Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative

This thesis investigates analytically the magnetohydrodynamics (MHD) transport of Newtonian and non-Newtonian fluids flows inside a circular channel. The flow was subjected to an external electric field for the Newtonian model and a uniform transverse magnetic field for all models. Pressure gradient or oscillating boundary condition was employed to drive the flow. In the first model Newtonian fluid flow without stenotic porous tube was considered and in the second model stenotic porous tube was taken into account. The third model is concerned with the temperature distribution and Nusselt number. The fourth model investigates the non-Newtonian second grade fluid velocity affected by the heat distribution and oscillating walls. Last model study the velocity, acceleration and flow rate of third grade non-Newtonian fluid flow in the porous tube. The non-linear governing equations were solved using the Caputo-Fabrizio time fractional order model without singular kernel. The analytical solutions were obtained using Laplace transform, finite Hankel transforms and Robotnov and Hartley’s functions. The velocity profiles obtained from various physiological parameters were graphically analyzed using Mathematica. Results were compared with those reported in the previous studies and good agreement were found. Fractional derivative and electric field are in direct relation whereas magnetic field and porosity are in inverse relation with respect to the velocity profile in Newtonian flow case. Meanwhile, fractional derivative and Womersely number are in direct relation whereas magnetic field, third grade parameter, frequency ratio and porosity are in inverse relation in third grade non-Newtonian flow case. In the case of second grade fluid, Prandtl number, fractional derivative and Grashof number are in direct relation whereas second grade parameter and magnetic field are in inverse relation. The fluid flow model can be regulated by applying a sufficiently strong magnetic field

Micropolar pulsatile blood flow conveying nanoparticles in a stenotic tapered artery : non-Newtonian pharmacodynamic simulation

Two-dimensional rheological laminar hemodynamics through a diseased tapered artery with a mild stenosis present is simulated theoretically and computationally. The effect of different metallic nanoparticles homogeneously suspended in the blood is considered, motivated by drug delivery (pharmacology) applications. The Eringen micropolar model has been deployed for hemorheological characteristics in the whole arterial region. The conservation equations for mass, linear momentum, angular momentum (micro-rotation), and energy and nanoparticle species are normalized by employing suitable non-dimensional variables. The transformed equations are solved numerically subject to physically appropriate boundary conditions using the finite element method with the variational formulation scheme available in the FreeFEM++ code. A good correlation is achieved between the FreeFEM++ computations and existing results. The effect of selected parameters (taper angle, Prandtl number, Womersley parameter, pulsatile constants, and volumetric concentration) on velocity, temperature, and microrotational (Eringen angular) velocity has been calculated for a stenosed arterial segment. Wall shear stress, volumetric flow rate, and hemodynamic impedance of blood flow are also computed. Colour contours and graphs are employed to visualize the simulated blood flow characteristics. It is observed that by increasing Prandtl number (Pr), the micro-rotational velocity decreases i.e., microelement (blood cell) spin is suppressed. Wall shear stress decreases with the increment in pulsatile parameters (B and e), whereas linear velocity increases with a decrement in these parameters. Furthermore, the velocity decreases in the tapered region with elevation in the Womersley parameter (α). The simulations are relevant to transport phenomena in pharmacology and nano-drug targeted delivery in hematology

RADIATION-BRINKMAN NUMBER EFFECTS ON BLOOD FLOW IN A POROUS ATHEROSCLEROTIC MICROCHANNEL WITH THE PRESENCE OF A MAGNETIC FIELD, GROWTH RATE AND TREATMENT

