Numerical simulation of time-dependent non-Newtonian nano-pharmacodynamic transport phenomena in a tapered overlapping stenosed artery

Nanofluids are becoming increasingly popular in novel hematological treatments and also advanced nanoscale biomedical devices. Motivated by recent developments in this area, a theoretical and numerical study is described for unsteady pulsatile flow, heat and mass transport through a tapered stenosed artery in the presence of nanoparticles. An appropriate geometric expression is employed to simulate the overlapping stenosed arterial segment. The Sisko non-Newtonian model is employed for hemodynamic rheology. Buongiorno’s formulation is employed to model nanoscale effects. The two-dimensional non-linear, coupled equations are simplified for the case of mild stenosis. An explicit forward time central space (FTCS) finite difference scheme is employed to obtain a numerical solution of these equations. Validation of the computations is achieved with another numerical method, namely the variational finite element method (FEM). The effects of various emerging rheological, nanoscale and thermofluid parameters on flow and heat/mass characteristics of blood are shown via several plots and discussed in detail. The circulating regions inside the flow field are also investigated through instantaneous patterns of streamlines. The work is relevant to nanopharmacological transport phenomena, a new and exciting area of modern medical fluid dynamics which integrates coupled diffusion, viscous flow and nanoscale drug delivery mechanisms

Unsteady hybrid nanoparticle-mediated magneto-hemodynamics and heat transfer through an overlapped stenotic artery : biomedical drug delivery simulation

Two-dimensional laminar hemodynamics through a diseased artery featuring an overlapped stenosis was simulated theoretically and computationally. This study presented a mathematical model for the unsteady blood flow with hybrid biocompatible nanoparticles (Silver and Gold) inspired by drug delivery applications. A modified Tiwari-Das volume fraction model was adopted for nanoscale effects. Motivated by the magnetohemodynamics effects, a uniform magnetic field was applied in the radial direction to the blood flow. For realistic blood behavior, Reynolds’ viscosity model was applied in the formulation to represent the temperature dependency of blood. Fourier’s heat conduction law was assumed, and heat generation effects were included. Therefore, the governing equations were an extension of the Navier-Stokes equations with magneto-hydrodynamic body force included. The two-dimensional governing equations were transformed and normalized with appropriate variables, and the mild stenotic approximation was implemented. The strongly nonlinear nature of the resulting dimensionless boundary value problem required a robust numerical method, and therefore the FTCS algorithm was deployed. Validation of solutions for the particular case of constant viscosity and non-magnetic blood flow was included. Using clinically realistic hemodynamic data, comprehensive solutions were presented for silver, and silver-gold hybrid mediated blood flow. A comparison between silver and hybrid nanofluid was also included, emphasizing the use of hybrid nanoparticles for minimizing the hemodynamics. Enhancement in magnetic parameter decelerated the axial blood flow in stenotic region. Colored streamline plots for blood, silver nano-doped blood, and hybrid nano-doped blood were also presented. The simulations were relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial disease

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

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

Numerical computation of nonlinear oscillatory two-immiscible magnetohydrodynamic flow in dual porous media system : FTCS and FEM study

The transient Hartmann magnetohydrodynamic (MHD) flow of two immiscible fluids flowing through a horizontal channel containing two porous media with oscillating lateral wall mass flux is studied. A two-dimensional spatial model is developed for the two fluids, one of which is electrically-conducting and the other electrically-insulating (as is the wall in the second region). Both fluid regimes are driven by a common pressure gradient. A Darcy-Forchheimer drag force model is used to simulate the porous medium effects on the flow in both fluid regions. Special boundary conditions are imposed at the interface. The governing second order nonlinear partial differential equations are non-dimensionalized for each region using a set of transformations. The resulting transport equations are shown to be controlled by the Hartmann hydromagnetic parameter (Ha), viscosity ratio parameter (α), two Darcy numbers (Da1, Da2), two Forchheimer numbers (Fs1, Fs2), two Reynolds numbers (Re1, Re2), frequency parameter (εA) associated with the transpiration (lateral wall flux) velocity and a periodic frequency parameter (ω*t*). Numerical FTCS finite difference solutions are obtained for a wide range of the governing parameters. Benchmarking is performed with a Galerkin finite element method code (MAGNETO-FEM) and the results are found to be in excellent agreement. Applications of the model include magnetic cleanup operations in coastal/ocean seabed oil spills and electromagnetic purification of petroleum reservoir fluids

Finite element analysis of non-Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

