An approach is presented that provides a justification for the use of the discrete Fourier transform in magnetic resonance (MR) image reconstruction. Without a priori knowledge of the Fourier transform, an imaging experiment is described that corresponds to the common spatial encoding process by means of magnetic field gradients. A regular matrix, the so-called encoding matrix, describing a linear system of equations is obtained. The presented approach consists of numerical optimization of the encoding matrix by minimizing its condition number. To accomplish this, the necessary concepts of numerical analysis are thoroughly introduced, which reflects the educational character of the manuscript. As a result, we will see that a numerically optimized encoding matrix is equal to the discrete Fourier transform matrix; thus, an explanation for the use of the discrete Fourier transform in MR image reconstruction is obtained.
Discocyte erythrocytes (red blood cells, RBCs) undergo spontaneous alignment in a uniform magnetic field, B0—a phenomenon initially observed via optical dispersion and light microscopy and later confirmed with nuclear magnetic resonance (NMR) spectroscopy. The phenomenon arises due to the diamagnetic anisotropy of membrane lipids and proteins, which have different energies when oriented parallel or perpendicular to the magnetic field. This behavior is directly relevant to modern NMR experiments performed on cells, in particular multiple quantum filtering of quadrupolar nuclei with nuclear spin quantum number I > ½, which are sensitive to the degree of alignment in intact cells and tissues, forming the basis of our present investigations. Using a quartic equation to represent the surface of a discocyte cell and the boundary element method to integrate over a triangular mesh, we compute the minimum-energy orientation of an RBC in B0. At a field strength of B0 = 9.4 T, the energy difference between parallel and orthogonal alignments was calculated to be ∼1200 kBT, the latter being Boltzmann’s constant kB times the absolute temperature T, which is the thermal energy of a single particle in solution. Using hydrodynamic theory, we estimate a characteristic realignment time (which has a theoretical 1/||B0||2 dependence) of ∼300 ms at this field strength and extend this to consider the effects of collective behavior in densely packed RBC suspensions. Our findings agree with experimental data showing subsecond reorientational dynamics in strong magnetic fields and provide a physical framework for interpreting magnetic-field-induced structural order in biological tissues, which inform the development of new NMR and magnetic resonance imaging (MRI) methodologies for probing anisotropy, membrane architecture, and cellular organization in vivo.
This study develops an optimized personalized microwave hyperthermia framework for glioblastoma treatment, integrating a 19-channel radiofrequency array of geometrically and electromagnetically co-optimized cosine-curved dipole antennas. We initiated the design by optimizing the conductor geometry (amplitude, wavelength, and phase offset) to reshape the current distribution. Concurrently, resonant coupling loops were incorporated to provide additional degrees of freedom for impedance tuning. This combined approach establishes a synergistic mechanism, thereby overcoming the limitations of ultra-high-frequency dipoles and achieving enhanced impedance matching at 2.45 GHz, which is demonstrated by an S11 value of -19.2 dB obtained through particle swarm optimization. The semidefinite relaxation (SDR) algorithm optimizes channel excitations under a 72-W total power constraint to maximize the tumor-specific absorption rate while minimizing exposure to healthy tissue. Multianatomical electromagnetic-thermal validation confirms a treatment planning time of 0.31 min, representing a 50% speed improvement over particle swarm optimization. This delivers a precise 41.69 degrees C mean tumor temperature with superior targeting quantified by a specific absorption rate amplification factor (SAF) of 4.46 and a hotspot-to-target quotient (HTQ) of 0.81. Parametric analysis reveals depth-progressive SAF attenuation from 4.33 at superficial positions to 2.67 at 4 cm depth alongside improved large-tumor targeting achieving SAF 4.63 and HTQ 0.75 at 5 cm diameter. A pediatric model exhibits heightened electromagnetic sensitivity showing SAF 5.02 versus less than 5% variation in adult models, establishing a clinically translatable pathway for precision brain hyperthermia. This work is a computational study validated entirely through in silico simulations, without involving in vivo or clinical experiments.