Mathematical models representing blood flow through a microchannel with the effect of radiation-Brinkman number with an external magnetic field were formulated. The atherosclerosis is due to an exponential growth of cholesterol in the blood and trans fat consumption. The geometry of atherosclerosis was assumed to be growth rate and time dependent. The blood flow is considered nonlinear, incompressible, viscous, and fully developed. The nonlinear equations under suitable boundary conditions were scaled to a system of dimensionless PDE, which were reduced further to ordinary differential equations using the perturbation conditions. The perturbed system of ordinary differential equations was solved using the Laplace method. The blood flow profiles, such as velocity, volumetric flow rate, lipid concentration profiles such as lipid concentration and rate of mass of the lipid transfer, and temperature profiles such as blood temperature and the rate of heat transfer are obtained and the effects of the pertinent parameters such as magnetic field, radiation absorption, and Brinkman Number were discussed. The results show that the velocity increases with an increase in Brinkman number, Grashof number, solutal Grashof number and the porosity, while it decreases with an increase in Schmidt number, Prandtl number, radiation absorption, chemical reaction, and magnetic field. From the investigation, we could deduce that there is an increase in blood temperature with the increase in Brinkman number and a decrease in temperature due to an increase in Schmidt number, Prandtl number, radiation absorption, chemical reaction, and oscillatory frequency. In conclusion, we have been able to formulate a mathematical representation of blood flow through a sclerotic microchannel, obtained an exact solution to the problem, and presented results that might be useful for mathematicians and clinicians

A review on recent advancements in the hemodynamics of nano-drug delivery systems

Cardiovascular disease (CVD) is a leading cause of mortality and morbidity in developed countries. CVD is produced by atherosclerotic lesions that reduce arterial lumen size through plaque formation and arterial thickening. This decreases blood flow to the heart and frequently manifests in severe hemodynamic complications like myocardial infarction or angina pectoris. A drug delivery system (DDS) is a clinical methodology (formulation or device) which enables the introduction of a therapeutic substance into the body and improves its efficacy and safety by controlling the rate, time, and place of release of drugs in the body. Drug delivery technologies modify drug release profile, absorption, distribution and elimination for the benefit of improving product effectiveness and patient convenience and compliance. The review explores extensively hemodynamic aspects of the cardiovascular system and diseases which can be treated via nanodrug delivery with a comprehensive overview of research efforts in these areas. Nanomedicine is an expeditiously growing science in which biomaterials (drugs) engineered at the nanoscale are implemented to enhance therapeutic performance and improve patient treatments. Among the many other diverse applications of nanomaterials in medicine (e.g. bio-UIRtribology, tissue repair, orthopaedic implants etc), nano-drug delivery systems have emerged as among the most promising. This technology has evolved into a significant platform for delivering successfully remedial agents to diseased sites with substantially greater target control, precision and sophistication. By greatly increasing site specificity, lowering toxicity and target-oriented 2 delivery, nanotechnological drug delivery (“nano-pharmacodynamics”) has consistently achieved very impressive consistency, benefits and has aided massively in the fight against potentially lethal haemotological diseases. Recently, nanomedicine has embraced an even wider range of applications including the administration of chemotherapeutic agents, biological agents, diabetes regulation, sterilization, cancer and tumour inhibition, rheumatic fever mitigation etc. The current review presents a comprehensive appraisal of nano-drug delivery systems, simulation with engineering methods, types of nanodrugs and their effectiveness. The excellent targeting properties attainable with magnetic nanoparticles as engineering pharmacodynamic agents, in particular, offers huge potential in the treatment of many complex hemodynamic disorders. Furthermore, the present review summarizes the efficiency of drug carrier nanoparticles in mitigating the adverse effects of stenosed blood vessels and outlines other future potential uses for nano-drugs in biomedical applications

Computational simulations of hybrid mediated nano-hemodynamics (ag-au/blood) through an irregular symmetric stenosis

