A Novel Pulmonary Valve Replacement Surgery Strategy Using Contracting Band for Patients With Repaired Tetralogy of Fallot: An MRI-Based Multipatient Modeling Study

Patients with repaired Tetralogy of Fallot (ToF), a congenital heart defect which includes a ventricular septal defect and severe right ventricular outflow obstruction, account for the majority of cases with late-onset right ventricle (RV) failure. Current surgery procedures, including pulmonary valve replacement (PVR) with right ventricle remodeling, yield mixed results. PVR with active band insertion was hypothesized to be of clinical usage on improving RV function measured by ejection fraction (EF). In lieu of risky open-heart surgeries and experiments on animal and human, computational biomechanical models were adapted to study the impact of PVR with five band insertion options. Cardiac magnetic resonance (CMR) images were acquired from seven TOF patients before PVR surgery for model construction. For each patient, five different surgery plans combined with passive and active contraction band with contraction ratio of 20, 15, and 10% were studied. Those five plans include three single-band plans with different band locations; one plan with two bands, and one plan with three bands. Including the seven no-band models, 147 computational bi-ventricle models were constructed to simulate RV cardiac functions and identify optimal band plans. Patient variations with different band plans were investigated. Surgery plan with three active contraction bands and band active contraction ratio of 20% had the best performance on improving RV function. The mean ± SD RV ejection fraction value from the seven patients was 42.90 ± 5.68%, presenting a 4.19% absolute improvement or a 10.82% relative improvement, when compared with the baseline models (38.71 ± 5.73%, p = 0.016). The EF improvements from the seven patients varied from 2.87 to 6.01%. Surgical procedures using active contraction bands have great potential to improve RV function measured by ejection fraction for patients with repaired ToF. It is possible to have higher right ventricle ejection fraction improvement with more bands and higher band active contraction ratio. Our findings with computational models need to be further validated by animal experiments before clinical trial could become possible.

Patients with repaired Tetralogy of Fallot (ToF), a congenital heart defect which includes a ventricular septal defect and severe right ventricular outflow obstruction, account for the majority of cases with late-onset right ventricle (RV) failure. Current surgery procedures, including pulmonary valve replacement (PVR) with right ventricle remodeling, yield mixed results. PVR with active band insertion was hypothesized to be of clinical usage on improving RV function measured by ejection fraction (EF). In lieu of risky open-heart surgeries and experiments on animal and human, computational biomechanical models were adapted to study the impact of PVR with five band insertion options. Cardiac magnetic resonance (CMR) images were acquired from seven TOF patients before PVR surgery for model construction. For each patient, five different surgery plans combined with passive and active contraction band with contraction ratio of 20, 15, and 10% were studied. Those five plans include three single-band plans with different band locations; one plan with two bands, and one plan with three bands. Including the seven no-band models, 147 computational bi-ventricle models were constructed to simulate RV cardiac functions and identify optimal band plans. Patient variations with different band plans were investigated. Surgery plan with three active contraction bands and band active contraction ratio of 20% had the best performance on improving RV function. The mean ± SD RV ejection fraction value from the seven patients was 42.90 ± 5.68%, presenting a 4.19% absolute improvement or a 10.82% relative improvement, when compared with the baseline models (38.71 ± 5.73%, p = 0.016). The EF improvements from the seven patients varied from 2.87 to 6.01%. Surgical procedures using active contraction bands have great potential to improve RV function measured by ejection

