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Research Papers

# Three-Dimensional Simulations in Glenn Patients: Clinically Based Boundary Conditions, Hemodynamic Results and Sensitivity to Input Data

[+] Author and Article Information
G. Troianowski

Institute for Computational and Mathematical Engineering,  Stanford University, Stanford, CA 94305

C. A. Taylor

Bioengineering Department, Stanford University, Stanford, CA 94305; Surgery Department,  Stanford University, Stanford, CA 94305

J. A. Feinstein

Bioengineering Department, Stanford University, Stanford, CA 94305; Pediatrics Department,  Stanford University, Stanford, CA 94305

I. E. Vignon-Clementel

INRIA Paris-Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France

J Biomech Eng 133(11), 111006 (Dec 01, 2011) (16 pages) doi:10.1115/1.4005377 History: Received January 28, 2011; Revised August 17, 2011; Published December 01, 2011; Online December 01, 2011

## Abstract

While many congenital heart defects can be treated without significant long term sequelae, some achieve successful palliation as their definitive endpoints. The single-ventricle defect is one such defect and leaves the child with only one operational ventricle, requiring the systemic and the pulmonary circulations to be placed in series through several operations performed during early childhood. Numerical simulations may be used to investigate these hemodynamic conditions and their relation to post-operative sequelae; however, they rely heavily on boundary condition prescription. In this study, we investigate the impact of hemodynamic input data uncertainties on simulation results. Imaged-based patient-specific models of the multi-branched pulmonary arteries and superior vena cava were built for five cavopulmonary connection (i.e. Glenn) patients. Magnetic resonance imaging and catheterization data were acquired for each patient prior to their Fontan surgery. Inflow and outflow boundary conditions were constructed to match available clinical data and resulted in the development of a framework to incorporate these types of clinical data into patient-specific simulations. Three-dimensional computational fluid dynamics simulations were run and hemodynamic indicators were computed. Power loss was low (and efficiency very high) and a linear correlation was found between power loss and cardiac index among the five patients. Other indicators such as low wall shear stress were considered to better characterize these patients. Flow was complex and oscillatory near the anastomosis, and laminar in the smaller branches. While common trends were seen among patients, results showed differences among patients, especially in the 3D maps, strengthening the importance of patient-specific simulations. A sensitivity analysis was performed to investigate the impact of input data (clinical and modeling) to construct boundary conditions on several indicators. Overall, the sensitivity of the output indicators to the input data was small but non-negligible. The sensitivity of commonly used hemodynamic indicators to compare patients is discussed in this context. Power efficiency was much more sensitive to pressure variation than power loss. To increase the precision of such indicators, mean flow split between right and left lungs needs to be measured with more accuracy with higher priority than refining the model of how the flow is distributed on average among the smaller branches. Although $±10%$ flow split imprecision seemed reasonable in terms of patient comparison, this study suggests that the common practice of imposing a right pulmonary artery/left pulmonary artery flow split of $55%/45%$ when performing patient specific simulations should be avoided. This study constitutes a first step towards understanding the hemodynamic differences between pre- and post Fontan surgery, predicting these differences, and evaluating surgical outcomes based on preoperative data.

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## Figures

Figure 1

Description of the four steps of geometry construction: Definition of paths along the main first and second generation vessels, segmentation of the MRI, orthogonally to the vessels’ path, lofting of those contours to define a 3D volume and blending of those individual volumes leading to a complete 3D geometry of the anastomosis

Figure 2

TOP: Velocity magnitude cuts after the main bifurcation in the RPA and LPA for the 0.5 M element mesh (left) and the 2 M element mesh (right) steady simulation. BOTTOM: wall shear stress for the 0.5 M element mesh (left) and the 2 M element mesh (right) steady simulation. Blue to red: 0 to 20dyn.cm−2 .

Figure 3

Solid model of the five patients, superimposed on a volume rendering of the MRI data

Figure 4

Pressure probed at different locations between inflow (blue) and RUL outflow (green), showing the pressure wave propagation in Patient A

Figure 5

Pressure and flow waveforms for patient A probed at the inlet (blue) and outlet of RUL (green), LPA (purple) and RPA (orange). The mean value of the flow at the inlet is 27.8cm3 .s−1 (1.67L. min−1 ) while the mean flow at the outlets are 2.99cm3 .s−1 (0.18 L. min-1) at the LPA, 2.54cm3 .s−1 (0.15L. min−1 ) at the RPA and 1.36cm3 .s−1 (0.08L. min1 ) at the RUL.

Figure 9

Isocontours of the residence index (as defined in the methods section) for particles released at peak deceleration in the five patients geometries. The isocontour of value 2 corresponds to an already high value of particle residence time.

Figure 10

Power loss (top) and MWSS (bottom) versus flow split for patients A (left) and D (right), and their quadratic or linear correlations

Figure 6

Stream line representation of the flow at peak deceleration (left) and maximum flow (right) at the anastomosis for the five patients

Figure 7

Power loss and efficiency in the 3D domain versus cardiac index for the five patients, and their linear trendlines

Figure 8

Wall shear stress (left) and oscillatory flow index (right) averaged over time for the five patients

Figure 11

Power loss (left) and MWSS (right) versus the branch parameter α, and their quadratic or linear correlations

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