Model Of Blood Flow Research Articles

Study of Effect of Different Shapes of Nanoparticles in Three-Layer Model for Blood Flow in Arterioles

Arterioles are pivotal console of hemodynamics as they are significant contributors to pressure. Under various physiological conditions like administration of a drug, arterioles ascertain divergent mechanical forces. The current communication discusses the effect of different shapes of copper nanoparticles inoculated as nano drugs in arterioles. The blood is assumed to be a non-Newtonian fluid and is delineated as nanofluids. The three-layer model is used for modeling the blood flow as it aptly describes the flow of blood in narrow vessels of diameter less than 100 μm. The Hamilton-Crosser model is implemented to describe the thermal conductivity of nanofluid as this model holds in accordance with experimental as well as theoretical results. The expressions are also obtained for density, thermal expansion and viscosity of the considered nanofluid. The equations are solved analytically and graphs have been plotted using MATLAB. The relative consequence of various shapes of nanoparticles like platelets, blades, cylinders and bricks is observed in temperature, velocity and flow rate. It has been investigated through the graphs that brick-shaped nanoparticles have shown a maximum rise in temperature, velocity and flow rate. And reverse results are observed for blade-shaped nanoparticles. The effect of volume fraction, heat source parameter and Grashof number have also been inspected. The considered analysis shows that a suitable shape of nanoparticle can be used to develop the nano drug according to biomedical needs.

Galcanezumab modulates Capsaicin-induced C-fiber reactivity.

The vasodilatory calcitonin-gene related peptide (CGRP) is understood as pivotal mediator in migraine pathophysiology. Blocking CGRP with small molecules or monoclonal antibodies (CGRP-mAb) reduces migraine frequency. However, prescription of CGRP-mAbs is still regulated and possible predictive measures of therapeutic success would be useful. Using standardized capsaicin-induced dermal blood flow model, 29 migraine patients underwent a laser speckle imaging measurement before and after administration of galcanezumab. At both sessions dermal blood flow before and after capsaicin stimulation as well as flare size were analyzed over all three trigeminal branches and the volar forearm for extracranial control. Long-term measures were repeated in 14 patients after continuous treatment ranging from 6 to 12 months. Resting dermal blood flow remained unchanged after administration of galcanezumab. Capsaicin-induced dermal blood flow decreased significantly after CGRP-mAb in all tested areas compared to baseline and this was consistent even after 12 months of treatment. However, following galcanezumab administration, the flare size decreased only in the three trigeminal dermatomes, not the arm and was therefore specific for the trigemino-vascular system. None of these two markers distinguished between responders and non-responders. CGRP-mAb changed blood flow response to capsaicin stimulation profoundly and this effect did not change over a 12-month application. Neither capsaicin-induced flare nor dermal blood flow can be used as a predictor for treatment efficacy. These data suggest that the mechanism of headache development in migraine is not entirely CGRP-mediated.

Study of radiative magneto-non-Newtonian fluid flow over a nonlinearly elongating sheet with Soret and Dufour effects

Casson fluid model is extensively used for modeling of blood flow in thin arteries at low shear rates. The current article investigates the Soret and Dufour effects on free convective flow of Casson fluid over a nonlinearly elongating sheet embedded in a porous medium. Free convection: Flows arising solely due to the difference in density caused by temperature differences. The exponential space-based heat source/sink and thermal radiation are also incorporated in the heat transfer equation. Similarity solution was obtained by using suitable transformations and the transformed equations are solved by using the Runge–Kutta fourth-order method with a shooting technique by the help of the MATLAB code. The impacts of operating parameters on velocity, temperature, and concentration distributions are explained through graphs and tables. Important findings of the analysis are: Dufour and Soret effects serve as the surface coolant and maintenance of solutal deposition-free surface. Applied magnetic field and heavier diffusing species with suction lead to thinner boundary condition preventing vorticity diffusion.

A mathematical model of blood flow in a stenosed artery with post-stenotic dilatation and a forced field.

Arterial stenosis is a common cardiovascular disease that restricts blood flow. A stenotic blood vessel creates tangent stress pressure, which lessens the arterial side and causes an aneurysm. The primary purpose of this study is to investigate blood flowing via an inclination pipe with stricture and expansion after stricture (widening) underneath the influence of a constant incompressible Casson liquid flowing with the magnetism field. The relations for surface shearing stress, pressure drop, flow resistance, and velocity are calculated analytically by applying a mild stenosis approximation. The effect of different physical characteristics on liquid impedance to flowing, velocity, and surface shearing stress are studied. With a non-Newtonian aspect of the Casson liquid, the surface shearing stress declines, and an impedance upturn. Side resistivity and shear-stress increase with the elevations of stricture, whilst together decreasing with a dilatation height.

