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

https://doi.org/10.1016/j.cmpb.2015.04.005Get rights and content

Highlights

  • We applied computational fluid dynamics modeling to 11 pulmonary vascular trees.

  • Patient-specific cardiac output is necessary to obtain accurate wall shear stress.

  • Spatially averaged wall shear stress is highly correlated with pulmonary vascular resistance.

  • Spatially averaged wall shear stress is highly correlated with arterial compliance.

  • Structured-tree outflow boundary conditions improve these correlations.

Abstract

Computational fluid dynamics (CFD) modeling of the pulmonary vasculature has the potential to reveal continuum metrics associated with the hemodynamic stress acting on the vascular endothelium. It is widely accepted that the endothelium responds to flow-induced stress by releasing vasoactive substances that can dilate and constrict blood vessels locally. The objectives of this study are to examine the extent of patient specificity required to obtain a significant association of CFD output metrics and clinical measures in models of the pulmonary arterial circulation, and to evaluate the potential correlation of wall shear stress (WSS) with established metrics indicative of right ventricular (RV) afterload in pulmonary hypertension (PH). Right Heart Catheterization (RHC) hemodynamic data and contrast-enhanced computed tomography (CT) imaging were retrospectively acquired for 10 PH patients and processed to simulate blood flow in the pulmonary arteries. While conducting CFD modeling of the reconstructed patient-specific vasculatures, we experimented with three different outflow boundary conditions to investigate the potential for using computationally derived spatially averaged wall shear stress (SAWSS) as a metric of RV afterload. SAWSS was correlated with both pulmonary vascular resistance (PVR) (R2 = 0.77, P < 0.05) and arterial compliance (C) (R2 = 0.63, P < 0.05), but the extent of the correlation was affected by the degree of patient specificity incorporated in the fluid flow boundary conditions. We found that decreasing the distal PVR alters the flow distribution and changes the local velocity profile in the distal vessels, thereby increasing the local WSS. Nevertheless, implementing generic outflow boundary conditions still resulted in statistically significant SAWSS correlations with respect to both metrics of RV afterload, suggesting that the CFD model could be executed without the need for complex outflow boundary conditions that require invasively obtained patient-specific data. A preliminary study investigating the relationship between outlet diameter and flow distribution in the pulmonary tree offers a potential computationally inexpensive alternative to pressure based outflow boundary conditions.

Introduction

Pulmonary hypertension (PH) is a degenerative disease that eventually leads to right heart failure [1], [2]. In this work, we present a preliminary investigation of the role of wall shear stress (WSS), estimated by time averaged computational fluid dynamics (CFD), in PH disease progression. Previous studies have shown that WSS decreases in PH patients relative to healthy controls [3], [4], making it a potential comprehensive prognostic characteristic encompassing fluid flow kinematics, vessel wall structural mechanics, bulk hemodynamics, and an underlying biological response.

There are three primary domains in the PH pathological cardio-pulmonary system: RV, proximal pulmonary vasculature, and the distal pulmonary vasculature. The proximal arteries act as a hydraulic damper to the distal vasculature [5]. Endothelial cells lining the distal vessels respond to local flow conditions by adjusting their cross-sectional area [6], thereby influencing the local pressure, wave reflection dynamics [7], and arterial tension in the (upstream) proximal vasculature. Therefore, these two domains are undoubtedly coupled (each domain responds to and impacts the other) and must share common characteristics in the maintenance of total system behavior, likely having a synergetic effect on PH disease progression. Furthermore, given that proximal-distal pulmonary coupling influences wave reflection phenomena and distensibility, the interaction between these domains will strongly influence flow pattern formation in the proximal vasculature.

While PH originates in the pulmonary vasculature, the resulting lethality lies in the inevitable RV dysfunction that occurs as a result of increased afterload [8]. The steady and pulsatile components of afterload are believed to be dictated by distal constriction and proximal stiffness, respectively [2], [9]. Therefore, pulmonary vascular resistance (PVR) and compliance (C) are the dominating patient disease progression characteristics available from Right Heart Catheterization (RHC), which are indicative of both the resistive and reactive components of impedance [10], respectively. Therefore, these metrics must be strongly coupled to the local flow dynamics and continuum metrics (e.g., WSS) common to both domains.

Intrinsic pressure regulation mechanisms signal smooth muscle cells (SMC) to adjust conduit area and regulate blood flow to match the local perfusion needs of tissue [11]. 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. For intrinsic pressure regulation, EC release vaso-constrictors/dilators and control their orientation based on the pulsatility and mean direction of WSS [6], [12], [14]. Intramural stress and WSS can also alter gene expression and signal collagen synthesis to increase vessel thickness and decrease compliance [6], [15].

