Postdoctoral Research Fellow, University Malaysia Pahang, Pahang, Malaysia
Mathematical model for prediction of effective treatment of cancer cells
Blood is considered as non-Newtonian fluid comprising of red blood cells (RBCs) and plasma. In the development of therapeutic and drug delivery the blood mediated nanoparticles is an emerging and growing filed. The nanoparticle properties such as, shape, size and surface chemistry can be controlled to enhance the effectiveness and efficacy of the drug delivery to targeted effective zone. The ability of the nanoparticles to target and enter the effective zone is extremely depends on their behaviour in the blood fluid. Here we introduce a new model of nanoparticle behaviour under blood flow and how their trajectory can be controlled by application of an external magnetic field. In other words, a mathematical model of magnetohydrodynamics (MHD) nanoparticles based micropolar blood flow through blood vessels is studied. The governing coupled nonlinear partial differential equations of the problem are non-dimensionalized by using appropriate similarity transformations. These non-dimensional equations along with the corresponding boundary conditions are solved numerically using the finite difference method in MATLAB for different emerging parameters. The results showed that the effect of particle size and morphology are two important parameters which should be considered for an effective treatment of diseased cells. Especially the models is helpful for prediction of effective treatment of cancer cells.
Abstract: In the paper, we use a mathematical model to study the population dyna mics of replicating malaria parasites and their interaction with the immune cells within a human host. The model is formulated as a system of age-structured partial differential equations that are then integrated over age to obtain a system of nonlinear delay differential equations. Our model incorporates an intracellular time delay between the infection of the red blood cells by the merozoites that grow and replicate within the infected cells to produce new merozoites. The infected red blood cells burst approximately every 48 h releasing daughter parasites to renew the cycle. The dynamical processes of the parasites within the human host are subjected to pressures exerted by the human immunological responses. The system is then solved using a first-order, finite difference method to give a discrete system. Numerical simulations carried out to illustrate stability of the system reveal that the populations undergo damped oscillations that stabilise to steady states.
Pub.: 22 Nov '07, Pinned: 11 Oct '17
Abstract: This paper presents an analysis of momentum, angular momentum and heat transfer during the unsteady natural convection in micropolar nanofluids. Presented phenomena are modelled in the vicinity of a vertical plate and heat flux which rises suddenly at a given moment, using the boundary layer concept. Differential equations of angular momentum conservation are used according to the theory of micropolar fluids developed by Eringen. Finite difference method is used to solve the equations for conservation of mass, energy, momentum and angular momentum. Selected nanofluids treated as single phase fluids contain small particles with diameter size d = 10 nm and d = 38.4 nm. In particular, two ethylene glycol based nanofluids and one water-based nanofluid are analysed. Volume fraction of these solutions is 6%. First ethylene glycol solution contain Al2 O3 nanoparticles (d = 38.4 nm), and the second ethylene glycol solution contained Cu nanoparticles (d = 10 nm). Water based nanofluid contain Al2 O3 nanoparticles (d = 38.4 nm). As a result of solving conservation equations, unsteady velocity field (U, V), temperature (T), microrotation component normal to (x, y) plane (N), velocity gradient ∂U/∂Y and temperature gradient ∂T/∂Y are obtained. These results are compared to theoretical and experimental results presented in literature. At the end of this paper, heat transfer enhancement for analysed nanofluids is estimated.
Pub.: 26 Aug '16, Pinned: 11 Oct '17