INTRODUCTION
Tetralogy of Fallot (TOF) is a common congenital heart disease. The symptoms include ventricular septal defect, pulmonary valve stenosis, aorta overriding, and right ventricular hypertrophy. Corrective surgery allows TOF patients to extend their life expectancy, and some patients manage to survive into adulthood (Murphy et al., 1993). Many repaired TOF survivors are left with some residual symptoms including pulmonary regurgitation causing progressive RV dysfunction and dilation (Geva et al., 2004;Kim and Emily, 2016). Anagnostopoulos et al. (2007) hypothesized that pulmonary valve cusp augmentation with pericardium would decrease pulmonary insufluciency and improve the early outcome for transatrial-transpulmonary TOF repair requiring transannular patch. Their procedure had some success in reducing the incidence of clinically significant postoperative pulmonary insufluciency (Anagnostopoulos et al., 2007). For pulmonary valve (PV) sparing repair procedure which may be associated with residual pulmonary stenosis, Sen et al. (2016) reported that valve-sparing transannular (VSTAR) repair had better short-term and comparable midterm results and may be appropriate for TOF repair in patients with small PV. For repaired TOF patients with pulmonary regurgitation or unsuitable for pulmonary valve sparing procedure, current surgical approach [pulmonary valve replacement (PVR)] yield mixed results with some patients failing to recover their RV function (Geva et al., 2004(Geva et al., , 2010Kim and Emily, 2016). Recent advanced techniques include transcatheter strategies and using tissue-engineered valves (Motta et al., 2017;Jones and Qureshi, 2018). Del Nido and Geva et al. (2004) proposed a RV remodeling surgery by trimming scar tissue on RV wall and replacing the original patch with a smaller one during the PVR. In a clinic trial (NIH 5P50HL074734, Geva, and del Nido), 34 TOF cases were randomly assigned to PVR and RV remodeling surgery as experimental group and other 30 TOF cases underwent PVR alone as control group. Results showed insignificant statistical difference in RV EF variance after the surgery between the two groups (−2 ± 7% vs. −1 ± 7%; p = 0.38) (Geva et al., 2004). In search for innovative PVR surgical procedures to improve postsurgery RV cardiac functions, computational simulations for a PVR procedure with active contracting band insertions were performed using cardiac magnetic resonance (CMR) data from one TOF patient to investigate the effect of band material stiffness variations, band length, and active contraction ratios . The initial modeling results were promising Yang et al., 2013).
Recent development in computational modeling made it possible for patient-specific ventricle models to be used for heart disease study and surgical optimizations. Peskin (1977Peskin ( , 1989) pioneered ventricle models with free moving boundaries and introduced early cardiac simulation models using immersed boundary method. McCulloch et al. (1992) developed a threedimensional finite element method for large elastic deformations of ventricular myocardium, presenting the first practical opportunity to solve large-scale anatomically detailed models for cardiac stress analysis. Kerckhoffs et al. (2007) presented a novel method to couple the finite element cardiac mechanical model into a closed-loop lumped circulation models. Sacks and Chuong (1993) and Billiar and Sacks (2000) used biaxial mechanical test to acquire ventricle anisotropic material properties. Saber et al. (2001) and Axel (2002) proposed early magnetic resonance imaging (MRI)-based ventricle mechanical analysis. Nordsletten et al. (2011) developed a solid/fluid coupled left ventricle model to quantitate blood flow, pressure distributions, and mechanical energy loss caused by viscous dissipation.
Efforts were also made in moving ventricular computational models closer to clinical and surgical applications (Tang et al., 2008Yang et al., 2013;Deng et al., 2018;Yu et al., 2019Yu et al., , 2020. Using CT-based mechanical fluid-solid interaction (FSI) ventricle model, Deng et al. (2018) studied systolic anterior motion of the mitral valve in hypertrophic obstructive cardiomyopathy. Our previous work included using bi-ventricular model to search surgical options, identify possible factors for post-PVR outcome prediction, estimate right ventricle myocardium stiffness, and study the impact of patch size, scar tissue removal, and RV remodeling on right ventricular function (Tang et al., 2008Yang et al., 2013;Yu et al., 2019). Our pilot study using ventricle mechanical model of one TOF patient showed the surgery plan of inserting three bands with band active contraction ratio of 20% could improve RV ejection fraction from 37.38 to 41.58% (Yu et al., 2020).
We hypothesized that PVR with active contracting bands would improve RV cardiac function measured by ejection fraction (EF). RV EF was selected since it is easy to calculate and it is the single most commonly used measure for RV cardiac function in clinical practice. It is sufficient for the RV function assessment of our preliminary study. The normal RV EF range is 47-68% for a healthy male and 50-72% for a healthy female, respectively (Alfakih et al., 2010). In lieu of risky surgery with animals or TOF patients, patient-specific computational ventricle models based on CMR imaging data were used to quantify ventricle motion and evaluate RV ejection fraction before and after the band insert surgery. CMR data from seven repaired TOF patients were used to construct a total of 147 models combining five different band insertion options and four different contraction ratios. Results from these models were analyzed to seek optimized band insertion options with the best post-PVR outcome.