Resting-state functional MRI (rsfMRI) analysis relies on complex mathematical operations whose properties and pitfalls are often poorly understood, leading to interpretational errors and suboptimal processing choices. This work presents novel mathematical insights for rsfMRI analysis through three key contributions: (1) a unified geometric framework showing that all common preprocessing and analysis operations can be understood as rotations in time-series vector space, (2) identification of rotationally invariant properties that remain stable across different processing choices, and (3) mathematical equivalences between seemingly different connectivity measures. We demonstrate how the hemodynamic response function acts as a rotation operator in frequency space, derive closed-form expressions for the impact of preprocessing on effective degrees of freedom, and show that correlation and coherence measures can be unified through frequency-weighted integration. Common mathematical errors in the literature are identified and corrected with worked examples. This framework provides practical guidance for choosing connectivity measures, ordering preprocessing steps, and understanding the mathematical constraints imposed by operations such as global signal regression. By connecting abstract mathematical concepts to concrete rsfMRI applications, this work serves as both a theoretical foundation and a practical guide for researchers using functional connectivity methods. Practical applications include detecting network disruption in neuropsychiatric disorders (e.g., schizophrenia) with dramatically improved sensitivity, harmonizing multisite data without complex corrections, optimizing scan protocols for specific effect sizes, and providing robust quality control metrics that outperform traditional approaches.
MR images are often acquired using a phased array of radiofrequency (RF) channels, with each RF channel being sensitive to only part of the object being scanned. The images collected from each RF channel are combined to generate a single image with higher SNR and more uniform sensitivity than can be obtained with a single channel alone. It is generally desirable to combine the images before performing any analysis in a quantitative imaging (QI) experiment—this way, the voxel-level signals input into the fitting model have high SNR. Computationally, it is often also more efficient than performing a quantitative fitting process on each channel image individually. Although fitting is typically performed on a voxel-level signal magnitude, certain pulse sequences like phase-cycled balanced steady-state free precession (pc-bSSFP) encode important information about tissue properties in the signal phase as well. Therefore, it is desirable to preserve the complex signal during the coil combination process in order for QI analyses to be reliable. While a variety of different coil combination techniques exist, there is little information on which ones best preserve phase for pc-bSSFP. Pc-bSSFP is of particular interest as the complex-valued images are used for relaxometry. This study compared the phase preservation performance of various coil combination techniques: Eigenvalue-based approach for iterative self-consistent parallel imaging reconstruction (ESPIRiT), simple phase robust coil combination (SRCC), full phase robust coil combination (FRCC), adaptive reconstruction (AR), and intrinsic multi-channel phase alignment (IMPA). These techniques were tested on pc-bSSFP data in both a simulated phantom and in vivo knee cartilage. The comparisons were conducted across a range of SNR levels to reflect realistic scenarios. Results showed that ESPIRiT, AR, and IMPA best preserved phase across the range of SNR levels tested.
In this paper, we contrast frequentist and Bayesian approaches to parameter estimation for a magnetic resonance (MR) relaxometry signal model which takes the form of a two-dimensional biexponential decay. The signal consists of two terms, each parameterized by an amplitude and a transverse and longitudinal relaxation time constant. There are two user-selected parameters, defining the two-dimensional character of the signal; these are an inversion time TI and a set of echo times, TE. Of particular interest is the fact that for two values of TI, which we call the null points, the signal becomes a monoexponential function in TE. Extracting the two parameters—the amplitude and decay constant—from the signal observed at or near a null point is particularly ill-posed since the monoexponential signal is highly overparameterized by the four parameter biexponential models. We seek to estimate these null points, which directly provide values for the longitudinal relaxation time constants, using both frequentist and Bayesian techniques. The frequentist approach uses nonlinear least squares (NLLS), and the Bayesian approach uses the Metropolis–Hastings algorithm. In addition to point estimates, both methods generate point clouds of parameter estimates representing uncertainties. Due to the symmetry of the biexponential model, these point clouds consist of two clusters. The variance of a single cluster and the separation between the two clusters, both of which capture the size of the point clouds, may be used as metrics for ill-posedness. Increasing point cloud size, indicating an undesired greater flexibility in parameter choice, illustrates a greater degree of ill-posedness. We find that both the frequentist and Bayesian approaches can estimate the null points using the extrema of these metrics and yield qualitatively similar and consistent results.
