Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2*-weighted magnetic resonance imaging at 7 T

Model-free phasor image analysis of quantitative myocardial T1 mapping

Model-free phasor image analysis, well established in fluorescence lifetime imaging and only recently applied to qMRI [Formula: see text] data processing, is here adapted and validated for myocardial qMRI [Formula: see text] mapping. Contrarily to routine mono-exponential fitting procedures, phasor enables mapping the lifetime information from all image voxels to a single plot, without resorting to any regression fitting analysis, and describing multi-exponential qMRI decays without biases due to violated modelling assumptions. In this feasibility study, we test the performance of our recently developed full-harmonics phasor method for unravelling partial-volume effects, motion or pathological tissue alteration, respectively on a numerically-simulated dataset, a healthy subject scan, and two pilot patient datasets. Our results show that phasor analysis can be used, as alternative method to fitting analysis or other model-free approaches, to identify motion artifacts or partial-volume effects at the myocardium-blood interface as characteristic deviations, or delineations of scar and remote myocardial tissue in patient data.

Review of fractional epidemic models

The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.

Quantitative MR relaxation using MR fingerprinting with fractional-order signal evolution

The fractional-order Bloch equations have been shown to describe a wider range of experimental situations involving heterogeneous, porous, or composite materials. This paper introduces a novel dictionary of quantitative MR fingerprinting generated by signal evolution model with fractional-order Bloch equations to describe magnetic resonance (MR) relaxation. Here, the fractional-order relaxation models are implemented into Bloch equations through phase transitions using EPG simulation. In the phantom experiments, the fractional-order analysis showed smaller root mean squared error (T1: RMSE = 5.21%, T2: RMSE=3.75%) using the proposed method compared to using conventional method. Among the in vivo experiments of human brains, the estimated T1 and T2 values (mean ± SD) were 843 ± 46.3 ms and 70 ± 4.7 ms in white matter, 1323 ± 28.5 ms and 95 ± 3.8 ms in gray matter. So the proposed method can provide well extensions of current MR fingerprinting and has shown potential to apply into the phantom experiments and the in vivo applications to approach the standard methods for quantitative imaging.

Estimation of Parameter of Fractional Order Covid -19 SIQR Epidemic Model

Epidemic model have been broadly used in different forms for studying and forecasting epidemiological processes the spread of dengue, zika virus , HIV, SARS and recently , the 2019–20 corona virus which is an ongoing pandemic of corona virus disease (COVID-19). In the present paper, an inverse problem to find the parameters for the single term (multi term) fractional order system of an outbreak of COVID-19 is considered. In the starting, we propose a numerical method for fractional order corona virus system based on the Gorenflo-Mainardi-Moretti-Paradisi (GMMP) scheme, and then to find the parameters we use GMMP method and the modified hybrid Nelder-Mead Simplex search and particle swarm optimization algorithm. With the new fractional orders and parameters our fractional order corona virus system is capable to providing numerical results that agree well with the real data.

T1rho Fractional-order Relaxation of Human Articular Cartilage

T1rho imaging is a promising non-invasive diagnostic tool for early detection of articular cartilage degeneration. A mono-exponential model is normally used to describe the T1rho relaxation process. However, mono-exponentials may not adequately to describe NMR relaxation in complex, heterogeneous, and anisotropic materials, such as articular cartilage. Fractional-order models have been used successfully to describe complex relaxation phenomena in the laboratory frame in cartilage matrix components. In this paper, we develop a time-fractional order (T-FACT) model for T1rho fitting in human articular cartilage. Representative results demonstrate that the proposed method is able to fit the experimental data with smaller root mean squared error than the one from conventional mono-exponential relaxation model in human articular cartilage.

A fractional motion diffusion model for a twice-refocused spin-echo pulse sequence

The purpose of this study was to develop an analytical expression for a fractional motion (FM) diffusion model to characterize diffusion-induced signal attenuation in a twice-refocused spin-echo (TRSE) sequence that is resilient to eddy currents, and to demonstrate its applicability to human brain imaging in vivo. Based on the FM theory, which provides a unified statistical description for Langevin motions, the diffusion-weighted (DW) MR signal was measured with a TRSE sequence that balances the concomitant gradients. The analytical expression was fitted to a set of DW images acquired with 14 b-values (0-4000 s/mm² ) from a total of 10 healthy human subjects at 3 T, yielding three FM parameter maps based on anomalous diffusion coefficient D_{φ, ψ} , diffusion increment variance φ, and diffusion correlation ψ, respectively. These parameters were used to characterize different brain regions in gray matter (GM), white matter (WM), and cerebrospinal fluid. The analytical expression for the TRSE-based FM model accurately described diffusion signal attenuation in healthy brain tissues at high b-values. TRSE's robustness against eddy currents was illustrated by comparing results from an expression for a conventional Stejskal-Tanner sequence. The TRSE-based FM model also produced consistent GM-WM contrast (p < 0.01) across all brain regions studied, whereas the consistency was not observed with the Stejskal-Tanner-based FM model. This new analytical expression is expected to enable further investigations to probe tissue structures by exploiting anomalous diffusion properties without being hindered by eddy-current perturbations at high b-values.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Development of Ferrite-Based Temperature Sensors for Magnetic Resonance Imaging: A Study of Cu1-xZnxFe2O4

We investigate the use of Cu_1-x Zn _x Fe₂O₄ ferrites (0.60 < x < 0.76) as potential sensors for magnetic- resonance-imaging thermometry. Samples are prepared by a standard ceramic technique. Their structural and magnetic properties are determined using x-ray diffraction, scanning electron microscopy, super-conducting quantum-interference device magnetometry, and Mossbauer and 3-T nuclear-magnetic-resonance spectroscopies. We use the mass magnetization of powdered ferrites and transverse relaxivity r*₂ of water protons in Ringer's-solution-based agar gels with embedded micron-sized particles to determine the best composition for magnetic-resonance-imaging (MRI) temperature sensors in the (280-323)-K range. A preclinical 3-T MRI scanner is employed to acquire T*₂ weighted temperature-dependent images. The brightness of the MRI images is cross-correlated with the temperature of the phantoms, which allows for a temperature determination with approximately 1°C accuracy. We determine that the composition of 0.65 < x < 0.70 is the most suitable for MRI thermometry near human body temperature.