Numerical considerations for advection-diffusion problems in cardiovascular hemodynamics

Effects of non-Newtonian viscosity on arterial and venous flow and transport

It is well known that blood exhibits non-Newtonian viscosity, but it is generally modeled as a Newtonian fluid. However, in situations of low shear rate, the validity of the Newtonian assumption is questionable. In this study, we investigated differences between Newtonian and non-Newtonian hemodynamic metrics such as velocity, vorticity, and wall shear stress. In addition, we investigated cardiovascular transport using two different approaches, Eulerian mass transport and Lagrangian particle tracking. Non-Newtonian solutions revealed important differences in both hemodynamic and transport metrics relative to the Newtonian model. Most notably for the hemodynamic metrics, in-plane velocity and vorticity were consistently larger in the Newtonian approximation for both arterial and venous flows. Conversely, wall shear stresses were larger for the non-Newtonian case for both the arterial and venous models. Our results also indicate that for the Lagrangian metrics, the history of accumulated shear was consistently larger for both arterial and venous flows in the Newtonian approximation. Lastly, our results also suggest that the Newtonian model produces larger near wall and luminal mass transport values compared to the non-Newtonian model, likely due to the increased vorticity and recirculation. These findings demonstrate the importance of accounting for non-Newtonian behavior in cardiovascular flows exhibiting significant regions of low shear rate and recirculation.

Patient-Specific Computational Modeling of Different Cannulation Strategies for Extracorporeal Membrane Oxygenation

Institution of extracorporeal membrane oxygenation (ECMO) results in unique blood flow characteristics to the end-organ vascular beds. We studied the interplay between cardiac-driven and extracorporeal membrane oxygenation (ECMO)-driven flow to vascular beds in different ECMO configurations using a patient-specific computational fluid dynamics (CFD) analysis. A computational ECMO model (femoral artery cannulation [FAC]) was constructed using patient-specific imaging and hemodynamic data. Following model calibration, we augmented the 3D geometrical model to represent alternative ECMO configurations (ascending aorta cannulation [AAC] and subclavian artery cannulation [SAC]). We performed CFD analyses, including a novel virtual color-dye analysis to compare global and regional blood flow and pressure characteristics as well as contributions of cardiac and ECMO-derived flow to the various vascular beds. Flow waveforms at all the aortic branch vessels were pulsatile, despite low cardiac output and predominant nonpulsatile ECMO-driven hemodynamics. Virtual color-dye analysis revealed differential contribution of cardiac and ECMO-derived flow to the end-organ vascular beds in the FAC model, while this was more evenly distributed in the AAC and SAC models. While global hemodynamics were relatively similar between various ECMO configurations, several distinct hemodynamic indices, in particular wall shear stress and oscillatory shear patterns, as well as differential contribution of ECMO-derived flow to various vascular beds, showed remarkable differences. The clinical impact of this study highlighting the relevance of CFD modeling in assessment of complex hemodynamics in ECMO warrants further evaluation.

CRIMSON: An open-source software framework for cardiovascular integrated modelling and simulation

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization.