Diffusion tensor magnetic resonance imaging of the normal breast

Purpose

The objective of this study was to evaluate diffusion anisotropy of the breast parenchyma and assess the range and repeatability of diffusion tensor imaging (DTI) parameters in normal breast tissue.

Materials and Methods

The study was approved by our institutional review board and included 12 healthy females (median age, 36 years). Diffusion tensor imaging was performed at 1.5 T using a diffusion-weighted echo planar imaging sequence. Diffusion tensor imaging parameters including tensor eigenvalues (λ₁, λ₂, λ₃), fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured for anterior, central and posterior breast regions.

Results

Mean normal breast DTI measures were λ₁=2.51×10⁻³ mm²/s, λ₂=1.89×10⁻³ mm²/s, λ₃=1.39×10⁻³ mm²/s, ADC=1.95±0.24×10⁻³ mm²/s and FA=0.29±0.05 for b=600 s/mm². Significant regional differences were observed for both FA and ADC (P<.05), with higher ADC in the central breast and higher FA in the posterior breast. Comparison of DTI values calculated using b=0, 600 s/mm² vs. b=0, 1000 s/mm², showed significant differences in ADC (P<.001), but not FA. Repeatability assessment produced within-subject coefficient of variations of 4.5% for ADC and 11.4% for FA measures.

Conclusion

This study demonstrates anisotropy of water diffusion in normal breast tissue and establishes a normative range of breast FA values. Attention to the influence of breast region and b value on breast DTI measurements may be important for clinical interpretation and standardization of techniques.     

Diffusion tensor imaging of oral carcinoma: Clinical evaluation and comparison with histopathological findings

PurposeThis study aims to assess the usefulness of diffusion tensor imaging (DTI) as a noninvasive method for the evaluation of histological grade and lymph node metastasis in patients with oral carcinoma (OC).Materials and methodsThirty-six consecutive patients with histologically confirmed OC underwent examination by 3-T MRI. DTI was performed using a single-shot echo-planar imaging sequence with b values of 0 and 1000 s/mm² and motion-probing gradients in 12 noncollinear directions. Fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) maps were compared with histopathological findings. The DTI parameters were correlated with the histological grade of the OCs based on the World Health Organization grading criteria and the presence or absence of lymph node metastasis.ResultsThe FA values (0.275 ± 0.058) of OC were significantly lower than those of normal tongue, muscle, and parotid glands (P < 0.001 for all), and the MD, AD, and RD values (1.220 ± 0.149, 1.434 ± 0.172, and 1.019 ± 0.165 × 10⁻³ mm²/s, respectively) were significantly higher than their respective normal values (P < 0.001 for all). Significant inverse correlations with histological grades were shown for FA, MD, AD, and RD values in OC patients (r = −0.862, r = −0.797, r = −0.747, and r = −0.844, respectively; P < 0.001 for all). In addition, there was a significant difference in the FA values of metastatic and nonmetastatic lymph nodes (0.186 vs. 0.276), MD (0.923 vs. 1.242 × 10⁻³ mm²/s), AD (1.246 vs. 1.621 × 10⁻³ mm²/s), and RD (0.792 vs. 1.100 × 10⁻³ mm²/s; P < 0.001 for all).ConclusionsDTI may be clinically useful for the noninvasive evaluation of histological grade and lymph node metastasis in OC patients.     

Quantitative diffusion coefficient maps using fast spin-echo MRI

In this work, we have evaluated the performance of a diffusion-sensitive fast spin-echo (FSE) pulse sequence. The proposed pulse sequence utilises velocity-compensating diffusion-encoding gradients and includes the collection of navigator echoes. Spoiler gradients were inserted in the slice-selecting direction to minimise effects from stimulated echoes. Calculations of the b values showed that cross-terms between imaging gradients and diffusion gradients only led to a marginal increase of b values. Pixel-wise calculation of apparent diffusion coefficient (ADC) maps was performed numerically, considering cross-terms between diffusion-encoding and imaging gradients. The sequences investigated used echo train lengths of 16, 8 and 4 echoes and were encoded in either the slice-, frequency- or phase-encoding direction. In order to allow for higher b values a pulse-sequence version using non-motion compensating diffusion-encoding gradients was written. Phantom measurements were performed and the diffusion coefficients of water and acetone were reasonable. Seven healthy volunteers (age 28–50 years) were examined and apparent diffusion coefficient values agreed well with expected values. Diffusion-weighted images, apparent diffusion coefficient maps and images corresponding to the trace of the diffusion tensor of good quality were retrieved in vivo.     

