Non-Newtonian Rheology in Blood Circulation

Blood is a complex suspension that demonstrates several non-Newtonian rheological characteristics such as deformation-rate dependency, viscoelasticity and yield stress. In this paper we outline some issues related to the non-Newtonian effects in blood circulation system and present modeling approaches based mostly on the past work in this field.Comment: 26 pages, 5 figures, 2 table

Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement

We present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid-structure interaction (FSI) in blood flow allowing non-zero longitudinal displacement. Arterial walls are modeled by a {linearly viscoelastic, cylindrical Koiter shell model capturing both radial and longitudinal displacement}. Fluid flow is modeled by the Navier-Stokes equations for an incompressible, viscous fluid. The two are fully coupled via kinematic and dynamic coupling conditions. Our numerical scheme is based on a new modified Lie operator splitting that decouples the fluid and structure sub-problems in a way that leads to a loosely coupled scheme which is {unconditionally} stable. This was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub-problems, leading to an implicit coupling between the fluid and structure velocities. The proposed scheme is a modification of the recently introduced "kinematically coupled scheme" for which the newly proposed modified Lie splitting significantly increases the accuracy. The performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme. It was shown that the accuracy of our scheme was comparable to that of the monolithic scheme, while our scheme retains all the main advantages of partitioned schemes, such as modularity, simple implementation, and low computational costs

Advancements in blood rheology and hemodynamics simulation with a brief history

Blood rheology is a complex field of study that investigates blood flow behavior, vital for understanding its role in physiological and pathological conditions. This article delves into various rheological models that describe blood behavior, ranging from Generalized Newtonian models to more sophisticated thixotropic and elastoviscoplastic models. One such model, the Horner-Armstrong-Wagner-Beris (HAWB) model, offers valuable insights into the dynamic interplay of reversible and irreversible phenomena in blood flow. Recent advancements, such as the mHAWB framework, provide enhanced accuracy and versatility in modeling blood rheology, holding great potential for diagnostic and therapeutic applications. Moreover, microscopic and mesoscopic simulations have paved the way for deeper insights into blood behavior, bridging the gap between theory and experiment. Multiscale models offer a promising approach to capturing the complexities of blood rheology at various length scales. Finally, we explore the clinical implications of blood rheology, including its significance in conditions like polycythemia, neonatal respiratory distress, and circulatory inadequacy. By understanding blood rheology comprehensively, we can advance our knowledge of complex blood flow dynamics and its potential applications in healthcare

Methods and Algorithms for Cardiovascular Hemodynamics with Applications to Noninvasive Monitoring of Proximal Blood Pressure and Cardiac Output Using Pulse Transit Time

Advanced health monitoring and diagnostics technology are essential to reduce the unrivaled number of human fatalities due to cardiovascular diseases (CVDs). Traditionally, gold standard CVD diagnosis involves direct measurements of the aortic blood pressure (central BP) and flow by cardiac catheterization, which can lead to certain complications. Understanding the inner-workings of the cardiovascular system through patient-specific cardiovascular modeling can provide new means to CVD diagnosis and relating treatment. BP and flow waves propagate back and forth from heart to the peripheral sites, while carrying information about the properties of the arterial network. Their speed of propagation, magnitude and shape are directly related to the properties of blood and arterial vasculature. Obtaining functional and anatomical information about the arteries through clinical measurements and medical imaging, the digital twin of the arterial network of interest can be generated. The latter enables prediction of BP and flow waveforms along this network. Point of care devices (POCDs) can now conduct in-home measurements of cardiovascular signals, such as electrocardiogram (ECG), photoplethysmogram (PPG), ballistocardiogram (BCG) and even direct measurements of the pulse transit time (PTT). This vital information provides new opportunities for designing accurate patient-specific computational models eliminating, in many cases, the need for invasive measurements. One of the main efforts in this area is the development of noninvasive cuffless BP measurement using patient’s PTT. Commonly, BP prediction is carried out with regression models assuming direct or indirect relationships between BP and PTT. However, accounting for the nonlinear FSI mechanics of the arteries and the cardiac output is indispensable. In this work, a monotonicity-preserving quasi-1D FSI modeling platform is developed, capable of capturing the hyper-viscoelastic vessel wall deformation and nonlinear blood flow dynamics in arbitrary arterial networks. Special attention has been dedicated to the correct modeling of discontinuities, such as mechanical properties mismatch associated with the stent insertion, and the intertwining dynamics of multiscale 3D and 1D models when simulating the arterial network with an aneurysm. The developed platform, titled Cardiovascular Flow ANalysis (CardioFAN), is validated against well-known numerical, in vitro and in vivo arterial network measurements showing average prediction errors of 5.2%, 2.8% and 1.6% for blood flow, lumen cross-sectional area, and BP, respectively. CardioFAN evaluates the local PTT, which enables patient-specific calibration and its application to input signal reconstruction. The calibration is performed based on BP, stroke volume and PTT measured by POCDs. The calibrated model is then used in conjunction with noninvasively measured peripheral BP and PTT to inversely restore the cardiac output, proximal BP and aortic deformation in human subjects. The reconstructed results show average RMSEs of 1.4% for systolic and 4.6% for diastolic BPs, as well as 8.4% for cardiac output. This work is the first successful attempt in implementation of deterministic cardiovascular models as add-ons to wearable and smart POCD results, enabling continuous noninvasive monitoring of cardiovascular health to facilitate CVD diagnosis

