Blood flow in large vessels is typically modeled using the Navier-Stokes equations for the fluid domain and elasticity equations for the vessel wall. As the wall deforms, additional complications are introduced because the shape of the fluid domain changes, necessitating the use of a re-mapping or re-griding process for the fluid region. Typically, this system (fluid, solid, mapping) is solved using an iterative approach in which the fluid, elastic, and mapping equations are solved in series until the iterations converge. We present a new approach based on multilevel minimization of the finite element approximation error using a least-squares (LS) norm. This approach allows for minimization of the error for the entire system or in selected parts. The multilevel LS approach overcomes many shortcomings of standard techniques. Most notably, the computational cost of solving the problem increases linearly with the degrees of freedom and the associated least-squares functional provides an a posteriori error measure. This paper compares the LS finite element approach to other popular numerical methods, specifically, the commercial package CFD-ACE. The focus of the comparison is on accuracy, computational cost, scalability (both parallel and serial), and flexibility. We show that the multilevel LS finite element approach scales optimally (i.e., linearly in serial environments), while the other methods degrade substantially as the problem size increases.

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.

The goals of this study were to characterize normal patterns of longitudinal motion of atrioventricular annuli in the young, establish reference values and assess growth-related changes (n = 40). Sensitivity to changes in right ventricular volume and pressure load was assessed in patients with atrial septal defect (ASD) (n = 25) and with primary pulmonary hypertension (PPH) (n = 20). M-mode of the annuli were obtained from apical views. In healthy subjects, longitudinal %displacement decreased with growth, lateral tricuspid annulus had highest %displacement, velocity of annular descent did not change with growth, tricuspid lateral annulus had the highest velocity of descent, only ascent velocity of the lateral tricuspid annulus decreased with growth, velocities of ascent for the lateral annuli were similar and higher than the septum, and heart rate had no effect on parameters tested. In patients with ASD, the findings were an exaggerated normal pattern. In patients with PPH, %displacement and ascent velocities were blunted. Our results demonstrate the utility of this technique to assess annular dynamics in pediatric patients.

Aortic arch anomalies usually require surgical intervention preceded by precise anatomic definition. We studied 20 patients to evaluate the feasibility and accuracy of using intravascular ultrasound catheters from a transesophageal approach with 3-dimensional image reconstruction for the diagnosis of aortic arch anomalies in infants and children. All patients had transthoracic echocardiograms and/or angiograms or magnetic resonance imaging. A 12.5-MHz intravascular ultrasound catheter was positioned in the esophagus and withdrawn by using an electrocardiogram and a respiratory gated pullback device to acquire the mediastinal images. All patients with arch anomalies underwent surgical repair. Reconstructed images were analyzed in the "anyplane" mode and with surface rendering. Intravascular ultrasound 3-dimensional imaging was successfully accomplished without complications. Anatomy was correctly identified in all patients by both blinded and unblinded observers, thus confirming the sensitivity and accuracy of the technique. We foresee this new technique to be useful as an adjunctive imaging modality applicable at the bedside or in the cardiac imaging laboratory.

Beyond infancy, blood cyst of the aortic valve is not known to occur. We describe a 16-year-old girl who had aortic valve stenosis and regurgitation and giant blood cyst of the aortic valve. Serial echocardiograms over a 12-year period demonstrated gradual enlargement of the cyst.