Model Of Blood Flow Research Articles

Normal Tissue Complication Probability Modeling of Severe Radiation-Induced Lymphopenia Using Blood Dose for Patients With Hepatocellular Carcinoma

PurposeThis study aims to develop a normal tissue complication probability (NTCP) model to estimate the risk of severe radiation-induced lymphopenia (SRIL, absolute lymphocyte count (ALC) < 500/μL) by using the blood dose of hepatocellular carcinoma (HCC) patients. Methods and MaterialsWe retrospectively collected data from 75 HCC patients who received radiotherapy (RT) between 2015 and 2018. The hematological dose framework calculated blood dose-volume histograms (DVHs) using a predefined blood flow model, organ DVHs, the number of treatment fractions, and beam delivery time. A Lyman-Kutcher-Burman (LKB) model with a generalized equivalent dose was used to establish the NTCP model, reflecting the whole blood DVHs. The optimization of the LKB parameters was conducted by minimizing a negative log-likelihood function. ResultsThere were 6, 4, 18, 33, and 14 patients in the groups with radiation-induced lymphopenia grades 0, 1, 2, 3, and 4, respectively. The median pre/post-RT ALC were 1410/μL (range, 520–3710/μL) and 470/μL (range, 60–1760/μL), respectively. There was a correlation between blood mean dose and ALC depletion (Pearson r = -0.664; p < 0.001). The average blood mean doses in each radiation-induced lymphopenia group were 2.90 Gy (95% CI, 1.96–3.85 Gy) for grade 0–1, 5.29 Gy (95% CI, 4.12–6.45 Gy) for grade 2, 8.81 Gy (95% CI, 7.55–10.07 Gy) for grade 3, and 11.69 Gy (95% CI, 9.82–17.57 Gy) for grade 4. When applying developed an NTCP model to predict SRIL, the area under the receiver operating characteristic curve and Brier score were 0.89 and 0.12, respectively. ConclusionWe developed the first NTCP model based on whole blood DVHs for estimating SRIL after abdominal RT in HCC patients. Our results showed a strong correlation between blood dose and ALC depletion, suggesting the potential to predict the risk of SRIL occurrence for using blood dose.

Mechanical study of blood flow through a permeable capillary with slippery wall

This research presents the mechanical behavior of blood flow through capillary having smooth inner surface. In this study modelling of blood flow via permeable and lubricated capillary caused by nutrients re-absorption has been done by the help of laws of momentum and mass. The nutrients re-absorption is assumed to be constant and inner walls of the capillary are smooth and slippery therefore slip condition on the velocity and constant rate in vertical direction at the wall has considered. The Kelvin Voigt model is employed to simulate blood flow via capillaries, and results for pressure, blood flow pattern, and shear force necessary for blood flow are discovered by recursive approach. Numerical results for nutrient re-absorption from the blood and impact of smooth and slippery surfaces on blood flow are shown through graphs. The novelty of the research invents that the smoothness and slickness of capillary wall is a crucial presumption to examine the blood as non-Newtonian fluid via capillary.

Simulation of blood flow in a stenosed and bifurcating artery using Finite Volume Methods and OpenFOAM

The article focuses on the shear-thinning and viscoelastic constitutive modelling and numerical simulation of blood flow in a stenosed and bifurcating artery. Specifically, the shear-thinning and viscoelastic behaviour of blood are modelled and implemented via the Oldroyd-B and Generalized Oldroyd-B constitutive models. A robust and efficient general purpose numerical (and computational) methodology for the simulation of blood flow in a stenosed and bifurcating artery is also developed and implemented. The numerical algorithm is developed more generally to resolve the mathematical model equations arising out of the all-encompassing Generalized Giesekus constitutive model. This model reduces to the Generalized Oldroyd-B model and subsequently also to the standard Oldroyd-B model simply by switching off certain material parameters. The inclusion of the Generalized Giesekus model must therefore be viewed in this context, to facilitate the development of an all encompassing general purpose numerical code. The blood flow modelling is otherwise done via the Oldroyd-B and Generalized Oldroyd-B constitutive models. The shear-thinning effects are implemented via the Cross model for shear-viscosity. The Generalized Oldroyd-B model results all illustrate that the velocity is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher would the velocity spurt through the constriction. This velocity behaviour correspondingly enhances the wall shear-stresses as the constriction increases, caused by the presence of the stenosis. High wall shear-stresses greatly increase the possibility of rupture of the stenosis. This can lead to catastrophic consequences in the usual case where the stenosis is caused, say, by tumor growth. As demonstrated near the contraction of a standard 4:1 contraction flow geometry, dramatic fluid flow effects, which are attributable to the polymeric-stresses, specifically to the first normal stress difference, are observed in the vicinity of the constrictions resulting from the presence of the stenosis. Such effects, include, flow recirculation and reversal, vortex formation, and spurt phenomena.

