Statistical shape modeling reveals the link between right ventricular shape, hemodynamic force, and myocardial function in patients with repaired tetralogy of Fallot

Abstract

Patients with repaired tetralogy of Fallot (rTOF) can develop chronic pulmonary insufficiency (PI) with right ventricular (RV) dilation, progressive RV dysfunction, and decreased exercise capacity. Pulmonary valve replacement (PVR) can help reduce the amount of PI and RV dilation; however, optimal timing remains controversial; a better understanding of rTOF pathophysiology is of fundamental importance to inform clinical management of patients with rTOF and optimal timing of PVR. In this study, we hypothesize a tight interplay between RV shape, intracardiac biomechanics, and ventricular function in patients with rTOF. To explore this hypothesis and derive quantitative measures, we combined statistical shape modeling with physics-based analysis of in vivo 4D flow data in 36 patients with rTOF. Our study demonstrated for the first time a correlation between regional RV shape variations, hemodynamic forces (HDF), and clinical dysfunction in patients with rTOF. The main findings of this work include 1) general increase in RV size, due to both volume overload and physiological growth, correlated with decrease in strain magnitude in the respective directions, and with increased QRS; 2) regional PI-induced remodeling accounted for ∼10% of the shape variability of the population, and was associated with increased diastolic HDF along the diaphragm-to-right ventricular outflow tract (RVOT) direction, resulting in a net RV deformation along the same direction and decreased tricuspid annular plane systolic excursion (TAPSE); and 3) three shape modes independently correlated with systolic HDF and exercise capacity. Identification of patients based on the shape variations described in this study could help identify those at risk for irreversible dysfunction and guide optimal timing of PVR.

NEW & NOTEWORTHY We combine statistical shape modeling with physics-based analysis of 4D flow data to elucidate the interplay between RV shape, hemodynamic forces, and clinical dysfunction in repaired tetralogy of Fallot. We are the first to show that ventricular remodeling is related to hemodynamic force magnitude and direction, global and regional functional parameters, and exercise intolerance. Identification of patients based on the shape variations described in this study could help identify those at risk for irreversible dysfunction.

INTRODUCTION

In the modern era of congenital cardiovascular surgery, patients with tetralogy of Fallot (TOF) survive into adulthood but may suffer from sequelae of their initial repair (1, 2). Early surgical intervention is performed in infancy to address the issue of decreased pulmonary blood flow, but it also disrupts the integrity of the pulmonary valve. As a consequence, patients with repaired tetralogy of Fallot (rTOF) can develop chronic pulmonary insufficiency (PI) with right ventricular (RV) dilation (3), progressive RV dysfunction, decreased exercise capacity, and increased risk of ventricular arrhythmias and mortality (4). Although pulmonary valve replacement (PVR) in patients with rTOF can help reduce the amount of PI and RV size, the optimal timing of PVR remains controversial and is largely based on global and functional parameters by cardiac magnetic resonance (CMR), which are often reflective of late disease manifestations (5). These parameters do not consider other important aspects of myocardial function and physiology, including intracardiac flow dynamics and regional ventricular shape and deformation patterns. A deeper understanding of rTOF pathophysiology is highly warranted to inform clinical decisions in terms of indication and optimal timing of PVR.

The progression from PI-induced compensatory mechanisms to overt RV failure is a complex and multifactorial process, and the unique postrepair biomechanical environment is likely to play a key role in driving the pathophysiological response of the RV (6). Hemodynamic alterations post repair can lead to adaptations in RV geometry, myofiber architecture, and conduction (7). Previous studies have used in vitro experiments (8), computational fluid dynamics (9), and time-resolved phase-encoded MR imaging with velocity encoding in three directions (4D flow) (10) to study alterations to intracardiac flow (e.g., vorticity and viscous energy loss) (11) in patients with rTOF. We recently demonstrated that flow topology in the RV of patients with rTOF is distinct from other forms of chronic RV volume overload and contributes to RV dysfunction and exercise intolerance (10). With any intracardiac blood flow, there is a driving intraventricular pressure gradient (or flow acceleration/deceleration) over the entire ventricular volume; globally, this pressure gradient is exchanged with the myocardium in the form of hemodynamic force (HDF) (12). HDF has been shown to be abnormal in patients with rTOF (10, 13, 14), and its role in cardiac remodeling has been implicated in a number of pathologies. Thus, alterations in intracardiac flow and HDF may contribute to physiological and shape adaptations of the myocardium (15).