Multiscale Fluid-Structure Interaction Models Development and Applications to the 3D Elements of a Human Cardiovascular System

Cardiovascular diseases (CVD) are the number one cause of death of humans in the United States and worldwide. Accurate, non-invasive, and cheaper diagnosis methods have always been on demand as cardiovascular monitoring increase in prevalence. The primary causes of the various forms of these CVDs are atherosclerosis and aneurysms in the blood vessels. Current noninvasive methods (i.e., statistical/medical) permit fairly accurate detection of the disease once clinical symptoms are suggestive of the existence of hemodynamic disorders. Therefore, the recent surge of hemodynamics models facilitated the prediction of cardiovascular conditions. The hemodynamic modeling of a human circulatory system involves varying levels of complexity which must be accounted for and resolved. Pulse-wave propagation effects and high aspect-ratio segments of the vasculature are represented using a quasi-one-dimensional (1D), non-steady, averaged over the cross-section models. However, these reduced 1D models do not account for the blood flow patterns (recirculation zones), vessel wall shear stresses and quantification of repetitive mechanical stresses which helps to predict a vessel life. Even a whole three-dimensional (3D) modeling of the vasculature is computationally intensive and do not fit the timeline of practical use. Thus the intertwining of a quasi 1D global vasculature model with a specific/risk-prone 3D local vessel ones is imperative. This research forms part of a multiphysics project that aims to improve the detailed understanding of the hemodynamics by investigating a computational model of fluid-structure interaction (FSI) of in vivo blood flow. First idealized computational a 3D FSI artery model is configured and executed in ANSYS Workbench, forming an implicit coupling of the blood flow and vessel walls. Then the thesis focuses on an approach developed to employ commercial tools rather than in-house mathematical models in achieving multiscale simulations. A robust algorithm is constructed to combine stabilization techniques to simultaneously overcome the added-mass effect in 3D FSI simulation and mathematical difficulties such as the assignment of boundary conditions at the interface between the 3D-1D coupling. Applications can be of numerical examples evaluating the change of hemodynamic parameters and diagnosis of an abdominal aneurysm, deep vein thrombosis, and bifurcation areas

Viscoelastic Properties of Cardiovascular Tissues

The aims of this chapter are to review the current state of knowledge regarding the viscoelastic behavior of cardiovascular tissues. We begin with a brief, general discussion of measurement and modeling of cardiovascular tissue viscoelasticity. We then review known viscoelastic behavior of arteries, veins, capillaries, blood components, the heart, and lymphatics. For each tissue type, we highlight tissue-specific measurement methods, the cellular and extracellular components responsible for tissue viscoelasticity, and the clinical implications of energy loss due to viscoelasticity. We conclude with a summary and suggestions for future research

Numerical simulation and experimentation of pulsatile flows in axisymmetric arterial models