The present study considers two-dimensional mathematical modelling of non-Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second-grade differential viscoelastic constitutive model is adopted for blood to mimic non-Newtonian characteristics and blood is considered to contain a homogenous suspension of nanoparticles. Vogel’s model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier-Stokes equations with linear Boussinesq’s approximation and Buongiorno’s nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate non-dimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery and furthermore that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nano-particle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid-independence study is included. Blood flow, heat and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity and magnetic parameters i.e. stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (Ni), Brownian motion parameter (Nb) and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration and skin-friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nano-particle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multi-physical nanoscale and thermomagnetic behaviour and also the simultaneous presence of bio-rheological behaviour (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat and mass transfer characteristics. The simulations are relevant to diffusion of nanodrugs in magnetic targeted treatment of stenosed arterial disease

Performance of magnetic dipole contribution on ferromagnetic non-Newtonian radiative MHD blood flow: An application of biotechnology and medical sciences

Casson flow ferromagnetic liquid blood flow over stretching region is studied numerically. The domain is influence by radiation and blood flow velocity and thermal slip conditions. Blood acts an impenetrable magneto-dynamic liquid yields governing equations. The conservative governing nonlinear partial differential equations, reduced to ODEs by the help of similarity translation technique. The transport equations were transformed into first order ODEs and the resultant system are solved with help of 4th order R-K scheme. Performing a magnetic dipole with a Casson flow across a stretched region with Brownian motion and Thermophoresis is novelty of the problem. Significant applications of the study in some spheres are metallurgy, extrusion of polymers, production in papers and rubber manufactured sheets. Electronics, analytical instruments, medicine, friction reduction, angular momentum shift, heat transmission, etc. are only few of the many uses for ferromagnetic fluids. As ferromagnetic interaction parameter value improves, the skin-friction, Sherwood and Nusselt numbers depreciates. A comparative study of the present numerical scheme for specific situations reveals a splendid correlation with earlier published work. A change in blood flow velocity magnitude has been noted due to Casson parameter. Increasing change in blood flow temperature noted due to Casson parameter. Skin-friction strengthened and Nusselt number is declined with Casson parameter. The limitation of current work is a non-invasive magnetic blood flow collection system using commercially available magnetic sensors instead of SQUID or electrodes.Unai Fernandez-Gamiz was supported by Government of the Basque Country [ELKARTEK21/10KK-2021/00014 & ELKARTEK22/85]. Irfan Nurhidayat was supported by King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand [KDS2020/045]

Fluid Dynamic Modeling of Biological Fluids: From the Cerebrospinal Fluid to Blood Thrombosis

1noL'abstract è presente nell'allegato / the abstract is in the attachmentopen718. INGEGNERIA CIVILE E AMBIENTALEnoopenCardillo, Giuli

Development of Particle Image Velocimetry for In-Vitro Studies of Arterial Haemodynamics

Atherosclerosis and related cardiovascular diseases (CVDs) are amongst the largest causes of morbidity and mortality in the developed world, causing considerable monetary pressure on public health systems worldwide. Atherosclerosis is characterised by the build up of vascular plaque in medium and large arteries and is a direct precursor to acute vascular syndromes such a myocardial infarction, stroke or peripheral arterial diseases. The causative factors leading to CVD still remain relatively poorly understood, but are becoming increasingly identifiable as a dysfunction of the endothelial cells that line the arterial wall. It is well known that the endothelium responds to the prevailing fluid mechanic (i.e. haemodynamic) environment, which plays a crucial role in the localised occurrence of atherosclerosis near vessel bends and bifurcations. In these areas, disturbed haemodynamics lead to flow separation and very low wall shear stress (WSS), which directly affects the functionality of the endothelium and impedes the transport of important blood borne agonists and antagonists. Detailed full field measurements assessing complex haemodynamics are sparse and consequently this thesis aims to address some of the important questions related to arterial haemodynamics and CVD by performing in-vitro flow measurements in physiologically relevant conditions. In particular, this research develops and uses state-of-the-art Particle Image Velocimetry (PIV) techniques to measure three-dimensional velocity and WSS fields in scaled models of the human carotid artery. For this purpose, the necessary theoretical and experimental concepts are developed and in-depth analyses of the underlying factors affecting the local haemodynamics and their relation to CVD are carried out. In the first part, a methodology for the construct of transparent hydraulic flow phantoms from medical imaging data is developed. The arterial geometries are reproduced in optically clear silicone and the flowing blood is modelled with a refractive index matched blood analogue. Subsequently, planar and Stereo-PIV techniques are developed and verified. A novel interfacial PIV (iPIV) technique is introduced to directly measure WSS by inferring the velocity gradient from the recorded particle images. The new technique offers a maximal achievable resolution of 1 pixel and therefore removes the resolution limit near the wall usually associated with PIV. Furthermore, the iPIV performance is assessed on a number of numerical and experimental test cases and iPIV offers a significantly improved measurement accuracy compared to more traditional techniques. Subsequently, the developed methodologies are applied in three studies to characterise the velocity and WSS fields in the human carotid artery under a number of physiological and experimental conditions. The first study focuses on idealised vessel geometries with and without disease and establishes a general understanding of the haemodynamic environment. Secondly, a physiological accurate vessel geometry under pulsatile flow conditions is investigated to provide a more realistic representation of the true in-vivo flow conditions. The prevailing flow structure in both cases is characterised by flow separation, strong secondary flows and large spatial and temporal variations in WSS. Large spatial and temporal differences exist between the different geometries and flow conditions; spatial variations appear to be more significant than transient events. Thirdly, the three-dimensional flow structure in the physiological carotid artery model is investigated by means of stereoscopic and tomographic PIV, permitting for the first time the measurement of the full 3D-3C velocity field and shear stress tensor in such geometries. The flow field within the model is complex and three-dimensional and inherently determined by the vessel geometry and the build up of an adverse pressure gradient. The main features include strong heliocoidal flow motions and large spatial variations in WSS. Lastly, the physiological implications of the current results are discussed in detail and reference to previous work is given. In summary, the present research develops a novel and versatile PIV methodology for haemodynamic in vitro studies and the functionality and accuracy is demonstrated through a number of physiological relevant flow measurements

