Single ventricle hearts are congenital cardiovascular defects in which the heart has only one functional pumping chamber. The treatment for these conditions typically requires a three-staged operative process where Stage 1 is typically achieved by a shunt between the systemic and pulmonary arteries, and Stage 2 by connecting the superior venous return to the pulmonary circulation. Surgically, the Stage 2 circulation can be achieved through a procedure called the Hemi-Fontan, which reconstructs the right atrium and pulmonary artery to allow for an enlarged confluence with the superior vena cava. Based on pre-operative data obtained from two patients prior to Stage 2 surgery, we developed two patient-specific multi-scale computational models, each including the 3D geometrical model of the surgical junction constructed from magnetic resonance imaging, and a closed-loop systemic lumped-parameter network derived from clinical measurements. "Virtual" Hemi-Fontan surgery was performed on the 3D model with guidance from clinical surgeons, and a corresponding multi-scale simulation predicts the patient's post-operative hemodynamic and physiologic conditions. For each patient, a post-operative active scenario with an increase in the heart rate (HR) and a decrease in the pulmonary and systemic vascular resistance (PVR and SVR) was also performed. Results between the baseline and this "active" state were compared to evaluate the hemodynamic and physiologic implications of changing conditions. Simulation results revealed a characteristic swirling vortex in the Hemi-Fontan in both patients, with flow hugging the wall along the SVC to Hemi-Fontan confluence. One patient model had higher levels of swirling, recirculation, and flow stagnation. However, in both models, the power loss within the surgical junction was less than 13% of the total power loss in the pulmonary circulation, and less than 2% of the total ventricular power. This implies little impact of the surgical junction geometry on the SVC pressure, cardiac output, and other systemic parameters. In contrast, varying HR, PVR, and SVR led to significant changes in theses clinically relevant global parameters. Adopting a work-flow of customized virtual planning of the Hemi-Fontan procedure with patient-specific data, this study demonstrates the ability of multi-scale modeling to reproduce patient specific flow conditions under differing physiological states. Results demonstrate that the same operation performed in two different patients can lead to different hemodynamic characteristics, and that modeling can be used to uncover physiologic changes associated with different clinical conditions.

The adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions. We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero-dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs.

In patients with congenital heart disease and a single ventricle (SV), ventricular support of the circulation is inadequate, and staged palliative surgery (usually 3 stages) is needed for treatment. In the various palliative surgical stages individual differences in the circulation are important and patient-specific surgical planning is ideal. In this study, an integrated approach between clinicians and engineers has been developed, based on patient-specific multi-scale models, and is here applied to predict stage 2 surgical outcomes. This approach involves four distinct steps: (1) collection of pre-operative clinical data from a patient presenting for SV palliation, (2) construction of the pre-operative model, (3) creation of feasible virtual surgical options which couple a three-dimensional model of the surgical anatomy with a lumped parameter model (LPM) of the remainder of the circulation and (4) performance of post-operative simulations to aid clinical decision making. The pre-operative model is described, agreeing well with clinical flow tracings and mean pressures. Two surgical options (bi-directional Glenn and hemi-Fontan operations) are virtually performed and coupled to the pre-operative LPM, with the hemodynamics of both options reported. Results are validated against postoperative clinical data. Ultimately, this work represents the first patient-specific predictive modeling of stage 2 palliation using virtual surgery and closed-loop multi-scale modeling.

Single ventricle heart defects involve pathologies in which the heart has only one functional pumping chamber. In these conditions, treatment consists of three staged procedures. At stage 1 pulmonary flow is provided through an artificial shunt from the systemic circulation. Representative hemodynamics models able to explore different virtual surgical options can be built based on pre-operative imaging and patient data. In this context, the specification of boundary conditions is necessary to compute pressure and flow in the entire domain. However, these boundary conditions are rarely the measured variables. Moreover, to take into account the rest of the circulation outside of the three-dimensional modeled domain, a number of reduced order models exist. A simplified method is presented to iteratively, but automatically, tune reduced model parameters from hemodynamic data clinically measured before stage 2 surgery. Patient-specific local hemodynamics around the distal systemic-to-pulmonary shunt anastomosis and the connected pulmonary arteries are also analyzed. Multi-scale models of pre-stage 2 single ventricle patients are developed, including a 3D model of shunt-pulmonary connection and a number of pulmonary arteries. For each pulmonary outlet a total downstream resistance is identified, consistent with measured flow split and pressures. Target pressures such as minimum, maximum or average over one or both lungs are considered, depending on the clinical measurement. When possible, both steady and pulsatile identifications are performed. The methodology is demonstrated with six patient-specific models: the clinical target data are well-matched, except for one case where clinical data were subsequently found inconsistent. Inhomogeneous pressure, swirling blood flow patterns and very high wall shear stress 3D maps highlight similarities and differences among patients. Steady and pulsatile tuning results are similar. This work demonstrates (1) how to use routine clinical data to define boundary conditions for patient-specific 3D models in pre-stage 2 single ventricle circulations and (2) how simulations can help to check the coherence of clinical data, or provide insights to clinicians that are otherwise difficult to measure, such as in the presence of kinks. Finally, the choice of steady vs. pulsatile tuning, limitations and possible extensions of this work are discussed.

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11We present a new approach for the outflow boundary conditions of Navier-12 Stokes equations in hemodynamics. We first describe some existing 3D-0D cou-13 pling methods and highlight benefits and disadvantages of each of them. We then 14 introduce a new method that consists in adding a 3D artificial part where the 15 Navier-Stokes equations are modified to obtain an equivalent energy balance to 16 a standard coupling with a 3-element Windkessel model. We investigate theoreti-17 cally the stability of the system and compare it to previously introduced methods. 18 Finally we compare these coupling methods for numerical simulations of blood 19 flow in three patient-specific models, which represent different flow regimes in 20 the pulmonary and systemic circulations. The new method, especially in its hybrid 21 form, is a possible alternative to existing methods. It can be in particular convenient 22 in codes that do not allow users to implement non-standard boundary conditions.23

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Objectives: Patient-specific multiscale modeling simulates virtual surgeries of the Fontan procedure using three different graft options. Predictive modeling details post-operative outcomes that can help inform clinical decision support. Methods: Six patients underwent preoperative cardiac magnetic resonance imaging and catheterization. Virtual surgery is carried out for each patient to test the resulting hemodynamics of three Fontan graft options: ECC, 9mm Y-graft, and 12mm Y-graft. Results: 1) one-way ANOVA p>0.998 in all systemic pressures and flows between graft options, 2) p=0.706 for hepatic flow distribution between graft options, 3) local power loss differences do not affect the systemic circulation, 4) anastomosis positioning modification of the same Y-graft in the same patient changed left PA hepatic distribution from 0.66 to 0.49 Conclusions: Systemic pressures and blood flow after the Fontan procedure are not affected by graft selection but are well influenced by patient pulmonary vascular impedance. The hepatic distribution can be affected by anastomosis placement.