On network construction and module detection for molecular graph of titanium dioxide.

Titanium dioxide is the most common and valuable oxide among four types of oxides of titanium. Its physicochemical properties make it a very valuable compound. The main objective of this article is to initially detect the modules based on highly connected links of the network of the degree-based topological indices. This information is lately integrated with different physical properties of the chemical compound of titanium dioxide to develop different mathematical frameworks based on master regulatory indices of the modules. This connection can be helpful in studying the physical measures at a deeper level in the form of different degree based topological indices.Communicated by Ramaswamy H. Sarma.

Modeling the impact of the vaccine on the COVID-19 epidemic transmission via fractional derivative.

To achieve the goal of ceasing the spread of COVID-19 entirely it is essential to understand the dynamical behavior of the proliferation of the virus at an intense level. Studying this disease simply based on experimental analysis is very time consuming and expensive. Mathematical modeling might play a worthy role in this regard. By incorporating the mathematical frameworks with the available disease data it will be beneficial and economical to understand the key factors involved in the spread of COVID-19. As there are many vaccines available globally at present, henceforth, by including the effect of vaccination into the model will also support to understand the visible influence of the vaccine on the spread of COVID-19 virus. There are several ways to mathematically formulate the effect of disease on the population like deterministic modeling, stochastic modeling or fractional order modeling etc. Fractional order derivative modeling is one of the fundamental methods to understand real-world problems and evaluate accurate situations. In this article, a fractional order epidemic model S p E p I p E r p R p D p Q p V p on the spread of COVID-19 is presented. S p E p I p E r p R p D p Q p V p consists of eight compartments of population namely susceptible, exposed, infective, recovered, the quarantine population, recovered-exposed, and dead population. The fractional order derivative is considered in the Caputo sense. For the prophecy and tenacity of the epidemic, we compute the reproduction number R 0 . Using fixed point theory, the existence and uniqueness of the solutions of fractional order derivative have been studied. Furthermore, we are using the generalized Adams-Bashforth-Moulton method, to obtain the approximate solution of the fractional-order COVID-19 model. Finally, numerical results and illustrative graphic simulation are given. Our results suggest that to reduce the number of cases of COVID-19 we should reduce the contact rate of the people if the population is not fully vaccinated. However, to tackle the issue of reducing the social distancing and lock down, which have very negative impact on the economy as well as on the mental health of the people, it is much better to increase the vaccine rate and get the whole nation to be fully vaccinated.

Comparison amongst pulse sequences for enhanced contrast to noise ratio in magnetic resonance imaging.

OBJECTIVE: To provide optimised pulse sequence and imaging protocols for contrast-to-noise ratio and for tissues that have different signal intensities in magnetic resonance imaging. METHODS: A tissue equivalent material, ferrous benzoic xylenol orange gel, was prepared using gelatine, ferrous ammonium sulfate, sulfuric acid, xylenol orange tetrasodium salt and benzoic acid. The gel was irradiated using 6MV photons from a Varian Clinac 600C linear accelerator, with a dose of 5, 10, 15, 20 and 25 gray. Experimental variations in imaging parameters were performed in echo time and repetition time. The quantitative analysis consisted of contrast-to-noise ratio. RESULTS: Conventional spin echo and fast spin echo were equivalent for the tissues of comparable signal intensities and for entities moderate difference between signal intensities. Conventional spin echo provided remarkable contrast for tissues where signal intensity difference was extremely high in T1, T2-weighted study. An appropriate inversion time of fast fluid attenuated inversion recovery made it significant to measure contrast between tissues where signal intensity difference was the smallest and ordinary. CONCLUSIONS: Choice of pulse sequence and parameters played a vital role in developing fine image contrast.

Calcification in Globus Pallidus and Putamen of Multiple Sclerosis Patients Versus Healthy Subjects Using Quantitative Susceptibility Mapping.