The heteronuclear single quantum correlation (HSQC) NMR method is widely used for the structural characterization of complex mixtures. In this study, the application range of multiplicity-enhanced HSQC (HSQC-ME) spectroscopy was broadened to quantitative analysis on low-field NMR devices with standard measurement possibilities. Acquisition parameters such as number of scans and t1 increments as well as repetition time were optimized to achieve the best signal-to-ratio and resolution requiring minimum measurement time. Standardization with internal standard using correction factor and external calibration approaches for active pharmaceutical ingredients/stimulants in pharmaceutical products and dietary supplements showed average absolute bias of 5.0% and 7.7%, respectively. The HSQC-ME NMR spectroscopic method was characterized by measurement uncertainty below 4% and limits of detection below 3 mg/mL for 2-h measurement time. Semiquantitative HSQC-ME analysis of organic acids in e-cigarettes can be performed within the accuracy of 25% at low-field NMR instruments in case of overlap in 1D NMR dimension and in the presence of huge solvent signals.
The density matrix of an arbitrary pure state of a system consisting of two spin-1/2 particles is derived from the Pauli spin angular momentum operators. Mixed singlet and triplet states are then formed from linear combinations of pure states and their corresponding density matrices constructed. Singlet and triplet states are exemplified by the spin isomers parahydrogen and orthohydrogen, respectively. Partial mixing is illustrated with the example of bilinear spin–spin coupling. Various properties of the density matrices of pure and mixed states are discussed, including idempotence, factoring, and spin correlation.
An ESR spin probe technique with non-TEMPO radicals, such as nitronyl nitroxide (NN), benzonitronyl nitroxide (BzNN), and iminonitroxide (IN) radicals, was used for a porous metal-organic framework (MOF), [(ZnI2)3(TPT)2] (ZnTPT; TPT = tris(4-pyridyl)-1,3,5-triazine), at room temperature. The principal values of g and hyperfine coupling (A) tensors estimated from spectral reproduction were different from those for organic matrices for some of these radicals. These results indicate that host-guest interactions occur between the ZnTPT matrix and guest radicals. Thus, when using NN, BzNN, and IN radicals as spin probes for a porous MOF, the interaction between the metal atoms or organic ligands in host materials and guest radicals should be considered. The experimental ESR spectra for the derivatives of NN or BzNN radicals were reproduced only by the rigid-limit component in the ESR time scale. However, those for the derivatives of IN radicals were approximately reproduced only by rotational diffusion around the z-axis perpendicular to the plane in the IN group. Interestingly, this reproduction was not around the y-axis of the principal axes of the g tensors, parallel to the molecular long axis, as previously observed in a few organic matrices. The IN radicals dispersed in the ZnTPT matrix are expected to be accommodated in cylindrical or pseudocylindrical nanospaces sandwiched by the pyridyl or triazine rings of TPT in ZnTPT. These findings show that the ESR spin probe technique using non-TEMPO radicals can be used to investigate the chemical and biological structures of nanosized materials.