Shape analysis of the RV has been historically hindered by its complex geometry and lack of clear anatomical landmarks. Initial studies of the rTOF population relied on morphometric analysis and reported significant geometrical alterations with respect to normal subjects (16). Recent advances in statistical shape modeling (SSM), in conjunction with data-reduction techniques, have opened new avenues for handling anatomical complexity with a relatively low number of parameters. With the use of SSM, recent studies have demonstrated distinct shape remodeling patterns in the RV induced by PI; particularly, patients with rTOF have dilation of the right ventricular outflow tract (RVOT) and bulging of the basal free wall (17, 18). However, the interplay between ventricular shape, myocardial function, and HDF has not been investigated. In this study, we hypothesize a tight interplay between RV shape, intracardiac biomechanics, and ventricular function in patients with rTOF. To explore this hypothesis and derive quantitative measures, we combined statistical shape modeling with physics-based analysis of in vivo 4D flow data in 36 patients with rTOF.

MATERIALS AND METHODS

Study Design

This was an Institutional Review Board-approved retrospective study. Waiver of consent was obtained. All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000. CMR database was initially queried for patients with a diagnosis of TOF. Inclusion criteria included 1) diagnosis of patients with TOF with pulmonary stenosis, 2) history of transannular/infundibular patch repair, and 3) diagnostic quality CMR performed between 2013 and 2020. Exclusion criteria included 1) diagnosis of any other form of TOF variant, including TOF with pulmonary atresia or TOF with major aortopulmonary collaterals; 2) history of surgical repair that would confound the RVOT anatomy, specifically right ventricle-to-pulmonary artery conduits; 3) poor quality CMR from significant sternal/stent artifact; 4) evidence of elevated pulmonary vascular resistance (confirmed by cardiac catheterization); and 5) evidence of significant tricuspid valve regurgitation as measured by CMR (beyond regurgitant fraction of 20%). These criteria allowed for identification of patients with rTOF with similar surgical intervention on the RVOT and similar mechanism of volume overload on the RV.

Cardiac MRI

All CMR studies were performed with a Siemens 1.5 T scanner. CMR data included cine imaging (long-axis and short-axis cine), contrast-enhanced magnetic resonance angiography (MRA), noncontrast three-dimensional steady-state free precession imaging (3-D SSFP) gated for end diastole, and two-dimensional phase contrast across the pulmonary valve (V_enc set between 2 m/s and 2.5 m/s) and 4D flow. The 4D flow sequence parameters included field of view (FOV) = 280–480 × 140–230 mm, matrix = 160 × 77, T_E = 2.19 ms, T_R = 37.9–59.4 ms (dependent on number of segments per RR and RR interval; either 2 segments for RR < 750 ms or 3 segments for RR > 750 ms), flip angle = 15, slice thickness = 1.8 or 2.8 mm (dependent on patient size, either 1.8 mm for body surface area (BSA) < 1.5 m²; 2.8 mm for BSA > 1.5 m²), V_enc = 2 m/s–2.5 m/s and number of reconstructed phases = 20–30. The MRA and 3-D SSFP covered the entire heart with voxel size ∼1.4 × 1.4 × 1.4 mm. Standard clinical measurements of RV end diastolic volume index (EDVi), RV end-systolic volume index (ESVi), RV ejection fraction (EF)%, and regurgitant fraction (RF)% were obtained. Electrocardiogram and cardiopulmonary exercise stress test results were also collected for QRS duration, V̇o_2max, and %predicted V̇o_2max.

Definition of MRI-Based Reference Frame

A reference system based on the individual RV anatomy was defined to aid the subsequent analyses. Following Sjöberg et al. (13), the apical-to-basal direction was defined as perpendicular to the short-axis cine plane (positive direction toward base). The septal-to-free wall direction is defined as perpendicular to both the short-axis cine plane and the three-chamber cine plane (positive direction toward free wall). Finally, the diaphragm-to-RVOT direction was derived as the cross product between the two previously defined vectors (positive toward RVOT). The reference system is schematically illustrated in Fig. 1.

Figure 1.

Cardiac magnetic resonance (CMR) images of a patient with repaired tetralogy of Fallot in the oblique/frontal plane (left), four chamber view (middle), and long axis right ventricular outflow tract (RVOT) view (right). MRI-based reference frame in the right ventricle (RV) demonstrating apical-to-basal (red), diaphragm-to-RVOT (blue), and septal-to-free wall (green) coordinate axes.

Segmentation and Creation of 3-D Models

Three-dimensional end-diastolic models of the RV were created from noncontrast 3-D SSFP, according to laboratory standard segmentation (19, 20) using commercially available software (Mimics; Materialise, Leuven, The Netherlands). The tricuspid inflow, RV body, and RVOT were segmented as a single mask. In cases of significant phase dispersion artifact, the contrast-enhanced MRA was used for verification of RVOT anatomy. The segmentations were also overlaid against the end-diastolic phase of the cine data to ensure that the 3-D model accurately represented the endocardial contours of the RV at end diastole.

