Computational simulations of the total cavo-pulmonary connection: insights in optimizing numerical solutions.

The Fontan procedure is a palliative surgical technique that is used to treat patients with congenital heart defects that include complex lesions such as those with a hypoplastic ventricle. In vitro, in vivo, and computational models of a set of modifications to the Fontan procedure, called the total cavopulmonary connection (TCPC), have been developed. Using these modeling methods, attempts have been made at finding the most energy efficient TCPC circuit. Computational modeling has distinct advantages to other modeling methods. However, discrepancies have been found in validation studies of TCPC computational models. There is little in the literature available to help explain and correct for such discrepancies. Differences in computational results can occur when choosing between steady flow versus transient flow numerical solvers. In this study transient flow solver results were shown to be more consistent with results from previous TCPC in vitro experiments. Using a transient flow solver we found complex fluctuating flow patterns can exist with steady inflow boundary conditions in computational models of the TCPC. To date such findings have not been reported in the literature. Furthermore, our computational modeling results suggest fluctuating flow patterns as well as the magnitudes of these secondary flow structures diminish if the TCPC offset between vena cavae is increased or if flanged connections are added. An association was found between these modifications and improvements in TCPC circuit flow efficiencies. In summary, development of accurate computational simulations in the validation process is critical to efforts in finding the most efficient TCPC circuits, efforts aimed at potentially improving the long term outcome for Fontan patients.

Insights into the effect of aortic compliance on Doppler diastolic flow patterns seen in coarctation of the aorta: a numeric study.

BACKGROUND: In the echocardiographic evaluation of coarctation of the aorta, the degree of antegrade diastolic flow (diastolic runoff) noted on spectral Doppler tracings traditionally was thought to be solely dependent on lesion severity. However, recent in vitro experiments suggest the presence of this spectral Doppler pattern is as much related to the severity of coarctation as it is with changes in aortic compliance. Using state-of-the-art, multidisciplinary, numeric analysis tools, the purpose of this study was to investigate the specific fluid and wall mechanics present in coarctation of the aorta to further understand these relationships. METHODS: Three computational numeric models of coarctation were developed with high, low, and no wall compliance. Flow simulations were run representing high- and low-flow states. RESULTS: In both the low- and high-flow states, the degree of diastolic runoff increased with increasing vessel compliance. The high compliance model had larger changes in aortic dilatation in the precoarctation region compared with the low compliance model. CONCLUSIONS: Increased aortic compliance brings about greater dilatation of the precoarctation aorta in systole, resulting in a persistence of stored upstream energy. This stored energy, released downstream in diastole as the precoarctation aortic walls contract, leads to increased degrees of diastolic runoff. Numeric methods offer a unique perspective into the mechanisms behind such clinical measures.

Reverse flow in compliant vessels and its implications for the Fontan procedure: numerical studies.

The Total Cavopulmonary Connection (TCPC), a variant of the Fontan operation used for palliative cardiovascular repair of patients with single ventricle physiology, creates a passive system of blood flow into the pulmonary circulation for which energy efficiency may be critical to long term outcome. Clinical studies have shown that reverse flow in the TCPC is an indication of poor clinical status in these patients. Using numerical simulations, we demonstrate that reverse flow leads to increased energy losses in compliant vessels. Such an effect can potentially set off a series of spiraling negative events with decreased ventricular function leading to reverse flow, which causes decreased energy efficiency, which in turn leads to worsening function, and so forth, thereby suggesting one cause of progressive heart failure in this patient group.

First-order system least squares for elastohydrodynamics with application to flow in compliant blood vessels.

Mathematical modeling of compliant blood vessels generally involves the Navier-Stokes equations on the evolving fluid domain and constitutive structural equations on the tissue domain. Coupling these systems while accounting for the changing shape of the fluid domain is a major challenge in numerical simulation. Many techniques have been developed to model compliant vessels, but all suffer from disproportionate increase in computational cost as problem complexity increases (i.e., larger domains, more dimensions, and more variables.). Even the best standard methods result in computational cost that typically grows quadratically with the degrees of freedom. Using a least-squares formulation of the problem, elliptic grid generation for the changing fluid domain, and an algebraic multigrid solver for the linear system can overcome many shortcomings of standard techniques. Most notably, the computational cost of solving the problem increases linearly with the degrees of freedom and the associated functional provides an a posteriori error measurement. Least squares represents a systematic approach for formulating the original problem so that the numerical process becomes straightforward and optimal, and it avoids restrictions that often limit other methods. Results are presented for a two-dimensional test problem consisting of a Newtonian fluid with properties of blood in a linear-elastic vessel with properties of smooth muscle.