Correlation between spinal cord diffusion tensor imaging and postural response latencies in persons with multiple sclerosis: A pilot study

PurposeLonger latency of postural response in multiple sclerosis (MS) may be linked to imbalance and increased likelihood of falls. It may be caused by the compromised microstructural integrity in the spinal cord, as evidenced by slowed somatosensory conduction in the spinal cord. Thus, the purpose of this study is to investigate the correlation between latency of postural responses and microstructural integrity of the cervical spinal cord, the region particularly related to the disease severity in MS, using diffusion tensor imaging (DTI) metrics.MethodsSeventeen persons with MS with mild-to-moderate disease severity were enrolled in this study. Postural response latencies of each patient were measured using electromyography of the tibialis anterior muscle (TA) and gastrocnemius muscle (GN) in response to surface perturbations. Cervical spinal cord DTI images were obtained from each patient. DTI mean, radial, axial diffusivity, and fractional anisotropy (FA) were measured between segments C4 and C6. Correlations of DTI metrics with postural response latencies, expanded disability status scale (EDSS) scores, and 25-foot walk (T25FW) were assessed using the Spearman's rank correlation coefficient at α = 0.05.ResultsLower FA was significantly correlated with longer latencies measured on right TA in response to forward postural perturbations (r = −0.51, p = .04). DTI metrics showed no significant correlations with EDSS scores (r = −0.06–0.09, p = .73–0.95) or T25FW (r = −0.1–0.14, p = .6–0.94). DTI metrics showed no significant differences between subjects with and without spinal cord lesions (p = .2–0.7).ConclusionsOur results showed a significant correlation between lower FA in the cervical spinal cord and longer latencies measured on right TA in response to forward postural perturbations in persons with MS, suggesting that impaired cervical spinal cord microstructure assessed by DTI may be associated with the delayed postural responses.     

Diffusion-weighted magnetic resonance imaging of human skeletal muscles: gender-, age- and muscle-related differences in apparent diffusion coefficient

Purpose

To evaluate the apparent diffusion coefficient (ADC) of skeletal muscle based on signal intensity (SI) attenuation vs. increasing b values and to determine ADC differences in skeletal muscles between genders, age groups and muscles.

Materials and Methods

Diffusion-weighted images (b values in the range of 0–750 s/mm² at increments of 50 s/mm²) of the ankle dorsiflexors (116 subjects) and the erector spinae muscles (86 subjects) were acquired with a 1.5-T MR device. From the two different slopes obtained in SI vs. b-value logarithmic plots, ADC^b0–50 (b values=0 and 50 s/mm²) reflected diffusion and perfusion, while ADC^b50–750 (b values in the range of 50–750 s/mm² at increments of 50 s/mm²) approximated the true diffusion coefficient. Moreover, to evaluate whether this b-value combination is appropriate for assessing the flow component within muscles, diffusion-weighted images of the ankle dorsiflexors (10 subjects) were obtained before and during temporal arterial occlusion.

Results

ADC^b0–50 and ADC^b50–750 were found to be 2.64×10^–3 and 1.44×10^–3 mm²/s in the ankle dorsiflexors, and 3.02×10^–3 and 1.49×10^–3 mm²/s in the erector spinae muscles, respectively. ADC^b0–50 was significantly higher than ADC^b50–750 in each muscle (P<.01). The erector spinae muscles showed significantly higher ADC values than the ankle dorsiflexors (P<.01). However, for each muscle, there were few significant gender- and age-related ADC differences. Following temporal occlusion, ADC^b0–50 of the ankle dorsiflexors decreased significantly from 2.49 to 1.6×10^–3 mm²/s (P<.01); however, ADC^b50–750 showed no significant change.

Conclusion

Based on the SI attenuation pattern, muscle ADC could be divided into ADC that reflects both diffusion and perfusion, and ADC that approximates a true diffusion coefficient. There were significant differences in ADC of functionally distinct muscles. However, we barely found any gender- or age-related ADC differences for each muscle.     

