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A new application of fractional derivatives for predicting human glioblastoma multiforme tumor growth

Glioblastoma is the most common and deadly primary brain tumor in adults. To optimize the treatment strategies, it is essential to understand the tumor growth dynamics in different periods. In this study, we use image processing techniques to combine the available early-stage imaging data and applied a fractional reaction–diffusion equation to predict the human glioblastoma multiforme tumor growth. We consider the heterogeneity of the brain tissue by assigning different diffusion coefficients for the three regions of the human brain. A meshfree method based on the thin plate spline radial basis function is used for the numerical solution of nonlinear time fractional Proliferation-Invasion equation. The results show that the proposed model has a better fit with the experimental data. The prediction of tumor growth at any desired time with no need to repeated imaging is another advantages of the model which could reduce the side effects and cost of diagnostic and therapeutic methods. The model can also incorporate the effects of various treatment modalities such as hyperthermia, radiation, and surgery on tumor growth. Furthermore, it can enable the use of patient-specific characteristics in diagnosis and treatment and facilitate the development of personalized medicine approaches.

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Lattice <scp>Boltzmann</scp> simulation of effects of realistic boundary conditions on volumetric radiation‐conduction melting of a novel cylindrical enclosure filled with phase change materials

AbstractIn this research, a novel solar latent heat thermal energy storage (LHTES) system, including the cylindrical enclosures filled with a phase change material (PCM), is proposed, which can be installed on the building windows to alleviate the drawbacks of traditional PCM‐filled double‐glazed windows, such as daylight hindrance and leakage. The lattice Boltzmann method (LBM) is used to simulate the volumetric radiation‐conduction melting of the PCM within a single cylinder of the proposed LHTES system with considering more realistic conditions such as convective boundary condition, shadow effect, and variable solar radiation angle compared with the available works in the literature. As such, several boundary conditions are assessed, and parameters such as cylinder diameter, extinction coefficient, scattering albedo, solar angle, shadow effect, and natural convection heat transfer coefficient are studied on the time history of the melting fraction and charging time. The results revealed that considering the applied conditions, such as convection heat loss to the environment and shadow, significantly affects the charging time of the system. It is shown that the charging time for convective boundary condition with , , and increases, respectively, by 11%, 30%, and 50% relative to a case with the insulated boundary condition without the shadow effect and 38%, 91%, and 175% compared with the insulated case with a 90° shadow.

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