Statistical Shape Analysis

The digital 3-D models of the RV obtained from segmentation were uniformly remeshed and rigidly aligned using the iterative closest point technique (21). The template shape of the population was computed using an iterative technique based on the large deformation diffeomorphic metric mapping (LDDMM) implemented into the open-source software Deformetrica (22). Along with the template, this method simultaneously computes nonlinear deformations (mappings) that transform the template into each of the patient geometries. To identify the physical directions of the remodeling and shape variation patterns, the net deformation vector was computed for each patient by averaging the pointwise difference between each patient’s shape and the template. The orientation of the deformation vector was quantified in terms of the angles between the vector and the three positive coordinate axes. Shape modes were computed using the principal component analysis (PCA) technique implemented into inhouse MATLAB software. The overall procedure is explained in detail in appendix.

Computation of HDF

Each 4D flow data set was postprocessed to compute the hemodynamic force vector. Time-resolved 3-D models of the RV endocardium were used to isolate the domain of interest; these dynamic masks were obtained from the segmented static diastolic models using a novel technique based on cine-MRI data and feature-tracking software, as described in previous work (9). This procedure also yields the time profile of the RV volume V(t) over the cardiac cycle. Custom MATLAB codes were then used to compute the global HDF vector, defined as the volume integral of the sum of the inertial and convective terms of the momentum equation:

$$\overrightarrow{\mathit{F}}\left(t\right)=\rho \underset{V\left(t\right)}{{\displaystyle \int }}\left(\frac{\partial \overrightarrow{v}}{\partial t}+\overrightarrow{v}·\nabla \overrightarrow{v}\right)\text{d}V$$

where ρ is the blood density (assumed to be equal to 1,060 kg/m³) and $\overrightarrow{v}\left(\overrightarrow{x},t\right)$ is the velocity field within the RV. The HDF physically represents the blood acceleration (per unit mass); also, as a consequence of Newton’s third law, it is inherently associated with a counterforce exerted on the myocardium at any instant in time. The force vector $\overrightarrow{\mathit{F}}\left(t\right)$ was normalized with the instantaneous RV volume V(t) to facilitate comparison between subjects and projected onto the previously defined reference frame. To allow for quantitative analysis, several physically based parameters were extracted from the time profile of volume-normalized HDF: 1) the average amplitude, computed as the root mean square (RMS) over the whole cardiac cycle of each component, as well as of the HDF magnitude; 2) the average amplitude during systole only and 3) during diastole; and 4) the mean diastolic alignment of the force with the RVOT axis, an angle ranging from 0° (perfect alignment with HDF axis, pointing toward RVOT) to 180° (HDF vector pointing toward diaphragm).

Statistical Analyses

Correlations between continuous variables were assessed using Pearson’s correlation coefficient. For all comparisons, a P values < 0.05 was considered statistically significant.

RESULTS

Demographics

This study analyzed 3-D models constructed from CMR data of 36 patients with rTOF. The study included patients with TOF who underwent repair with either transannular or infundibular patch. The average age was 20.7 ± 12.8 yr, BSA was 1.54 ± 0.4 m², and 18 (50%) were females. The patients overall had normal RV EF 51.4 ± 5.26%. The average RV EDVi was 134.4 ± 34.9 mL/m² with a pulmonary RF of 29.9 ± 17.3%. Twelve patients had exercise stress test results for analysis. Additional functional and volumetric demographics are outlined in Table 1. Significant correlations between shape variations and the orientation of the deformation vector with parameters including size, function, and HDF are summarized in Fig. 2.

Table 1.

Patient characteristics

	Mean	SD
BSA, m2	1.5	0.4
Age, yr	20.7	12.8
Female sex, n (%)	18 (50)	N/A
RV EDVi, mL/m2	134	34.9
RV ESVi, mL/m2	66.2	22.5
RV EF, %	51.4	5.3
Pulmonary RF, %	29.9	17.3
RV GLS, %	−22.8	−5.0
RV GCS, %	−12.2	−5.2
RV free wall strain, %	−26.3	−5.9
RV septal strain, %	−17.6	−6.1
RV annular excursion, mm	13.7	3.7
LV EDVi, mL/m2	75.8	17.4
LV EF, %	59.3	5.4
LV GLS, %	−21.0	−3.8
LV GCS, %	−28.6	−4.7
LV lateral wall strain, %	−26.6	−5.1
LV septal strain, %	−15.4	−4.4
LV annular excursion, mm	13.7	3.8

Values are means and standard deviations; n, number of patients. Thirty-six patients with repaired tetralogy of Fallot were included. BSA, body surface area; EDVi, end-diastolic volume index; EF, ejection fraction; ESVi, end-systolic volume index; GCS global circumferential strain; GLS, global longitudinal strain; LV, left ventricular; N/A, not applicable; RF, regurgitant fraction; RV, right ventricle.

Figure 2.

