The Enduring Impact of Shape Following Perfect Coarctation of the Aorta Repair

Abstract

Objectives: Aortic arch appearances can be associated with worse cardiac function and chronic hypertension late after coarctation of the aorta (CoA) repair, even without residual obstruction. Statistical shape modeling (SSM) has identified specific 3D arch shapes linked to poorer cardiovascular outcomes. We sought a mechanistic explanation. Methods: From 53 asymptomatic patients late after CoA repair with no residual obstruction (age: 22.3 ± 5.6 years; 12-38 years after operation), eight aortic arch shapes associated with the four best and four worst cardiovascular parameters were obtained from 3D SSM. Four favorable shapes were affiliated with left ventricular (LV) ejection fraction +2 standard deviation (SD) values from the mean, and indexed LV end diastolic volume/indexed LV mass/resting systolic blood pressure that were −2SD. Four unfavorable shapes were defined by the reverse. Computational Fluid Dynamics modeling was carried out to assess differences in pressure gradient across the aortic arch and viscous energy loss (VEL) between favorable and unfavorable aortic arches. Results: In all aortic arches, the pressure gradients were clinically insignificant (<8 mm Hg). However, in the four unfavorable aortic arches, VEL were uniformly higher than those in the favorable shapes (VEL difference: 15%-32%). There was increased turbulence and more complex propagation of VEL along with the unfavorable aortic arches. Conclusions: This study reveals the variable flow dynamics that underpin the association of aortic arch shapes with worse cardiovascular outcomes late after successful CoA repair. Higher VEL persists in the unfavorable aortic arch shapes. Further understanding of the mechanism of viscous energy loss in cardiovascular maladaptation may afford mitigating strategies to monitor and modify this unrelenting liability.

Keywords

coarctation of the aorta statistical shape modeling computational fluid dynamics viscous energy loss

Introduction

Coarctation of the aorta (CoA) is a lesion with well-established surgical and interventional approaches for correction.^1,2 However, despite undergoing a “successful” repair with good early outcomes, many patients with CoA face late complications and morbidities, including medically refractory hypertension, reduced heart function, and exercise capacity.^3–5 While the etiology for these challenges is likely to be multifactorial, an awareness is emerging that the aortic arch shape, long after initial repair, may be an important mechanistic contributor.^6–9 To overcome the limitation of using 2-dimensional (2D), that is, height-width ratio or angulation, to describe the 3-dimensional (3D) aortic arch,^10–13 we reported using statistical shape modeling (SSM) to leverage large medical imaging datasets to assess a population of aortic arch anatomies in a 3D space.^14,15 These studies reveal specific 3D aortic arch shapes associated with worse cardiac function/hypertension late after CoA repair (Figure 1).^16,17

To further understand how 3D aortic arch shape can impact late cardiac outcomes in patients without residual aortic arch obstruction or clinically relevant arch pressure gradients, we adopted novel computational fluid dynamics (CFD) modeling in conjunction with the SSM phenomenological approach. We hypothesized that unique mechanistic metrics, gleaned from CFD, are associated with those aortic arch shape features linked to previously reported unfavorable late cardiac function.¹⁷

Materials and Methods

Geometry

The analysis is based on the shape modes generated by the SSM, as previously reported, from 53 asymptomatic patients late after isolated surgical CoA repair (age = 22.3 ± 5.6 years; 12-38 years after initial operation) with no clinically important residual obstruction or stenosis.¹⁷ We analyzed routine follow-up cardiac magnetic resonance (CMR) imaging data (1.5 T Avanto MR scanner, Siemens Medical Solutions) of 53 asymptomatic patients late following isolated aortic coarctation repair (CoA; mean age 22.3 ± 5.6 years), including scans from 2007 to 2015. The CMRs were obtained 12 to 38 years (mean 20.6 ± 5.0 years) following initial CoA repair, and none had hemodynamically significant residual aortic arch obstruction or CoA requiring revision/reintervention as determined by Doppler echocardiographic interrogation. Thirty-six (68%) patients had initial repair during the first year of life, seven patients in second year, and ten patients more than five years after birth (with the oldest age at repair at ten years). Patients with additional left-sided obstructive lesions (including hypoplastic left heart syndrome) or hypoplastic aortic arch/interrupted aortic arch were excluded, as well as those with aneurysmal dilatation and those with imaging artifacts due to stents or valve prosthesis. Approximately 80% of the cohort had an end-to-end (E-E) CoA repair, while nearly one-half had a bicuspid aortic valve (Table 1). Ethical approval was obtained for the use of image data for research, and all patients or legal guardians gave informed consent.