Equilibrium of 1:2:3 CLBLCO superconductors with oxygen: reaction equation,thermodynamics and improvement of homogeneity

Equilibrium of 1:2:3 superconductors (Ca_xLa_1−x)(Ba_1.75−xLa_0.25+x)Cu₃O_y (this compound has in the past variously denoted as CLBLCO, CLBCO or CaLaBaCuO) with oxygen was studied for x=0.1 and x=0.4 in the temperature range of 150–950 °C under 1 atm. O₂. The main process is the reversible reaction −Cu₃²⁺O_6.625+0.25O₂=−Cu₂²⁺Cu³⁺O_7.125 which is completed with the formation of one Cu³⁺. The enthalpy (in kJ/mol CLBLCO) and entropy (in J(mol CLBLCO)⁻¹K⁻¹) of this reaction were calculated from the temperature dependence of the equilibrium constant. The values are ΔH=−33.1 and ΔS=−29.9 for x=0.1 and ΔH=−49.4 and ΔS=−42.7 for x=0.4.It was found that the equilibrium of ceramic pellet of CLBLCO with oxygen cannot be practically achieved below 300 °C while the equilibrium for powder is achieved even at 200 °C. Low rate of reaction of CLBLCO with oxygen causes the problem in low temperature equilibration. In contrast, diffusion of oxygen ions in the ceramics is observed even at 200 °C. This diffusion proceeds without the change of the oxygen content and may be applied in order to improve the homogeneity of the distribution of oxygen ions.     

Diffusion tensor parameters and principal eigenvector coherence: Relation to b-value intervals and field strength

Diffusion-weighted MRI images acquired at b-value greater than 1000 s mm^− 2 measure the diffusion of a restricted pool of water molecules. High b-value images are accompanied by a reduction in signal-to-noise ratio (SNR) due to the application of large diffusion gradients. By fitting the diffusion tensor model to data acquired at incremental b-value intervals, we determined the effect of SNR on tensor parameters in normal human brains, in vivo. In addition, we also investigated the impact of field strength on the diffusion tensor model. Data were acquired at 1.5 and 3 T, at b-values 0, 1000, 2000 and 3000 s mm^− 2 in twenty diffusion-sensitised directions. Fractional anisotropy (FA), mean diffusivity (MD) and principal eigenvector coherence (κ) were calculated from diffusion tensors fitted between datasets with b-values 0–1000, 0–2000, 0–3000, 1000–2000 and 2000–3000 s mm^− 2. Field strength and b-value effects on diffusion parameters were analysed in white and grey matter regions of interest. Decreases in FA, κ and MD were found with increasing b-value in white matter. Univariate analysis showed a significant increase in FA with increasing field strength in highly organised white matter. These results suggest there are significant differences in diffusion parameters at 1.5 and 3 T and that the optimal results, in terms of the highest values of FA in white matter, are obtained at 3 T with a maximum b = 1000 s mm^− 2.     

Intravoxel incoherent motion magnetic resonance imaging for breast cancer: A comparison with molecular subtypes and histological grades

PurposeThe purpose of this paper is to investigate whether the IVIM parameters (D, D *, f) helps to determine the molecular subtypes and histological grades of breast cancer.MethodsFifty-one patients with breast cancer were included in the study. All subjects were examined by 3 T Magnetic Resonance Imaging (MRI). Diffusion-weighted imaging (DWI) was undertaken with 16 b-values. IVIM parameters [D (true diffusion coefficient), D* (pseudo-diffusion coefficient), f (perfusion fraction)] were calculated. Histopathological reports were reviewed to histological grade, histological type, and immunohistochemistry. IVIM parameters of tumors with different histological grades and molecular subtypes were compared.ResultsD* and f were significantly different between molecular subtypes (p = 0.019, p = 0.03 respectively). D* and f were higher in the HER-2 group and lower in Triple negative (−) group (D*:36.8 × 10⁻³ ± 5.3 × 10⁻³ mm²/s, f:29.5%, D*:29.8 × 10⁻³ ± 5.6 × 10⁻³ mm²/s, f:21.5% respectively). There was a significant difference in D* and f between HER-2 and Triple (−) subgroups (p = 0,028, p = 0.024, respectively). D* was also significantly different between the HER-2 group and the Luminal group (p = 0,041). While histological grades increase, D and f values tend to decrease, and D* tends to increase. While the Ki-67 index increases, D* and f values tend to increase, and D tend to decrease.ConclusionD* and f values measured with IVIM imaging were useful for assessing breast cancer molecular subtyping. IVIM imaging may be an alternative to breast biopsy for sub-typing of breast cancer with further research.     