Pulmonary vascular compliance can be approximated as the ratio of the stroke volume to the pulse pressure (PP), which is known to be linearly proportional to the true compliance, but is a slight overestimation of the compliance calculated from the parameter optimization of a Windkessel model [16]. The stiffness of the proximal vasculature and resistance of the distal vasculature both contribute to RV afterload, and are linearly related [2]. Thus, the two metrics are not independent, as an increase in distal resistance will increase the proximal pressure, causing the vessel walls to be taut [15]. Moreover, prolonged exposure to elevated pressures will result in collagen synthesis, thereby altering the inherent mechanical properties of the proximal vessels [17] and undoubtedly weaken its ability to act as a hydraulic damper to the distal vasculature [18].

Pulmonary arterial flow patterns can be visualized from imaging modalities [19], [20] or predicted with computational models. 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.

Tang et al. [21] implemented CFD analysis to show that increased cardiac output (CO), resulting from exercise, results in an increase in WSS. Further computational work, comparing pulmonary hemodynamics in the PH patient population with a healthy dataset, revealed a decreased WSS in PH [4], which we recently correlated with an increase in impedance using a similar computational framework [22]. However, the considerations critical to computational modeling of the pulmonary vasculature or the mechanisms driving this WSS decrease remain unaddressed. Similarly, Hunter et al. [14] used computational modeling to show that mitigation of hypertension in pediatric patients can reduce WSS. They simulated the hemodynamics in the proximal pulmonary arteries of two patient-specific geometries. In one case, a decrease in CO and vascular stiffness as the result of a septal defect closure led to reduced WSS. In the second case, a decrease in distal resistance and vascular stiffness did not have a significant impact on WSS. Su et al. [23] used an ideal fluid–structure interaction (FSI) model to investigate the influence of stiffness on local hemodynamics. They found that chronic increases in pressure, likely due to increased distal resistance, resulted in decreased WSS in the proximal vasculature.

As all systematic changes associated with PH disease progression are strongly coupled to the WSS acting on the proximal and distal endothelium, we hypothesize that spatially averaged wall shear stress (SAWSS), estimated using a patient-specific CFD model, will decrease in patients with PH concomitant with the reactive and resistive components of RV afterload. If true, it is conceivable that changes in WSS precede morphological remodeling, thereby leading to significant breakthroughs in strategies for risk stratification, and frequently monitoring disease progression and treatment efficacy. Furthermore, WSS could dictate pathological vs. adaptive vascular remodeling, alluding to disease reversibility and driving treatment decision making [24].

Clinicians must be equipped with tools for evaluating treatment efficacy that are reproducible, affordable, and minimally invasive for the patient. The current protocol for patients admitted with PH symptoms is to perform RHC [25] to measure CO, pressure in the main pulmonary artery (MPA), pulmonary capillary wedge pressure (PCWP) and, from these, compute PVR [26]. These metrics can give an indication of RV workload at the onset of PH, where regulation of RV function is typically homeometric [27]. RHC is invasive and occasionally requires the patient to be sedated. Therefore, essential RHC data is only available to the physician as a pre-treatment baseline and it may be unfeasible to obtain repeatedly for assessing disease progression and treatment efficacy. A fast and reliable CFD model would have a vast clinical application, but the feasibility and reliability of modern day CFD analysis in pulmonary hemodynamics remains largely unexplored.

In this study, we present an efficient computational estimate of WSS in adult patients with PH and interrogate the association between computed SAWSS with PVR (resistive impedance) and C (reactive impedance). We utilize the flexibility of computational modeling to identify patient phenotypes (e.g., morphology, hemodynamics) that dictate the relationship between computed SAWSS and afterload. Furthermore, modeling is used to explain the flow distribution in a 6-generation pulmonary tree structure, which could be used in future modeling studies to dictate the outflow boundary condition and estimate local WSS in distal vessels. The overall goal of the present work is to utilize CFD for assessing WSS in pulmonary arterial geometries of human subjects with PH. As evidence shows WSS to decrease in PH patients when compared with healthy controls [4], the objectives of this work are two-fold: (i) to examine the extent of patient specificity required to obtain a significant association of CFD output metrics and clinical measures, and (ii) to evaluate the potential correlation of WSS with established metrics indicative of RV afterload in PH. Particularly, we correlate WSS with the most clinically universal metric of RV workload: PVR. In addition, as RV workload and distal flow dynamics are also influenced by proximal compliance [5], [23] we show that SAWSS can also be used to assess pulmonary vasculature characteristics that are typically associated with the reactive component of vascular impedance [10].