Data Acquisition
Boston Children's Hospital Committee on Clinical Investigation approved this study. The approval number is IRB-CRM09-04-0237. Written informed consent was obtained from participants. CMR data was acquired from seven TOF patients 6 months before and after PVR (four males, average age: 31.81 years). Demographic and ejection fraction (EF) data of the seven TOF patients are given in Table 1. Post-PVR EF data served as a benchmark for us to check if the new surgery strategy with active contracting bands could provide better post-PVR cardiac outcome. CMR image segmentation was performed at Children's Hospital-Boston, Harvard Medical School using a commercial software QMass (Medis Medical Imaging Systems, Leiden, the Netherlands). The locations of patch, scar, and valve were identified based on cine MRI, flow velocity data, and delayed enhancement CMR and with inspections by cardiac surgeon Dr. del Nido (PJdN, over 30 years of experience) who performed the PVR surgeries. Each acquired cardiac cycle data set included 30 discrete time points, and each time point had a 3D CMR image data. End-diastolic volume (EDV) and end-systolic volume (ESV) were computed with Simpson's method. Figure 1 gives two sample CMR image slices at end ejection, their segmented contours, constructed 3D RV/LV model with scar, patch, and myocardium fiber orientation and recorded RV pressure via cardiac catheterization procedures.