Dependence on b-value of the direction-averaged diffusion-weighted imaging signal in brain

PurposeThe dependence of the direction-averaged diffusion-weighted imaging (DWI) signal in brain was studied as a function of b-value in order to help elucidate the relationship between diffusion weighting and brain microstructure.MethodsHigh angular resolution diffusion imaging (HARDI) data were acquired from two human volunteers with 128 diffusion-encoding directions and six b-value shells ranging from 1000 to 6000 s/mm² in increments of 1000 s/mm². The direction-averaged signal was calculated for each shell by averaging over all diffusion-encoding directions, and the signal was plotted as a function of b-value for selected regions of interest. As a supplementary analysis, similar methods were also applied to retrospective DWI data obtained from the human connectome project (HCP), which includes b-values up to 10,000 s/mm².ResultsFor all regions of interest, a simple power law relationship accurately described the observed dependence of the direction-averaged signal as a function of the diffusion weighting. In white matter, the characteristic exponent was 0.56 ± 0.05, while in gray matter it was 0.88 ± 0.11. Comparable results were found with the HCP data.ConclusionThe direction-averaged DWI signal varies, to a good approximation, as a power of the b-value, for b-values between 1000 and 6000 s/mm². The exponents characterizing this power law behavior were markedly different for white and gray matter, indicative of sharply contrasting microstructural environments. These results may inform the construction of microstructural models used to interpret the DWI signal.     

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis

Object

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg–Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data.

Materials and Methods

MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm²), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction.

Results

The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC = 0.60 ± 0.09 (10^− 3 mm²/s), D* = 28 ± 9 (10^− 3 mm²/s) and perfusion fraction = 14% ± 6%. The values obtained by the LM bi-exponential fit were: ADC = 0.45 ± 0.27 (10^− 3 mm²/s), D* = 63 ± 145 (10^− 3 mm²/s) and perfusion fraction = 27% ± 17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis.

Conclusion

The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior.     

Localized high-resolution DTI of the human midbrain using single-shot EPI,parallel imaging,and outer-volume suppression at 7 T

Localized high-resolution diffusion tensor images (DTI) from the midbrain were obtained using reduced field-of-view (rFOV) methods combined with SENSE parallel imaging and single-shot echo planar (EPI) acquisitions at 7 T. This combination aimed to diminish sensitivities of DTI to motion, susceptibility variations, and EPI artifacts at ultra-high field. Outer-volume suppression (OVS) was applied in DTI acquisitions at 2- and 1-mm² resolutions, b = 1000 s/mm², and six diffusion directions, resulting in scans of 7- and 14-min durations. Mean apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values were measured in various fiber tract locations at the two resolutions and compared. Geometric distortion and signal-to-noise ratio (SNR) were additionally measured and compared for reduced-FOV and full-FOV DTI scans. Up to an eight-fold data reduction was achieved using DTI-OVS with SENSE at 1 mm², and geometric distortion was halved. The localization of fiber tracts was improved, enabling targeted FA and ADC measurements. Significant differences in diffusion properties were observed between resolutions for a number of regions suggesting that FA values are impacted by partial volume effects even at a 2-mm² resolution. The combined SENSE DTI-OVS approach allows large reductions in DTI data acquisition and provides improved quality for high-resolution diffusion studies of the human brain.     

Differential detection of metastatic and inflammatory lymph nodes using intravoxel incoherent motion diffusion-weighted imaging

PurposeThis study sought to monitor the dynamic process of lymph node (LN) metastasis with intravoxel incoherent motion diffusion-weighted imaging (IVIM-DWI), and to investigate the impact of disease course on the detection of metastatic LNs by IVIM-DWI.MethodsTwenty female New Zealand rabbits with 2.5–3.0 kg body weight were studied. VX2 cells and egg yolk emulsion were randomly inoculated into one thigh to induce metastatic and inflammatory popliteal LNs, respectively. Eight rabbits underwent IVIM-DWI (14 b values, 0–2000 s/mm²) 2 h prior to, and 14, 21, and 28 days after inoculation (D0, D14, D21, D28). The apparent diffusion coefficient (ADC), true diffusion coefficient (D), pseudodiffusion coefficient (D*), and perfusion fraction (f) were measured and compared between the metastatic and the inflammatory groups at each time point. Three rabbits randomly chosen from the remaining twelve rabbits were sacrificed at each time point to perform hematoxylin and eosin staining and histologic evaluation.ResultsThe patterns of dynamic change of D*, ADC, and D were different between the metastatic and the inflammatory LNs. The metastatic group had a lower D* value at D14 (p = .003), and greater ADC and D values at both D21 (p = .001, p = .001) and D28 (p = .021, p = .001), compared to the inflammatory group. The f value of the metastatic group was greater than that of the inflammatory only at D28 (p = .001).ConclusionsIVIM-DWI can reflect the dynamic process of LN metastasis, and disease course has a significant influence on the ability of IVIM-DWI to detect metastatic nodes.     