A Report of Generalized Blood Flow Model with Heat Conduction Between Blood and Particles

This paper examines the magneto hydrodynamic two-phase blood (Casson fluid) flow in a vessel with heat conduction between blood and particles. The temperature of both phases is also considered. The model for the flow under consideration is formulated in terms of partial differential equations. Then the classical model is generalized by utilizing the Caputo fractional order derivative. The generalized equations are then non-dimensionalized by using appropriate dimensionless variables. The exact dimensionless solutions are obtained via the joint application of Laplace & Hankel integral transforms. The influence of various embedded parameters on both the velocities (blood and magnetic particles) and the temperature distribution are presented graphically. It is worth noting that the particle and blood velocities decrease for increasing the values of magnetic parameter (H) which is useful to control the blood flow during magnetic therapy (for treating pain, such as the back, foot, or joint pain) and surgeries. It is worth noting that fractional model better describes the flow behavior than classical model by providing virous integral curves as shown in Fig.

Dependence of Temperature Rise on the Position of Catheters and Implants Power Sources Due to the Heat Transfer into the Blood Flow

This work provides a numerical analysis of heat transfer from medical devices such as catheters and implants to the blood flow by considering the relative position of such power sources to the vessel wall. We have used COMSOL Multiphysics® software to simulate the heat transfer in the blood flow, using the finite element method and Carreau-–Yasuda fluid model (a non-Newtonian model for blood flow). The location of the power source is changed (from the center to near the wall) in the blood vessel with small steps, while the blood flow takes different velocities. The numerical simulations show that when the catheter/implant approaches the vessel wall, the temperature increases linearly for ~90% of the radial displacement from the centerline position to the vessel wall, while for the last 10% of the radial displacement, the temperature increases exponentially. As a result, the temperature is increased significantly, when changing the position of the catheter/implant from the centerline to the area adjacent to the vessel wall.

Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory

A mathematical model of cerebral blood flow in the form of a dynamical system is studied. The cerebral blood flow autoregulation modeling problem is treated as a nonlinear control problem and the potential and applicability of the nonlinear control theory techniques are analyzed in this respect. It is shown that the cerebral hemodynamics model in question is differentially flat. Then, the integrator backstepping approach combined with barrier Lyapunov functions is applied to construct the control laws that recover the cerebral autoregulation performance of a healthy human. Simulation results confirm the good performance and flexibility of the suggested cerebral blood flow autoregulation design. The conducted research should enrich our understanding of the mathematics behind the cerebral blood flow autoregulation mechanisms and medical treatments to compensate for impaired cerebral autoregulation, e.g., in preterm infants.

Pulmonary gas exchange evaluated by machine learning: a computer simulation

Using computer simulation we investigated whether machine learning (ML) analysis of selected ICU monitoring data can quantify pulmonary gas exchange in multi-compartment format. A 21 compartment ventilation/perfusion (V/Q) model of pulmonary blood flow processed 34,551 combinations of cardiac output, hemoglobin concentration, standard P50, base excess, VO2 and VCO2 plus three model-defining parameters: shunt, log SD and mean V/Q. From these inputs the model produced paired arterial blood gases, first with the inspired O2 fraction (FiO2) adjusted to arterial saturation (SaO2) = 0.90, and second with FiO2 increased by 0.1. ‘Stacked regressor’ ML ensembles were trained/validated on 90% of this dataset. The remainder with shunt, log SD, and mean ‘held back’ formed the test-set. ‘Two-Point’ ML estimates of shunt, log SD and mean utilized data from both FiO2 settings. ‘Single-Point’ estimates used only data from SaO2 = 0.90. From 3454 test gas exchange scenarios, two-point shunt, log SD and mean estimates produced linear regression models versus true values with slopes ~ 1.00, intercepts ~ 0.00 and R2 ~ 1.00. Kernel density and Bland–Altman plots confirmed close agreement. Single-point estimates were less accurate: R2 = 0.77–0.89, slope = 0.991–0.993, intercept = 0.009–0.334. ML applications using blood gas, indirect calorimetry, and cardiac output data can quantify pulmonary gas exchange in terms describing a 20 compartment V/Q model of pulmonary blood flow. High fidelity reports require data from two FiO2 settings.

