Considerations for Numerical Modeling of the Pulmonary Circulation—A Review With a Focus on Pulmonary Hypertension

Abstract

Both in academic research and in clinical settings, virtual simulation of the cardiovascular system can be used to rapidly assess complex multivariable interactions between blood vessels, blood flow, and the heart. Moreover, metrics that can only be predicted with computational simulations (e.g., mechanical wall stress, oscillatory shear index, etc.) can be used to assess disease progression, for presurgical planning, and for interventional outcomes. Because the pulmonary vasculature is susceptible to a wide range of pathologies that directly impact and are affected by the hemodynamics (e.g., pulmonary hypertension), the ability to develop numerical models of pulmonary blood flow can be invaluable to the clinical scientist. Pulmonary hypertension is a devastating disease that can directly benefit from computational hemodynamics when used for diagnosis and basic research. In the present work, we provide a clinical overview of pulmonary hypertension with a focus on the hemodynamics, current treatments, and their limitations. Even with a rich history in computational modeling of the human circulation, hemodynamics in the pulmonary vasculature remains largely unexplored. Thus, we review the tasks involved in developing a computational model of pulmonary blood flow, namely vasculature reconstruction, meshing, and boundary conditions. We also address how inconsistencies between models can result in drastically different flow solutions and suggest avenues for future research opportunities. In its current state, the interpretation of this modeling technology can be subjective in a research environment and impractical for clinical practice. Therefore, considerations must be taken into account to make modeling reliable and reproducible in a laboratory setting and amenable to the vascular clinic. Finally, we discuss relevant existing models and how they have been used to gain insight into cardiopulmonary physiology and pathology.

Patient-specific computational modeling of blood flow in the pulmonary arterial circulation

“…Noteworthy is that the distal resistance used in the structured tree outflow boundary condition dictates the flow split rather than total pulmonary resistance, as it was iteratively tuned to yield the RHC measured inlet pressure (mPAP). The strong correlation of SAWSS with PVR and C suggests that: (1) as endothelial cells lining the pulmonary vasculature have been shown to respond to shear by proliferation and the release of vasoactive agents, a change in SAWSS could be partially responsible for the cycle that perpetuates the progression of the disease [13]; and (2) SAWSS derived from CFD analysis could be used as a non-invasive alternative to PVR and C for assessing disease progression.…”

“…A tetrahedral mesh, progressively growing in element size from the endoluminal surface to the volume core, was generated for each patient-specific vasculature. A WSS-based grid independence study was conducted according to the protocol outlined in [13, 28]. Each patient-specific geometry varied in size and morphology, therefore requiring different mesh densities to generate the CFD models.…”

“…Endothelial cells (EC) are responsible for maintaining homeostasis by sensing non-physiological flow and signaling SMC to adjust accordingly. Impaired endothelial response can lead to vascular disease [12] and initiate a destructive cycle that will ultimately lead to stiffening of the proximal pulmonary vessels and RV dysfunction [13]. Currently, it is not yet known what triggers the change that results in the pulmonary vasculature's inability to regulate pressure and vascular resistance.…”

“…4D magnetic resonance imaging (MRI) is noisy and offers low temporal and spatial resolution, which is a shortcoming for estimating fluid shear. Computational models have been used previously to simulate the pulmonary flow dynamics [13]. They offer unparalleled advantages over reconstructing patient-specific flow patterns with 4D MRI, in terms of spatial and temporal resolution, and can be used to simulate pathological hemodynamic challenges.…”

The Role of Wall Shear Stress in the Assessment of Right Ventricle Hydraulic Workload

“…WSS is bound by 50 dyn/cm 2 , because of regions of high stress concentrations that can arise in the CFD simulations from geometric anomalies in distal vessels reconstructed from poor image resolution. 7 WSS was evaluated in the form of the following metrics: (1) WSS integrated over the entire pulmonary geom- etry and normalized by the endothelial surface area, i.e., SAWSS (eq. [13]), and (2) WSS averaged along the perimeter of an arbitrary circumferential location (see Fig.…”