Pionic contribution to the scalar and longitudinal N-Δ transition quadrupole form factors

The pionic contribution to the scalar and longitudinal p → Δ⁺ transition quadrupole form factors is calculated. It is shown that the πN channel contributes +0.023 − i 0.093 fm² at photon momentum q = 400 MeV (EMR ≈ (+1.4 − i 5.7) %). This might be larger than the “core” quadrupole moment, and one should be careful in comparing experimental data and theoretical predictions. This pionic contribution makes the measurement of the phase of the quadrupole moment more interesting.     

Voxelwise analysis of diffusion MRI of cervical spinal cord using tract-based spatial statistics

Robust voxelwise analysis using tract-based spatial statistics (TBSS) together with permutation statistical method is standardly used in analyzing diffusion tensor imaging (DTI) of brain. A similar analytical method could be useful when studying DTI of cervical spinal cord.Based on anatomical data of sixty-four healthy volunteers, white (WM) and gray matter (GM) masks were created and subsequently registered into DTI space. Using TBSS, two skeleton types were created (single line and dilated for WM as well as GM). From anatomical data, percentage rates of overlap were calculated for all skeletons in relation to WM and GM masks.Voxelwise analysis of fractional anisotropy values depending on age and sex was conducted. Correlation of fraction anisotropy values with age of subjects was also evaluated. The two WM skeleton types showed a high overlap rate with WM masks (~94%); GM skeletons showed lower rates (56% and 42%, respectively, for single line and dilated). WM and GM areas where fraction anisotropy values differ between sexes were identified (p < .05). Furthermore, using voxelwise analysis such WM voxels were identified where fraction anisotropy values differ depending on age (p < .05) and in these voxels linear dependence of fraction anisotropy and age (r = −0.57, p < .001) was confirmed by regression analysis. This dependence was not proven when using WM anatomical masks (r = −0.21, p = .10).The analytical approach presented shown to be useful for group analysis of DTI data for cervical spinal cord.     

The anomalous quasi isotropic [g] tensor found for CdBr2:Ag2+ and AgBr0.15Cl0.85:Ag2+: An explanation through strong covalency

The “anomalous” quasi-isotropic [g] tensor observed in systems containing the elongated AgBr⁴⁻₆ unit (g_∥ = 2.078 ± 0.003; g⊥ = 2.065 ± 0.003) is reasonably explained, within a rigorous Molecular Orbital framework, in terms of a very high covalency, consistent with the optical electronegativity of Ag²⁺ and previous results on other Cu²⁺ and Ag²⁺ complexes. For the antibonding level 3b_1g(x² − y²) about 90% of the electronic charges should be on bromine ions. The present analysis reveals that g_∥ − g₀ is dominated by charge-transfer excitations while g_⊥− g₀ is dominated by crystal-field excitations.     

Random walks in a simple percolation model with two jump frequencies

We consider transport properties of the system in which the good-conducting bonds lie in parallel planes linked by poor-conducting bonds and the concentration p of good-conducting bonds is close to the two-dimensional percolation threshold p_c. The diffusion coefficient D(τ) which describes the random walking in directions along the planes is calculated as a function of variable τ = p − p_c. For τ → 0 the asymptotic relation D(τ)/D(0) − 1 | ∼ |τ|^α is found w α = 2ν − s. Here s is the superconductivity exponent and ν is the correlation length exponent. It is argued that such behavior is to be expected also for more general models.     

Microwave Spectrum,Nuclear Quadrupole Coupling Constants,and Structure of Bromodifluoromethane