Solid-state deuterium NMR is well suited to the study of the conformational dynamics of DNA. Deuterium quadrupole echo spectra for a particular motional model can be calculated and matched to the experimental spectrum to extract information on the DNA dynamics; however, doing so can be very time-intensive. The two-axis motion used to model the dynamics of either 2″ or 5′/5″ furanose ring deuteron is particularly complex with up to ten independent variables that can be optimized. Here, we present a program which automates both the input script generation and searches the parameter space for the best fit using a simulated annealing algorithm. The parameter, χred2, provides a relative measure of goodness of fit. This method reduces the overall time to determine the best fit of a line shape to a few days, in most cases, when running on a low-power desktop PC. The automated fitting program presented here can be easily modified to generate input scripts for new models, incorporate a weighting factor to the χred2 calculation to emphasize key line shape features, or fit nonsymmetrized data. This adaptable program will make simulation of solid-state deuterium spectra accessible to a broader audience.
This study was aimed to investigate the application value of magnetic resonance imaging (MRI) scanning examination in the preoperative treatment of functional glioma and to analyze the application effect of nursing intervention in the operating room in the treatment of fiber surgery. In this study, 80 patients with functional glioma were included as research objects and randomly rolled into the control group (routine nursing) and the experimental group (comfort nursing intervention in the operating room), with 40 cases in each group. All patients underwent craniocerebral MRI plain scan plus enhanced scan before surgery. The levels of the heart rate, systolic blood pressure, diastolic blood pressure, interleukin-6 (IL-6), cortisol, and anxiety before and after the intervention in the two groups were compared when patients entered the operating room (T1), when anesthesia took effect (T2), at the end of surgery (T3), when patients regained consciousness after surgery (T4), and 1 day after surgery (T5). MRI showed that the main glioma sites were located in the basal ganglia region (26.25%), followed by the central region (20.00%) and the Broca region (17.5%). The levels of IL-6 at T2, T3, and T4 in the control group were 186.45 ± 64.55 ng/L, 287.68 ± 34.59 ng/L, and 488.69 ± 81.14 ng/L, respectively, which were inferior to those at T2 (167.44 ± 15.59 ng/L), T3 (186.25 ± 52.64 ng/L), and T4 (356.57 ± 48.22 ng/L) in the test group. The SAS score of the test group after intervention (45.38 ± 2.02) was lower than that of the control group (51.03 ± 3.65) (P<0.05). The levels of cortisol in the test group (T2 (8.89 1.23 ng/L), T3 (9.23 1.25 ng/L), and T4 (11.78 1.27 ng/L) were lower than those in the control group (T2 (11.58 ± 2.48 ng/L), T3 (12.06 ± 2.82 ng/L), and T4 (13.04 ± 11.78)). In short, preoperative MRI scanning was beneficial to detect the location of glioma in functional area. Comfort nursing in the operating room can effectively relieve the anxiety and depression of glioma patients and improve the adverse psychological conditions of the patients.
To investigate the effects of early nursing intervention on brain injury among premature infants, 100 premature infants diagnosed with brain injury were included in the research and randomly divided into the control group (50 cases) and the experimental group (50 cases). The patients in the two groups were performed with the same conventional comprehensive treatment. The patients in the control group received conventional nursing while those in the experimental group underwent early nursing intervention. During follow-up, neurodevelopment, motor behavior, the incidence rate of brain injury, and nursing satisfaction of the infants in the two groups were compared. It was demonstrated that the five neurodevelopment scores of the experimental group were all higher than those of the control group. The differences showed statistical significance ( P < 0.05 ). The total effective rate of motor development of the experimental group reached 94%, while that of the control group amounted to 80%. Obviously, the total effective rate of motor development of the experimental group was higher than that of the control group. The difference was statistically significant ( P < 0.05 ). The nursing satisfaction of the experimental group reached 98%, which was apparently higher than that of the control group (74%). The difference suggested statistical significance ( P < 0.05 ). The rates of brain injury at 1 and 2 years after the birth of the experimental group were 6% and 2%, respectively. The rates of brain injury at 1 and 2 years after the birth of the control group amounted to 18% and 14%, respectively. The rates of brain injury at 1 and 2 years after the birth of the experimental group were lower than those of the control group. The difference revealed statistical significance ( P < 0.05 ). Hence, the early nursing intervention of premature infants with brain injury could promote brain development, improve neurological function, reduce the incidence of brain injury, and achieve an ideal nursing effect.