Significant correlations between shape variations (modes M0, M1, M2, M7, M10) and orientation of the deformation vector [i.e., the angle between the vector and the apical-basal, septal-free wall, diaphragm-right ventricular outflow tract (RVOT) axes] with parameters including right ventricular size, function, and hemodynamic force (HDF). The map reports the value of Pearson’s correlation coefficient. BSA, body surface area; EDVi, end diastolic volume index; EF, ejection fraction; ESVi, end systolic volume index; GCS, global circumferential strain; GLS, global longitudinal strain; RF, regurgitant fraction; RV, right ventricle; TAPSE, tricuspid annular plane systolic excursion.

Statistical Shape Analysis

The computed template geometry is shown in Fig. 3 (in red), along with the individual patient geometries, showing that it is well centered within the cohort. Figure 4 visually demonstrates the deformation vector in two different cases: one where the ventricle is preferentially remodeled along the diaphragm-to-RVOT direction, and one in which it is mainly deformed along the apical-to-basal direction (with respect to the average shape of the population). From the PCA analysis, 35 independent principal component modes were extracted. The first four modes encoded 58% of the total shape variability, while more than 80% of shape variance was achieved by the 10th mode. Five shape modes, in particular, correlated with several parameters related to function, strain, and hemodynamic forces, and are shown in Fig. 5. Shape mode 0 (M0), contributing 34.6% to the cohort variability, was mostly associated with general growth and change in RV shape in response to increased volume. Shape mode 1 (M1) demonstrated RV remodeling in response to PI, with development of an RV apical bulge and enlargement of the RVOT diameter and accounted for 10.7% of the total shape variance. Shape mode 2 (M2, 6.8%) demonstrated longitudinal shortening from the RV apex to base and an overall more globular RV with increased angle between the inflow and outflow regions. Shape mode 7 (M7, 3.1%) was associated with an increase in the angle between the inflow and outflow regions, as well as slight bulging at the RV apex. Shape mode 10 (M10, 2.2%) showed significant RV apical bulging, as well as a shorter, more dilated RVOT. In addition, M10 notably demonstrated increased inflow length from apex to base and increased circumference of the inflow portion of the RV.

Figure 3.

Individual patient geometries (in gray) superimposed with the computed template geometry (in red).

Figure 4.

Visual demonstration of the net deformation vector. The template is shown in red, while the individual patient geometry is shown in gray. The vectors connecting each pair of corresponding points between the template and the patient shape are averaged to get the net deformation vector (shown in black). In A, a case where the right ventricle (RV) is deformed preferentially along the apical-to-basal direction is shown; a patient where the deformation vector is mostly aligned along the diaphragm-to-right ventricular outflow tract (RVOT) axis is instead shown in B. Note that the vector points toward the net direction of deformation with respect to the template. The magnitude of the deformation vectors shown was magnified for visualization purposes.

Figure 5.

Shape variations of the right ventricle in patients with repaired tetralogy of Fallot. The entire right ventricle (RV) shape is opacified, with the RV outlined along the oblique/frontal, long-axis (LAX) and short-axis (SAX) planes, respectively. Blue shade/outline denotes −2SD from the template shape and red shade/outline denotes +2SD toward the shape variation of interest. The darker shaded parts noted in LAX view represent the inner curvature of the ventricular septum. M0, global increase in RV size; M1, RV apical bulge and enlargement of the right ventricular outflow tract (RVOT) diameter; M2, longitudinal shortening from RV apex to base and an overall more globular RV with increased angle between the inflow and outflow regions; M7, increase in the angle between the inflow and outflow regions, as well as slight bulging at the RV apex; M10, significant RV apical bulging, increased inflow length from apex to base, increased circumference of the inflow portion of the RV, as well as a shorter, more dilated RVOT.

Hemodynamic Forces

The time evolution of the mean components of the HDF over the cardiac cycle is shown in Fig. 6, while Table 2 reports the mean values of the volume-normalized parameters. Qualitatively, HDF was mainly directed toward the RVOT in early systole, consistent with blood acceleration; a slight deceleration is visible in late systole, as revealed by the force reversal. In diastole, forces were initially negative (i.e., directed toward apex and diaphragm), reflecting acceleration of the blood entering the ventricle. During the latter part of early diastolic inflow, the apex-to-base and diaphragm-to-RVOT HDF components become positive as a result of blood deceleration along both directions, due to inflow from the tricuspid valve and regurgitant flow, respectively.

Figure 6.

Time evolution of mean hemodynamic force components over the cardiac cycle; the bars show the standard deviation. HDF, hemodynamic force; rTOF, repaired tetralogy of Fallot; RVOT, right ventricular outflow tract.

Table 2.

Mean hemodynamic force

Hemodynamic Force, N/L	Systolic RMS	Diastolic RMS
n	36	36
Apical-to-basal	0.97 (0.39)	0.71 (0.25)
Septal-to-free wall	0.45 (0.30)	0.29 (0.11)
Diaphragm-to-RVOT	1.12 (0.49)	0.43 (0.19)

Values are mean systolic and diastolic root mean squared (RMS) hemodynamic forces for 36 patients with repaired tetralogy of Fallot in the apex-to-base, septal-to-free wall, and diaphragm-to-right ventricular outflow tract (RVOT) axes. n, number of patients.