The microwave spectrum of bromodifluoromethane, CHBrF₂(Halon 1201) has been studied for the first time from 7 to 40 GHz. A least-squares analysis of the observedc-type transition frequencies gave rotational and centrifugal distortion constants and components of the bromine nuclear quadrupole coupling constant tensor in the principal axes system as follows:A= 10199.7186(62) MHz,B= 2903.4150(26) MHz,C= 2360.1521(23) MHz, Δ_J= 0.660(14) kHz, Δ_JK= 2.87(11) kHz, Δ_K= 8.95 kHz, δ_J= 0.1344(24) kHz, δ_K= 3.22(15) kHz, χ_aa= 521.281(92) MHz, χ_bb− χ_cc= −38.32(9) MHz, and |χ_ac| = 187.1(26) MHz for the⁷⁹Br species;A= 10199.5567(54) MHz,B= 2876.5588(20) MHz,C= 2342.3796(18) MHz, Δ_J= 0.652(12) kHz, Δ_JK= 2.77(9) kHz, Δ_K= 8.21(61) kHz, δ_J= 0.1300(19) kHz, δ_K= 2.97(13) kHz, χ_aa= 435.61(10) MHz, χ_bb− χ_cc= −32.08(8) MHz, and |χ_ac| = 148.5(29) MHz for the⁸¹Br species. The structural parameters are calculated from all these rotational constants and the electronic properties of the carbon–bromine bond in bromodifluoromethane are evaluated from the observed nuclear quadrupole coupling constants. These molecular properties are compared with those of other related molecules.     

Usefulness of diffusion derived vessel density computed from a simplified IVIM imaging protocol: An experimental study with rat biliary duct blockage induced liver fibrosis

ObjectivesLiver vessel density can be evaluated by DDVD (diffusion derived vessel density): DDVD_(b0b1) = Sb0/ROIarea0 – Sb1/ROIarea1, where Sb0 and Sb1 refer to the liver signal when b is 0 or 1 s/mm². Sb1 and ROIarea1 may be replaced by other b-values. With a rat biliary duct ligation (BDL) model, this study assesses the usefulness of liver DDVD computed from a simplified IVIM imaging protocol using b = 25 and b = 50 to replace b = 1 s/mm², alone and in combination with other IVIM parameters.MethodsMale Sprague-Dawley rats were used. The rat number was 5, 5, 5, and 3 respectively, for the timepoints of 7, 14, 21, 28 days post-BDL surgery. 12 rats had partial biliary duct recanalization performed after the rats had BDL for 7 days and then again followed-up for a mean of 14 days. Liver diffusion MRIs were acquired at 3.0 T with a b-value distribution of 0, 25, 50, 75, 100, 150, 300, 700, 1000 s/mm². DDVD_mean (control rats n = 6) was the mean of DDVD_(b0b25) and DDVD_(b0b50). IVIM fitting started from b = 0 s/mm² with segmented fitting and a threshold b of 50 s/mm² (n = 5 for control rats). Three 3-D spaces were constructed using a combination of the four diffusion parameters.ResultsThe control rats and BDL rats (n = 18) had a liver DDVD_mean of 84.0 ± 26.2 and 44.7 ± 14.4 au/pixel (p < 0.001). All 3-D spaces totally separated healthy livers and all fibrotic livers (n = 30, BDL rats and recanalization rats). The mean relative distance between healthy liver cluster and fibrotic liver cluster was 0.331 for PF, D_slow, and D_fast; 0.381 for PF, D_fast, and DDVD_mean; and 0.384 for PF, D_slow, and DDVD_mean.ConclusionA combination of PF, D_slow, and D_fast allows total separation of healthy livers and fibrotic livers and the integration of DDVD improved the separation.     

Emergence of new magic numbers,N = 16 and 32 by tensor interaction in Skyrme–Hartree–Fock theory

Melting of N = 20 shell and development of N = 16 and 32 shells for neutron-rich nuclei have been studied extensively by including tensor interaction in Skyrme–Hartree–Fock theory optimized to reproduce the splitting Δ1f shells of ^40,48Ca and ⁵⁶Ni nuclei. Evolution of gap generated by the energy difference of single-particle levels ν2s _1/2 and ν1d _3/2 has been found to be responsible for shell closure at N = 16. The splitting pattern of spin–orbit partners 2p shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates the formation of a new shell at N = 32 region.     

On the cosmological equations in the presence of a spatially homogeneous torsion field

It is shown that Einstein's equations obtained from the Friedmann Ansatz for the metric and an arbitrary cosmological term can be consistently extended on include a spatiall]y homogeneous contorsion field K_abc = ϵ _abc K(t), K(t) = η/R(t); η an arbitrary constant. This mechanism which guarantees covariant conservation of the Einstein tensor, amounts to replacing the arbitrary constant. This mechanism which guarantees covariant conservation of the Einstein tensor, amounts to replacing the signature parameter ϵ = ( +1: spherical space, 0: flat space, −1: hyperbolic space) by ϵ₁ = ϵ − η².