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Technical Briefs

Left Ventricular Finite Element Model Bounded by a Systemic Circulation Model

[+] Author and Article Information
A. I. Veress

Department of Mechanical Engineering,
Department of Bioengineering,
University of Washington,
Seattle, WA 98195

G. M. Raymond, J. B. Bassingthwaighte

Department of Bioengineering,
University of Washington,
Seattle, WA 98195

G. T. Gullberg

Life Science Division,
E. O. Lawrence Berkeley National Laboratory,
Berkeley, CA 94720;
Department of Radiology,
University of California San Francisco,
San Francisco, CA 94122

For more information, see www.continuity.ucsd.edu.

For more information, see www.physiome.org.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received June 19, 2012; final manuscript received January 3, 2013; accepted manuscript posted February 19, 2013; published online April 24, 2013. Assoc. Editor: Jeffrey W. Holmes.

J Biomech Eng 135(5), 054502 (Apr 24, 2013) (6 pages) Paper No: BIO-12-1239; doi: 10.1115/1.4023697 History: Received June 19, 2012; Revised January 03, 2013; Accepted February 19, 2013

A series of models were developed in which a circulatory system model was coupled to an existing series of finite element (FE) models of the left ventricle (LV). The circulatory models were used to provide realistic boundary conditions for the LV models. This was developed for the JSim analysis package and was composed of a systemic arterial, capillary, and venous system in a closed loop with a varying elastance LV and left atria to provide the driving pressures and flows matching those of the FE model. Three coupled models were developed, a normal LV under normotensive aortic loading (116/80 mm Hg), a mild hypertension (137/89 mm Hg) model, and a moderate hypertension model (165/100 mm Hg). The initial step in the modeling analysis was that the circulation was optimized to the end-diastolic pressure and volume values of the LV model. The cardiac FE models were then optimized to the systolic pressure/volume characteristics of the steady-state JSim circulatory model solution. Comparison of the stress predictions for the three models indicated that the mild hypertensive case produced a 21% increase in the average fiber stress levels, and the moderate hypertension case had a 36% increase in average stress. The circulatory work increased by 18% and 43% over that of the control for the mild and moderate hypertensive cases, respectively.

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Figures

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Fig. 1

Schematic of the systemic JSim model of FE heart model and model of circulatory system. The labels are P for the pressure values, F for the flow, R for the resistance, C for the compliance, and L for the inertance at the given locations shown above. The left atria and ventricle are represented as a time varying elastance units.

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Fig. 2

The left ventricle FE model in the end-diastolic (left) and end-systolic (right) configurations

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Fig. 3

Schematic of the coupled system analysis protocol. The initial step is the optimization of the circulation to the end-diastolic pressure and volume values produced by an initial run of the FE model. JSim was then run until equilibrium was achieved in the model. This was followed by optimization of the FE model to reproduce the JSim pressure and volume values at each of the four time points. Once the correct values were achieved for a given time point, the process was repeated for the next time point until all of the time points had been optimized.

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Fig. 4

(a) Aortic pressure curves (dashed black) and the left ventricular pressure curve (solid black) defined in the JSim circulatory system are given. (b) The JSim derived LV volume curve (black) used in the mild hypertensive systolic optimizations. The vertical gray lines indicate the four systolic time points for both graphs.

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Fig. 5

Optimization to the JSim systolic volume values (gray) was achieved after four iterations all of the time points in each of the cases: normotensive (top), mild hypertension (middle), and moderate hypertension (bottom)

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Fig. 6

Hypertension increases the fiber stress as seen in these ventricular short axis slices. These are fiber strain distributions for normal, mild, and moderate hypertension (left). The location of the slices is shown on the right.

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