination of textures 1 and 2 on scanner A. The plot shows the number of times a feature is able to discriminate texture 1 and 2 if extracted from original and filtered images acquired on scanner A, as a function on the VOI size. Due to the selection of features with ICC>0.9, not all the features were extracted from all the available image types (10 in total: original + 9 filtered images), so the maximum count a feature could reach is indicated next to the feature name on y axis.

Figure 1. Identified VOIs and textures. Three phantom inserts were chosen as representative of three textures, from a finer texture (1) to a coarser one (3), through a medium texture (2). The volumes of the selected VOIs were: 29.8 cm³ (red), 20.7 cm³ (green), 13.3 cm³ (blue), 7.4 cm³ (yellow), 3.3 cm³ (pink), and 0.8 cm³ (cyan).

Figure 1: Flow chart describing the “lactate-bSSFP” and “GRE-all” experiments. The novelty in this work is the bSSFP rate constant fitting (green square).

Figure 4: For all three types of in vivo data, an example of a lactate image acquired in the “lactate-bSSFP” experiment and the corresponding localizers. The kidney ROI for healthy rats and the tumor ROI for mouse prostate and human studies are outlined in blue. The signal from the ROI was averaged to get the time courses. The plots show “GRE-all” time courses fit using the GRE fitting and the “lactate-bSSFP” experiment time courses fit with the bSSFP fitting.

Figure 1. Pulse sequence used to produce flow-compensated (dashed line) and non-flow-compensated (solid line) diffusion encoding. The delays marked in red and blue were increased/decreased to vary the encoding time (T). The sum of the red and blue delays was kept constant to achieve a fixed echo time

Figure 4. Signal vs. b-value for different encoding times. The signal was averaged over voxels where assuming the ballistic regime provided a better fit to data than assuming the diffusive regime, using data from the shortest encoding time (T = 25 ms). The rationale behind this is that only these voxels were assumed to possibly show an encoding-time dependence, given that other voxels already were in the diffusive regime

Figure 1. Intracellular and extracellular compartment models.

Table 1. Mean [STD] of Biophysical Parameters on a Slab from the Left Ventricle Wall. The 𝜶₂ and 𝜶₃ are the dispersion about the primary eigenvector in the sheetlet plane and sheetlet-normal plane. Reported physiological range from literature for intracellular, extracellular and vessels volume fractions are 65.0±3.6, 31.2±5.8, and 7.7±2.2 percent ⁸. Myocyte radii along the short and long axes are 6.0±0.7 and 15.3±1.0 𝜇m ⁷. Assuming a circular cross-section, the radius is 9.5±0.5 𝜇m ⁷.

Figure 2. Diffusion parameter maps based on D, α_QDI, α_T-FROC, and τ at different TM values in row a), b), c), and d), respectively.

Figure 1. A diffusion phase diagram with respect to temporal fractional derivative α, and spatial fractional derivative β. Two special cases (β = 2, and 2α = β) in this study were marked with dash lines. Note that the circled point corresponds to Gaussian diffusion.

Figure 1: Three-site model used in the kinetic model. The model considers unidirectional conversion of hyperpolarized substrate [1-13C]aKG to either [1-13C] 2HG or [1-13C] glutamate.

Figure 3: Fits for dataset 1 using the overlapped fitting method. Experimentally measured substrate (A), measured product signal (B), and computed fits (C, D) are shown. For the cell lysate data, separate 2HG measurement (B) was possible. A larger amount of 2HG was detected when C5aKG+2HG was used as input (C) than the case when C5aKG alone (D) was inputted in the model. Fits for C5aKG (red) and 2HG (yellow) are derived for the best summed fit (purple) w.r.t the measured input signal (blue).

Figure 3. Comparison of diffusivity and kurtosis estimated from (a) the sub-diffusion and (b) DKI models. Top row: axial view; bottom row: mid-sagittal view. $$$D^*$$$ and $$$K^*$$$ have been computed based on sub-diffusion model parameters $$$D_{SUB}$$$ and $$$\beta$$$; $$$D_{DKI}$$$ and $$$K_{DKI}$$$ have been estimated by fitting the standard DKI model to the data.