To explore the functional changes in the whole brain network in patients with sudden sensorineural hearing loss (SHL) at the acute stage from functional magnetic resonance imaging (fMRI) imaging evaluation results, 80 patients with sudden right SHL were selected as subjects (patient group). In addition, 40 healthy volunteers who underwent physical examination in the hospital during the same period were recruited as a control group. fMRI imaging was performed to analyze functional parameters and core nodes of the whole brain network. It was found that at all thresholds, the fMRI parameters Cp and Lp of the patient group were dramatically superior to those of the control group. The fMRI parameter Eglobal of the patient group was substantially lower than that of the control group ( P < 0.05 ). At most of the thresholds, the fMRI parameter λ in patients was dramatically superior to that in the control group ( P < 0.05 ). There were ten specific network core nodes in patients, including the right parahippocampal gyrus, right supra-occipital gyrus, left suboccipital gyrus, right fusiform gyrus, right parietal lobule, right subparietal lobule, right superior temporal gyrus, left superior marginal gyrus, and right superior temporal gyrus. In summary, the whole brains of patients with sudden SHL still had small-world attributes, but some characteristics of the brain network had changed, and there was a trend of transformation to a regular network. The connection between the auditory brain area and the functional areas related to language and vision was weakened, and the distribution of core nodes changed. This study provides a reference basis for exploring the changes in local brain and connectome levels in patients with sudden sensorineural hearing loss in the acute phase based on resting-state fMRI.
The MR diffusion-weighted imaging technique was used to evaluate the efficacy and safety of CalliSpheres drug-loaded microspheres for transarterial chemoembolization in the treatment of advanced bladder cancer. 35 patients with advanced bladder cancer were treated with CalliSpheres DLMS for transarterial chemoembolization. Imaging techniques such as magnetic resonance (MR) diffusion-weighted imaging were used to evaluate the therapeutic effect. The changes in serum tumor markers, immune function indexes, and oxidative stress indexes in patients before and after treatment were compared, and the quality of life of patients and the incidence of adverse reactions during follow-up were also evaluated. The results showed that the overall response rate (ORR) was 74.29% and that the disease control rate (DCR) was 97.14%. Compared with that before treatment, the ADC value of the tumor in patients with advanced bladder cancer detected by MR diffusion-weighted imaging technology was significantly increased after treatment and the maximum tumor diameter was significantly decreased P < 0.05 . Compared with those before treatment, the levels of serum tumor markers (CA199, CA724, and CA125) in advanced bladder cancer patients after treatment decreased P < 0.05 . The levels of T-lymphocyte subsets (CD3+ and CD4+) decreased, and CD8+ levels increased P < 0.05 . The levels of superoxide dismutase decreased P > 0.05 . At the same time, the subscale evaluation of function, symptoms, quality of life, adverse reactions, and economics of patients with advanced bladder cancer on the QLQ-C30 scale improved after treatment, and the incidence rate and recurrence rate during the follow-up period were 8.57% and 11.43%, respectively. It showed that CalliSpheres DLMS had a good clinical effect and high safety in the treatment of advanced bladder cancer and was a safe and feasible treatment method. The use of MR diffusion-weighted imaging technology could achieve quantitative evaluation of clinical efficacy of advanced bladder cancer.
