Predicted airway obstruction distribution based on dynamical lung ventilation data: A coupled modeling-machine learning methodology.

In asthma and chronic obstructive pulmonary disease, some airways of the tracheobronchial tree can be constricted, from moderate narrowing up to closure. Those pathological patterns of obstructions affect the lung ventilation distribution. While some imaging techniques enable visualization and quantification of constrictions in proximal generations, no noninvasive technique exists to provide the airway morphology and obstruction distribution in distal areas. In this work, we propose a method that exploits lung ventilation measures to access positions of airway obstructions (restrictions and closures) in the tree. This identification approach combines a lung ventilation model, in which a 0D tree is strongly coupled to a 3D parenchyma description, along with a machine learning approach. On the basis of synthetic data generated with typical temporal and spatial resolutions as well as reconstruction errors, we obtain very encouraging results of the obstruction distribution, with a detection rate higher than 85%.

Calculated ventilation and effort distribution as a measure of respiratory disease and Heliox effectiveness.

In spite of numerous clinical studies, there is no consensus on the benefit Heliox mixtures can bring to asthmatic patients in terms of work of breathing and ventilation distribution. In this article we use a 3D finite element mathematical model of the lung to study the impact of asthma on effort and ventilation distribution along with the effect of Heliox compared to air. Lung surface displacement fields extracted from computed tomography medical images are used to prescribe realistic boundary conditions to the model. Asthma is simulated by imposing bronchoconstrictions to some airways of the tracheo-bronchial tree based on statistical laws deduced from the literature. This study illuminates potential mechanisms for patient responsiveness to Heliox when affected by obstructive pulmonary diseases. Responsiveness appears to be function of the pathology severity, as well as its distal position in the tracheo-bronchial tree and geometrical position within the lung.

A reduced-order modeling for efficient design study of artificial valve in enlarged ventricular outflow tracts.

A computational approach is proposed for efficient design study of a reducer stent to be percutaneously implanted in enlarged right ventricular outflow tracts (RVOT). The need for such a device is driven by the absence of bovine or artificial valves which could be implanted in these RVOT to replace the absent or incompetent native valve, as is often the case over time after Tetralogy of Fallot repair. Hemodynamics are simulated in the stented RVOT via a reduce order model based on proper orthogonal decomposition, while the artificial valve is modeled as a thin resistive surface. The reduced order model is obtained from the numerical solution on a reference device configuration, then varying the geometrical parameters (diameter) for design purposes. To validate the approach, forces exerted on the valve and on the reducer are monitored, varying with geometrical parameters, and compared with the results of full CFD simulations. Such an approach could also be useful for uncertainty quantification.

Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation.

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.

A methodological paradigm for patient-specific multi-scale CFD simulations: from clinical measurements to parameter estimates for individual analysis.

A new framework for estimation of lumped (for instance, Windkessel) model parameters from uncertain clinical measurements is presented. The ultimate aim is to perform patient-specific haemodynamic analysis. This framework is based on sensitivity analysis tools and the sequential estimation approach of the unscented Kalman filter. Sensitivity analysis and parameter estimation are performed in lumped parameter models, which act as reduced order surrogates of the 3D domain for haemodynamic analysis. While the goal of sensitivity analysis is to assess potential identifiability problems, the unscented Kalman filter estimation leads to parameter estimates based on clinical measurements and modelling assumptions. An application of such analysis and parameter estimation methodology is demonstrated for synthetic and real data. Equality constraints on various physiological parameters are enforced. Since the accuracy of the Windkessel parameter estimates depends on the lumped parameter representativeness, the latter is iteratively improved by running few 3D simulations while simultaneously improving the former. Such a method is applied on a patient-specific aortic coarctation case. Less than 3% and 9% errors between the clinically measured quantities and 3D simulation results for rest and stress are obtained, respectively. Knowledge on how these Windkessel parameters change from rest to stress can thus be learned by such an approach. Lastly, it is demonstrated that the proposed approach is capable of dealing with a wide variety of measurements and cases where the pressure and flow clinical measurements are not taken simultaneously.

Three-dimensional simulations in Glenn patients: clinically based boundary conditions, hemodynamic results and sensitivity to input data.

