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TECHNICAL PAPERS: Fluids/Heat/Transport

# Application of A Microstructural Constitutive Model of the Pulmonary Artery to Patient-Specific Studies: Validation and Effect of Orthotropy

[+] Author and Article Information
Yanhang Zhang

Department of Aerospace and Mechanical Engineering,  Boston University, Boston, MA 02215

Martin L. Dunn

Department of Mechanical Engineering,  University of Colorado at Boulder, Boulder, CO 80309

Kendall S. Hunter, Craig Lanning, D. Dunbar Ivy, Lori Claussen

Division of Cardiology,  The Children’s Hospital of Denver, Denver, CO 80218

S. James Chen

Department of Medicine, Division of Cardiology,  University of Colorado at Denverand  Health Sciences Center, Denver, CO 80262

Robin Shandas

Department of Mechanical Engineering, 427 UCB,  University of Colorado, Boulder, CO 80309 and Division of Cardiology,  The Children’s Hospital of Denver, Denver, CO 80218robin.shandas@colorado.edu

J Biomech Eng 129(2), 193-201 (Aug 22, 2006) (9 pages) doi:10.1115/1.2485780 History: Received October 07, 2005; Revised August 22, 2006

## Abstract

We applied a statistical mechanics based microstructural model of pulmonary artery mechanics, developed from our previous studies of rats with pulmonary arterial hypertension (PAH), to patient-specific clinical studies of children with PAH. Our previous animal studies provoked the hypothesis that increased cross-linking density of the molecular chains may be one biological remodeling mechanism by which the PA stiffens in PAH. This study appears to further confirm this hypothesis since varying molecular cross-linking density in the model allows us to simulate the changes in the $P‐D$ loops between normotensive and hypertensive conditions reasonably well. The model was combined with patient-specific three-dimensional vascular anatomy to obtain detailed information on the topography of stresses and strains within the proximal branches of the pulmonary vasculature. The effect of orthotropy on stress∕strain within the main and branch PAs obtained from a patient was explored. This initial study also puts forward important questions that need to be considered before combining the microstructural model with complex patient-specific vascular geometries.

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## Figures

Figure 1

Schematic of the artery wall and the eight-chain orthotropic unit element to model the orthotropic behavior of synthetic network structure in the intimal-medial layer

Figure 2

Finite element mesh of a 3D patient-specific proximal pulmonary vascular structure reconstructed from biplane angiography images. Three end movement planes are applied to constrain the movement of the 3D anatomy. The nodes at the ends of the MPA, LPA, and RPA are allowed to move only in the end movement plane.

Figure 3

Input wall thickness of the finite-element model of the 3D patient-specific pulmonary vascular structure

Figure 4

Predicted P‐D responses using a simple tube inflation model. The artery wall is assumed to be isotropic with material parameters HI from Table 1. Curves from right to left correspond to axial stretch λz from 1.0 to 1.5 in increments of 0.1.

Figure 5

Predicted (a) circumferential and (b) longitudinal stresses versus diameter for the P‐D responses in Fig. 4. Axial stretch λz is increased from 1.0 to 1.5 in increments of 0.1.

Figure 6

P‐D loops of a normotensive subject (squares) and a hypertensive patient (circles). Linear regression lines of pressure versus diameter for each loop are also shown. Simulations were based on a tube inflation model. Solid lines correspond to simulations using material parameters HI and dashed lines correspond to simulations using material parameters NI from Table 1. Initial diameters of the tube vary from 0.75cmto1.25cm to account for the different sizes of the arteries due to the different ages of the patients.

Figure 7

Contours of longitudinal strain (a) at pressure of 40.5mmHg when the artery wall is assumed to be isotropic with material parameters HI from Table 1; (b) at pressure of 40.5mmHg when the artery wall is assumed to be orthotropic and stiffer in the longitudinal direction with material parameters HOL from Table 1; and (c) at pressure of 39.6mmHg when the artery wall is assumed to be orthotropic and stiffer in the circumferential direction with material parameters HOC from Table 1

Figure 8

Contours of circumferential strain (a) at pressure of 40.5mmHg when the artery wall is assumed to be isotropic with material parameters HI from Table 1; (b) at pressure of 40.5mmHg when the artery wall is assumed to be orthotropic and stiffer in the longitudinal direction with material parameters HOL from Table 1; (c) at pressure of 39.6mmHg when the artery wall is assumed to be orthotropic and stiffer in the circumferential direction with material parameters HOC from Table 1

Figure 9

Contours of stresses in the circumferential (left) and longitudinal (right) directions: (a) at pressure of 40.5mmHg when the artery wall is assumed to be isotropic with material parameters HI from Table 1; (b) at pressure of 40.5mmHg when the artery wall is assumed to be orthotropic and stiffer in the longitudinal direction with material parameters HOL from Table 1; (b) at pressure of 39.6mmHg when the artery wall is assumed to be orthotropic and stiffer in the circumferential direction with material parameters HOC from Table 1

Figure 10

Predicted P‐D responses at the midpoint of RPA when the artery wall is assumed to be isotropic with material parameters HI, orthotropic and stiffer in the longitudinal direction with material parameters HOL, and orthotropic and stiffer in the circumferential direction with material parameters HOC from Table 1. Sensitivity study on the thickness of the arterial wall was performed by increasing the nodal thickness from 10% (HI) to 12% and 16% of the local diameter.

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