Water diffusion in biomedical systems as related to magnetic resonance imaging

Water diffusion within the brain is studied numerically for various clinical conditions. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. A wide range of pertinent parameters such as Lewis number, cell volume, and the buoyancy ratio are considered in the present study. Comparisons with previously published work show excellent agreement. The results show that the diffusion coefficient, cell volume, and the buoyancy ratio play significant roles on the characterization of the mass and heat transfer mechanisms within the cell. Concentration maps are developed for various clinical conditions. Pertinent results for the streamlines, isotherms and the mass and heat transfer rates in terms of the average Sherwood and Nusselt numbers are presented and discussed for different parametric values. Experimental tests are also conducted to produce an 8 Tesla image which is compared with our numerical simulation. The present study provides essential maps for brain disorders classified based on several pertinent clinical attributes.     

Non-Darcian Effects on Buoyancy-Induced Heat Transfer in a Partially Divided Square Enclosure with Internal Heat Generation

The present investigation addresses non-Darcian effects on the buoyancy-induced heat transfer in a partially divided square enclosure with internal heat generation. The generalized model of the momentum equation, which is also known as the Forchheimer–Brinkman extended Darcy model, which takes into account boundary and inertia effects, was used in representing the fluid motion inside the porous layer. The local thermal equilibrium condition was assumed to be valid for the range of the thermophysical parameters considered in the present investigation. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used was ascertained by comparing our results with previously published results. Results were obtained in terms of streamlines, isotherms, and Nusselt number for various geometrical parameters specifying the height and width of the partition. In addition, the effects of external and internal Rayleigh numbers and Darcy number were highlighted in the proposed study.     

Applications of nanofluids in porous medium

Journal of Thermal Analysis and Calorimetry - This investigation provides a review on the applications of nanofluids in porous media. The transport phenomena in porous media have been of continuing...     

Unsteady numerical simulation of double diffusive convection heat transfer in a pulsating horizontal heating annulus

A numerical study is conducted on time-dependent double-diffusive natural convection heat transfer in a horizontal annulus. The inner cylinder is heated with sinusoidally-varying temperature while the outer cylinder is maintained at a cold constant temperature. The numerical procedure used in the present work is based on the Galerkin weighted residual method of finite-element formulation by incorporating a non-uniform mesh size. Comparisons with previous studies are performed and the results show excellent agreement. In addition, the effects of pertinent dimensionless parameters such as the thermal Rayleigh number, Buoyancy ratio, Lewis number, and the amplitude of the thermal forcing on the flow and heat transfer characteristics are considered in the present study. Furthermore, the amplitude and frequency of the heated inner cylinder is found to cause significant augmentation in heat transfer rate. The predictions of the temporal variation of Nusselt and Sherwood numbers are obtained and discussed.     

Fluid–structure interaction of turbulent pulsatile flow within a flexible wall axisymmetric aortic aneurysm model

Pulsatile turbulent flow characteristics in an axisymmetric aortic aneurysm (AA) model were analyzed numerically using a simulated physiological waveform. The transport equations were solved using the finite element formulation based on the Galerkin method of weighted residuals. A fully-coupled fluid–structure interaction (FSI) analysis was utilized in this work. We investigated the effects of turbulent flow characteristics on the distribution of wall stress and flow patterns in AA models. Wall stress distributions were calculated by computational solid stress (CSS) model, which ignores the effect of the blood flow, and the FSI model that takes into account flow and solid mechanics. Our results showed that peak wall stress and peak deformation were found to occur shortly after peak systolic flow in the FSI model and at the peak luminal pressure condition in the CSS model. Further, CSS model underestimated wall stress calculations when compared to the FSI model. There were also significant differences in the structure of flow fields between the flexible and rigid wall aneurysm models. Contour plots of kinetic energy dissipation and the application of the Kolmogorov microscale suggest that the conditions that result in red blood cell damage and platelet activation most likely occur in the near-wall region of AA during turbulent flow.     

New lower bounds for bin packing problems with conflicts

The bin packing problem with conflicts (BPC) consists of minimizing the number of bins used to pack a set of items, where some items cannot be packed together in the same bin due to compatibility restrictions. The concepts of dual-feasible functions (DFF) and data-dependent dual-feasible functions (DDFF) have been used in the literature to improve the resolution of several cutting and packing problems. In this paper, we propose a general framework for deriving new DDFF as well as a new concept of generalized data-dependent dual-feasible functions (GDDFF), a conflict generalization of DDFF. The GDDFF take into account the structure of the conflict graph using the techniques of graph triangulation and tree-decomposition. Then we show how these techniques can be used in order to improve the existing lower bounds.     

The role of porous media in biomedical engineering as related to magnetic resonance imaging and drug delivery

Pertinent works associated with magnetic resonance imaging (MRI) and drug delivery are reviewed in this work to demonstrate the role of transport theory in porous media in advancing the progress in biomedical applications. Diffusion process is considered significant in many therapies such as delivering drugs to the brain. Progress in development of the diffusion equation using local volume-averaging technique and evaluation of the applications associated with the diffusion equation are analyzed. Tortuosity and porosity have a significant effect on the diffusion transport. Different relevant models of tortuosity are presented and mathematical modeling of drug release from biodegradable delivery systems are analyzed in this investigation. New models for the kinetics of drug release from porous biodegradable polymeric microspheres under bulk erosion and surface erosion of the polymer matrix are presented in this study. Diffusion of the dissolved drug, dissolution of the drug from the solid phase, and erosion of the polymer matrix are found to play a central role in controlling the overall drug release process. This study paves the road for the researchers in the area of MRI and drug delivery to develop comprehensive models based on porous media theory utilizing fewer assumptions as compared to other approaches.     

Computational modeling of transport phenomena in chemical vapor deposition

Fluid flow, heat and mass transport processes in a two-dimensional converging channel with a heated susceptor are investigated numerically for various pertinent parameters. A model is developed to analyze the impact of the transport mechanisms on the deposition process of a typical chemical vapor deposition. Discretization of the governing equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases are performed and found to be in excellent agreement. Various results for the streamlines, isotherms, and isoconcentrations are presented and discussed for different parametric values. The results of the present investigation show that the tilted susceptor can produce a greater deposition and a more even distribution of material than a non-tilted susceptor. Moreover, the tilted susceptor is found to suppress the effect of transverse recirculation regions inside the reactor.     

Computational modeling of cerebral diffusion-application to stroke imaging

Water diffusion within the structure of a brain extracellular space is analyzed numerically for various diffusion parameters of brain tissue namely extracellular space porosity and tortuosity. An algorithm for predicting diffusion pattern of water molecules within human brain considering the mechanics of water diffusion within porous media is developed. The extracellular space is modeled as a homogeneous porous medium with uniform porosity and permeability. Discretization of the fluid flow, heat transfer and mass transport equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Concentration maps are developed in this study for various clinical conditions. The effect of the space porosity and the turtousity on the heat and mass transport within the extracellular space are found to be significant. The results presented in this work play an important role in producing more effective imaging techniques for brain injury based on the apparent diffusion coefficient.