Shape Correlations with Functional Parameters and HDF

Net deformation vector.

The apical-to-basal and septal-to-free wall angles of the net deformation vector correlated with dimensional parameters such as BSA (r = 0.57, P = < 0.001 and r = 0.67, P < 0.001, respectively). They also correlated with each other (r = 0.49, P = 0.003), indicating that net deviations from the template shape along these two directions occurred preferentially together and were associated with physiological growth factors.

In addition, the apical-to-basal angle of the net deformation vector correlated with functional parameters such as RV free wall strain (r = 0.53, P = 0.001), RV free wall annular excursion (r = 0.41, P = 0.014), and QRS duration (r = 0.43, P = 0.012). Uniquely, the decrease in the angle between the deformation vector and the apical-to-basal axis correlated with increased magnitude of RV global longitudinal strain (GLS) (r = 0.48, P = 0.004), demonstrating the relationship between shape variation in the apical-to-basal axis and improved longitudinal shortening.

The septal-to-free wall angle of the net deformation vector also correlated with RV free wall strain (r = 0.43, P = 0.009), RV free wall annular excursion (r = 0.39, P = 0.022), and QRS duration (r = 0.48, P = 0.004). The angle between the deformation vector and the septal-to-free wall axis correlated with RV size, specifically RV EDVi (r = 0.39, P = 0.018) and RV ESVi (r = 0.37, P = 0.029), as well as RV global circumferential strain (GCS) (r = 0.37, P = 0.028).

On the other hand, the angle between the deformation vector and the diaphragm-to-RVOT axis was associated with RF (r = 0.37, P = 0.027) and even more so with diastolic force parameters, particularly with diaphragm-to-RVOT RMS HDF (r = 0.58, P = <0.001). This relationship demonstrates an important link between PI-induced HDF and pathological remodeling patterns along the same direction.

Shape mode M0—correlates with general RV size and myocardial function.

M0 was largely representative of the rTOF population and was associated with general increase in RV size. M0 correlated directly with absolute RV end-diastolic volume (EDV) (r = 0.94, P < 0.001), RV EDVi (r = 0.724, P < 0.0001), body surface area (r = 0.754, P < 0.0001), and increased RF (r = 0.60, P < 0.001).

M0 also correlated with myocardial function: increased propensity toward M0 correlated with decrease in magnitude of RV global longitudinal strain (GLS) and RV free wall strain (r = −0.47, P = 0.005 and r = −0.49, P = 0.003) (Fig. 7A). M0 also correlated with increased QRS duration (r = 0.66, P < 0.001), demonstrating electromechanical dyssynchrony with increasing volume.

Figure 7.

Relationship of shape modes M0 and M1 with strain, QRS duration, regurgitant fraction (RF), and hemodynamic force (HDF). Increased propensity toward M0 correlates with decrease in magnitude of right ventricle global longitudinal strain (RV GLS) and RV free wall strain (A) and increased QRS duration (B). Increased propensity toward M1 correlates with increased RF (C) and increased diastolic diaphragm-to-right ventricular outflow tract (RVOT) and diastolic magnitude HDF (D).

Finally, with shape variation M0, the mean angle between the diastolic HDF vector and the septal-to-free wall direction was decreased (r = −0.35, P = 0.039). This finding demonstrates deviation of the total force away from the typical apex-to-base direction and toward the free wall with increased RV volume.

Shape mode M1—correlates with myocardial function and diastolic hemodynamic force.

Shape mode M1 was representative of RV apical bulging and enlargement of the RVOT, which correlated with increased regurgitant fraction (r = 0.55, P = < 0.001) (Fig. 7C). M1 also correlated with decreased RV systolic wall motion in the form of tricuspid annular plane systolic excursion (TAPSE) (r = −0.45, P = 0.007).

M1 was related to several HDF parameters including increased diastolic apex-to-base RMS HDF (r = 0.51, P = 0.001), increased diastolic septum-to-free wall RMS HDF (r = 0.45, P = 0.006), increased diastolic diaphragm-to-RVOT RMS HDF (r = 0.55, P = <0.001), and increased diastolic magnitude RMS HDF (r = 0.58, P = < 0.001) (Fig. 7D). An increasingly remodeled RV, represented by shape variation M1, was associated with a decrease in angle between the direction of the global force vector and the RVOT axis (r = −0.47, P = 0.004). This finding represents an overall misalignment of HDF from predominantly apical-to-basal axis to instead over the RVOT axis (Fig. 8).

Figure 8.