Radiofrequency (RF) transmit field (B-1) mapping is a promising method in mitigating the B-1 inhomogeneity in various magnetic resonance imaging (MRI) applications. Although several phase- or magnitude-based B-1 mapping methods have been proposed, these methods often require complex modeling, long acquisition time, or specialized MRI sequences. A recently introduced simultaneous echo refocusing (SER) technique can be applied in the B-1 mapping method to extend the three-dimensional (3D) spatial coverage only without long data acquisition. Therefore, in this study, a multislice B-1 mapping method using composite spin echo sequences and SER techniques is proposed to obtain more accurate B-1 mapping with short data acquisition time. To evaluate the performance of the proposed B-1 mapping method, computational simulations were performed and compared with Morrell's method, double angle method, and Yarnykh's method. These results showed that the angle-to-noise ratio of the proposed B-1 mapping method has wider B-1 range compared to that of other B-1 mapping methods. In addition, the proposed B-1 mapping methods were compared to the multislice iterative signal intensity mapping method in both phantom and in vivo human experiments, and there was no remarkable difference between the two methods regarding the flip angle distribution in these experiments. Based on these results, this study demonstrated that the proposed B-1 mapping method is suitable for accurately measuring B-1 propagation under the condition providing reduced scan time and wider 3D coverage of B-1 mapping by applying composite RF pulse and SER techniques into the phase-sensitive method.
The dynamics of an identical pair of entangled spin-1/2 particles, both subjected to the same random magnetic field, are studied. The dynamics of the pure joint state of the pair are derived using stochastic calculus. An ensemble of such pure states is combined using the modified spin joint density matrix, and the joint relaxation time for the pair of spin-1/2 particles is obtained. The dynamics can be interpreted as a special kind of correlation involving the spatial components of the Bloch polarization vectors of the constituent entangled spin-1/2 particles.
This research was aimed to investigate the magnetic resonance imaging (MRI) features of brain structure and neuroendocrine levels in patients with first-episode schizophrenia. 25 hospitalized patients with first-episode schizophrenia were selected as the observation group, while 25 healthy people were selected as the control group. All the objects underwent MRI examination, and the images as well as gray matter density of the original image data were analyzed under voxel-based morphometry (VBM). The cortisol and prolactin in the observation group were detected, and the levels were compared. The Pearson correlation analysis was adopted to analyze the correlation between cortisol and prolactin levels and the total score of the Positive and Negative Syndrome Scale (PANSS). The results showed that the gray matter volume of the precentral gyrus, superior frontal gyrus, middle frontal gyrus, inferior frontal gyrus, postcentral gyrus, inferior parietal lobule, superior parietal lobule, and anterior cingulate cortex of the observation group decreased, while the volume of cerebellar gray matter increased. The levels of cortisol and prolactin in the observation group (387.54 ± 117.69 μg/L and 804.16 ± 267.13 μIU/mL, respectively) were significantly higher than those in the control group (138.46 ± 62.47 μg/L and 397.54 ± 203.82 μIU/mL, respectively), and the differences were statistically significant ( P < 0.05 ). The results of the Pearson correlation test showed that the higher the cortisol level, the more severe the schizophrenia (r = 0.421 and P = 0.013 ), while the prolactin level was not directly related to the severity of schizophrenia (r = 0.019 and P = 0.568 ). In conclusion, the MRI features based on the VBM technology can accurately assess the changes of gray matter; the levels of cortisol and prolactin in patients with first-episode schizophrenia were significantly higher than those in healthy people; and the higher the cortisol level, the more severe the schizophrenia symptoms. This study provided a certain research basis for MRI features of brain structure and neuroendocrine changes in patients with first-episode schizophrenia.
