This retrospective study was approved by the Children’s National Hospital Institutional Review Board (number Pro00010748, approved August 24, 2018). Patients with repaired CoA were included if they had a CMR study and an exercise stress test within one year measuring peak oxygen consumption (VO2max) and peak respiratory exchange ratio ≥ 1.1, indicating maximal effort. Subjects were excluded with recurrent CoA requiring intervention or if additional medical morbidities were present, such as complex congenital heart disease (i.e. single ventricle), significant valvar regurgitation or stenosis, or significant pulmonary, musculoskeletal, or metabolic problems that affect exercise capacity. The presence of a bicuspid aortic valve was not an exclusion criterion given the high prevalence in this population. Exercise capacity was defined as percent predicted VO2max for age and sex. Per clinical protocol, predicted VO2max was calculated using the James equation  for pediatric patients (ages 7–15 years) and the Wasserman equation  for adult patients (ages 16–54 years).
In vivo imaging
All clinical CMR imaging was performed to the lab standard and consistent with Society for Cardiovascular Magnetic Resonance congenital heart disease guidelines  on a 1.5 T CMR system (Aera, Siemens Healthineers, Erlangen, Germany) including 3D steady state free precession and angiography with typical parameters to achieve a slice thickness of 1.2–1.5 mm and pixel resolution between 1.2 × 1.2 mm and 1.5 × 1.5 mm, as well as phase contrast imaging and cine volumetry.
AAo and DAo diameters were measured using 3D data sequences and flow was calculated from 2D phase contrast imaging using standard techniques (Medis, Leiden, The Netherlands). Percent DAo flow was calculated to calibrate the in vitro model. Where available, LV ejection fraction (LVEF) and LV mass were obtained from the clinical CMR cine imaging.
The echocardiogram most recent to the exercise stress test was reviewed. LVEF or fractional shortening was measured if the LVEF was not measured by CMR. Additionally, peak DAo velocity, corrected for increased proximal velocity (> 2 m/s), was assessed.
In vitro model
The details of the CMR-compatible mock circulatory flow loop were previously described . Briefly, a patient-specific three-dimensional model was created using standard segmentation techniques in commercial software (Materialise Mimics/3-matic, Leuven, Belgium). In the cases of stents, there was assumed to be no in-stent stenosis based on review of peak velocity by echocardiogram and dark blood CMR. Therefore, the inner diameter of the vessel was segmented as the same diameter as the proximal and distal native vessel. Models were printed in a rigid plastic (Accura 60; 3D Systems Corporation, Rock Hill, South Carolina, USA) by an additive manufacturing company (Xometry, Gaithersburg, Maryland, USA). To simulate the effect of the aortic shape on hemodynamics, both during rest and exercise conditions, the aorta models and flow parameters were scaled to accommodate the operating limits of the flow pump (CardioFlow 5000MR; Shelley Medical Imaging Technologies, London, Ontario, Canada), requiring a peak instantaneous flow rate less than 300 mL/s. Dimensional analysis, a standard engineering technique, was used to scale flow by decreasing fluid viscosity and arch size while maintaining the same flow conditions . Viscosity was decreased by using water instead of blood-like fluid. The models were scaled linearly by each axis to a body surface area (BSA) of 1 m2 based on defined normal values of aorta size in the range of adolescent and adult BSA . By scaling to the same body surface area (BSA), the indexed flow conditions of rest and exercise remained identical for all models (3 L/min/m2 and 9 L/min/m2, respectively). Flow curves were derived from the AAo flow profile from in vivo CMR.
The printed models were placed in a mock circulatory flow loop. The aorta model was placed in a box filled with water and saline bags for stabilization. The head vessels were combined as a single outflow. Compliance and resistance components were added using standard techniques , mimicking in vivo vessel compliance and systemic vascular resistance. The outlet valves were adjusted until the desired flow distribution among head vessels and DAo matched in vivo CMR conditions and remained unchanged between rest and exercise conditions. Therefore, the only the change between the rest and exercise condition was in increase in flow from 3 to 9 L/min/m2.
Pressure was measured at access points in the proximal AAo and distal DAo using MR-conditional pressure transducers (Utah Medical Products, Midvale, Utah, USA) with data acquisition via LabView (National Instruments, Austin, Texas, USA). The peak pressure gradient (ΔP) was calculated for rest and exercise conditions by subtracting the DAo peak pressure from the AAo peak pressure averaged over at least ten cardiac cycles.
In vitro CMR
A standard amount of gadolinium contrast was added to the flow circuit and the CMR-compatible mock circulatory flow loop was centered in the bore of a 1.5 T CMR system (Aera, Siemens Healthineers). Acquisitions were gated to the flow pump using the above CMR-conditional pressure sensors . An in-plane 2D phase contrast sequence was used to determine the appropriate encoding velocity to avoid aliasing for exercise flow. 4D flow acquisitions were performed using encoding velocity 200 cm/s for rest and 200–400 cm/s for exercise, echo time 2.2 ms, repetition time 38 ms, flip angle 15 degrees. The acquired matrix size was approximately 72 × 160 with a field of view of 190 mm × 270 mm to obtain a reconstructed resolution of 1.7 mm × 1.7 mm with a slice thickness of 1.8 mm. 4D flow sequences were exported for off-line analysis.
4D flow analysis
Each dataset was segmented to isolate the velocity flow fields within the region of interest. To obtain consistent results, a semi-automated threshold technique was developed based on a modified Otsu method  using the logarithm of the histogram to avoid bias toward the larger background region . Further post-processing was performed using iTFlow, commercially available software (Cardio Flow Design, Tokyo, Japan), for qualitative assessment of streamline flow and quantitative assessment of peak systolic WSS, vorticity, and helicity. Peak WSS was measured in the AAo, aortic arch, and DAo, defined by standard landmarks . Peak vorticity, and right (positive) and left-handed (negative) helicity were measured in the entire aorta model and normalized by the volume of the segmented region as they are all dependent on voxel volume. Each parameter was measured in rest and exercise conditions, and the ratio of the exercise to rest condition was calculated. Background correction was not applied as there was no static tissue in the in vitro setup to be used for correction. Flow measurements from 4D flow were validated using a clamp-on ultrasonic flow meter (PXL Flowsensor; Transonic, Ithaca, New York, USA). In order to test the hypothesis that increased turbulence in the DAo is related to exercise capacity, the Reynolds number in the DAo (ReDAo) was estimated using the average diameter in the DAo (by centerline analysis) and the flow at peak systole in the DAo during rest and exercise, both measured with iTFlow.
All statistical analyses were performed with Prism 8 (Graphpad, San Diego, California, USA). A paired two-tailed t-test was used to evaluate the mean difference of ΔP at rest and exercise. All correlations were performed using Pearson’s correlation coefficient (r) including ΔP at rest and exercise with percent predicted VO2max, the ratio of exercise to rest for each 4D flow parameter (peak WSS, vorticity, and helicity) with DAAo/DDAo and percent predicted VO2max, and the estimated ReDAo at rest and exercise with percent predicted VO2max.