Research Papers

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

[+] Author and Article Information
V. O. Kheyfets

Department of Biomedical Engineering,
The University of Texas at San Antonio,
AET 1.360, One UTSA Circle,
San Antonio, TX 78249

W. O'Dell

Department of Radiation Oncology,
University of Florida,
Shands Cancer Center,
P.O. Box 100385,
2033 Mowry Road,
Gainesville, FL 32610

T. Smith

Western Allegheny Health System,
Allegheny General Hospital,
Gerald McGinnis Cardiovascular Institute,
320 East North Avenue,
Pittsburgh, PA 15212

J. J. Reilly

Department of Medicine,
The University of Pittsburgh,
1218 Scaife Hall,
3550 Terrace Street,
Pittsburgh, PA 15261

E. A. Finol

Department of Biomedical Engineering,
The University of Texas at San Antonio,
AET 1.360, One UTSA Circle,
San Antonio, TX 78249
e-mail: ender.finol@utsa.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received December 6, 2012; final manuscript received March 25, 2013; accepted manuscript posted April 4, 2013; published online May 9, 2013. Assoc. Editor: Dalin Tang.

J Biomech Eng 135(6), 061011 (May 09, 2013) (15 pages) Paper No: BIO-12-1598; doi: 10.1115/1.4024141 History: Received December 06, 2012; Revised March 25, 2013; Accepted April 04, 2013

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.

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Fig. 1

Outline of disease progression in chronic pulmonary hypertension. The white boxes refer to effects on the pulmonary arterial vasculature (vessel wall thickness, vessel wall stiffness, arterial pressure). The orange box refers to effects on the right ventricle. Note: EC = endothelial cells; SMC = smooth muscle cells; RV = right ventricle; Q = flow; σz = longitudinal stress; σθ = circumferential stress; τw = wall shear stress; eNO = endothelial nitric oxide; ET-1 = endothelin-1.

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Fig. 2

Procedure for conducting patient-specific computational modeling of pulmonary vasculature. (a) Starting with a thoracic CT scan of the patient, (b) a 3D solid model of the pulmonary vasculature is reconstructed. (c) The model outlets are truncated normal to the centerline and fixed to outlet extensions measuring 10 times the outlet diameter in length. (d) A volume mesh is applied to the entire solid model, which is imported into a numerical CFD/FSI simulation. Note: CFD = computational fluid dynamics; FSI = fluid-structure interaction.

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Fig. 3

Resulting arterial trees, reconstructed using different automated and manual techniques from in vivo human volumetric CT scans. Different degrees of fine structure reconstruction are due, in part, to differences in image resolution: [65]-Buelow (voxel dimensions not given); [66] Shikata (0.6 × 0.6 × 1.3 mm); [67] Kaftan (0.6 × 0.6 × 0.6 mm); [68] Dongen (submillimeter, isotropic, but not specified); [69] Ebrahimdoost (0.66 × 0.66 × 1.0 mm); [70] Burrowes (0.68 × 0.68 × 1.4 mm).

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Fig. 4

Vasculature generated by manual segmentation using Mimics. Magnification: example segmentation fault requiring manual intervention. Circled parts show branches that could not be fully segmented due to inadequate image resolution.

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Fig. 5

Wall shear stress distribution of patient-specific pulmonary vasculature, at two levels of segmentation (A and B). The hemodynamics are dependent on the number of tree generations that are segmented and the inlet-to-outlet cross-sectional area ratio. Both simulations are carried out with a zero traction outflow boundary condition. The segmentation with a greater total outlet cross-sectional area (B) develops lower pressure at the inlet and lower velocities in the terminal vessels (not indicated in figure).

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Fig. 6

(a) Region of analysis for the mesh independence convergence study. (b) Mesh independence convergence data for pulmonary vasculature obtained with a commercial solver, Fluent (ANSYS), using steady state inlet plug flow with zero traction outflow boundary conditions. The graph depicts the residual error in the estimated wall shear stress (WSS) as a function of the number of elements in the mesh used for calculation.

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Fig. 7

(a) Inlet waveforms measured for pulmonary vasculature: solid—Henk et al. [129]; dashed—Swan–Ganz balloon tip catheter measurements of normal subject, taken at University of Pittsburgh Medical Center; (b) inlet of typical segmented pulmonary artery and Schwarz–Christoffel (SC) mapping procedure: A unit circle is superimposed onto the inlet. Any point within the domain can be represented as a complex number: R∧ = x+iy, in which the modulus corresponds to the distance from the center of gravity (CG).

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Fig. 8

Outflow boundary conditions applied to pulmonary vascular models. (a) The pure resistance model consists of a single resistor causing a linear relationship between the outlet pressure and flow. (b) The Windkessel models extend the pure resistance model with a compliance term but do not capture fully the complex flow patterns through compliant vascular networks. (c) The structured tree model is a hypothetical reconstruction of the compliant vascular tree distal to each truncated outlet. The pressure-flow relationship at each outlet is calculated by computing the tree impedance. (d) The fluid-structure interaction (FSI) boundary condition is a useful add-on to any FSI simulation, which encompasses all the sophistication of the compliant structured tree.

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Fig. 9

(a) Wall shear stress (WSS) distribution calculated from Tang et al. [40]. (b) Magnification showing nonphysiological stress concentrations arising from uncompensated errors in segmentation using our model, which did not assume cylindrical vessels in the distal arteries but with similar inflow and outflow boundary conditions as used by Tang et al.



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