Data was collected from a 6-year-old ALGS patient undergoing a hybrid X-ray catheter/DSMRI study as described previously. Combined acquisition of functional (flow and volumes) at rest and peak dobutamine stress (20 mug/kg/minute) and three-dimensional (3D) morphologic MRI data (dual-phase), with concomitant central pressure monitoring, was performed and used to parameterize the computational simulations. Images were acquired using a 1.5T MR-scanner (Achieva, Philips, Best, Netherlands) and a Philips BV Pulsera cardiac X-Ray unit under general anesthesia, which was maintained constant throughout the procedure. Details of the imaging parameters are provided in Table A in S1 File.
A novel modeling framework that integrates image data and detailed invasive/non-invasive measurements was used to obtain a faithful computational representation of the patient's physiology. A brief description of key aspects of the model is provided in the following sections (further details are available in the Technical Note in S1 File).
The CRIMSON custom software (CardiovasculaR Integrated Modeling and SimulatiON; http://www.crimson.software/) was used to segment the aorta and main branches, including the coronaries, and the central pulmonary arteries, using a semi-automatic segmentation method to produce an analytical representation of the vessels (Fig 1) from the diastolic phase of the 3D-Steady-state free precession (SSFP) sequence. Details regarding this segmentation approach are found elsewhere. The 3D geometry was discretized into a volumetric finite element mesh consisting of 1,687,949 tetrahedral elements (characteristic dimension h = 0.8mm) and 325,463 nodes, with curvature-based refinement.
Blood was modeled as an incompressible Newtonian fluid (density rho = 0.00106 g/mm3 and viscosity mu = 0.004g/mm s). Blood vessels were modeled using the Coupled Momentum Method, whereby an incompressible linear elastic membrane with spatially-varying structural stiffness is monolithically-coupled to the fluid domain. The linearized stiffness (E) of the aorta, its branches, and the central pulmonary arteries were prescribed according to the equation:  where Psyst and Pdiast represent the catheter-derived systolic and diastolic pressures, respectively, and Dsyst and Ddiast the 3D-SSFP-derived systolic and diastolic diameters at the level of the aortic and pulmonary artery roots, respectively. Wall thickness was prescribed to be 1 mm throughout. This produced a linearized stiffness of 2.26 x 105 g/mm s2 for the systemic and 1.30 x 105 g/mm s2 for the pulmonary arteries.
Expanding on previous developments by our group, we have designed a closed-loop coupled-multidomain (3D-0D) model consisting of image-based portions of the pulmonary and systemic circulations (where image data was available), and LPN (0D) models of the heart chambers and the arterial and venous distal circulations (see Fig 1). Parameter values for the LPN models for each condition are given in Tables B-F of the Technical Note in S1 File.
Metabolic control of the coronary microcirculation was achieved using a method develop by our group, which has been tested against invasive patient data. The foundation of this LPN model relies on using CBF as a surrogate of myocardial oxygen delivery, and on dynamically adapting coronary microvascular resistance to eliminate any "myocardial hunger" (i.e. mismatch between oxygen demand and supply). The myocardial oxygen demand per heartbeat was computed from the cardiac workload, determined by the 0D heart model, after integrating the area of the ventricular pressure-volumes curves and the ventricular elastance function. Because the CMCM can reproduce patient coronary vasomotor responses to changes in cardiac workload, it has the ability to predict CBF adaptations in response to changes in the myocardial oxygen demand and coronary perfusion pressure gradient. This permits simulation of the coronary response to a generalized vasodilation state as seen during liver reperfusion and enables specific probing of the complex coronary microcirculatory responses.
The model assumed a fixed oxygen extraction of 40% and 80% for the RCA and LCA respectively at Rest and 100% for both coronary circulations at Stress.
RV and LV elastance functions were derived from ventricular cines and catheterization data, describing cyclic ventricular volume and intraventricular pressures, respectively, using methods described in Arthurs et al. Ventricular volume curves, obtained by manually contouring the endocardial borders of all cardiac phases of the cardiac MRI short-axis cines, were matched with the corresponding R-wave in the invasive pressure recordings to obtain time-varying elastance functions (further details in the Technical Note in S1 File). Ventricular volumetric parameters for the Rest and Stress conditions used to define their corresponding elastance functions are listed in Table 1.
At peak DSMRI, cardiac output increased by ~45% from baseline. No regional wall motion abnormalities were noted. Tissue stiffness was kept constant through all three experimental conditions. The PRS condition was defined by imposing a 31% drop in MAP relative to the Stress condition, following Hilmi et al. definition of significant PRS.
All simulations were performed in our custom parallel blood flow solver CRIMSON using 128 processors on a SGI Altix UV, using a total simulation time of 150 hours per case.