Outline of right ventricle (RV) in the oblique/frontal view. Blue outline denotes −2SD from the template shape and red outline denotes +2SD toward the shape variation of interest. An increased propensity toward M1 (red) is associated with a more acute angle between the direction of the total force vector (hemodynamic force, HDF) and the right ventricular outflow tract (RVOT) axis. There is increased contribution of the RVOT force to the overall HDF as the two vectors become more parallel to each other (red).

Shape mode M2—correlates with systolic hemodynamic force.

M2 was representative of longitudinal shortening of the RV and was associated with decreased systolic apex-to-base RMS HDF (r = 0.39, P = 0.035), decreased systolic RVOT-to-diaphragm RMS HDF (r = 0.35, P = 0.035), and decreased systolic RV magnitude RMS HDF (r = 0.42, P = 0.001) (Fig. 9A).

Figure 9.

Relationship of shape modes M2, M7, and M10 with hemodynamic force (HDF), strain, and exercise capacity. A: increase propensity toward M2 correlates with decreased systolic apex-to-base and magnitude HDF. B and C: increased propensity toward M7 correlates with decreased magnitude of right ventricle global circumferential strain (RV GCS) (B) and decreased V̇o_2max (C). D: increased propensity toward M10 correlates with decreased %predicted V̇o_2max.

Shape mode M7—correlates with myocardial function and exercise capacity.

M7 was representative of slight bulging at the RV apex and tilting of the tricuspid inflow relative to the outflow region, which correlated with decreased magnitude of RV global circumferential strain (GCS) (r = 0.41, P = 0.016) (Fig. 9B). M7 also correlated with increased QRS duration (r = 0.37, P = 0.034). In addition, of the 12 patients with exercise stress test data, M7 correlated with decrease in V̇o_2max (r = −0.68, P = 0.012) (Fig. 9C).

Shape mode M10—correlates with exercise capacity.

Finally, M10 was representative of more pronounced RV apical bulging, a short dilated RVOT, and increased inflow length, which correlated with decreased percent predicted V̇o_2max (r = −0.75, P = 0.005) (Fig. 9D).

DISCUSSION

Our study demonstrated for the first time a connection between regional RV shape variations, hemodynamic forces, and clinical dysfunction in patients with rTOF. The main findings of this work include 1) homogeneous increase in RV size, due to both volume overload and physiological growth, correlated with decrease in strain magnitude in the respective directions, and with increased QRS; 2) regional PI-induced remodeling accounted for ∼10% of the shape variability of the population and was associated with increased diastolic HDF along the diaphragm-to-RVOT direction, resulting in a net RV deformation along the same direction and decreased TAPSE; and 3) three shape modes independently correlated with systolic HDF (M2) and exercise capacity (M7 and M10). This study also demonstrated that a combination of data-driven statistical shape modeling techniques with physics-based analysis of intracardiac flow is a promising approach to gain insights into cardiac biomechanics and ventricular function.

The rTOF population represents our best chance to understand the long-term ventricular adaptations to the “iatrogenic” hemodynamic environment of chronic insufficiency. Prior work has shown that chronic PI results in increased myocardial workload and inefficiency of the RV leading to eventual dysfunction over time (23). However, the progression toward RV failure is likely a complex, multifactorial process. For example, RV biomechanics is already adversely affected by scar tissue or patch material in the RVOT, where late gadolinium enhancement is associated with regional RV dysfunction (6).

In turn, alterations in the intracardiac biomechanical environment in rTOF (5, 9–11, 15, 24, 25) may lead to myocardial adaptation that takes place in response to shear forces generated by, e.g., diastolic vortex formation (26). There may be variable epigenetic mechanisms of cardiac remodeling in response to abnormal flow patterns and biomechanical forces (27) that disrupt the physiological dynamic balance between blood flow and myocardial tissue. On a macro scale, the remodeling of the RV manifests as alterations in shape, whereas intracardiac flow exchanges its pressure load with the myocardium in the form of HDF. Now we have provided quantitative evidence of a correlation between shape, HDF, and function.

The temporal profiles of HDF were qualitatively and quantitatively in line with previous studies (13). There was a persistent diastolic force component along the diaphragm-to-RVOT direction that is typically absent in healthy subjects (13, 14), leading to a misalignment of the diastolic HDF with respect to the typical apex-base direction. As the link between flow and shape remodeling, HDF may have utility as an early indicator for biomechanical dysfunction in patients with rTOF. Recent studies have demonstrated the limitations of conventional CMR measurements in patients with rTOF. The degree of PI is not correlated with impaired clinical status (28). Furthermore, metrics of clinical function including RV EF and exercise capacity often remain unchanged after PVR (17, 29). HDF adds directional information to PI and may be a better physics-based measure of the physical effect of regurgitation on the myocardium, by accounting for the net result of the complex interaction between the PI jet and the tricuspid inflow in diastole (9, 10). As HDF drives the intraventricular pressure gradient exchanged within the myocardium, it may be associated with increased wall shear stress and thus with stimulation of diastolic mechanoreceptors in the endocardium, provoking activation of intracellular pathways involved in cardiac adaptation and remodeling (30, 31). On the other hand, HDF may also be useful in detecting systolic pumping alterations. Previous studies have investigated HDF as an early biomarker of dysfunction in patients with heart failure with preserved EF (32), albeit with mixed results (33). Identification of minor kinetic dysfunction at the blood-tissue interface may be possible through HDF analysis, leading to detection of mechanical abnormalities in asymptomatic patients (12).