Influence of parent vessel feature on the risk of internal carotid artery aneurysm rupture via computational method

In this study, the role of sac section area and parent vessel diameter on the hemodynamic feature of the blood flow in selected internal carotid artery (ICA) aneurysms is comprehensively investigated. The changes of wall shear stress, pressure, and oscillatory shear index (OSI) of blood stream on the vessel for various aneurysms with coiling treatment. To attain hemodynamic factors, computational technique is used for the modeling of non-Newtonian transient blood flow inside the three different ICA aneurysms. Three different saccular models with various Parent vessel mean Diameter is investigated in this study. The achieved outcomes show that increasing the diameter of the parent vessel directly decreases the OSI value on the sac surface. In addition, the mean wall shear stress decreases with the increase of the parent vessel diameter.

Variable separated physics-informed neural networks based on adaptive weighted loss functions for blood flow model

Physics-informed neural networks (PINN) architectures have been recently explored to accelerate hemodynamics simulations by leveraging mathematical models for blood flow and empirical data. In this paper, a variable separated physics-informed neural networks based on adaptive weighted loss functions (AW-vsPINN) is developed for blood flow model in arteries. In particular, sub-neural networks are proposed to separately predict the unknown scalar state variables by sharing the same input layer. The AW-vsPINN adaptively adjusts the weights of loss terms by the minmax algorithm, which will be updated synchronously along with the network parameters and can balance the contributions of different loss terms during training. The two-stage optimization is implemented to train the neural networks. Specifically, the Adam optimizer is iterated for initial steps with the learning rate generated by the inverse time decay scheduler, and then the L-BFGS optimizer continues to train until the loss converges. Numerical results illustrate that the AW-vsPINN can remarkably improve prediction accuracy and enhance the ability of generalization compared to the conventional PINN. The proposed AW-vsPINN framework has high potential in predicting the blood flow information in cardiovascular disease.

Numerical analysis of the behavior of two-phase blood flow in locally magnetized vessel

The main purpose of this study is to analyze the behavior of non-Newtonian blood flow under localized magnetic field. To that end, we consider a 2-dimensional and two-phase fully-developed biomagnetic fluid model in a rectangular artery. The blood flow model considers the ferrohydrodynamic (FHD) and magnetohydrodynamics (MHD) parameters, which differ from the traditional model based upon Navier-Stokes equations. An external user-defined (UDF) source code was used to define fully-developed flow, viscosity, FHD and MHD properties in magnetic and non-magnetic regions. The numerical outcomes are evaluated in consideration of their potential uses in the field of magneto-hemorheology. All the physical parameters used to interpret the findings are consistent with the pathological conditions. The solutions are displayed as velocity, stream function, temperature contours. The study reveals that blood flow can be regulated by modifying the magnetic field strength, artery diameter, and concentration of red blood cells within the artery. In particular, it could be useful for surgical treatments of cancer and dengue diseases in the extraction of affected red blood cells from the bloodstream.