Five PVR Surgical Plans With Active Contracting Bands and Band Active Contraction
Five band insertion plans with band location and number variations are proposed to find optimal surgical plan using active contracting bands. An illustration of the five band plans is given by Figure 2. The five band plans included three plans with single band at different band locations, one plan with two bands, and one plan with three bands (Figure 2 and Table 2). The details were introduced in our previous publication (Yu et al., 2020). These five band plans led to 20 models for each patient with one passive band model and three active band models with different contraction ratios. Including the no-band baseline model, 21 models were constructed for each patient. Since we used seven TOF patients, a total of 147 models were included in our paper.
The innovative PVR surgical plan using active contracting band was motivated by the fact that poor RV cardiac function indicated by low EF values were caused partially by RV's weak contraction ability due to RV dilation. The contracting bands were used with the expectation that they would help RV to contract and improve its cardiac function. Passive elastic bands would not help since while they seem to be able to help RV to contract, they would hold the ventricle during its expansion (diastole) and defeat the purpose. Active contracting bands could help the ventricle to contract through active contraction and also allow the ventricle to re-expand through active relaxation. It is commonly known that myocardium active contraction is achieved by sarcomere shortening. However, active relaxation is equally important for the band models to work. Figure 3 gives plots of selected band zero-stress lengths in systole and diastole and band stress/strain curves in a cardiac cycle. When transitioning from diastole to systole (active contraction), the band zero-stress length changes from its diastole zero-stress length to systole zero-stress length (shortening) which results in strain and stress increases. When transitioning from systole to diastole (active relaxation), the band zero-stress length changed from its systole zero-stress length to diastole zero-stress length results in strain and stress decreases. Band material stress-strain curves are given in section "The RV/LV/Patch/Band Model and Material Models for Ventricle, Patch and Band." The RV/LV/Patch/Band Model and Material Models for Ventricle, Patch, and Band The RV/LV/patch/band model includes governing equations, boundary conditions, and material models for ventricle tissue, scar tissue, patch, and bands. The governing equations are the same for all structure components (Tang et al., 2008Yang et al., 2013;Yu et al., 2019): ρv i,tt = σ ij,j , i, j = 1, 2, 3; sum over j.
(1)  (H) Recorded RV pressure profile (Tang et al., 2008Yang et al., 2013;Yu et al., 2019Yu et al., , 2020. RV/LV combined geometry for each patient was obtained from CMR data and reconstructed following established procedures . Patch and scar locations were determined by our cardiac surgeon (PJ del Nido) and radiologist (T. Geva). No-slip conditions and natural boundary conditions were imposed automatically by ADINA (ADINA R&D, Watertown, MA, United States) at all interfaces of different structure components (ventricle, band, scar, and patch). RV and Combination of plan C and D Plan A models are models with a band at anterior to the middle of PM. They are named as AXXX, where A is short for anterior, and XXX represents band active contraction ratio, for example, 010 = 10%. Plan B models are models with a band at posterior to the middle of PM. They are named PXXX, where P is short for posterior. Plan D models has a band at the base of PM. They are called BXXX, where B is short for base. For multiband plans, plan C models are named as APXXX since plan C is the combination of A and B; and Plan E is named as APBXXX because plan E is the combination of A, P, and B. PM, papillary muscle.
LV inner-pressure conditions were prescribed as (Tang et al., 2008Yang et al., 2013;Yu et al., 2019Yu et al., , 2020: where p RV and p LV were blood pressure conditions specified on RV and LV inner surfaces. Pressure on the RV/LV outsurface was set to be zero. Patch, scar, and band materials were assumed to be hyper-elastic, isotropic, nearly incompressible, and homogeneous. The isotropic Mooney-Rivlin strain energy function is given by (Tang et al., 2008Yang et al., 2013;Yu et al., 2019Yu et al., , 2020, where c 1 , c 2 , D 1 , and D 2 are material constants and I 1 and I 2 are the first and second invariants of Cauchy-Green strain, where C ij is the Cauchy-Green deformation tensor. Ventricle tissue material was assumed to be hyper-elastic, anisotropic, nearly incompressible, and homogeneous. The non-linear anisotropic modified Mooney-Rivlin model was obtained by adding an additional anisotropic term in Eq. (4) : where I 4 = C ij (n f ) i (n f ) j , n f is the fiber direction, and K 1 and K 2 are material constants. With parameters chosen properly, the modified Mooney-Rivlin model described in Eq. (6) could fit the directly measured myocardium stress-strain data from our biaxial test experiment Yu et al., 2019Yu et al., , 2020. In our models, patent-specific ventricle material parameter values were selected to match CMR-measured volume data. A two-layer construction process was used to make our RV/LV models to take myocardium fiber orientations into consideration (see Figure 1D). Patient-specific fiber orientation data was not available for our study. Fiber orientation data from available literature were used in our models (Sanchez-Quintana et al., 1996;Nash and Hunter, 2000;Hunter et al., 2003). Fiber orientations were specified for every element on the inner and outer layers of our models. For left ventricle, the fiber orientation was approximately −60 • (relative to circumferential direction) at the outer layer and +80 • at the inner layer. RV fiber orientation was −45 • at the outer layer and +40 • at the inner layer (see Figure 1).

Preshrink Process to Obtain Ventricle Zero-Load Geometries and Patient-Specific Ventricle Material Parameter Quantification
Patient ventricle CMR images were obtained under in vivo conditions. Zero-load ventricular geometries were not available from in vivo CMR images and were obtained using a preshrink iterative process. In our modeling process, the approximate zero-load geometries were obtained by shrinking segmented contours on each slice (short-axis direction) with a short-axis shrinking rate and reducing distance between each slice (longaxis direction) with a long-axis shrinking rate (3%). The shrink ratio for inner contours was 2-3% based on the RV endsystole volume (minimum volume in a cardiac cycle) and the corresponding RV pressure. The outer contours shrink ratio was determined to meet the conservation of mass of the total ventricular wall. Figure 4 gives an illustration of the preshrink process. Three material parameter values c 1 , d 1 , and K 1 in Eqs.
(4)-(7) were adjusted iteratively until the relative error between the pressurized computational RV volume and CMR-measured in vivo volume data was less than 0.2%. This process was done semiautomatically using a secant method for fast convergence to in vivo RV volume. Figure 5 shows stress-stretch relations of patient 5 RV tissue, patch, scar, and band at begin filling and begin ejection, respectively. The corresponding material parameter values for those material models are shown in Table 3. For our seven no-band baseline models, the mean ± SD RV volume was 226.84 ± 121.20 ml at begin filling (same as endsystole volume ESV) and 359.19 ± 158.41 ml at begin ejection (same as end-diastole volume EDV), in agreement with the CMR data: 225.84 ± 120.13 ml at begin filling (p = 0.313) and 359.53 ± 158.61 ml at begin ejection (p = 0.438). Details were described in Tang et al. (2013Tang et al. ( , 2008, Yang et al. (2013), and Yu et al. (2019Yu et al. ( , 2020.