Table 1.

Overview of Patient Characteristics.^a

Variables	Mean ± standard deviation
Number of patients	53
Age at time of CMR [years]	22.3 ± 5.6
Height [cm]	170.5 ± 9.5
BSA [m²]	1.83 ± 0.21
Aortic valve morphology (TAV/BAV/fBAV)	(21/26/6)
Type of initial repair (E-E/ExtE-E/Flap/Patch/Balloon)	(42/1/6/3/1)
LVEF [%]	64.1 ± 7.3
iLVEDV [mL/m²]	78.5 ± 14.6
iLVM [g/m²]	64.1 ± 14.7
BP [mm Hg]	130.0 ± 17.1

Abbreviations: BAV, bicuspid aortic valve; fBAV, functionally bicuspid aortic valve; BP, systolic resting blood pressure; BSA, body surface area; E-E, end-to-end anastomosis; ExtE-E, extended end-to-end anastomosis; ILVEDV, indexed left ventricular end-diastolic volume; iLVM, indexed left ventricular mass; LVEF, left ventricular ejection fraction; TAV, tricuspid aortic valve.

Lower case i indicates parameters indexed to patient BSA.

For each of the four cardiac function parameters (LVEF, iLVEDV, iLVM, and BP), two unique aortic arch shapes are extracted from partial least squares (PLS) to match high (+2SD) or low (−2SD) cardiac function values. For example, for LVEF, an aortic arch shape associated with LVEF that is +2 SD from the cohort mean is obtained, along with one associated with LVEF that is −2 SD from the mean. Thus, four pairs (or eight total) of aortic arch shapes were generated, and further postprocessed using the Vascular Modelling Toolkit (VMTK) software (Orobix) to prepare for CFD modeling.¹⁸

Pipe-like flow extensions were added at the transverse aortic arch sections (Figure 2A) to account for the volume of flow through the head and neck vessels. Flow extensions, of length 0.5 and 10 times their diameters, were added to the inlet and outlets of each geometry, respectively, to avoid recirculation at the outlets and allow boundary condition imposition at the inlet. An example of the resulting processed shapes is shown in Figure 2.

Computational Fluid Dynamics

All eight geometries were meshed using ANSYS Integrated Computer Engineering Modelling for Computational Fluid Dynamics (ANSYS Inc) software package and simulations were carried out in ANSYS Fluent v19.0. Postprocessing and result analysis were conducted in ParaView v5.9.0 (Kitware). The computational mesh comprised tetrahedral cells in the lumen of the aorta and thin prismatic cells in the near-wall region. Mesh sensitivity analysis that confirmed independence with ∼2 million cells, and error of <2% is detailed in the Supplemental Material.

A transient parabolic inlet velocity profile was adapted from the literature,¹⁹ obtained from phase contrasted CMR for a patient with a healthy aorta. Through linear scaling, the volumetric flow rate plot (Figure 2) was generated for a peak volumetric flow rate of 400 mL/s, at 0.11 s, for CoA patients post-repair.²⁰ Cardiac cycle was 1 s which corresponds to a heart rate of 60 BPM.

Similar to previous studies,²¹ outlet boundary conditions were defined as flow, where the total inlet flow is divided 1:1 between head-neck vessels and the descending aorta. A k-ω SST turbulence model with 5% turbulence intensity was used in the simulation.²⁰ Two cardiac cycles were simulated to reach stable solution. Blood was modeled as an incompressible, Newtonian fluid with a density of 1,060 kg·m⁻³ and dynamic viscosity of 0.0036 kg·m⁻¹·s⁻¹.