This article examines theoretically and numerically the unsteady two-dimensional blood flow through a diseased artery featuring an irregular stenosis. An appropriate geometric model is adopted to simulate the irregular stenotic artery. Inspired by drug delivery applications for blood vessels, the impact of hybrid nanoparticles on blood flow using a modified Tiwari-Das model is discussed. The blood is examined to have a homogenous suspension of hybrid nanoparticles. Reynolds’ viscosity model is applied in the formulation to represent the temperature dependency of blood. The two-dimensional governing conservation equations for momentum and heat transfer with buoyancy effect are simplified by considering the mild stenotic approximation. A finite-difference technique is deployed to numerically discretize the transformed non-dimensional model. Extensive graphical results for blood flow characteristics are obtained by MATLAB code. Comprehensive visualization of the effects of hemodynamic, geometric and nanoscale parameters on transport characteristics is provided. The problem is conducted for silver and silver-gold hybrid mediated blood flow models, and experimental values of blood and these biocompatible metallic nanoparticles. A comparison between silver and hybrid nanofluid is obtained which promotes the use of hybrid nanoparticles in successfully achieving clinically more beneficial results associated with nano-drug delivery in diseased hemodynamics. Enhancement in viscosity parameter induces axial flow acceleration in the stenotic region while lower thermal conductivity decreases the temperature magnitudes. Furthermore, with time variation, the pressure gradient is found to be lower in coronary arteries comparatively to femoral arteries. The simulations are relevant to transport phenomenon in nano-drug targeted delivery in haematology

Cilia-assisted hydromagnetic pumping of biorheological couple stress fluids

A theoretical study is conducted for magnetohydrodynamic pumping of electro-conductive couple stress physiological liquids (e.g. blood) through a two-dimensional ciliated channel. A geometric model is employed for the cilia which are distributed at equal intervals and produce a whip-like motion under fluid interaction which obeys an elliptic trajectory. A metachronal wave is mobilized by the synchronous beating of cilia and the direction of wave propagation is parallel to the direction of fluid flow. A transverse static magnetic field is imposed transverse to the channel length. The Stokes’ couple stress (polar) rheological model is utilized to characterize the liquid. The normalized two-dimensional conservation equations for mass, longitudinal and transverse momentum are reduced with lubrication approximations (long wavelength and low Reynolds number assumptions) and feature a fourth order linear derivative in axial velocity representing couple stress contribution. A coordinate transformation is employed to map the unsteady problem from the wave laboratory frame to a steady problem in the wave frame. No slip conditions are imposed at the channel walls. The emerging linearized boundary value problem is solved analytically, and expressions presented for axial (longitudinal) velocity, volumetric flow rate, shear stress function and pressure rise. The flow is effectively controlled by three geometric parameters, viz cilia eccentricity parameter, wave number and cilia length and two physical parameters, namely magnetohydrodynamic body force parameter and couple stress non-Newtonian parameter. Analytical solutions are numerically evaluated with MATLAB software. Axial velocity is observed to be enhanced in the core region with greater wave number whereas it is suppressed markedly with increasing cilia length, couple stress and magnetic parameters, with significant flattening of profiles with the latter two parameters. Axial pressure gradient is decreased with eccentricity parameter whereas it is elevated with cilia length, in the channel core region. Increasing couple stress and magnetic field parameter respectively enhance and suppress pressure gradient across the entire channel width. The pressure-flow rate relationship is confirmed to be inversely linear and pumping, free pumping and augmented pumping zones are all examined. Bolus trapping is also analyzed. The study is relevant to MHD biomimetic blood pumps

In-Vitro and In-Silico Investigations of Alternative Surgical Techniques for Single Ventricular Disease

Single ventricle (SV) anomalies account for one-fourth of all cases of congenital Heart disease. The conventional second and third stage i.e. Comprehensive stage II and Fontan procedure of the existing three-staged surgical approach serving as a palliative treatment for this anomaly, entails multiple complications and achieves a survival rate of 50%. Hence, to reduce the morbidity and mortality rate associated with the second and third stages of the existing palliative procedure, the novel alternative techniques called “Hybrid Comprehensive Stage II” (HCSII), and a “Self-powered Fontan circulation” have been proposed. The goal of this research is to conduct in-vitro investigations to validate computational and clinical findings on these proposed novel surgical techniques. The research involves the development of a benchtop study of HCSII and self-powered Fontan circulation

Book of Abstracts 15th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering and 3rd Conference on Imaging and Visualization