The key RV shape variations in this study are in line with other statistical shape modeling studies in rTOF (17, 18, 34). We have now also demonstrated several shape relationships with HDF and with global and regional functional parameters. General increase in RV size, as seen in M0, was related to both physiological growth (BSA) and volume overload (RF), irrespective of HDF, and correlated with decreased magnitude of RV GLS and RV free wall strain. Interestingly, increased propensity toward M0 and M7 correlated with increased QRS duration, suggesting electromechanical dyssynchrony with these shape variations. On the other hand, RV apical bulging and RVOT dilation, as seen with M1, correlated with increased RF, increased diastolic force parameters, and decreased function, evidenced by lower TAPSE. Upon inspection of the newly introduced net deformation vector, we could establish a clear and directional correlation between the diastolic HDF and the RV remodeling pattern, compatible with the epigenetic mechanisms mentioned earlier.

Most interestingly, RV shape deformation in the apical-to-basal axis is directly related to RV GLS, whereas deformation in the septal-to-free wall plane is related to RV GCS. This finding is consistent with the directionality of the muscle fibers in the RV, with the superficial and deep muscles aligned horizontally, aiding in longitudinal shortening from apex to base, while the middle layer is circumferential, allowing for circumferential contraction (7, 35). CMR strain analysis of patients with rTOF has proven RV GCS to be more predictive than RV GLS in meeting criteria for PVR (35).

The association of M7 and M10 with exercise capacity raises interesting possibilities related to the role of RVOT in exercise capacity. In this study as well as in our prior research, the traditional CMR metrics of function did not correlate with exercise capacity (10). M7 was associated with V̇o_2max, whereas M10 was associated %predicted V̇o_2max (age and sex independent). Both involve RV apical bulging, which is generally associated with RV dilation found in other shape modes (and also sensitive to age and sex). M10 also involves the widening of the RVOT; in our previous study, 4D flow abnormalities in the RVOT were also implicated in reduced exercise capacity in both V̇o₂ and %predicted V̇o₂ (10). The results imply that the combination of RV apical bulging and widening of the RVOT are associated with exercise capacity independent of age and sex, although the sample size of this cohort was rather small (n = 12) and further investigation is required.

Our study is the first to define the relationship between RV shape and HDF in patients with rTOF, and in general, among the first to combine SSM with intracardiac flow analysis. Prior work has defined the unique properties of HDF in patients with rTOF (13) and described the key variations in RV shape due to remodeling (18); however, the link between HDF and RV shape has not been defined until now. During the preparation of this manuscript, a SSM study was published reporting a relationship between global RV vorticity and two subtle shape modes, independent of RF, albeit in a modest rTOF cohort (36). We also analyzed the flow metrics reported in our previous work (not shown here); in the current cohort, vorticity was always associated with RF, whereas we found a modest correlation between diastolic viscous energy loss and shape mode M4, independent of PI. These correlations may be interpreted as a consequence of shape variability, and not as the cause. Nonetheless, future investigation should focus on the relationship between the mechanisms of HDF generation and their relationship with vortex formation, as well as on the direct coupling between HDF and RV myocardial deformation, to further elucidate the mechanobiological mechanisms responsible for the remodeling process. Shape analysis should also be applied to larger rTOF cohorts such as those from the INDICATOR study (2), to investigate shape changes before-and-after PVR, the utility of shape modes to detect clinical dysfunction, and the relationship between shape and exercise capacity.

This study is limited by its relatively small sample size, although in line with (or larger than) previous SSM studies. The shape modeling analysis was only performed for end-diastolic shape as derived from 3-D SSFP imaging; the end-systolic shape could also have been derived from cine imaging, although there would be limitations in 3-D features of the RVOT when compared with 3-D SSFP. End-systolic shape can conceivably be derived from high-quality, ferumoxytol-enhanced 4D flow data, which will be considered for future studies. The computation of HDF may be slightly affected by imperfect definition of the region of interest, although preliminary analyses showed that HDF is relatively robust with respect to small variations of the mask. Finally, this study was of a cross-sectional nature, and as such, caution should be taken when interpreting cause-and-effect relationships between the factors at play. Based on the findings and physics-based reasoning, we conjectured a pathophysiological picture where diastolic hemodynamic forces contribute to drive the remodeling of the RV, which in turn is linked to alterations in myocardial functional parameters. Nonetheless, further longitudinal and biomechanical modeling studies are needed to consolidate and refine these conclusions.