Figure 2. Link between sub-diffusion and DKI models: (a) plot of the natural logarithm of the sub-diffusion model and its approximations. Mono-exponential (MONO) and DKI are the first- and second-order approximations of the sub-diffusion model, respectively; (b) relationship between kurtosis $$$K^*$$$ and $$$\beta$$$; (c) relationship between the ratio $$$D^*/D_{SUB}$$$ and $$$\beta$$$. $$$D^*$$$ and $$$K^*$$$ are the diffusivity and kurtosis computed from sub-diffusion model parameters $$$D_{SUB}$$$ and $$$\beta$$$.

Figure 3. The light gray curves comprise samples of an aMRI library of >4000 simulated SDE b-space decays. Experimental data from murine colorectal tumor (circles),⁷ human prostate lesion (stars) and NA tissue (triangles), brain GM (diamonds), and bladder (squares) single voxels are shown. Different aMRI model k_io, r, and V parameter sets produce the colored library simulated curves matching the disparate data. More importantly, the model parameters for each curve are in generally good agreement with measures from independent ex vivo studies of these tissues (Figure 4).

Figure 1. Simulated SDE decay curves showing the dependence on each of the aMRI parameters: the mean cellular water efflux rate constant k_io (a), the cell density r (b), and the mean cell volume V (c), while the other two are held constant. Thus, for (a) r = 1,200,000 cells/μL, V = 0.54 pL, for (b) k_io = 39 s^-1, V = 0.54 pL, and for (c) k_io = 39 s^-1, r = 1,200,000 cells/μL. In these semi-log plots, all decays are curved [non‑Gaussian] except those for pure water: r = 0 in (b), and V = 0 in (c).

Figure 1: Visual representation of SMT (intracellular volume fraction $$$v_{in}$$$ and intrinsic diffusivity $$$\lambda \ [\mathrm{mm}^2/\mathrm{s}]$$$) and NODDI (orientation dispersion index $$$OD$$$, intracellular volume fraction $$$v_{ic}$$$ and isotropic volume fraction $$$v_{iso}$$$) parameters under different inversion times.

Figure 2: Mean values and first and third quartiles for SMT (intracellular volume fraction $$$v_{in}$$$ and intrinsic diffusivity $$$\lambda \ [\mathrm{mm}^2/\mathrm{s}]$$$) and NODDI (mean orientation of Watson distribution $$$\mu = (\theta, \phi) \ [\mathrm{rad}]$$$, orientation dispersion index $$$OD$$$, intracellular volume fraction $$$v_{ic}$$$ and isotropic volume fraction $$$v_{iso}$$$) over regions-of-interests and changes in TI. WM - white matter, GM - grey matter, CSF - cerebrospinal fluid.

Figure 1. Reproduction of the “tissue compartment” results of a single-shell free-water study of aging white matter, simulated using the constant tissue-trace constraint. Metrics derived from the tissue compartment, as per Eq. 6, represent variation in the shape of the tissue tensor while the size remains constant, since all isotropic variations are allotted to the free water compartment. For a biological interpretation of these results, see ref. 6.

Figure 2. Reproduction of the “free water compartment” results of a single-shell free-water study of aging white matter, simulated using the constant tissue-trace constraint. The constant tissue-trace relationship between f and MD (Eq. 3) is nonlinear, so the linear correlation coefficients exhibited by f and MD differ. If MD better follows a quadratic distribution, as is thought to be the case in aging, f follows a distribution that can be better approximated by a line.

Fig.1. Method and Experiment design. (A)-(C) illustrates the multimodal registration and template generation. The transformation generated with multimodal images is applied to the FOD data, which are then averaged to generate each FOD template. (D) illustrates the population FOD template generation based on single modality FOD-based registration.

Fig.2 FOD templates generated from 50 HCP subjects with 4 methods shown in Fig.1. The FOD butterfly patterns (overlaid on the L0 term of the FOD expansion, which corresponds to the total apparent fiber density). The white boxes highlight the FODs with crossing-fibers and near-cortex white matter.

Figure 1. The pH dependence of NMR and Z-spectral intensities for oyster glycogen (100 mM glucose units) in 95% D₂O/5% H₂O. (a) 1D NMR spectra at different pH. (b) Z-spectra at three pH values (4s continuous RF irradiation, B1 = 0.4 µT). (c) Lorentzian fitted peak intensities (S/S₀) at +1.2, +0.6 and -1.0 ppm as a function of pH. (d) GlycoNOE (-1 ppm) intensity as a function of B₁ (16s continuous RF) at two pH values. The curve was fitted using Eq. 1.