A stochastic model of blood flow to calculate blood dose during radiotherapy

Purpose. Lymphopenia is a common side effect in patients treated with radiotherapy, potentially caused by direct cell killing of circulating lymphocytes in the blood. To investigate this hypothesis, a method to assess dose to circulating lymphocytes is needed. Methods. A stochastic model to simulate systemic blood flow in the human body was developed based on a previously designed compartment model. Blood dose was obtained by superimposing the spatiotemporal distribution of blood particles with a time-varying dose rate field, and used as a surrogate for dose to circulating lymphocytes. We discuss relevant theory on compartmental modeling and how to combine it with models of explicit organ vasculature. Results. A general workflow was established which can be used for any anatomical site. Stochastic compartments can be replaced by explicit models of organ vasculatures for improved spatial resolution, and tumor compartments can be dynamically assigned. Generating a patient-specific blood flow distribution takes about one minute, fast enough to investigate the effect of varying treatment parameters such as the dose rate. Furthermore, the anatomical structures contributing most to the overall blood dose can be identified, which could potentially be used for lymphocyte-sparing treatment planning. Conclusion. The ability to report the blood dose distribution during radiotherapy is imperative to test and act upon the current paradigm that radiation-induced lymphopenia is caused by direct cell killing of lymphocytes in the blood. We have built a general model that can do so for various treatment sites. The presented framework is publicly available at http://github.com/mghro/hedos.

MHD blood flow effects of Casson fluid with Caputo-Fabrizio fractional derivatives through an inclined blood vessels with thermal radiation

This study investigates a fractional-order time derivative model of non-Newtonian magnetic blood flow in the presence of thermal radiation and body acceleration through an inclined artery. The blood flow is formulated using the Casson fluid model under the control of a uniformly distributed magnetic field and an oscillating pressure gradient. Caputo-Fabrizio's fractional derivative mathematical model was used, along with Laplace transform and the finite Hankel transform technique. Analytical expressions were obtained for the velocity of blood flow, magnetic particle distribution, and temperature profile. These distributions are presented graphically using Mathcad software. The results show that the velocity increases with the time, Reynolds number and Casson fluid parameters, and diminishes when Hartmann number increases. Moreover, fractional parameters, radiation values, and metabolic heat source play an essential role in controlling the blood temperature. More precisely, these results are beneficial for the diagnosis and treatment of certain medical issues.

Analysis Of Two-Layered Model Of Blood Flow Through Stenosed Tube With Permeable Walls In The Presence Of Magnetic Field Considering Blood As Couple Stress Fluid With Variable Viscosity And Slip Velocity

The paper investigates the “two-layered model of blood flow” as steady incompressible couple stress fluid through one-dimensional channel in multi-stenosed blood vessel. Within the core region, the blood flow is conceptualized as a dynamic entity exhibiting the attributes of a couple stress fluid, distinguished by variable viscosity orchestrated in accordance with the precepts delineated by the Einstein relation and the peripheral region of the tube comprises of plasma which is considered as “Newtonian fluid with constant viscosity”. The governing equations of the blood flow are solved using the Frobenius technique using the slip boundary condition and the expressions are derived for peripheral and central velocities along with shear stress and pressure gradient. The effects of various parameters on the flow variables have been emphasised. MATLAB programming software is used to visualize the results regarding shear stress and pressure gradient. The study further interrogates the effect of change in thickness of peripheral layer on pressure gradient under the influence of magnetic field and slip velocity.

Myocardial perfusion segmentation and partitioning methods in personalized models of coronary blood flow

Abstract In this work we present methods and algorithms for construction of a personalized model of coronary haemodynamics based on computed tomography images. This model provides estimations of fractional flow reserve, coronary flow reserve, and instantaneous wave-free ratio taking into account transmural perfusion ratio indices obtained from perfusion images. The presented pipeline consists of the following steps: aorta segmentation, left ventricle wall segmentation, coronary arteries segmentation, construction of 1D network of vessels, partitioning of left ventricle wall, and personalization of the model parameters. We focus on a new technique, which generates specific perfusion zones and computes transmural perfusion ratio according to the quality of available medical images with a limited number of visible terminal coronary vessels. Numerical experiments show that accurate evaluation of stenosis before precutaneous coronary intervention should take into account both fractional flow reserve indices and myocardial perfusion, as well as other indices, in order to avoid misdiagnosis. The presented model provides better understanding of the background of clinical recommendations for possible surgical treatment of a stenosed coronary artery.

