Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device

Abstract

Left ventricular assist devices (LVADs) are continuous flow pumps that are employed in patients with severe heart failure. Although their emergence has significantly improved therapeutic options for patients with heart failure, detailed studies of the impact of LVADs on hemodynamics are notably lacking. To this end we initiate a computational study of the Jarvik 2000 LVAD model employing isogeometric fluid–structure interaction analysis. We focus on a patient-specific configuration in which the LVAD is implanted in the descending thoracic aorta. We perform computations for three pump settings and report our observations for several quantities of hemodynamic interest. It should be noted that this paper presents the first three-dimensional, patient-specific fluid–structure interaction simulation of LVADs.

Introduction

Cardiovascular disease is the number one killer of men and women in the US and is the primary cause of congestive heart failure (CHF), which afflicts over 5.2 million Americans. There are 550,000 new cases of CHF reported annually. Cardiovascular diseases produce a number of physiological changes to the tissue of the cardiovascular system (e.g., loss of elasticity of the arteries as in arteriosclerosis, ischemic damage and cardiomyopathies). These change the hemodynamics of the cardiovascular system with potentially disastrous consequences. When other treatments fail, implanted circulation support devices can be used to reestablish interrupted or inadequate flow. The emergence of axial flow assist devices has significantly advanced therapeutic options for patients with severe heart failure. These devices deliver continuous blood flow and provide distinct advantages with regard to reduction in size, weight, and energy demands, simplified implantation technique, and device control [21].

New, small, efficient non-pulsatile axial flow left ventricle assist devices (LVADs) are currently being studied as bridges to transplant, destination therapy and recovery for CHF. These pumps are highly engineered, optimized devices, but the design of their most effective implant configurations and operating conditions has been more difficult. This is unfortunate because LVADs greatly alter the hemodynamics of the heart and aorta, which can be either helpful, as intended, or harmful, leading to significant complications. Tools to optimize LVAD device design and placement are notably lacking, though both have a significant effect on hemodynamics. Of particular concern regarding hemodynamics is the occurrence of regions in which the blood is stagnant, thought to be a key factor leading to thrombogenesis [58]. Flow stasis was seen clinically using trans-esophageal echo technology in patients with the pump outlet graft in the descending aorta and the LVAD on high speed. Stasis or mild wall shear stress has been correlated with thrombotic events [36].

Currently there is very little work on numerical simulation of LVADs. In [39] an idealized LVAD configuration was studied using steady-state computational fluid dynamics (CFD). In [29], a time-dependent simulation of an idealized two-dimensional aortic arch with the LVAD was performed using time-dependent CFD. In both cases, the arterial wall was considered rigid. In this work, we perform fluid–structure interaction simulation of a three-dimensional patient-specific model of the aorta, from the aortic valve to the descending thoracic aorta, including flow into branch vessels, and include the effect of the LVAD. The effect of an LVAD on hemodynamics is complex and demands a locally three-dimensional model of the flow in the aortic valve and aorta. We focus on this section of the aorta because this is the region in which the hemodynamics are most affected by the introduction of an LVAD. It is also the region in which hemodynamics has the greatest effect on the health of the heart. Our modeling and simulation efforts are motivated by ongoing clinical studies, which suggest that it is the gross features of the configuration and operating conditions of the device that are in most need of assessment and optimization [29].

For this study we constructed a patient-specific model of the thoracic aorta with an added LVAD branch in the descending location. We consider three different flow conditions: (1) LVAD is off and all the blood flow occurs through the aortic root; (2) LVAD is operating in the regime where over one half of the blood supplied to the aorta comes from the pump; (3) LVAD is operating in the regime where nearly all the flow comes from the LVAD. Inflow data for our patient-specific model was obtained from a lumped-parameter closed-loop multiscale model of the cardiovascular system that was developed in [18]. The latter allows for the inclusion of assist devices.

We use NURBS-based isogeometric analysis for geometry modeling and simulation. (See Refs. [25], [9], [5] for the basics of isogeometric analysis and Refs. [3], [59] for application of NURBS-based isogeometric analysis to modeling and simulation of fluid–structure interaction applied to vascular flows.) We use numerical procedures developed in [2] with the following modification to the coupled system solution strategy: at the nonlinear iteration stage we omit the so-called shape derivatives from the left-hand side tangent matrix, resulting in a simplified coupled solution procedure. No significant influence of this on the nonlinear convergence was observed. This so-called “quasi-direct” approach for fluid–structure coupling was advocated in [56], [53], [54]. For investigations of the effect of including shape derivatives in the left-hand side matrix on the overall convergence of monolithic fluid–structure interaction algorithms see [13], [10].

The paper is organized as follows. In Section 2 we present the coupled fluid–structure interaction formulation of vascular blood flow at the continuous level. In this formulation, the blood is modeled as an incompressible viscous fluid and the arterial wall is modeled as a hyperelastic solid. The formulation allows for large structural motions. In Section 3 the semi-discrete formulation of the coupled problem is given and the algorithm to advance the fluid–structure equations in time is described. In Section 4 we present the setup and numerical results of the simulation of blood flow and arterial wall motion in the model of a patient-specific thoracic aorta with LVAD implanted in the descending location. We give a detailed discussion of imposition of initial and boundary conditions. In particular, we present a stable modification of the outflow boundary condition to account for possible cases of locally reversed flow through outflow boundaries. Numerical results obtained for the descending aortic distal anastomosis are in agreement with clinical observations and findings for this configuration. In Section 5, we draw conclusions and outline future research directions.