BACKGROUND: Calcification has been well reported in basal ganglia and it grows rapidly in globus pallidus (GP) followed by putamen (PUT) and caudate nucleus because of their high metabolic rate and displays high susceptibility effects. Therefore, the current study focused on magnetic susceptibility effect of calcium content in normal and diseased tissue due to metabolic changes. OBJECTIVES: To evaluate calcium content in GP and PUT structures of multiple sclerosis (MS) patients versus healthy subjects using quantitative susceptibility mapping. PATIENTS AND METHODS: We compared 10 MS patients with mean age of 48.3 years (standard deviation [SD]=11.89) with 10 healthy subjects with mean age of 39.6 years (SD=11.52). Scanning of subjects was performed with high resolution (0.5×0.5×2 mm3) using susceptibility weighted imaging sequence on 3 Tesla (Trio-Siemens, Erlangen, Germany). Data was processed in homemade SPIN software to produce susceptibility mapping. Threshold was set in healthy subjects to detect calcium content in PUT and GP structures. RESULTS: Magnetic susceptibility(x) of calcium content was assessed by number of pixels induced by GP and PUT in MS patients as well as healthy subjects. Two sample t-test was used to assess the difference between susceptibilities of GP and PUT of MS patients (P = 0.06, P > 0.05). Susceptibilities of GP and PUT also showed P = 0.3 in healthy subjects. One way analysis of variance was used to assess the difference of susceptibilities in four variables of both populations. Insignificant results (P = 0.7, P > 0.05) were found among four variables. There was no statistically significant difference between magnetic susceptibilities of both populations. CONCLUSION: Statistical analysis of susceptibilities of MS patients versus healthy subjects found no excess deposition of calcium content in deep gray matter of MS patients. Calcification may not be considered as a biomarker of prognosis in MS.

Choice of the pulse sequence and parameters for improved signal-to-noise ratio in T1-weighted study of MRI.

OBJECTIVE: To investigate the practical impact of alteration of imaging parameters on signal-to-noise ratio for the most commonly used T1-weighted magnetic resonance sequences. METHODS: The study was conducted in the Department of Medical Physics, Ninewells Hospital and Medical School, Dundee, UK, in 2007. Magnetic resonance images of a tissue-equivalent material were generated with a set of T1 and T2 values. Experimental variations in the imaging parameters were performed in echo time and repetition time. Quantitative analysis consisted of signal-to-noise ratio. RESULTS: Percentage inaccuracy in signal-to-noise ratio was the result of inappropriate choice of parameters. We have investigated conventional spin echo, fast spin echo and fast fluid attenuated inversion recovery with one of corresponding percentage errors 28.68%, -36.65% and -40.34%, respectively. Conventional spin echo presented moderately low percentage error with the choice of repetition time and echo time. Factual error in fast spin echo was slightly higher than conventional spin echo. Fast fluid attenuated inversion recovery could create outstanding signal-to-noise ratio of high T1/T2 value phantoms in T1-weighted images. CONCLUSIONS: The role of repetition time and echo time in T1-weighted images was crucial to sustain the image quality.

The impact of variation in the pulse sequence parameters on image uniformity in magnetic resonance imaging.

OBJECTIVE: To evaluate the practical impact of alteration of key imaging parameters of Magnetic Resonance Imaging on image quality and effectiveness provided by widely available fast imaging pulse sequences. METHODS: A tissue equivalent material for Magnetic resonance Imaging (MRI) has been produced from a polysaccharide gel, agros, containing gadolinium chloride chelated to Ethylene Diamine Tetra- Acetic acid (EDTA) with a sort of T1 and T2 values. Experimental variations in key parameters included echo time (TE) and repetition time TR. Quantitative analysis consisted of image nonuniformity. RESULTS: In T2 weighted images; any change in TE played a critical role in the signal homogeneity in all pulse sequences. The percentage of nonuniformity was incredibly high in T2 weighted image but the change of TR was insignificant in T2-weighted study. Involving T1 weighted images, percentage of nonuniformity was high in gradient recalled echo (GRE), also noticeable in fast fluid attenuated recovery (FLAIR) but quite acceptable in fast spin echo (FSE) and conventional spin echo (CSE). CONCLUSION: Selection of parameters relatively simple in CSE both in T1, T2-weighted study that maintains image uniformity and quality as well. GRE is a very sensitive pulse sequence for any variation in parameters and loose signal uniformity rapidly.