Solution Methods, Data Extraction, and Statistical Analysis
The 147 models were constructed and solved with ADINA using unstructured finite elements and the Newton-Raphson iteration method (Tang et al., 2008Yang et al., 2013;Yu et al., 2019;Yu et al., 2020). Simulations were performed for several cardiac cycles until the solution relative differences between the last two cycles in L 2 norm were less than 0.1%. The L 2 norm of a given function F was computed with: where T is the period (one cardiac cycle), F will be | S(t)−S(t+T)| as the function difference over one period where S(t) stands for either stress-P 1 (maximum principal stress) or strain-P 1 (maximum principal strain), the integration is taken over the  entire RV domain and one cardiac cycle with discretization performed utilizing all available nodes and time steps. The results from the last period were recorded for analysis. For all 147 simulations, only three cycles were needed to obtain the solution. For each model, stress and strain data from 100 evenly spaced points for each slice of RV inner surface were extracted. Maximum principal stress and strain values were chosen to represent the stress and strain state of these points, and their mean values at begin filling (BF) and begin ejection (BE) were recorded as the stress and strain value of this model. RV Ejection fraction was used as the index (marker) for evaluating ventricle cardiac function. RV ejection fraction (EF) is defined as: where RV EDV is right ventricle end-diastole volume and RV ESV is right ventricle end-systole volume. Higher EF value indicates that the ventricle is more efficient in pumping blood. Difference between pre-and post-PVR EF denoted by EF was used to measure PVR (with and without active contracting bands) improvement: Preoperation (no-band) RV/LV models were regarded as the baseline model. The paired test Wilcoxon signed rank test was used to compare the differences of EF, stress, and strain values between band and baseline models and the differences between different surgery plans. The test was performed using the function: p = signrank(a,b) from MATLAB statistical tool box.

Three-Band Surgical Option Had Best Improvement for RV Ejection Fraction
Simulation results from the seven patients using five band options with band contraction ratio of 20% are given in Table 4. Surgery plan with three active bands (plan E) had the best RV EF improvement among the five band plans. The mean ± SD RV ejection fraction value from the seven patients with plan E was 42.90 ± 5.68%, representing a 4.19% absolute improvement or 10.82% relative improvement over the mean value of the baseline no-band models (38.71 ± 5.73%, p = 0.016). Absolute EF improvements for each patient varied from 2.87 to 6%. Mean ± SD EF values of the seven patients for band options A-D were 2.51 ± 0.80%, 2.13 ± 0.53%, 3.36 ± 1.07%, 1.90 ± 0.40%, respectively. The two-band plan (option C) had the second best performance. Similar results were also found when the band active contraction ratio was 15 or 10%, respectively.