Deep Learning for Computational Hemodynamics: A Brief Review of Recent Advances

Computational fluid dynamics (CFD) modeling of blood flow plays an important role in better understanding various medical conditions, designing more effective drug delivery systems, and developing novel diagnostic methods and treatments. However, despite significant advances in computational technology and resources, the expensive computational cost of these simulations still hinders their transformation from a research interest to a clinical tool. This bottleneck is even more severe for image-based, patient-specific CFD simulations with realistic boundary conditions and complex computational domains, which make such simulations excessively expensive. To address this issue, deep learning approaches have been recently explored to accelerate computational hemodynamics simulations. In this study, we review recent efforts to integrate deep learning with CFD and discuss the applications of this approach in solving hemodynamics problems, such as blood flow behavior in aorta and cerebral arteries. We also discuss potential future directions in the field. In this review, we suggest that incorporating physiologic understandings and underlying fluid mechanics laws in deep learning models will soon lead to a paradigm shift in the development novel non-invasive computational medical decisions.

A Two-Layered Model of Blood Flow for Stenosed Artery along with the Peripheral Layer

A Two-Layered Model of Blood Flow for Stenosed Artery along with the Peripheral Layer

Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid–structure interaction system

A noteworthy aspect in blood flow modeling is the definition of the mechanical interaction between the fluid flow and the biological structure that contains it, namely the vessel wall. Particularly, it has been demonstrated that the addition of a viscous contribution to the mechanical characterization of vessels brings positive results when compared to in-vivo measurements. In this context, the numerical implementation of boundary conditions able to keep memory of the viscoelastic contribution of vessel walls assumes an important role, especially when dealing with large circulatory systems. In this work, viscoelasticity is taken into account in entire networks via the Standard Linear Solid Model. The implementation of the viscoelastic contribution at boundaries (inlet, outlet and junctions), is carried out considering the hyperbolic nature of the mathematical model. Specifically, a non-linear system is established based on the definition of the Riemann Problem at junctions, characterized by rarefaction waves separated by contact discontinuities, among which the mass and the total energy are conserved. Basic junction tests are analyzed, such as a trivial 2–vessels junction, for both a generic artery and a generic vein, and a simple 3–vessels junction, considering an aortic bifurcation scenario. The chosen asymptotic-preserving IMEX Runge-Kutta Finite Volume scheme is demonstrated to be second-order accurate in the whole domain and well-balanced, even when including junctions. Two different benchmark models of the arterial network are then implemented, differing in number of vessels and in viscoelastic parameters. Comparison of the results obtained in the two networks underlines the high sensitivity of the model to the chosen viscoelastic parameters. In these numerical tests, the conservation of the contribution provided by the viscoelastic characterization of vessel walls is assessed in the whole network, including junctions and boundary conditions.

Distributed lumped parameter modeling of blood flow in compliant vessels

We extend our previous distributed lumped parameter (DLP) modeling approach to take into account blood vessel wall deformability. This is achieved by adding a compliance term for each vascular segment based on 1D NS equations. The results of the proposed method are compared against 1D Navier–Stokes and 3D fluid–structure interaction (FSI) modeling in idealized and patient-specific models. We show that 1D Navier–Stokes blood flow modeling can be highly inaccurate in predicting flow and pressure dynamics in diseased cases, while in comparison the DLP approach produces consistently accurate flow and pressure waveforms as compared to 3D FSI modeling. The relative accuracy and computational efficiency of the proposed DLP approach offer the possibility to replace or augment 1D or 3D modeling to study hemodynamics in a variety of applications.

Optimal Decay Rates of Solutions to a Blood Flow Model

Optimal Decay Rates of Solutions to a Blood Flow Model

Inverse problems in blood flow modeling: A review.

Mathematical and computational modeling of the cardiovascular system is increasingly providing non‐invasive alternatives to traditional invasive clinical procedures. Moreover, it has the potential for generating additional diagnostic markers. In blood flow computations, the personalization of spatially distributed (i.e., 3D) models is a key step which relies on the formulation and numerical solution of inverse problems using clinical data, typically medical images for measuring both anatomy and function of the vasculature. In the last years, the development and application of inverse methods has rapidly expanded most likely due to the increased availability of data in clinical centers and the growing interest of modelers and clinicians in collaborating. Therefore, this work aims to provide a wide and comparative overview of literature within the last decade. We review the current state of the art of inverse problems in blood flows, focusing on studies considering fully dimensional fluid and fluid–solid models. The relevant physical models and hemodynamic measurement techniques are introduced, followed by a survey of mathematical data assimilation approaches used to solve different kinds of inverse problems, namely state and parameter estimation. An exhaustive discussion of the literature of the last decade is presented, structured by types of problems, models and available data.

