A closed-loop lumped parameter model of blood circulation is considered for single-ventricle shunt physiology. Its parameters are estimated by an inverse problem based on patient-specific haemodynamics measurements. As opposed to a black-box approach, maximizing the number of parameters that are related to physically measurable quantities motivates the present model. Heart chambers are described by a single-fibre mechanics model, and valve function is modelled with smooth opening and closure. A model for valve prolapse leading to valve regurgitation is proposed. The method of data assimilation, in particular the unscented Kalman filter, is used to estimate the model parameters from time-varying clinical measurements. This method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements. Two patient-specific cases - one without regurgitation and one with atrioventricular valve regurgitation - are presented. Pulmonary and systemic circulation parameters are successfully estimated, without assumptions on their relationships. Parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics, or estimated. Results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure. The model and the estimation method are shown to successfully capture patient-specific clinical observations, even with regurgitation, such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings. Lastly, biomechanical implications of the results are discussed.

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.

BackgroundWave intensity analysis, traditionally derived from pressure and velocity data, can be formulated using velocity and area. Flow-velocity and area can both be derived from high-resolution phase-contrast cardiovascular magnetic resonance (PC-CMR). In this study, very high temporal resolution PC-CMR data is processed using an integrated and semi-automatic technique to derive wave intensity.MethodsWave intensity was derived in terms of area and velocity changes. These data were directly derived from PC-CMR using a breath-hold spiral sequence accelerated with sensitivity encoding (SENSE). Image processing was integrated in a plug-in for the DICOM viewer OsiriX, including calculations of wave speed and wave intensity. Ascending and descending aortic data from 15 healthy volunteers (30 ± 6 years) data were used to test the method for feasibility, and intra- and inter-observer variability. Ascending aortic data were also compared with results from 15 patients with coronary heart disease (61 ± 13 years) to assess the clinical usefulness of the method.ResultsRapid image acquisition (11 s breath-hold) and image processing was feasible in all volunteers. Wave speed was physiological (5.8 ± 1.3 m/s ascending aorta, 5.0 ± 0.7 m/s descending aorta) and the wave intensity pattern was consistent with traditionally formulated wave intensity. Wave speed, peak forward compression wave in early systole and peak forward expansion wave in late systole at both locations exhibited overall good intra- and inter-observer variability. Patients with coronary heart disease had higher wave speed (p <0.0001), and lower forward compression wave (p <0.0001) and forward expansion wave (p <0.0005) peaks. This difference is likely related to the older age of the patients’ cohort, indicating stiffer aortas, as well as compromised ventricular function due to their underlying condition.ConclusionA non-invasive, semi-automated and reproducible method for performing wave intensity analysis is presented. Its application is facilitated by the use of a very high temporal resolution spiral sequence. A formulation of wave intensity based on area change has also been proposed, involving no assumptions about the cross-sectional shape of the vessel.

Using a novel, noninvasive technique based on image analysis, we have demonstrated that aortic arch reconstruction in children with hypoplastic left heart syndrome is associated with reduced aortic distensibility and unfavorable ventricular-vascular coupling compared with those with single ventricle physiology without aortic arch reconstruction.

Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).

The effects of <65% stenosis on SCPC hemodynamics and physiology were minor and may not justify the increased complexity of adding LPA arterioplasty to the SCPC operation. However, in the longer term, pulmonary augmentation may affect outcomes of the Fontan completion surgery, as pulmonary artery distortion is a risk factor that may influence stage III physiology.