Development of Particle Image Velocimetry for In-Vitro Studies of Arterial Haemodynamics

Atherosclerosis and related cardiovascular diseases (CVDs) are amongst the largest causes of morbidity and mortality in the developed world, causing considerable monetary pressure on public health systems worldwide. Atherosclerosis is characterised by the build up of vascular plaque in medium and large arteries and is a direct precursor to acute vascular syndromes such a myocardial infarction, stroke or peripheral arterial diseases. The causative factors leading to CVD still remain relatively poorly understood, but are becoming increasingly identifiable as a dysfunction of the endothelial cells that line the arterial wall. It is well known that the endothelium responds to the prevailing fluid mechanic (i.e. haemodynamic) environment, which plays a crucial role in the localised occurrence of atherosclerosis near vessel bends and bifurcations. In these areas, disturbed haemodynamics lead to flow separation and very low wall shear stress (WSS), which directly affects the functionality of the endothelium and impedes the transport of important blood borne agonists and antagonists. Detailed full field measurements assessing complex haemodynamics are sparse and consequently this thesis aims to address some of the important questions related to arterial haemodynamics and CVD by performing in-vitro flow measurements in physiologically relevant conditions. In particular, this research develops and uses state-of-the-art Particle Image Velocimetry (PIV) techniques to measure three-dimensional velocity and WSS fields in scaled models of the human carotid artery. For this purpose, the necessary theoretical and experimental concepts are developed and in-depth analyses of the underlying factors affecting the local haemodynamics and their relation to CVD are carried out. In the first part, a methodology for the construct of transparent hydraulic flow phantoms from medical imaging data is developed. The arterial geometries are reproduced in optically clear silicone and the flowing blood is modelled with a refractive index matched blood analogue. Subsequently, planar and Stereo-PIV techniques are developed and verified. A novel interfacial PIV (iPIV) technique is introduced to directly measure WSS by inferring the velocity gradient from the recorded particle images. The new technique offers a maximal achievable resolution of 1 pixel and therefore removes the resolution limit near the wall usually associated with PIV. Furthermore, the iPIV performance is assessed on a number of numerical and experimental test cases and iPIV offers a significantly improved measurement accuracy compared to more traditional techniques. Subsequently, the developed methodologies are applied in three studies to characterise the velocity and WSS fields in the human carotid artery under a number of physiological and experimental conditions. The first study focuses on idealised vessel geometries with and without disease and establishes a general understanding of the haemodynamic environment. Secondly, a physiological accurate vessel geometry under pulsatile flow conditions is investigated to provide a more realistic representation of the true in-vivo flow conditions. The prevailing flow structure in both cases is characterised by flow separation, strong secondary flows and large spatial and temporal variations in WSS. Large spatial and temporal differences exist between the different geometries and flow conditions; spatial variations appear to be more significant than transient events. Thirdly, the three-dimensional flow structure in the physiological carotid artery model is investigated by means of stereoscopic and tomographic PIV, permitting for the first time the measurement of the full 3D-3C velocity field and shear stress tensor in such geometries. The flow field within the model is complex and three-dimensional and inherently determined by the vessel geometry and the build up of an adverse pressure gradient. The main features include strong heliocoidal flow motions and large spatial variations in WSS. Lastly, the physiological implications of the current results are discussed in detail and reference to previous work is given. In summary, the present research develops a novel and versatile PIV methodology for haemodynamic in vitro studies and the functionality and accuracy is demonstrated through a number of physiological relevant flow measurements