Analysis

To characterize flow performance, for each of the eight models, two flow dynamic values, known for effects on cardiovascular maladaptation and clinical outcomes, were extracted from CFD: (1) peak pressure gradient ( $Δ P$ ) between the ascending and descending aorta (shown as planes i and ii in Figure 2) and (2) viscous power loss ( ${E^{'}}_{L}$ ).^22,23

The peak pressure gradient at maximal systolic flow rate was calculated through equation (1):

Δ P = P_{A A o} - P_{D A o}

E_{L}^{'}

was calculated as reported previously²⁴:

E_{L}^{'} = μ \sum_{m = 1}^{n} ϕ_{v} V_{m}

where:

µ = 0.0036 kg·m⁻¹·s⁻¹

$n = number of cells$

$ϕ_{v} = \frac{1}{2} \sum_{i} \sum_{j} {[(\frac{\partial v_{i}}{\partial x_{j}} + \frac{\partial v_{j}}{\partial x_{i}}) - \frac{2}{3} (\nabla \cdot v) δ_{i j}]}^{2}$ with δ_ij = 1 for i = j and 0 otherwise (for each cell)

$V_{m} = volume of cell m$

E_{L}^{'}

represents the viscous power loss in the fluid volume at each point in time. The peak and the average

E_{L}^{'}

—calculated as the area under each curve, divided by the period of the cardiac cycle (Supplemental Material)—were obtained.

For each cardiac function parameter, to compare $Δ P$ and $E_{L}^{'}$ between the 2 shapes (favorable vs unfavorable), we also reported the percentage differences of the $Δ P$ or $E_{L}^{'}$ of the “low” (−2 SD) shape to the “high” (+2 SD) shape.

Velocity streamlines and $E_{L}^{'}$ contours at the time of maximum systolic flow rate were also generated for all eight shape modes to visually illustrate the spatial arrangement variabilities within the different geometries.

Results

Table 1 summarizes the peak (systolic) pressure gradients, $Δ P$ , for each geometry. Flows through the “unfavorable” shapes, that is, those associated with low LVEF, high iLVEDV, high iLVM, and high BP, produced higher pressure gradients (in red) than their “favorable” counterparts (in green). This corroborated previous phenomenological findings.¹⁷ $Δ P$ reached values between 3.7 and 7.6 mm Hg. The highest ΔP was seen in the aortic shape linked with high BP (+2SD).

Each shape mode's respective $E_{L}^{'}$ transient plot is shown in Figure 3. Highest (worst) maximum and average $E_{L}^{'}$ values were seen in aortic shapes associated with low LVEF, high iLVEDV, high iLVM, and high BP (Table 2). Percentage differences of the peak values ranged from 9.2% to 26.9%, and the average over a cardiac cycle between 15.1% and 32%. Maximum instantaneous $E_{L}^{'}$ ranging from 66.90 mW to 91.56 mW, while average $E_{L}^{'}$ ranged between 10.77 mW and 15.24 mW.

Table 2.

Maximum Pressure Gradient ( $Δ P$ ) Between the Ascending and Descending Aorta, and Maximum and Average Viscous Energy Loss ( $E_{L}^{'}$ ), Derived From CFD.^a

The velocity streamlines in Figure 4 qualitatively show how, given the same input flow conditions, the blood flow distributes differently in response to the specific aortic arch shape. The main differences between favorable and unfavorable shape modes in the $E_{L}^{'}$ contour plots (Figure 5) can be seen in the descending aorta: the flow, as it travels over the transverse arch, either propagates $E_{L}^{'}$ from the inner to the outer curvature (seen in the high iLVM case) or courses uniformly around the inner curvature. This is also reflected in the velocity fields, where regions of flow acceleration (turbulence) coincide with higher $E_{L}^{'}$ . Unfavorable shape modes with $E_{L}^{'}$ mapped a traversing contour, crossing from the inner to the outer curvature, are observed throughout a cardiac cycle and are associated with worse cardiac functions (low LVEF, high iLVEDV, high iLVM, and high BP) (Figure 3).