Numerical study of irreversibility analysis on pulsatile flow of blood through a ω-shaped stenotic artery

The mathematical modeling of blood flow in a stenotic blood vessel is very important for understanding the effects of various geometric and rheological parameters on the normal flow of blood. The present study is concerned with the heat and mass transfer in the blood flow of a non-Newtonian fluid through a ω-shaped stenotic arterial segment. The non-Newtonian behavior of blood is described mathematically by employing the constitutive equation of the Herschel-Bulkley fluid. The wall of the artery is considered to be rigid having ω-shaped constriction in its lumen. The mild stenosis assumption is used to simplify the fully coupled momentum, energy, and concentration equations as well as the constitutive equation of the Herschel-Bulkley fluid. Numerical solutions for fluid velocity, temperature, mass concentration, and entropy generation are evaluated by using the explicit finite difference scheme. The effects of various emerging parameters on the velocity, wall shear stress, flow rate, temperature, concentration, and entropy distributions have been analyzed in detail. A comparison between different fluid models has also been presented. It is found that the temperature in the Herschel-Bulkley fluid is marginally lower than that of the Newtonian, Power law, and Bingham fluids whereas an opposite trend is noticed in the case of mass concentration.

Human whole-brain models of cerebral blood flow and oxygen transport

The cerebral vasculature plays a critical role in the transport of oxygen and other nutrients to brain tissue. However, the size, complexity, and paucity of detailed anatomical information of this system makes understanding cerebral behaviour in normal and pathological conditions, as well as its response to stimuli, highly challenging. Whole-brain mathematical models have a valuable role to play in the understanding and measurement of cerebral parameters. However, for the same reasons, whole-brain models are highly complex to construct. In this study, we propose a novel multi-compartment approach to blood flow and oxygen transport. Building on prior models, we propose a new formulation based on a multiple compartment porous medium approach. Using non-dimensional analysis, we derive the most compact form of the equations and constrain the parameter space using clinically measurable quantities, such as baseline perfusion and blood volume. We illustrate the spatially and temporally varying response of the brain by simulating the response to changes in both arterial blood pressure and arterial oxygen saturation, showing that the oxygen response is strongly dependent upon depth, with large but slow responses being found deep in the brain and small but fast responses nearer the surface, whereas the flow response is very rapid in comparison. Blood flow and oxygenation are thus shown to exhibit very different characteristic time scales. This has significant implications for how we consider the response of the brain to external stimuli, such the autoregulation and reactivity responses, and how we model the brain at different time scales.Statement of Significance: In this study we present a new mathematical model for simulations of blood flow and oxygen transport in the human brain. A compact representation is obtained from analysis of the governing equations and different time scales are identified. We show that the behaviour is strongly depth dependent and that 3D models exhibit very different behaviour from simplified 1D models. This will be important in developing further models of the brain, particularly in simulating its active response.

A semi-implicit finite volume scheme for blood flow in elastic and viscoelastic vessels

A novel staggered semi-implicit finite volume method for the simulation of one-dimensional blood flow in networks of elastic and viscoelastic vessels is proposed. The one-dimensional blood flow model is split into three subsystems: one containing the nonlinear convective terms, a second one for the viscoelastic terms and a final subsystem for the pressure-related terms. An explicit approach is then employed to discretize the convective subsystem, while the viscous and pressure terms are treated implicitly. This leads to a CFL-type time step restriction which depends only on the bulk velocity of the flow and not on the speed of the pressure waves or on the visco elasticity. As such, the method is computationally efficient in case of low speed index, which is equivalent to a low Mach regime for the Navier-Stokes equations. To extend the proposed methodology to the case of networks, a novel and very simple 3D approach for the treatment of junctions is proposed. Each junction is represented by a unique three-dimensional primal cell and the Euler equations are employed to approximate the velocity and pressure unknowns. A multidimensional numerical flux then takes into account the elementary information of the junction geometry, namely normal vectors and areas of the incident vessels, when approximating the blood flow at the cell interfaces embedded in the 3D cell. As such, the final scheme, based on guaranteeing mass and momentum conservation through the junction, is able to capture reflecting waves properly considering the effect of the different incident angles of vessels at a junction. The proposed methodology is carefully validated in the context of single elastic and viscoelastic vessels and small networks showing a good agreement with available analytical, experimental and numerical data.

Numerical Model Validation of the Blood Flow through a Microchannel Hyperbolic Contraction.

