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RESEARCH PAPERS

# Finite Element Modeling of the Left Atrium to Facilitate the Design of an Endoscopic Atrial Retractor

[+] Author and Article Information
S. R. Jernigan

Department of Mechanical and Aerospace Engineering, North Carolina State University, NCSU Box 7910, Raleigh, NC 27695srjernig@ncsu.edu

G. D. Buckner, J. W. Eischen

Department of Mechanical and Aerospace Engineering, North Carolina State University, NCSU Box 7910, Raleigh, NC 27695

D. R. Cormier

Department of Industrial Engineering, North Carolina State University, NCSU Box 7906, Raleigh, NC 27695

J Biomech Eng 129(6), 825-837 (Mar 15, 2007) (13 pages) doi:10.1115/1.2801650 History: Received February 13, 2006; Revised March 15, 2007

## Abstract

With the worldwide prevalence of cardiovascular diseases, much attention has been focused on simulating the characteristics of the human heart to better understand and treat cardiac disorders. The purpose of this study is to build a finite element model of the left atrium (LA) that incorporates detailed anatomical features and realistic material characteristics to investigate the interaction of heart tissue and surgical instruments. This model is used to facilitate the design of an endoscopically deployable atrial retractor for use in minimally invasive, robotically assisted mitral valve repair. Magnetic resonance imaging (MRI) scans of a pressurized explanted porcine heart were taken to provide a 3D solid model of the heart geometry, while uniaxial tensile tests of porcine left atrial tissue were conducted to obtain realistic material properties for noncontractile cardiac tissue. A finite element model of the LA was constructed using ANSYS ™ Release 9.0 software and the MRI data. The Mooney–Rivlin hyperelastic material model was chosen to characterize the passive left atrial tissue; material constants were derived from tensile test data. Finite element analysis (FEA) models of a CardioVations Port Access™ retractor and a prototype endoscopic retractor were constructed to simulate interaction between each instrument and the LA. These contact simulations were used to compare the quality of retraction between the two instruments and to optimize the design of the prototype retractor. Model accuracy was verified by comparing simulated cardiac wall deflections to those measured by MRI. FEA simulations revealed that peak forces of approximately $2.85N$ and $2.46N$ were required to retract the LA using the Port Access™ and prototype retractors, respectively. These forces varied nonlinearly with retractor blade displacement. Dilation of the atrial walls and rigid body motion of the chamber were approximately the same for both retractors. Finite element analysis is shown to be an effective tool for analyzing instrument/tissue interactions and for designing surgical instruments. The benefits of this approach to medical device design are significant when compared to the alternatives: constructing prototypes and evaluating them via animal or clinical trials.

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## Figures

Figure 1

Explanted porcine heart with pressurized LA: (a) MRI scan at 0mmHg, (b) MRI scan at 30mmHg, and (c) MRI scan at 60mmHg

Figure 2

Explanted porcine heart showing muscle fiber orientations on surface of LA: (a) anterolateral tissue and (b) left atrial appendage tissue

Figure 3

Experimental true (Cauchy) stress-strain curves for left atrial tissue: (a) anterolateral, (b) posterolateral, (c) appendage, and (d) average curves for the three regions. Note that graphs on the left represent data for specimens elongated perpendicular to the observed fiber direction; graphs on the right represent data for specimens elongated parallel to observed fiber direction.

Figure 4

FEA model of porcine LA after meshing and application of boundary conditions: (a) posterolateral and (b) anterolateral views. Constrained nodes are designated by triangular markers.

Figure 5

Element thicknesses of the left atrial model as defined per area; (a) posterolateral and (b) anterolateral views

Figure 6

Atrial wall deflections resulting from internal pressurization (0–30mmHg): (a) posterolateral view of MRI data, (b) anterolateral view of MRI data, (c) posterolateral view of FEA simulation data, and (d) anterolateral view of FEA simulation data

Figure 7

Spherical coordinate system and vectors used in the correlation coefficient calculations: (a) computation of Δr and (b) calculation of α

Figure 8

CardioVations Port Access™ retractor (45×50mm2): (a) outside the patient, (b) application in minimally invasive MVR, and (c) mitral valve exposure provided by the retractor (endoscopic view)

Figure 9

Meshed components for atrial retraction analysis: (a) CardioVations Port Access™ retractor (35×60mm2) and (b) retractor placement in the LA showing incision, boundary conditions, contact elements, and direction of gravitational acceleration (z axis extends directly into the page)

Figure 10

Meshed components of endoscopic retractor prototype: (a) entire retractor and (b) detail of wire tips

Figure 11

Atrial retraction with the endoscopic instrument: (a) 0% arm deployment, (b) 66% arm deployment, and (c) 100% arm deployment (white arrows indicate extent of arm deployment)

Figure 12

Rigid body motion of the LA during retraction with the endoscopic instrument: (a) unretracted (left) and fully retracted (right) cross sections of LA model (28mm from the mitral annulus) and (b) translocation evaluated at cross sections with varying distances from the mitral annulus (calculated at area centroids)

Figure 13

Dilation of the LA during retraction: change in cross-sectional areas (compared to unretracted case) versus distance from mitral annulus

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