Plants are reservoirs of naturally occurring chemical constituents with a wide range of structural diversity. These biological compounds can be derived from different parts of plants such as leaves, barks, seeds, seed coats, flowers, and roots. A broad array of secondary metabolic compounds is present in the plants such as antibiotics, alkaloids, antimicrobials, food-grade pigments, and phenolics which have been reported to possess numerous health-related benefits, including antioxidant, anti-inflammatory, anticancer, and antiobesity activities. Therefore, the identification and detection of these compounds are of utmost importance in order to utilise their benefits into various fields. Wherein, magnetic resonance techniques, such as NMR (nuclear magnetic resonance), MRI (magnetic resonance imaging), and EPR (electron paramagnetic resonance), being far more reproducible, nondestructive, than other analytical techniques such as liquid chromatography, mass spectroscopy, and high-performance liquid chromatography cover a much wider dynamic range of metabolites with easy sample preparation techniques with high speed and fidelity. Hence, these magnetic resonance techniques have been proven to be extremely useful in plant metabolite profiling and disease metabolomics, along with structural elucidation of bioactive compounds from plant sources. Therefore, the present review focuses on the effectiveness of magnetic resonance for the detection of plant-derived metabolites that may lead to new areas of research in various fields such as drug discovery and development, metabolomics, combinatorial chemistry, and assessing overall food safety and quality.
This study was aimed to investigate the changes of brain MRI features and serum biological parameters in patients with TLE. 30 patients with unilateral TLE confirmed by surgical pathology were selected as study subjects, and 30 subjects without a history of epilepsy who underwent health examinations during the same period were selected as controls. The brain MRI features of the patients were explored and the T2 relaxation time (HCT2) indexes of the bilateral hippocampus were extracted. The differences in levels of peripheral blood T lymphocyte subsets, inflammatory cytokines, and miRNAs were measured. The results showed that the hippocampal volume of TLE patients was significantly reduced, and the HCT2 value of the hippocampus was greater than that of the control group ( P < 0.05). CD 3+ (77.9 ± 4.4)%, CD 4+ (45.6 ± 2.2)%, CD 8+ (22.1 ± 1.9)%, and CD 3+ /CD 8+ (2.24 ± 0.22) in peripheral blood T lymphocyte subsets of epileptic patients, compared with control group, CD 3+ , CD 4+ , and CD 4+ /CD 8+ levels were significantly increased and CD 8 + concentration was significantly decreased in epileptic patients ( P < 0.05); inflammatory cytokines TNF- α was (2.63 ± 0.26) pg/mL, IL-1 β was (4.61 ± 0.57) pg/mL, IL-2 was (1.59 ± 0.21) pg/mL, IL-6 was (2.28 ± 0.19) pg/mL, and ICAM-1 was (1.89 ± 0.30) pg/mL in peripheral blood of epileptic patients, which was significantly increased compared with control group, while IL-10 was significantly decreased in epileptic patients ( P < 0.05); miR-146a was (2.14 ± 0.28) and miR-210 was (1.89 ± 0.31), miR-221 (2.44 ± 0.35), miR-34a (0.59 ± 0.14), miR-135b (10.17 ± 0.16), miR-33 (0.26 ± 0.09) in peripheral blood miRNA levels of epileptic patients, and miR-146a, miR-210, miR-221, and miR-34a levels of epileptic patients were significantly increased compared with control group, while MiR-135b and miR-33 levels of epileptic patients were significantly reduced ( P < 0.05). In summary, patients with TLE have hippocampal lesions, which may be related to peripheral blood T lymphocyte subsets imbalance, chronic inflammatory response, and abnormal expression of miRNAs.
The Clebsch–Gordan coefficients are extremely useful in magnetic resonance theory, yet have an infamous perceived level of complexity by many students. The Clebsch–Gordan coefficients are used to determine both the matrix elements of the spherical tensor operators and the total angular momentum states of a system of component angular momenta. Full derivations of these coefficients are rarely worked through step by step. Instead, students are provided with tables accompanied by little or no explanation of where the values in it originated from. This lack of direction is often a source of confusion for students. For this reason, we work through two common examples of the application of the Clebsch–Gordan coefficients to magnetic resonance experiments. In the first, we determine the components of the magnetic resonance Hamiltonian of ranks 0, 1, and 2 and use these to identify the secular portion of the static, heteronuclear dipolar Hamiltonian. In the second, we derive the singlet and triplet states that arise from the interaction of two identical spin- 1 / 2 particles.
