Multi-Scale Cardiovascular Flow Analysis by an Integrated Meshless-Lumped Parameter Model

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage of the integrated surface discretization and automated point distribution used for the Meshless collocation. The local hemodynamics are integrated with the peripheral circulation via compartments that account for branch viscous resistance (R), flow inertia (L), and vessel compliance (C), namely RLC electric circuit analogies. The cardiac function is modeled via time-varying capacitors simulating the ventricles and constant capacitors simulating the atria, connected by diodes and resistors simulating the atrioventricular and ventricular-arterial valves. This multi-scale integration in an in-house developed computational tool opens the possibility for model automation of patient-specific anatomies from medical imaging, elastodynamics analysis of vessel wall deformation for fluid-structure interaction, automated model refinement, and inverse analysis for parameter estimation

Meshless 2D direct numerical simulation and heat transfer in a backward-facing step with heat conduction in the step

A meshless direct pressure-velocity coupling procedure is presented to perform Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent incompressible flows in regular and irregular geometries. The proposed method is a combination of several efficient techniques found in different Computational Fluid Dynamic (CFD) procedures. With this new procedure, preliminary calculations with 2D steady state flows show that viscous effects become negligible faster that ever predicted numerically. The fundamental idea of this method lays on several important inconsistencies found in three of the most popular techniques used in CFD, segregated procedures, as well as in other formulations. The inconsistencies found become important in elliptic flows and they might lead to some wrong solutions. Preliminary calculations done in 2D laminar flows, suggest that the numerical diffusion and interpolation error are much important at low speeds, mainly when both, viscous and inertia forces are present. With this competitive and efficient procedure, the solution of the 2D Direct Numerical Simulation of turbulent flow with heat transfer on a backward-facing step is presented. The thermal energy is going to be transferred to the fluid through conduction on the step, with both constant temperature and heat flux conditions in the back wall of the step. The variation of the local Nusselt Number through the wall will be studied and its corresponding effect in the energy transfer to the fluid

Left Ventricular Assist Devices: Engineering Design Considerations

Patients with end-stage congestive heart failure awaiting heart transplantation often wait long periods of time (300 days or more on the average) before a suitable donor heart becomes available. The medical community has placed increased emphasis on the use of Left Ventricular Assist Devices or LVADs that can substitute for, or enhance, the function of the natural heart while the patient is waiting for the heart transplant (Poirier, 1997; Frazier & Myers, 1999). Essentially, a rotary LVAD is a pump that operates continuously directing blood from the left ventricle into the aorta by avoiding the aortic valve. Generally speaking, the goal of the LVAD is to assist the native heart in pumping blood through the circulatory system so as to provide the patient with as close to a normal lifestyle as possible until a donor heart becomes available or, in some cases, until the patient’s heart recovers. In many situations, this means allowing the patient to return home and/or to the workforce

Left Ventricular Assist Devices: Engineering Design Considerations

Patients with end-stage congestive heart failure awaiting heart transplantation often wait long periods of time (300 days or more on the average) before a suitable donor heart becomes available. The medical community has placed increased emphasis on the use of Left Ventricular Assist Devices or LVADs that can substitute for, or enhance, the function of the natural heart while the patient is waiting for the heart transplant (Poirier, 1997; Frazier & Myers, 1999). Essentially, a rotary LVAD is a pump that operates continuously directing blood from the left ventricle into the aorta by avoiding the aortic valve. Generally speaking, the goal of the LVAD is to assist the native heart in pumping blood through the circulatory system so as to provide the patient with as close to a normal lifestyle as possible until a donor heart becomes available or, in some cases, until the patient’s heart recovers. In many situations, this means allowing the patient to return home and/or to the workforce

An Inverse POD-RBF Network Approach to Parameter Estimation in Mechanics

An inverse approach is formulated using proper orthogonal decomposition (POD) integrated with a trained radial basis function (RBF) network to estimate various physical parameters of a specimen with little prior knowledge of the system. To generate the truncated POD-RBF network utilized in the inverse problem, a series of direct solutions based on FEM, BEM or exact analytical solutions are used to generate a data set of temperatures or deformations within the system or body, each produced for a unique set of physical parameters. The data set is then transformed via POD to generate an orthonormal basis to accurately solve for the desired material characteristics using the Levenberg-Marquardt (LM) algorithm to minimize the objective least squares functional. While the POD-RBF inverse approach outlined in this paper focuses primarily in application to conduction heat transfer, elasticity, and fracture mechanics, this technique is designed to be directly applicable to other realistic conditions and/or relevant industrial problems

In-Vitro Analysis of the Fenestration in the Injection Jet Shunt Assisted Fontan Circulation

