Efficiency differences in computational simulations of the total cavo-pulmonary circulation with and without compliant vessel walls
Introduction
The Fontan operation is a palliative surgical procedure performed on children born with congenital defects of the heart that have yielded these children only one functioning ventricle. This procedure is performed when a two ventricular repair is not possible [1], [2]. In the preferred modification of this procedure, the total cavo-pulmonary connection (TCPC) [3], the superior vena cava (SVC), and inferior vena cava (IVC) are routed directly to the pulmonary arteries (see Fig. 1) using various techniques. The single ventricle alone then must supply the energy needed to push blood through both the systemic and pulmonary circulations now connected in series. Despite their widespread use these procedures have mixed short and long term clinical results.
In efforts to improve clinical outcomes, a key design criterion for investigators of the Fontan connection is that of circuit efficiency. A common measure of efficiency is pressure drop, i.e. how much the pressure in the vessels decreases between the inflows of the Fontan circuit (i.e. pressure average between the vena cava—VC) and the outflows of the Fontan circuit (i.e. pressure average between the pulmonary arteries—PA). Factoring not just pressure drops but also flow rate in an efficiency measure is an important consideration in evaluating non-steady flow systems like the Fontan circuit [4], [5], [6]. A more complete determiner of efficiency in Fontan circuits used by investigators is the energy loss or rate of energy loss (power loss) between the vena cava and pulmonary arteries through the cardiac cycle.
There have been a number of recent reports in the literature regarding Fontan hemodynamics using in vitro models [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], numerical models [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], animal models [31], and clinical studies [32], [33], [34], [35], [36], [37], [38]. The role of numerical modeling (also known as computational fluid dynamic (CFD) modeling) has been increasing in studying this and other biomedical phenomena, since it provides distinct advantages over other forms of investigation: a complete array of data at any and all times, a wide parameter range for study, and a completely non-invasive procedure.
The studies referred to previously have addressed issues as to the effect on efficiency due to: SVC:IVC flow rate ratio, relative angle of vessels, offset of IVC versus SVC, actual vessel geometry with pulsatile flow, use of atrium versus extra-atrial conduit versus intra-atrial tunnel [39], etc. However, little data is available in the literature assessing simultaneously two of the key complicating features of Fontan flow in models of the Fontan circuit, namely: (a) pulsatility, which is found clinically in the Fontan connection [5], [6], [28], and (b) compliance of the vessel walls. We believe these features are crucial to proper cardiovascular (CV) simulation of the TCPC circuit and hence here we have used a model that simulates both the flow of the fluid and the deformation of the walls. Our hypothesis is that measures of efficiency will differ when comparing TCPC computational models having rigid versus elastic walled vessels. If our hypothesis is correct then inclusion of elasticity into numerical models of the TCPC circuit is important when determining efficiencies through such cardiovascular models.
Section snippets
Solution method
To represent the TCPC, an idealized “cross” configuration was used for the geometry, with four cylindrical vessels lying in a single plane and meeting in a central junction. Each vessel has its own homogenous material parameters, which are listed below.
Numerical simulations were performed to model blood flow through the connection using commercially available software. The package CFD-ACE(U)™ (CFD Research Company, Huntsville, AL) was used to solve simultaneously for the motion of the fluid and
Results
Time averages over a cardiac cycle of the pressure drop and power loss are given in the Table 1 for both the rigid and elastic vessel cases. For the elastic case, an estimate for the power loss was used based on the mean of the approximations for (Appendix A).
Discussion
Recent strides in technology have allowed for sophisticated computational modeling of complex biomechanical systems. In particular, such strides have allowed for the development of advanced computational fluid dynamic models for various parts of the cardiovascular system [63].
Though there are a multitude of modeling studies reported in the literature on the total cavo-pulmonary connection (TCPC) [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23],
Conclusions
This numerical study demonstrates that differences in efficiency exist between the rigid versus elastic walled numerical total cavo-pulmonary connection models considered here.
We compared simulations in rigid versus elastic vessel wall total cavo-pulmonary connection models and documented the differences in pressure drop and power loss through each. In order to develop total cavo-pulmonary connection computational models that better represent the clinical setting, these results suggest a need
Acknowledgements
This work was supported by a National American Heart Association Scientist Development Award, #9730235N. We would like to thank Dr. Matthew Slaby at CFD Research Corporation, for his efficient and patient help with grid development and solution suggestions.
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