Figure 2. Numerical simulations agree with the analytical results. (a, d) Numerically simulated Z-spectra for different hydroxyl exchange rates. (b, d) The dependence of the numerically simulated glycoNOE (black circles) intensities on B₁ field strengthis in agreement with that using the analytical solution (red line, using Eq. 1). (c, f) Values for the enhancement factor (e) for numerically and analytically simulated data are the same.

Figure 3. Bloch fitted k_ex with different fitting conditions for the 5.6 ppm amide proton in 25 mM iopamidol solutions with different T₁ values. The analyzed spectra were acquired at 37 °C with a saturation power of 3.0 μT and a saturation time of 6.0 sec.

Figure 4. The computation time for the Bloch-fitting process with different fitting conditions. For each fitting condition, the computation time presented includes data for the fitting of the spectra of twenty-four 25 mM iopamidol samples scanned at five temperatures (i.e. 120 spectra per fitting condition).

Figure 1: Left: Single-heart cavity model coupled with the circulation system via system of diodes and a two-stage Windkessel. Right: Example of acquired and processed CMR and pressure data of LV rTOF patient #1.

2D illustration of the virtual histology-based geometry used in the simulations. Myocytes are triangular meshes (polyhedra). The extra-cellular volume fraction is 22%.

FA and MD values for two extreme permeability cases ($$$\kappa$$$=0 and 0.05μm/ms). All simulations have been computed considering a STEAM sequence with increasing $$$\Delta$$$ and constant gradient strength and duration. Parameters: $$$N_p$$$=10⁴ walkers, $$$D_\text{ICS}$$$=1.5µm²/ms and $$$D_\text{ECS}$$$=3µm²/ms.

(Top) Sheetlet segmented from histological images. (Bottom) Synthesised sheetlet after completion of the packing algorithm and after removing ghost cells, which leave distinct pockets of ECS between myocytes. The sheetlet outline was used as the target region and myocytes were created to match cell geometries from histology.

Illustration of the presented packing algorithm. Bounding circles are used to quickly reject objects from intersection computation. Objects in grey are the buffer zone and "ghost cells", which will be removed at the end of the simulation, leaving the myocyte objects.

Fig.1| Cerebellar vermis and hemisphere showed different fMRI signals in humans in vivo^1,2. In order to explore the neurophysiological basis of such difference we characterized capillary responses ex-vivo in vermis lobule V and hemisphere lobule VI in acute mouse cerebellar slices (left: vascular organization of these regions) and recorded neuronal activity with an HD-MEA (right: LFP signals recorded from the granular layer). Then, we validated a biophysical realistic model with the electrophysiological data and used it to dissect the neuronal contribution to the NVC.

Fig. 2| Capillary dilation differed between cerebellar vermis and hemisphere in response to mossy fibers stimulation, and vascular responses did not show linear trends while increasing the input frequency. Granular layer neuronal responses recorded as Local Field Potentials (N_2a-N_2b peaks) differed in cerebellar vermis and hemisphere, and the N_2b peak presented a non-linear frequency dependent trend. Importantly N_2b peak is informative of N-methyl-D-aspartate receptors (NMDA) activation and the NMDAR-NO pathway is known to regulate cerebellar neurovascular coupling³.

Fig.1 Realistic VAN model of mouse cortex. (A) Anatomical reconstruction of full vascular network (600 micron cube). Arteries (red), capillaries (green), veins (blue). The inputs and outputs to the network are indicated in magenta. The boundary conditions must be computed to emulate the behavior within the VAN as if it were connected to large feeding arteries and draining veins as it is in the brain. (B) The distribution of Young’s elasticity modulus indicating the characteristic difference between pial veins and the intra cortical diving veins and capillaries (logarithmic scale).

Fig.2 Determination of boundary conditions using a whole-brain stylistic VAN. (A) Vascular network for mouse brain (diving artery:vein ratio 1:3; arteries red, capillaries green, veins blue). Cyan indicates the path used for analysis, the area representing the realistic VAN is shaded, magenta dots show the VAN boundary nodes. (B) Pressure and (C) blood volume along the path in (A) for baseline and active conditions for short and long-duration stimuli. Magenta lines indicate the boundary nodes in (A). (D) Pressure increases at the boundary nodes for different stimulus durations.

Figure.2 Behavioral assay,1,7,14 and 30 days after operation. ( A ) Gait disturbance score: There was no significant difference among the three groups;(B and C) Hot-Plate and acetone assay: Compared with the normal group and sham group, the DLBP group showed a decreased in pain and temperature threshold; (D,E and F) Grip force and tail suspension assay: The DLBP group showed reduced grip and struggle time and increased bending time due to axial pain in the waist and back (#P < 0.05).