Numerical Modeling and Simulation of Blood Flow in a Rat Kidney: Coupling of the Myogenic Response and the Vascular Structure

A numerical simulation was carried out to investigate the blood flow behavior (i.e., flow rate and pressure) and coupling of a renal vascular network and the myogenic response to various conditions. A vascular segment and an entire kidney vascular network were modeled by assuming one single vessel as a straight pipe whose diameter was determined by Murray’s law. The myogenic response was tested on individual AA (afferent artery)–GC (glomerular capillaries)–EA (efferent artery) systems, thereby regulating blood flow throughout the vascular network. Blood flow in the vascular structure was calculated by network analysis based on Hagen–Poiseuille’s law to various boundary conditions. Simulation results demonstrated that, in the vascular segment, the inlet pressure Pinlet and the vascular structure act together on the myogenic response of each individual AA–GC–EA subsystem, such that the early-branching subsystems in the vascular network reached the well-regulated state first, with an interval of the inlet as Pinlet = 10.5–21.0 kPa, whereas the one that branched last exhibited a later interval with Pinlet = 13.0–24.0 kPa. In the entire vascular network, in contrast to the Pinlet interval (13.0–20.0 kPa) of the unified well-regulated state for all AA–GC–EA subsystems of the symmetric model, the asymmetric model exhibited the differences among subsystems with Pinlet ranging from 12.0–17.0 to 16.0–20.0 kPa, eventually achieving a well-regulated state of 13.0–18.5 kPa for the entire kidney. Furthermore, when Pinlet continued to rise (e.g., 21.0 kPa) beyond the vasoconstriction range of the myogenic response, high glomerular pressure was also related to vascular structure, where PGC of early-branching subsystems was 9.0 kPa and of late-branching one was 7.5 kPa. These findings demonstrate how the myogenic response regulates renal blood flow in vascular network system that comprises a large number of vessel elements.

Herschel-Bulkley Model of Blood Flow through an Asymmetric Stenosed Artery on Unsteady Reactive Solute Dispersion

This study examined the effects of chemical reaction, stenosis shape parameter and non-Newtonian behaviour on solute dispersion in blood flow via an asymmetric stenosed artery using the generalised dispersion model (GDM). The Herschel–Bulkley (H-B) fluid model, which consists of a yield stress and power-law index, is used to represent the non-Newtonian characteristics of blood in a narrow artery at a low shear rate. The impact of stenosis shape parameter, chemical reaction, power-law index and plug flow radius on the dispersion coefficient and effective axial diffusion of solute is shown. The findings showed that the aforementioned parameters significantly impact the overall process of the chemically reactive solute in a bulk flow. The dispersion coefficient and effective axial diffusion decreases with an increase in the chemical reaction rate, stenosis shape parameter and power-law index. As time passes, the dispersion process slows and becomes almost constant implying a steady state of diffusion. In short, this study provides further insights into the physiological processes involved in the dispersion of drugs and nutrients in the circulatory system.

Structure (Epicardial Stenosis) and Function (Microvascular Dysfunction) That Influence Coronary Fractional Flow Reserve Estimation

Background. The treatment of coronary stenosis is decided by performing high risk invasive surgery to generate the fractional flow reserve diagnostics index, a ratio of distal to proximal pressures in respect of coronary atherosclerotic plaques. Non-invasive methods are a need of the times that necessitate the use of mathematical models of coronary hemodynamic physiology. This study proposes an extensible mathematical description of the coronary vasculature that provides an estimate of coronary fractional flow reserve. Methods. By adapting an existing computational model of human coronary blood flow, the effects of large vessel stenosis and microvascular disease on fractional flow reserve were quantified. Several simulations generated flow and pressure information, which was used to compute fractional flow reserve under several conditions including focal stenosis, diffuse stenosis, and microvascular disease. Sensitivity analysis was used to uncover the influence of model parameters on fractional flow reserve. The model was simulated as coupled non-linear ordinary differential equations and numerically solved using our implicit higher order method. Results. Large vessel stenosis affected fractional flow reserve. The model predicts that the presence, rather than severity, of microvascular disease affects coronary flow deleteriously. Conclusions. The model provides a computationally inexpensive instrument for future in silico coronary blood flow investigations as well as clinical-imaging decision making. A combination of focal and diffuse stenosis appears to be essential to limit coronary flow. In addition to pressure measurements in the large epicardial vessels, diagnosis of microvascular disease is essential. The independence of the index with respect to heart rate suggests that computationally inexpensive steady state simulations may provide sufficient information to reliably compute the index.