Discussion

In our 2017 study titled “How Successful is Successful?,” we asked two questions: (1) can the 3D shape of an aortic arch, late after CoA repair, be fully and quantitatively accounted for and (2) is 3D aortic arch shape, in and by itself, associated with better/worse cardiovascular outcomes?¹⁷ The novelty of that study was therefore two-fold: introducing SSM to fully characterize the 3D properties of the aortic arch in a large cohort of patients, and discovering distinct 3D aortic arch shapes that independently correspond with poorer cardiovascular function. While shedding light on the importance of the aortic shape, that study was descriptive in nature and could not afford a mechanistic insight into how differences in shape contributed to outcomes, such as worse ventricular performance and hypertension. In a series of studies using 4D CMR to examine flow characteristics in the aortic arch in various congenital heart diseases, Schaeffer's group observed that flow inefficiencies, characterized by increased viscous energy loss (VEL), are associated with both natural and surgically reconstructed aortas, such as those in tetralogy of Fallot and following Norwood-type aortic reconstruction.^13,22 Nonetheless, these studies did not address aortic arch shape relationships late after CoA repair, nor reported arterial pressures or pressure gradients across an aortic arch. Therefore, we employed well-established CFD methods to uncover the flow dynamic differences; that is, VEL and peak pressure gradient, that may underpin the observed relationship between aortic arch shapes and cardiovascular outcomes. Adopting the same cohort of patients who are doing well with no clinically important anatomic arch obstruction late after CoA repair, we identified two distinct aortic arch shapes that are associated with +2 and −2 SD values for each cardiovascular parameter. Computational fluid dynamics simulations revealed worse VELs were uniformly present in (unfavorable) aortic arch shapes corresponding with low LV function, more LV dilatation, high LV mass, and worse hypertension. Conversely, ranging from 3.7 and 7.6 mm Hg, peak pressure gradients were not hemodynamically or clinically significant. Moreover, calculated contour mapping suggests that a more complex propagation of VEL along with the aortic arch into the descending aorta is linked with unfavorable outcomes.

Viscous energy loss is not a familiar nomenclature because it is not a clinically measurable quantity. However, in the fields of fluid mechanics and heat/mass transfer, it signifies the undesirable loss of mechanical energy that powers fluid motion due to viscosity. As a viscous fluid, blood motion can produce friction and shear that will partially convert kinetic and potential energies to viscosity-related energy transfers that become permanent, unrecoverable losses to the usable mechanical energy of the system. Therefore, the observed VEL relationship in this study provides a mechanistic link to the previously reported association between aortic arch and worse cardiovascular outcomes, such as systemic hypertension, long after successful CoA repair. This suggests that specific aortic arch shapes that result in increased VEL may contribute (in part) to late cardiovascular maladaptation, such as lower LVEF or higher iLVM. Unlike the pronounced kinetic energy loss (reflected by large pressure gradients) caused by significant (re-)stenosis or obstruction that typically mandates intervention, shape-related VEL in patients with successful CoA repair is subtle but can chronically persist in the background despite acceptable echocardiographic interrogation, or even angiographic assessment. Rather, VEL will not produce discernible, or even clinically measurable, pressure gradients. This is evident by the underwhelming peak pressure gradients obtained from the CFD simulations. While the impact of high-grade aortic arch obstruction on cardiac function and distal organ perfusion is readily diagnosed, how shape-related chronic VEL, acting under the radar, contributes to poorer late cardiovascular outcome will require further investigation. It is likely that VEL is a part of a larger set of factors, including inherent biological variances/vascular properties/genetic predispositions, that result in increased cardiovascular risks for patients with repaired CoA.

To isolate aortic arch shape as the independent focus of the study, the patient cohort represents those who are clinically well without residual anatomic aortic arch obstruction. With peak systolic pressure gradients ranging from 3.7 and 7.6 mm Hg in the eight CFD models, the numerical simulation not only validated our patient selection but also shed light on the challenges to clinically evaluate and monitor shape-related VEL. It is worth highlighting that for each aortic arch shape pair, the favorable and unfavorable shapes were separated by 4 standard deviations in clinical outcomes. Despite this wide divide in each of the four outcome measures, none of the unfavorable aortic arch shapes produced peak pressure gradients that would have registered clinical concern or mandated intervention. What is clear then is that pressure gradient as the traditional measure of adequacy of aortic arch reconstruction is unable to capture shape-related VEL because it does not produce sufficiently high flow resistance. While unsupported by the present study, it is possible that shape-related VEL continuously exerts a subtle and subclinical, but cumulative, long-term cardiovascular burden in patients after CoA repair. Or perhaps, rather than promote resistance and pressures, high VEL reflects exaggerated shear stress contour and/or disorganized wave propagation, two factors known to affect unfavorable ventricular-arterial coupling.^24,25 Due to this insidious nature, a more robust and lifelong follow-up within an established adult congenital heart program with regular echocardiograms may be indicated for all patients after CoA repair.