The Fontan circulation is a fragile system in which imperfections at any one of multiple levels may compromise quality of life, produce secondary pathophysiology, and shorten life span. Despite positive outcomes over the years, the Fontan circulation still presents survival rates of less than 50%. Increased inferior vena caval (IVC) pressure itself may play some role in “Fontan failure”. We propose to augment energy in the Fontan circulation with an injection jet shunt (IJS) drawing flow directly from the aortic arch, balanced by a conduit-to-atrial fenestration to approximately preserve the ratio of pulmonary flow (Qp) to systemic flow (Qs). Currently to mitigate IVC pressures surgeons often implement an orifice, called fenestration, between the IVC and the right atrium which bypasses the lungs. The amount of pressure relief is proportional to the size of the fenestration. Preliminary experimental results closely validate the detailed in-silico findings. Benchtop study shows that increasing the fenestration size can incrementally drop the IVC pressure, the systemic oxygen saturation can be adversely affected. Enlargement of the fenestration to 7 mm results in a significant IVC pressure drop with a reduction in systemic oxygen saturation.  Addition of an IJS to this Fontan model helps to preserve the IVC pressure drop while improves systemic oxygen saturation, hemodynamically insignificant volume load to the ventricle

Computational Analysis of Hybrid Norwood Circulation with Distal Aortic Arch Obstruction and Reverse Blalock-Taussig Shunt

BACKGROUND: The hemodynamics characteristics of the hybrid Norwood (HN) procedure differ from those of the conventional Norwood and are not fully understood. We present a multi-scale model of HN circulation to understand local hemodynamics and effects of aortic arch stenosis and a reverse Blalock-Taussig shunt (RBTS) on coronary and carotid perfusion. METHODS: Four 3-dimensional models of four HN anatomic variants were developed, with and without 90% distal preductal arch stenosis and with and without a 4-mm RBTS. A lumped parameter model of the circulation was coupled to a local 3-dimensional computational fluid dynamics model. Outputs from the lumped parameter model provided waveform boundary conditions for the computational fluid dynamics model. RESULTS: A 90% distal arch stenosis reduced pressure and net flow-rate through the coronary and carotid arteries by 30%. Addition of the RBTS completely restored pressure and flow rate to baseline in these vessels. Zones of flow stagnation, flow reversal, and recirculation in the presence of stenosis were rendered more orderly by addition of the RBTS. In the absence of stenosis, presence of the shunt resulted in extensive zones of disturbed flow within the RBTS and arch. CONCLUSIONS: We found that a 4-mm × 21-mm RBTS completely compensated for the effects of a 90% discrete stenosis of the distal aortic arch in the HN. Placed preventatively, the RBTS and arch displayed zones with thrombogenic potential showing recirculation and stagnation that persist for a substantial fraction of the cardiac cycle, indicating that anticoagulation should be considered with a prophylactic RBTS

A Coupled Localized Rbf Meshless/Drbem Formulation For Accurate Modeling Of Incompressible Fluid Flows

Velocity-pressure coupling schemes for the solution of incompressible fluid flow problems in Computational Fluid Dynamics (CFD) rely on the formulation of Poisson-like equations through projection methods. The solution of these Poisson-like equations represent the pressure correction and the velocity correction to ensure proper satisfaction of the conservation of mass equation at each step of a time-marching scheme or at each level of an iteration process. Inaccurate solutions of these Poisson-like equations result in meaningless instantaneous or intermediate approximations that do not represent the proper time-accurate behavior of the flow. The fact that these equations must be solved to convergence at every step of the overall solution process introduces a major bottleneck for the efficiency of the method. We present a formulation that achieves high levels of accuracy and efficiency by properly solving the Poisson equations at each step of the solution process by formulating a Localized RBF Collocation Meshless Method (LRC-MM) solution approach for the approximation of the diffusive and convective derivatives while employing the same framework to implement a Dual-Reciprocity Boundary Element Method (DR-BEM) for the solution of the ensuing Poisson equations. The same boundary discretization and point distribution employed in the LRC-MM is used for the DR-BEM. The methodology is implemented and tested in the solution of a backward-facing step problem

Multi-scale cardiovascular flow analysis by an integrated meshless-lumped parameter model

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage of the integrated surface discretization and automated point distribution used for the Meshless collocation. The local hemodynamics are integrated with the peripheral circulation via compartments that account for branch viscous resistance (R), flow inertia (L), and vessel compliance (C), namely RLC electric circuit analogies. The cardiac function is modeled via time-varying capacitors simulating the ventricles and constant capacitors simulating the atria, connected by diodes and resistors simulating the atrioventricular and ventricular-arterial valves. This multi-scale integration in an in-house developed computational tool opens the possibility for model automation of patient-specific anatomies from medical imaging, elastodynamics analysis of vessel wall deformation for fluid-structure interaction, automated model refinement, and inverse analysis for parameter estimation

Multi-Scale Cardiovascular Flow Analysis By An Integrated Meshless-Lumped Parameter Model

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage of the integrated surface discretization and automated point distribution used for the Meshless collocation. The local hemodynamics are integrated with the peripheral circulation via compartments that account for branch viscous resistance (R), flow inertia (L), and vessel compliance (C), namely RLC electric circuit analogies. The cardiac function is modeled via time-varying capacitors simulating the ventricles and constant capacitors simulating the atria, connected by diodes and resistors simulating the atrioventricular and ventricular-arterial valves. This multi-scale integration in an in-house developed computational tool opens the possibility for model automation of patient-specific anatomies from medical imaging, elastodynamics analysis of vessel wall deformation for fluid-structure interaction, automated model refinement, and inverse analysis for parameter estimation