Leveraging elasticity of blood stenosis to detect the role of a non-Newtonian flow midst an arterial tube: Mazumdar and Keller models

Blood stenosis is considered one of the most serious risks which face humanity nowadays. In addition, it is also one of the most apparent symptoms of COVID (19) (Corona Virus). Consequently, this research is shedding light on studying the blood flow in case of having blood clots and artery elasticity in the presence of stenosis during studying the flow. Hematopoiesis requires a model of the yield stress fluid, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). Navier stokes equation is used to simulate this subject in a mathematical way. The elasticity on the stenosis arterial walls is simulated by Rubinow & Keller model [24] and Mazumdar model [25]. The results reveal exciting behaviors that, in turn, require adequate study of non-Newtonian fluid flow phenomena, especially the results showed that the increase in the parameters related to the elasticity of the walls facilitating the flow of blood through the stenosis area. In addition, a comparison between two elasticity models (Rubinow & Keller model and Mazumdar model) is considered. Further, for normal artery without stenosis, our results are the same as those obtained by Vajravelu et.al [22].

The Effects of the Mechanical Properties of Vascular Grafts and an Anisotropic Hyperelastic Aortic Model on Local Hemodynamics during Modified Blalock-Taussig Shunt Operation, Assessed Using FSI Simulation.

Cardiovascular surgery requires the use of state-of-the-art artificial materials. For example, microporous polytetrafluoroethylene grafts manufactured by Gore-Tex® are used for the treatment of cyanotic heart defects (i.e., modified Blalock–Taussig shunt). Significant mortality during this palliative operation has led surgeons to adopt mathematical models to eliminate complications by performing fluid–solid interaction (FSI) simulations. To proceed with FSI modeling, it is necessary to know either the mechanical properties of the aorta and graft or the rheological properties of blood. The properties of the aorta and blood can be found in the literature, but there are no data about the mechanical properties of Gore-Tex® grafts. Experimental studies were carried out on the mechanical properties vascular grafts adopted for modified pediatric Blalock–Taussig shunts. Parameters of two models (the five-parameter Mooney–Rivlin model and the three-parameter Yeoh model) were determined by uniaxial experimental curve fitting. The obtained data were used for patient-specific FSI modeling of local blood flow in the “aorta-modified Blalock–Taussig shunt–pulmonary artery” system in three different shunt locations: central, right, and left. The anisotropic model of the aortic material showed higher stress values at the peak moment of systole, which may be a key factor determining the strength characteristics of the aorta and pulmonary artery. Additionally, this mechanical parameter is important when installing a central shunt, since it is in the area of the central anastomosis that an increase in stress on the aortic wall is observed. According to computations, the anisotropic model shows smaller values for the displacements of both the aorta and the shunt, which in turn may affect the success of preoperative predictions. Thus, it can be concluded that the anisotropic properties of the aorta play an important role in preoperative modeling.

Fibrin Strands Will Grow from Soluble Fibrin and Hang Up in an In Vitro Microcirculatory Viscoelastic Model: Is This a Major Cause of COVID-19 Associated Coagulopathy?

Viscoelastic testing (VET) by both TEG and ROTEM has demonstrated hypercoagulability early in corona virus disease 2019 (COVID-19) associated coagulopathy (CAC). Additional VET studies demonstrated fibrinolytic shutdown late in a majority of severely ill COVID-19 patients with an associated elevation of d-dimer. Elevated d-dimer confirms that coagulation, followed by fibrinolysis, has occurred. These findings imply that, during CAC, three enzymes—thrombin, Factor XIIIa and plasmin—must have acted in sequence. However, limitations in standard VET analyses preclude exploration of the earliest phases of clot induction, as well as clot formation and clot dissolution in flowing blood. Herein, we describe a novel method illuminating aspects of this unexplored area. In addition, we created an in vitro blood flow model in which the interactions of thrombin, Factor XIII and plasmin with fibrinogen can be studied, allowing the determination of soluble fibrin (SF), the highly unstable form of fibrin that precedes the appearance of a visible clot. This model allows the determination of the SF level at which fibrin microclots begin to form.