Finally, we are often asked (and rightly criticized for) how the additional insights from this exercise would be useful or actionable clinically; that is, how would one perform the initial CoA repair to ensure a favorable aortic arch shape? The answer, we are afraid, is that we do not know. The aortic arches studied here are from a cross-sectional population of patients at a late timepoint from the initial CoA repair. Thus, without the knowledge of what the aortic arch looked like immediately after surgery or at any other interceding timepoints, it is not possible to assess the evolution of the initial aortic arch shape to its late or final appearance. And without such a longitudinal, and patient-specific, understanding of aortic arch transformation with time and growth, it would be purely conjecture, and foolhardy, for us to suggest a specific operative technique or surgical modification to the standard CoA repairs. Since the vast majority (>80%) of the cohort had extended end-to-end repair, SSM is unable to reveal specific preoperative patient characteristics, intraoperative techniques, or postoperative management that may predict the late appearance of the repaired aortic arch.

Limitations

In this study, the CFD simulations of the eight aortic arch shape models used the same meshing parameters, uniform boundary conditions, and rigid-walled and modeling methods. While patient-specific modeling is currently popular, the application of a uniform boundary condition and simulation parameters in this study are logical means to focus on the comparative flow dynamics between different aortic arch shapes. By removing interpatient variabilities in the CFD simulations, in addition to vastly improving the efficiency of the investigation analysis, differences in both VEL and peak pressure gradients are singularly attributed to shape variations. It must be acknowledged that since aortic arch shape variations are associated with different cardiovascular functional outcomes, the boundary conditions, such as blood pressure and cardiac output and aortic wall properties that define each model could not be identical. However, as the scope of study is to uncover mechanistic effects of the aortic arch shape, this study is unable to account for all patient-specific adaptations, including variations in the aortic wall stiffness and compliance. For similar reasons, we did not adopt a multiscale approach with closed-loop simulation including linkage with a lumped parameter network model. Such an approach would not provide additional information that is gleaned from the granular details in the CFD models.

Conclusion

The present study builds upon our early work on 3D aortic arch shape to advance an insight into the variable flow dynamics that underpins the association of aortic arch shapes with worse cardiovascular outcomes late after successful CoA repair. Even in the absence of residual obstruction or clinically important pressure gradients, higher VELs persist in those aortic arch shapes associated with lower left ventricular ejection fraction and higher end-diastolic volume, left ventricular mass, and resting blood pressure. Future work needs to further the understanding of the mechanism by which the insidious dissipation of viscous energy in aortic arch flow results in cardiovascular maladaptation, and whether mitigating strategies can be discovered to modify this unrelenting liability.

Supplemental Material

sj-pdf-1-pch-10.1177_21501351241269868 - Supplemental material for The Enduring Impact of Shape Following Perfect Coarctation of the Aorta Repair

Supplemental material, sj-pdf-1-pch-10.1177_21501351241269868 for The Enduring Impact of Shape Following Perfect Coarctation of the Aorta Repair by Liam Swanson, Emilie Sauvage, Malebogo Ngoepe, Silvia Schievano, Jan L. Bruse and Tain-Yen Hsia in World Journal for Pediatric and Congenital Heart Surgery

Footnotes

Abbreviations

Acknowledgments

The authors are grateful for the present and past support from Leducq Foundatioin, the British Heart Foundation, and the FirstRand Foundation.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the First Rand Foundation, Fondation Leducq, British Heart Foundation.

ORCID iDs

Jan L. Bruse

Tain-Yen Hsia

Supplemental Material

Supplemental material for this article is available online.

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Supplementary Material

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