ABSTRACT NUMERICAL SIMULATION AND EXPERIMENTATION OF PULSATILE FLOWS IN AXISYMMETRIC ARTERIAL MODELS by TADESSE GEBREEGZIABHER December 2011 Co-advisors: 1. Dr. Emmanuel Ayorinde 2. Dr. Trilochan Singh Major: Mechanical Engineering Degree: Doctor of Philosophy The primary motivation for this dissertation is the fluid flow and structural response to unsteady blood flow in the human body. The research work is a synergistic merging of numerical simulation and experimentation. For the experiments, an all-encompassing, highly flexible experimental apparatus was designed and fabricated to facilitate a wide range of operating conditions, the range of which was chosen to accommodate mammalian cardiovascular system for both human and animal species. The parameters that were varied during the course of the experimentation include the frequency of the flow pulsation, tubular materials having various structural properties, and blockages of the tube cross sections to simulate the presence of plaque in arteries. The main outcome of the experimentation was a connection between the amplitude and frequency of the pulsations and the volumetric flow rate of the flowing fluid. Of equal importance is the extent of the response of the wall to the nature of the pulsating flow which was detected, located and characterized using a non-invasive acoustic emission equipment. The simulations that were performed represent a major advance over prior attempts to simulate pulsating flows in flexible- and rigid-walled tubes. That advance was embodied in the model that was used to characterize the flow. In most of prior studies, a particular flow regime was selected and used throughout the entire solution domain. This selection ignored the fact that flowing fluids passing through variable cross sections undergo changes of flow regime. In particular, a flow initiated in a relatively large upstream cross section may be laminar based on inlet conditions. However, as the fluid travels downstream and enters a constricted cross section, the laminar regime may undergo a transition and subsequently experience turbulence. The capability to accommodate all these flow regimes by a single model was first accomplished in this research. Of special relevance is that the capability to simulate the proper flow regime enabled a more realistic response of the bounding wall of the tube to the imposed pulsations. Comparisons were made between the experimental results and the predictions of the simulations for two purposes. One was to establish the ranges of applicability of the simulation model. The other established a body of archival-quality information based on confirming experimental and simulated results. Another unique contribution of this research is the determination of the presence of flow-induced acoustic emissions. The motivation for this part of this work is the development of a diagnostic tool to detect, locate, and characterize blockages in arterial models

Novel model of cerebrospinal fluid dynamics based on hemodynamically driven cyclic brain compliance variation

This study provides a novel explanation for the CerebrQ-Spinal Fluid (CSF) flow pattern observed in phase contrast cine-MRJ studies. CSF dynamics has been traditionally explained as a bulk flow from the site of production to the site of absorption. Studies done with phase contrast cine-MRI show a more complex CSF movement, that is not explainable by the bulk flow paradigm. This study describes a mechanism explaining how the energy delivered by the heart in each cycle is responsible not only for the blood flow, but also for the CSF circulation. This mechanism is based on a cyclic variation of brain compliance, dependent on the blood volume inside the brain vessels. As the cardiac cycle changes the blood volume inside the vessels, it also conditions a compliance cycle of the brain tissue. For better comprehension of the mechanism, a conceptual model, mathematical model and computer model are described. To capture the essence of CSF dynamics a three compartmental model is created representing: the ventricular system, the intracranial subarachnoideal space, and the spinal subarachnoideal space. The implemented driving function represents the blood volume variation with time produced by the cardiac cycle. In turn it detennines cyclic changes in brain parenchyma compliance. Brain parenchyma compliance changes as a function of the blood volume inside the brain vessels; therefore, during systole the compliance diminishes, during diastole compliance increases. As brain tissue compliance changes the CSF volume inside each compartment is redistributed. Cyclic compliance variation of brain tissue creates a pulsatile CSF flow. The CSF dynamics model is also used for the analysis of altered CSF dynamics; Normal Pressure Hydrocephalus and Idiopathic Intracranial Hypertension are explained as a consequence of altered compliance of the brain tissue

Nonlinear Dynamics of Human Aortas for Material Characterization

Evaluating the nonlinear dynamics of human descending thoracic aortas is essential for building the next generation of vascular prostheses. This study characterizes the nonlinear dynamics, viscoelastic material properties, and fluid-structure interaction of 11 ex-vivo human descending thoracic aortas the full range of physiological heart rates. The aortic segments are harvested from heart-beating donors screened for transplants. A mock circulatory loop is developed to reproduce physiological pulsatile pressure and flow. The results show cyclic axisymmetric diameter changes, which are satisfactorily compared to in-vivo measurements at a resting pulse rate of 60 bpm, with an additional bending vibration. An increase of the dynamic stiffness (i.e., storage modulus) with age is also observed. This increase is accompanied by a strong reduction with age of the cyclic diameter change during the heart pulsation at 60 bpm and by a significant reduction of the loss factor (i.e., damping). Large dissipation is observed at higher pulse rates due to the combined effects of fluid-structure interaction and viscoelasticity of the aortic wall. This study presents data necessary for developing innovative grafts that better mimic the dynamics of the aorta