In this edition, the two events will run together as a single conference, highlighting the strong connection with the Taylor & Francis journals: Computer Methods in Biomechanics and Biomedical Engineering (John Middleton and Christopher Jacobs, Eds.) and Computer Methods in Biomechanics and Biomedical Engineering: Imaging and Visualization (JoãoManuel R.S. Tavares, Ed.). The conference has become a major international meeting on computational biomechanics, imaging andvisualization. In this edition, the main program includes 212 presentations. In addition, sixteen renowned researchers will give plenary keynotes, addressing current challenges in computational biomechanics and biomedical imaging. In Lisbon, for the first time, a session dedicated to award the winner of the Best Paper in CMBBE Journal will take place. We believe that CMBBE2018 will have a strong impact on the development of computational biomechanics and biomedical imaging and visualization, identifying emerging areas of research and promoting the collaboration and networking between participants. This impact is evidenced through the well-known research groups, commercial companies and scientific organizations, who continue to support and sponsor the CMBBE meeting series. In fact, the conference is enriched with five workshops on specific scientific topics and commercial software.info:eu-repo/semantics/draf

Mathematical modelling of myocardial perfusion: coronary flow and myocardial mechanics

Coronary artery disease (CAD) is a condition characterised by the narrowing or blockage of the major blood vessels that supply blood to the heart muscle. This can cause insufficient myocardial perfusion to the heart and deficient cardiac outputs, leading to the possibility of heart failure. CAD is one of the leading causes of morbidity and mortality worldwide. Early and accurate diagnosis and treatment of CAD are essential to minimise the risk of complications, including heart attack or heart failure. In cardiovascular research, computational modelling of coronary circulation is proving to be a valuable tool for gaining insights and information. It enables researchers to isolate the effects of various physiological and pathological conditions on the coronary circulation. Thus, this thesis aimed to develop computational models of one dimensional (1D) coronary flow and three-dimensional (3D) heart. Both models included detailed geometric information tosimulate and predict physiologically realistic results. A one- way coupling of the coronary flow model and the heart model was achieved and produced physiologically accurate myocardial perfusion. Specifically, we first investigated the effect of intramyocardial pressure (IMP) on coronary flow and developed a 1D finite difference coronary flow model. A coronary network based on experimental data was constructed to simulate coronary flow along the complete path of the coronary vasculature. Utilising an assumed aortic pressure, right atrial pressure, and IMP, our simulated coronary pressure and flow rates were in good agreement with published experimental data. It was observed that the majority of the coronary arterial flow on the left side occurs during diastole, while the flow slows down or even reverses during systole. Secondly, we developed a 3D finite element model of the left ventricle (LV) to obtain a more realistic IMP. The LV model was constructed from a patient-specific geometry. The simulated pressure and volume of the LV cavity in repeated cardiac cycles, as well as the ejection fraction, were all within published physiological ranges. We further analysed the stress distributions within the LV wall. Thirdly, a brief review of experimental IMP, as well as calculations of IMP from lumped parameter models and 3D heart models, were presented. Through analysis, we determined a formula for calculating IMP from our 3D LV model. Additionally, we proposed an assignment scheme of the epicardial coronary arteries to the 17 segments of the LV wall recommended by the American Heart Association. Based on the assignment, we devised the one-way coupling framework between the coronary flow model and the LV model to investigate myocardial perfusion. We further developed a bi-ventricular model to investigate the effect of pulmonary regurgitation (PR) on cardiac function. The model provided a computational approach for exploring the influence of PR on right ventricle (RV) dilation and the interaction between LV and RV. Our simulated RV end-diastolic volumes under varying degrees ofPR were comparable with published magnetic resonance imaging data. Moreover, from the long-axis and short-axis views of the bi-ventricular geometry, we observed clearly the motion of the interventricular septum from the baseline case to the severe PR case. This bi-ventricular model was intended to further couple with the coronary flow model to investigate the interaction of right coronary arterial flow and left coronary arterial flow. However, due to time constraints, this has not yet been undertaken. The computational models of the coronary flow and heart developed in this thesis exhibit promising capabilities for providing physiologically accurate predictions of coronary flow and myocardial mechanics. Further application of these models has the potential to deepen our understanding of the underlying mechanisms in physiological coronary flow and various CAD