Search

Computer simulations of blood flow in patients with anomalous aortic origin of a coronary artery (AAOCA) have the promise to provide insight into this complex disease. They provide an in-silico experimental platform to explore possible mechanisms of myocardial ischemia, a potentially deadly complication for patients with this defect. This paper focuses on the question of model calibration for fluid-structure interaction models of pediatric AAOCA patients. Imaging and cardiac catheterization data provide partial information for model construction and calibration. However, parameters for downstream boundary conditions needed for these models are difficult to estimate. Further, important model predictions, like fractional flow reserve (FFR), are sensitive to these parameters. We describe an approach to calibrate downstream boundary condition parameters to clinical measurements of resting FFR. The calibrated models are then used to predict FFR at stress, an invasively measured quantity that can be used in the clinical evaluation of these patients. We find reasonable agreement between the model predicted and clinically measured FFR at stress, indicating the credibility of this modeling framework for predicting hemodynamics of pediatric AAOCA patients. This approach could lead to important clinical applications since it may serve as a tool for risk stratifying children with AAOCA.

Patients with congenital and acquired heart conditions often undergo studies using Magnetic Resonance Angiography (MRA) images and time-resolved four-dimensional phase-contrast magnetic resonance (4D Flow) images to noninvasively estimate blood flow properties such as flux, wall shear stress and vorticity. The 4D Flow image specifies velocity of blood within the imaging volume while the MRA image yields, via segmentation, an accurate representation of the geometry of the vessel walls. Both the geometry of the vessel walls and the velocity of the blood within them are required to generate accurate estimates of vessel flow properties. The images are not acquired simultaneously so the patient is subject to shifting between scans, resulting in misalignment of the images. Additionally, motion from the respiratory and cardiac cycles causes deformation within the anatomical structures themselves. This misalignment and deformation causes inaccuracy in estimates of blood flow properties. An approach is presented that partially alleviates these discrepancies thus facilitating more accurate estimation of blood flow properties.

In this paper, we develop a pulsatile compartmental model of the Fontan circulation and use it to explore the effects of a fenestration added to this physiology. A fenestration is a shunt between the systemic and pulmonary veins that is added either at the time of Fontan conversion or at a later time for the treatment of complications. This shunt increases cardiac output and decreases systemic venous pressure. However, these hemodynamic benefits are achieved at the expense of a decrease in the arterial oxygen saturation. The model developed this paper incorporates fenestration size as a parameter and describes both blood flow and oxygen transport. It is calibrated to clinical data from Fontan patients, and we use it to study the impact of a fenestration on several hemodynamic variables. In certain scenarios corresponding to high-risk Fontan physiology, we demonstrate the existence of an optimal fenestration size that maximizes oxygen delivery to the systemic tissues.

This paper describes computer models of three interventions used for treating refractory pulmonary hypertension (RPH). These procedures create either an atrial septal defect, a ventricular septal defect, or, in the case of a Potts shunt, a patent ductus arteriosus. The aim in all three cases is to generate a right-to-left shunt, allowing for either pressure or volume unloading of the right side of the heart in the setting of right ventricular failure, while maintaining cardiac output. These shunts are created, however, at the expense of introducing de-oxygenated blood into the systemic circulation, thereby lowering the systemic arterial oxygen saturation. The models developed in this paper are based on compartmental descriptions of human hemodynamics and oxygen transport. An important parameter included in our models is the cross-sectional area of the surgically created defect. Numerical simulations are performed to compare different interventions and various shunt sizes and to assess their impact on hemodynamic variables and oxygen saturations. We also create a model for exercise and use it to study exercise tolerance in simulated pre-intervention and post-intervention RPH patients.

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ greatly in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we systematically compare several reduced models of blood flow for physiologically relevant vessel parameters, network topology, and boundary data. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.

A method for engineering the behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numerical simulations that a polynomial, delayed feedback is a versatile tool to tune synchronization patterns. Dynamical states consisting of one to four clusters were engineered to demonstrate the application of synchronization engineering in an experimental electrochemical system., Comment: To appear in CHAOS