Newtonian Flow in Converging-Diverging Capillaries

The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously-derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier-Stokes are identical to those obtained from the lubrication approximation within a non-dimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.Comment: 23 pages, 5 figures, 1 table. This is an extended and improved version. arXiv admin note: substantial text overlap with arXiv:1006.151

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

Cardiovascular function and ballistocardiogram: a relationship interpreted via mathematical modeling

Objective: to develop quantitative methods for the clinical interpretation of the ballistocardiogram (BCG). Methods: a closed-loop mathematical model of the cardiovascular system is proposed to theoretically simulate the mechanisms generating the BCG signal, which is then compared with the signal acquired via accelerometry on a suspended bed. Results: simulated arterial pressure waveforms and ventricular functions are in good qualitative and quantitative agreement with those reported in the clinical literature. Simulated BCG signals exhibit the typical I, J, K, L, M and N peaks and show good qualitative and quantitative agreement with experimental measurements. Simulated BCG signals associated with reduced contractility and increased stiffness of the left ventricle exhibit different changes that are characteristic of the specific pathological condition. Conclusion: the proposed closed-loop model captures the predominant features of BCG signals and can predict pathological changes on the basis of fundamental mechanisms in cardiovascular physiology. Significance: this work provides a quantitative framework for the clinical interpretation of BCG signals and the optimization of BCG sensing devices. The present study considers an average human body and can potentially be extended to include variability among individuals

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