A computational fluid dynamics (CFD) model of blood flow through hyperbolic contraction with a discrete phase model (DPM) was experimentally validated. For this purpose, the positions and velocities of red blood cells (RBCs) flowing in a microchannel with hyperbolic contraction were experimentally assessed using image analysis techniques, and were subsequently compared with the numerical results. The numerically and experimentally obtained velocity fields were in good agreement, with errors smaller than 10%. Additionally, a nearly constant strain rate was observed in the contraction region, which can be attributed to the quasilinear increase in the velocity along the hyperbolic contraction. Therefore, the numerical technique used was validated due to the close similarity between the numerically and experimentally obtained results. The tested CFD model can be used to optimize the microchannel design by minimizing the need to fabricate prototypes and evaluate them experimentally.

Computational fluid dynamics of coronary arteries with implanted stents: Effects of Newtonian and non‐Newtonian blood flows

AbstractThis study introduces and compares computational fluid dynamics of Newtonian and non‐Newtonian blood flows in coronary arteries, with and without considering stents. Three blood flow models, including Newtonian, Carreau, and non‐Newtonian power‐law models, were simulated to investigate their effect, and the solution algorithm includes drawing the geometry, creating the desired mesh, and then simulating Newtonian and non‐Newtonian blood flow different models and comparing them with each other, is presented in the article. A Newtonian fluid model has been commonly used in the simulation of blood flow, whereas blood has non‐Newtonian properties due to the nature of a solution containing suspended particles. The goal of this research is to investigate the differences between the models built with Newtonian and non‐Newtonian fluid assumptions. In addition, a stent was designed and the effect of the stent on blood flow parameters was investigated for all three flow models, including Newtonian, Carreau, and non‐Newtonian power‐law models. Stents are medical devices that can be placed in arteries to open up blood flow in a blocked vessel. Stents can affect the wall shear stress. Knowing the slight deformation of the shear stress makes the importance of stent implantation and also helps to optimize the design of the intravascular stent, which can affect the occlusion of the vessels. The distribution of the velocity, pressure, and wall shear stress in all blood flow models with and without considering the effect of stents have been investigated and finally compared. Therefore, in general, the innovation of this article is to find the effect of implanted stents on blood flow parameters with different blood flow models, both Newtonian and non‐Newtonian. A comparison of Newtonian and non‐Newtonian flows showed that in the case of the Carreau non‐Newtonian model, the wall shear stress was higher. In addition, in the results of the geometric model with a stent effect compared to the geometric model without a stent effect, it is evident that there was a higher velocity and wall shear stress.

Mechanistic insights on age-related changes in heart-aorta-brain hemodynamic coupling using a pulse wave model of the entire circulatory system.

Age-related changes in aortic biomechanics can impact the brain by reducing blood flow and increasing pulsatile energy transmission. Clinical studies have shown that impaired cardiac function in patients with heart failure is associated with cognitive impairment. Although previous studies have attempted to elucidate the complex relationship between age-associated aortic stiffening and pulsatility transmission to the cerebral network, they have not adequately addressed the effect of interactions between aortic stiffness and left ventricle (LV) contractility (neither on energy transmission nor on brain perfusion). In this study, we use a well-established and validated one-dimensional blood flow and pulse wave computational model of the circulatory system to address how age-related changes in cardiac function and vasculature affect the underlying mechanisms involved in the LV-aorta-brain hemodynamic coupling. Our results reveal how LV contractility affects pulsatile energy transmission to the brain, even with preserved cardiac output. Our model demonstrates the existence of an optimal heart rate (near the normal human heart rate) that minimizes pulsatile energy transmission to the brain at different contractility levels. Our findings further suggest that the reduction in cerebral blood flow at low levels of LV contractility is more prominent in the setting of age-related aortic stiffening. Maintaining optimal blood flow to the brain requires either an increase in contractility or an increase in heart rate. The former consistently leads to higher pulsatile power transmission, and the latter can either increase or decrease subsequent pulsatile power transmission to the brain.NEW & NOTEWORTHY We investigated the impact of major aging mechanisms of the arterial system and cardiac function on brain hemodynamics. Our findings suggest that aging has a significant impact on heart-aorta-brain coupling through changes in both arterial stiffening and left ventricle (LV) contractility. Understanding the underlying physical mechanisms involved here can potentially be a key step for developing more effective therapeutic strategies that can mitigate the contributions of abnormal LV-arterial coupling toward neurodegenerative diseases and dementia.