Section snippets

Methods

Ten patients admitted to Allegheny General Hospital (Pittsburgh, PA) suspected of having PH underwent routine RHC. Table 1 shows measurements acquired during RHC, using a Swan-Ganz Standard Thermo-dilution Catheter, which were used to calculate PVR (Eq. (1)) and compliance (C) (Eq. (2)) [2]. Upon diagnosis of PH, disease severity and RV function were qualitatively assessed according to the World Health Organization Pulmonary Arterial Hypertension Function Classification.PVR=mPAPPCWPCOC=COHR×PP

Traditional clinical qualitative/quantitative assessment of the patient cohort

A trained cardiologist's assessment of RV morphology on echocardiograms revealed substantial RV remodeling and function changes in patients with high PVR. For example, the subject with the highest PVR (1316 dyn s/cm5) presented a severely dilated RV with severe RV dysfunction. The subject with the second highest PVR (777 dyn s/cm5) showed a mild to moderately dilated RV with severe systolic dysfunction. Finally, a third subject with elevated PVR (408 dyn s/cm5), but relatively low compared to the

Discussion

The data presented in this study is sufficient to reject the null hypothesis and confirm that SAWSS, estimated by CFD simulations with a constant flow rate, changes in PH manifestation concurrent with changes in afterload. Furthermore, as opposed to imaging modalities with limited spatial resolution (e.g., 4D MRI), CFD analysis can offer the resolution necessary for a reliable estimate of SAWSS, which is improved as boundary conditions are more representative of the patient-specific hemodynamic

Conclusion

Spatially averaged wall shear stress (SAWSS) computed from patient-specific CFD models is inversely correlated with distal pulmonary vascular resistance and compliance in subjects with pulmonary hypertension. In addition, SAWSS is statistically correlated with afterload when considering only patient specific geometry and CO. Implementing a structured tree outflow boundary condition in the CFD model further improves this correlation because elevated distal resistance acts to flatten the velocity

Acknowledgments

We acknowledge research funding from NIH award 1P01HL103455-01, The University of Pittsburgh, The University of Texas at San Antonio's Department of Biomedical Engineering, and The University of Texas System Board of Regents’ Science and Technology Acquisition and Retention (STARS) program. The use of ANSYS Fluent software was gratefully facilitated through an academic agreement with ANSYS, Inc. The content is solely the responsibility of the authors and does not necessarily represent the

References (39)

  • M.F. O’Rourke

    Vascular impedance in studies of arterial and cardiac function

    Physiol. Rev.

    (1982)
  • A. Bellofiore et al.

    Methods for measuring right ventricular function and hemodynamic coupling with the pulmonary vasculature

    Ann. Biomed. Eng.

    (2013)
  • Z. Wang et al.

    Role of collagen content and cross-linking in large pulmonary arterial stiffening after chronic hypoxia

    Biomech. Model. Mechanobiol.

    (2012)
  • M. Zamir

    The Physics of Pulsatile Flow

    (2000)
  • J.E. Hall

    Textbook of Medical Physiology

    (2011)
  • J. Ando et al.

    Vascular mechanobiology: endothelial cell responses to fluid shear stress

    Circ. J.

    (2009)
  • V.O. Kheyfets et al.

    Considerations for numerical modeling of the pulmonary circulation – a review with a focus on pulmonary hypertension

    J. Biomech. Eng.

    (2013)
  • K.S. Hunter et al.

    Simulations of congenital septal defect closure and reactivity testing in patient-specific models of the pediatric pulmonary vasculature: a 3D numerical study with fluid–structure interaction

    J. Biomech. Eng.

    (2006)
  • J.D. Humphrey

    Mechanisms of arterial remodeling in hypertension: coupled roles of wall shear and intramural stress

    Hypertension

    (2008)
  • Cited by (65)

    • Hemodynamics of the right ventricle and the pulmonary circulation

      2022, Applications in Engineering Science
      Citation Excerpt :

      As the pulmonary vasculature involves macroscopic components at the level of the pulmonary arteries all the way to the level of the microcirculation, multi-scale approaches have frequently been applied, along with different models for the surrounding lung parenchyma with fractal and anatomically-based models (Tawhai and Burrowes, 2008) to describe the distribution of pulmonary blood flow (Glenny and Robertson, 1985). Due to these variations in RV and PA anatomy, patient-specific computational modeling is critical for the main PA, segmental and subsegmental vessels (Kheyfets et al., 2015). Below we highlight some examples of modeling the RV-PA circuit in different disease states, including recent studies that have used computational techniques to provide insights into PA wall shear stress as a measure of RV afterload.

    • Flow and remodeling processes occurring within the body proper

      2022, Digital Human Modeling and Medicine: The Digital Twin
    View all citing articles on Scopus
    View full text