While many congenital heart defects can be treated without significant long term sequelae, some achieve successful palliation as their definitive endpoints. The single-ventricle defect is one such defect and leaves the child with only one operational ventricle, requiring the systemic and the pulmonary circulations to be placed in series through several operations performed during early childhood. Numerical simulations may be used to investigate these hemodynamic conditions and their relation to post-operative sequelae; however, they rely heavily on boundary condition prescription. In this study, we investigate the impact of hemodynamic input data uncertainties on simulation results. Imaged-based patient-specific models of the multi-branched pulmonary arteries and superior vena cava were built for five cavopulmonary connection (i.e. Glenn) patients. Magnetic resonance imaging and catheterization data were acquired for each patient prior to their Fontan surgery. Inflow and outflow boundary conditions were constructed to match available clinical data and resulted in the development of a framework to incorporate these types of clinical data into patient-specific simulations. Three-dimensional computational fluid dynamics simulations were run and hemodynamic indicators were computed. Power loss was low (and efficiency very high) and a linear correlation was found between power loss and cardiac index among the five patients. Other indicators such as low wall shear stress were considered to better characterize these patients. Flow was complex and oscillatory near the anastomosis, and laminar in the smaller branches. While common trends were seen among patients, results showed differences among patients, especially in the 3D maps, strengthening the importance of patient-specific simulations. A sensitivity analysis was performed to investigate the impact of input data (clinical and modeling) to construct boundary conditions on several indicators. Overall, the sensitivity of the output indicators to the input data was small but non-negligible. The sensitivity of commonly used hemodynamic indicators to compare patients is discussed in this context. Power efficiency was much more sensitive to pressure variation than power loss. To increase the precision of such indicators, mean flow split between right and left lungs needs to be measured with more accuracy with higher priority than refining the model of how the flow is distributed on average among the smaller branches. Although ± 10% flow split imprecision seemed reasonable in terms of patient comparison, this study suggests that the common practice of imposing a right pulmonary artery/left pulmonary artery flow split of 55%/45% when performing patient specific simulations should be avoided. This study constitutes a first step towards understanding the hemodynamic differences between pre- and post Fontan surgery, predicting these differences, and evaluating surgical outcomes based on preoperative data.

Virtual surgeries in patients with congenital heart disease: a multi-scale modelling test case.

The objective of this work is to perform a virtual planning of surgical repairs in patients with congenital heart diseases--to test the predictive capability of a closed-loop multi-scale model. As a first step, we reproduced the pre-operative state of a specific patient with a univentricular circulation and a bidirectional cavopulmonary anastomosis (BCPA), starting from the patient's clinical data. Namely, by adopting a closed-loop multi-scale approach, the boundary conditions at the inlet and outlet sections of the three-dimensional model were automatically calculated by a lumped parameter network. Successively, we simulated three alternative surgical designs of the total cavopulmonary connection (TCPC). In particular, a T-junction of the venae cavae to the pulmonary arteries (T-TCPC), a design with an offset between the venae cavae (O-TCPC) and a Y-graft design (Y-TCPC) were compared. A multi-scale closed-loop model consisting of a lumped parameter network representing the whole circulation and a patient-specific three-dimensional finite volume model of the BCPA with detailed pulmonary anatomy was built. The three TCPC alternatives were investigated in terms of energetics and haemodynamics. Effects of exercise were also investigated. Results showed that the pre-operative caval flows should not be used as boundary conditions in post-operative simulations owing to changes in the flow waveforms post-operatively. The multi-scale approach is a possible solution to overcome this incongruence. Power losses of the Y-TCPC were lower than all other TCPC models both at rest and under exercise conditions and it distributed the inferior vena cava flow evenly to both lungs. Further work is needed to correlate results from these simulations with clinical outcomes.

Patient-specific modeling of blood flow and pressure in human coronary arteries.

Coronary flow is different from the flow in other parts of the arterial system because it is influenced by the contraction and relaxation of the heart. To model coronary flow realistically, the compressive force of the heart acting on the coronary vessels needs to be included. In this study, we developed a method that predicts coronary flow and pressure of three-dimensional epicardial coronary arteries by considering models of the heart and arterial system and the interactions between the two models. For each coronary outlet, a lumped parameter coronary vascular bed model was assigned to represent the impedance of the downstream coronary vascular networks absent in the computational domain. The intramyocardial pressure was represented with either the left or right ventricular pressure depending on the location of the coronary arteries. The left and right ventricular pressure were solved from the lumped parameter heart models coupled to a closed loop system comprising a three-dimensional model of the aorta, three-element Windkessel models of the rest of the systemic circulation and the pulmonary circulation, and lumped parameter models for the left and right sides of the heart. The computed coronary flow and pressure and the aortic flow and pressure waveforms were realistic as compared to literature data.

Outflow boundary conditions for 3D simulations of non-periodic blood flow and pressure fields in deformable arteries.

The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congenital cardiovascular disease. The relevance of using boundary conditions that accommodate transient phenomena compared with boundary conditions that assume periodicity of the solution is discussed.

On coupling a lumped parameter heart model and a three-dimensional finite element aorta model.

Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure-volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.