Conclusions

Our findings support the interplay between myocardial shape variations, changes in HDF, functional parameters, and exercise tolerance. RV shape remodeling in patients with rTOF is related to alterations in HDF magnitude and direction, global and regional functional parameters, and decreased exercise tolerance. Identification of patients with rTOF with progression of myocardial shape toward the shape variations described in this study could help identify those at risk for early forms of failure such as exercise intolerance.

DATA AVAILABILITY

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

GRANTS

F. Capuano is a Serra Húnter Fellow. Y.-H. Loke receives partial salary support from National Heart, Lung, and Blood Institute Grants R01 HL143468-01 and R21 HL156045.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

S.K., Y-H.L., and F.C. conceived and designed research; S.K., Y-H.L., and F.C. performed experiments; S.K., Y-H.L., and F.C. analyzed data; S.K., Y-H.L., and F.C. interpreted results of experiments; S.K., Y-H.L., and F.C. prepared figures; S.K., Y-H.L., and F.C. drafted manuscript; S.K., E.B., Y-H.L., and F.C. edited and revised manuscript; S.K., E.B., L.J.O., Y.-H.L., and F.C. approved final version of manuscript.

APPENDIX: METHODS FOR STATISTICAL SHAPE ANALYSIS

The segmented 3-D models of the RV were remeshed using VMTK with an average resolution of ∼0.15 elements/mm², with the twofold aim of having a regular representation of the surface, and of reducing the costly computational effort required by the statistical shape model. It was verified that the remeshing process did not alter any important shape features; the total surface area of the remeshed models varied by less than 1% with respect to the original segmented surfaces.

The average patient shape was selected as the one with the volume closest to the average volume of the cohort; this shape was also selected as the initial reference geometry for the template computation. All the remeshed models were rigidly aligned to this shape using an iterative closest point technique. The template computation was carried out using the deterministic atlas function of the open-source software Deformetrica. This shape analysis software employs a mathematical framework based on a control-point instance of the large deformation diffeomorphic metric mapping (LDDMM). The algorithm simultaneously computes the template as well as the mappings that transform the template into each of the patient’s geometries. The kernel width of the deformation was progressively reduced from 32 mm, in steps of 4 mm. The kernel width controls the length scale of the deformation and the number of control points used to parameterize the mapping; larger widths imply “stiffer” transformations with fewer degrees of freedom, while smaller widths tend to improve the accuracy of the process. The metric employed to monitor the accuracy of the computed mappings was the Hausdorff distance between the reconstructed models (i.e., the models obtained by deforming the template shape) and the corresponding original geometries. This distance was made nondimensional using the average size of each model along the three directions. The refinement process was stopped at a kernel width equal to 24 mm, when the average nondimensional Hausdorff distance fell below 5%. This resulted in 75 control points used to parameterize the mappings.

Based on the computed template, the net deformation vector for each patient p was computed as follows:

$$\overrightarrow{d_{\text{p}}}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\left(\overrightarrow{G_{\text{p}}^i}-\overrightarrow{T^i}\right)$$

where n is the number of points of the reconstructed models (note that n is the same for all the reconstructed models and for the template), $\overrightarrow{G_{\text{p}}^i}$ is the coordinate vector of the ith point of the patient p’s geometry, and $\overrightarrow{T^i}$ is the coordinate vector of the corresponding point of the template. Conceptually, the mean deformation vector provides information about the direction and magnitude of the net remodeling pattern of each patient’s RV with respect to the template shape; it is therefore a simple and immediate measure that allows to correlate the directions of remodeling with the hemodynamic force as well as with other parameters. In this context, it is worth to explicitly notice that the template shape was derived from the rTOF cohort investigated in this work, and thus is itself representative of a diseased shape. The deformation vector lies in the reference frame of the rigidly aligned models; it was subsequently transformed back into each of the patient’s original reference frames, so to decompose it along the three clinically relevant directions defined in materials and methods.

In addition, a principal component analysis (PCA) was carried out to identify the main modes of shape variance in the cohort. To this aim, the momenta vectors that parameterize the LDDMM transformations were rearranged into a deformation matrix X of dimensions $3n_{\text{cp}}\times n_{\text{p}}$, where $n_{\text{cp}}=75$ is the number of control points and $n_{\text{p}}=36$ is the number of patients. The shape modes were then computed as the eigenvectors of the covariance matrix $S=\left(X-\overline{X}\right){\left(X-\overline{X}\right)}^T/n_{\text{p}}$, where $\overline{X}$ is the columnwise mean of $X$. Shape scores, indicating the weight with which each patient’s geometry encodes a certain shape mode, were calculated by projecting the mth mode eigenvector on the deformation matrix.