Figure.4 MRI T2 mapping (A and B) and BOLD (C and D),1 month after operation. Compared with the normal group and sham group, the T2 values of the L4/5 and L5/6 multifidus and erector spinae in the DLBP group were increased. There was no significant difference in R2*values of multifidus , erector spinae and psoas major among the three groups (#P < 0.05) .

Figure 2. The first row shows the pattern of the CBV change across the layers used in our simulation. Rows 2 to 5 show the BOLD and VASO simulated profiles. Profiles with RMSE 20% higher than the minimum RMSE are plotted as the shaded area. In all figures the horizontal axes show the relative cortical depth, vertical axes show the percentage of signal change, solid lines represent imaging data, dotted lines represent simulated responses, and error bars show the standard error of the mean.

Figure 1. A) Schematic representation of the modelled primary motor cortex centred on two adjacent principal veins of groups 3 and 4 (V3, V4) with artery to vein ratio of 2-1. B) Baseline blood volume in intracortical vessels and the laminar network (i.e. arterioles, capillaries, and venules) in the modelled area.

Figure 3. Wave images, curl maps and stiffness maps at 7T and 3T.

Figure 1. PVC head phantom and the setup of the MRE test.

Representative activation maps for the two processing methods, NEMO and SVarM, for different levels of B₀ and B₁⁺ inhomogeneities. On the right, corresponding plots of Dice score and surviving pixels ration (mean ± std). On the top, ground truth activation map, obtained from BOLD fMRI experiments, and representative B₀ and B₁⁺ field maps.

Simulated neuro-current time series with (a) or without (b) concomitant neural activation. Time courses (mean ± std) after each step of data processing. NEMO consists of a regression and high-pass filtering step to remove low frequency confounds (d), a rectification step converting variance differences in mean shifts (e) and extraction of the peak magnitude in the frequency spectrum at the task frequency (f). SVarM uses GLM regression to remove low frequency confounds (h), then pools the data into ON and OFF groups and tests the difference in their variance with Levene’s test (i-j).

Figure 2: Exemplary images of the original and UNICORN+B1 images of RRx1 to RRx8 of (A) FA = 126^o and (B) FA = 163^o. Each image was automatically windowed individually.

Figure 1: Quantitative ROI analysis and qualitative clinical evaluation for the eight different UNICORN settings RRx1 to RRx8 of FA = 126^o (top) and FA = 163^o (bottom). Each setting reconstructed three image series: original without UNICORN and B1 filtering (original, red), UNICORN without B1 filtering (UNICORN, green), and UNICORN with B1 filtering (UNICORN+B1, blue).

Example in vivo dataset. Estimation bias including moving average for individual voxels (A) and averaged over signal features (B). The area of markers is proportional to the number of voxels in the feature. (C) Example slice from the same 3D dataset. ¹⁹F-NPs are taken up by inflammatory cells, which then accumulate at sites of inflammation. The first row shows ¹⁹F-MR signal intensity for test data after RNBC (measured) and with model based bias correction (corrected), as well as the reference data. The second line shows estimation bias computed by comparison of test and reference data.

(A) Rician noise with known noise level is used for the forward model. (B) The true signal intensities are assumed to be drawn from a positively skewed probability distribution. Here a log-normal prior is shown. The measured data is thus drawn from a marginal distribution computed by integrating the product of forward model and prior distribution. The right shift of probability mass for signal levels above the detection threshold leads to the observed overestimation. (C) Posterior distributions for two measured signal levels. The posterior mean gives the corrected signal

Figure 1. The 3D vasculature from 7T TOF-MRA obtained by our progressive method.

Figure 2. Comparison between the segmentation results of our method and U-NET. (a) Origin image. (b) Ground truth. (c) Result of U-NET. (d) Result of our method.

Figure 1. Orthogonal representations of CBF, BAT, and aCBV maps of one subject for the different modelling strategies and conditions (air and hypercapnia). aCBV maps are only obtained when using strategies where the macrovascular component is modelled (M_art). M_artM_nodisp - model with macrovascular component but without dispersion, M_artM_disp - model with macrovascular and dispersion components, M_noartM_nodisp - model without macrovascular and dispersion components, M_noartM_disp - model with dispersion but without macrovascular component.