Multiscale Constitutive Framework of One-Dimensional Blood Flow Modeling: Asymptotic Limits and Numerical Methods

Multiscale Constitutive Framework of One-Dimensional Blood Flow Modeling: Asymptotic Limits and Numerical Methods

Modeling of blood flow in the framework of micropolar theory

In this paper, we study the blood flow through blood vessels of various radii (including the case of variable cross section as well as modeling the blood flow through venae and arteries). Two approaches are discussed in order to mimic the dependence of blood viscosity on red blood cells aggregation, which changes with the shear rate and position inside the vessel: Two microstructural parameters together with empirical constitutive equations as a characteristic of aggregation are proposed, namely the microinertia as well as the volume fraction of blood particles (erythrocytes, platelets and leukocytes). Consequently, the Navier–Stokes system of equations for an incompressible fluid is supplemented by a constitutive equation for the moment of inertia in one case and for the volume fraction in another. The problems are solved numerically by the finite volume method for vessels of various geometries in spatial description. A comparison with experimental data for a narrow capillary shows the efficiency of the proposed constitutive equations for describing blood flow. Also, velocity profiles are obtained on the basis of compiled empirical formula for various sections of a blood vessel of variable radius. In addition, the flow through vessels of the human circulatory system, such as the inferior vena cava and the carotid artery, are studied.

Patient-specific modeling of blood flow in the coronary arteries

Patient-specific models of blood flow in the coronary arteries have entered clinical practice worldwide to aid in the diagnosis and management of heart disease. This technology leverages modern AI-based image segmentation methods to extract the geometry of the coronary arteries from noninvasive computed tomography volumetric imaging, computational physiology methods to define boundary conditions and computational fluid dynamic techniques to compute coronary artery flow and pressure. The methods described herein have been used to compute the fractional flow reserve (FFR) in the coronary arteries, namely the ratio of pressure in a coronary artery to the reference aortic pressure under conditions of maximum hyperemia induced by the intravenous administration of a vasodilator to mimic increased coronary artery blood flow as occurs during physical activity. The fractional flow reserve derived from coronary computed tomography angiography (CCTA) using patient-specific models of coronary artery blood flow is referred to as FFRCT and has been validated against invasive measurements using pressure wires in several hundred patients and subsequently evaluated in clinical trials in several thousand patients. Patient-specific models of coronary artery blood flow can be used to predict outcomes of coronary artery revascularization procedures, to identify patients at risk of having a heart attack, and to model tissue perfusion of the microcirculation by coupling with emerging models of cardiac function. This paper provides a state-of-the-art review of computational methods for, and applications of, quantifying blood flow in patient-specific models of the coronary arteries.

Reduced order modeling of parametrized pulsatile blood flows: Hematocrit percentage and heart rate

This paper numerically evaluates the accuracy and performance of a stabilized finite element Reduced Order Modelling (ROM) approach that is designed to simulate pulsatile blood flows. The method is able to estimate fluid flow parametric solutions of interest in hemodynamics by considering the hematocrit percentage (Hct%) and the heart rate (fc) as parameters. The method estimates off-trained parametric scenarios which have not been included in the training data set composing the ROM basis and that can adopt arbitrary values from specific patient conditions. The hematocrit percentages modifies the viscous properties of blood, which are incorporated into the problem physics through a power-law model. The hematocrit percentages are 5≤Hct%≤50, ranging from severe anemia to physiological values. The pulsatile flow condition is modeled via a Womersley function, with fcbpm (beats per minute) ranging between 60bpm≤fc≤120bpm. These frequencies comprise physiological conditions of patients at rest and tachycardia or moderate exercise. Two-and-three-dimensional flows are simulated inside a representative geometry of a carotid artery, where the accuracy is tested by studying the effect of the number of components of the ROM approximating basis and the number of sampling points composing the training data set. The parametric calculation verifies that the proposed approach constitutes a valuable computational tool for simulating complex fluid flow hemodynamics and can be applied to clinical decision-making.