Figure 2. Regional analysis of the different haemodynamic parameters (CBF, BAT and aBV; rows) with the different modelling strategies (colors, correspondence detailed in Figure 1 legend) and conditions (columns). Statistically significant results are highlighted with * (p>0.05, corrected for multiple comparisons).

Fig.1| The Virtual Brain (TVB) simulation was performed in three different conditions: healthy (HC), Alzheimer’s disease (AD) and Frontotemporal Spectrum Disorder (FTSD). For each group a randomly chosen subject is reported as an example. Each row shows structural connectivity (SC), experimental functional connectivity (expFC) and simulated functional connectivity (simFC) obtained with three different networks: whole-brain, cortical subnetwork (CORTEX) and embedded cerebro-cerebellar subnetwork (CORTEXCRBL).

Fig.2| Boxplot of Pearson correlation coefficient (PCC) between experimental and simulated functional connectivity for all groups (healthy, HC Alzheimer’s disease, AD Frontotemporal Spectrum Disorder, FTSD) and networks. PCC values obtained integrating cerebro-cerebellar connections (CORTEXCRBL) are higher than PCC values obtained with the other networks (WHOLEBRAIN and CORTEX) both in healthy and pathological conditions.

Figure 1. Visualization of A) the first network and B) the other three networks both (Left Column) before and (Right Column) after the anatomical swapping of arteries and veins. Not only was the labeling swapped but the diameter spectra were also reassigned so that the newly assigned arteries have the same diameter distribution as the previous arteries and similarly the veins share the diameter spectra of the original veins. C) This topological matching is also reflected by plotting the diameter spectra of the arteries, capillaries, and veins from before and after swapping the anatomy.

Figure 4. Visualization of the cerebral blood volume (CBV) time course for all 4 VANs. The dilation in the experimental group (3:1 ratio) is significantly higher than the control counterpart in each case.

Figure 2. Signal amplitude and independence in resting-state data. a) The image shows the location of nine voxels crossing the cortical ribbon (“cross-cortex line”) that were used in the successive analysis. b) Power of low-frequency fluctuations at different points of the cross-cortex line calculated for ten different pre-processing pipelines. c) Mean homogeneity, assessed as correlation and coherence between pairs of voxels in the cross-cortex-line. Error bars represent standard error of the mean. Different letters indicate significantly different groups.

Figure 3. Identification of evoked responses. a) Line activation profiles, calculated as the mean beta-value across 20 lines (see inset on the bottom left), for two task-fMRI scans involving either motor-only (M) or motor and sensory processing induced by touch (M+T), computed after pre-processing with ten different pipelines. The dashed lines indicate the intensity of the mean functional image. b) ROIs selected for group analysis. c) The GM to CSF ratio of the t-statistic. Asterisks indicate significant differences between pre-processing pipelines (p<0.05).

Figure 1. Group mean atlased tSNR, identically viewed and windowed (rows 1-2), and masked to grey matter (rows 3-5). Control images shown in rows 1/4; LLR-denoised images, rows 2/5. For control data, global, masked, and default mode, auditory, and sensorimotor network seed mean and standard deviation tSNRs were 180.98 ± 17.19, 181.75 ± 18.40, 132.28 ± 7.29, 236.79 ± 28.67, and 246.87 ± 41.24 respectively; for LLR data, 454.10 ± 62.76, 436.63 ± 66.58, 237.83 ± 27.87, 498.25 ± 71.02, and 576.57 ± 161.65.

Figure 5. Group-level sensorimotor network connectivity statistical map. Left column shows control data; right column, LLR-denoised data. Shown for each variant and threshold are volumes (vol_SC) of the seed-containing cluster (blue arrows). Clusters are thresholded in volume to 40 voxels. Top row has maps thresholded to $$$p=1\times{10}^{-3}$$$; bottom row, $$$p=2.55\times{10}^{-4}$$$ (reduction to $$$25.5\%$$$ of baseline) for LLR-denoised data to replicate vol_SC of control. LLR-denoised data show a $$$98.58\%$$$ increase in vol_SC at $$$p=1\times{10}^{-3}$$$.

Figure1. Harmonisation of FA and MD on ROI-wise level via Z-scoring or ComBat was equally effective. While Z-scoring projected diffusion metrics independently (here to reference scheme 30x2), ComBat adjusted signal across all acquisition schemes.

Table 1. Coefficient of Variation of JHU ROI Means Before and After Data Harmonisation. All CV values displayed as mean [min, max] in %.