Higher Band Contraction Ratio Had
Better RV EF Improvement Table 5 summarizes results from the seven patients using band option E (three-band model) with 0, 10, 15, and 20% band contraction ratios and their EF differences compared with the no-band baseline model. The models with 0% contraction ratio corresponded to models with passive bands. Mean ± SD EF values of the seven patients for 10 and 15% band contraction ratio were 3.19 ± 1.00 and 2.27 ± 0.89%, respectively. Considering the results given in section "Three-Band Surgical Option had Best Improvement for RV Ejection Fraction": mean ± SD EF of seven patients for 20% band contraction ratio were 4.19 ± 1.11%, models with 20% band contraction ratio had higher EF and EF values than that with 15 and 10% band contraction ratios. Higher band contraction ratio improved RV EF more.
Intuitively, it might be reasonable to expect that a passive elastic band may be able to improve ejection fraction since elastic bands would help the ventricle to contract. Our simulations indicated that that was not the case. Mean EF of models with surgery option E and passive bands was −3.27%, and EF values ranged from −5.67 to −1.93%. For surgery option A-D, mean ± SD EF were −1.37 ± 0.50, −1.04 ± 0.44, −2.32 ± 0.85, and −1.23 ± 0.79%, respectively. RV EF decreased after passive bands were inserted. The reason is actually simple: passive elastic bands would not "relax" by themselves after they contracted. The bands would actually hold the ventricle and became resistance for ventricle expansion. Mean ± SD volume values of surgery options A-D with passive bands at begin ejection were 349.76 ± 158.75, 352.08 ± 157.36, 344.56 ± 157.62, 350.83 ± 157.53, and 339.24 ± 157.82 ml, respectively, whereas the baseline model was 359.19 ± 158.41 ml. On the other hand, active bands help ventricle to contract by active contraction and would not resist ventricle expansion since active bands would "relax" through active relaxation ( Table 6).

Stress/Strain Patterns Were Complex in Right Ventricle
Figures 6, 7 provides begin-ejection (maximum pressure) and begin-filling (minimum pressure) stress and strain plots on RV inner surface from four band models of patient 5. Stress and strain distributions have complex patterns. Band insertion changed local stress and strain distributions. Figures 6, 7 show that stress and strain values of RV tissues near band insert locations increased, whereas stress and strain relatively away from band decreased. Mean stress and strain values are given in Tables 2, 4  It should be noted that mean stress/strain values (average of seven patients) had very small variations for all five band options. At begin ejection, stress and strain values from models with active band were close to the baseline. RV mean ± SD strain values of options A-E with 20% band contraction ratio were 0.297 ± 0.067, 0.296 ± 0.067, 0.298 ± 0.066, 0.298 ± 0.066, and 0.304 ± 0.067, which were also close to mean ± SD stress value of baseline models: 0.292 ± 0.062. Table 5 comparing stress/strain values from models with different band contraction ratios. At begin ejection, average stress and strain values (seven patients) from models with 10% band contraction ratio were 16 and 5.6% higher than that from the passive band models. Average stress and strain values from models with 10, 15, and 20% band contraction ratios showed practically no differences (difference <2%).

Motivation of the Innovative PVR With Active Contracting Band Insertion Procedures
How to manage the residual symptoms for repaired ToF cases such as pulmonary regurgitation has gradually become a great challenge for clinicians. Even though PVR could be an effective treatment for pulmonary regurgitation, other symptoms such as 6 | Mean ± SD RV ejection fraction and wall stress/strain data of seven TOF patients from 140 RV/LV models with active or passive band(s) and seven models without band.

Plan
Begin RV dysfunction may sometimes be irreversible after the PVR surgery (Geva et al., 2004(Geva et al., , 2010Kim and Emily, 2016). del Nido and Geva et al. (2010) proposed an aggressive surgical treatment including removing scar tissue and remodeling RV in order to improve RV function after PVR. However, the randomized clinical trial showed that the addition of surgical remodeling of the RV during PVR resulted in no measurable improvement in RV function (Geva et al., 2010). PVR with active contracting band insertion aims to improve RV EF by assisting the ventricle to contract. In theory, the band should actively contract during systole, decreasing RV volume, and yet, the band should also be able to relax during diastole. These processes were reflected in our models: the mean ± SD RV volume values of models E020 at end ejection/begin filling were 211.73 ± 115.66 ml, which was lower than that of baseline models (226.84 ± 121.20 ml, p = 0.016). At end filling/begin ejection, no significant difference was found between E020 and baseline RV volume values (358.53 ± 158.63 ml vs. 359.19 ± 158.41 ml, p = 0.813) since the active bands were able to relax and did not resist the ventricle to expand in diastole phase (filling phase). Compared with our previous work on band insert surgery simulation, 147 models were constructed for seven patients with repaired TOF in this paper, vs. only one patient was used in previous paper (Yu et al., 2020). The purpose of this study was to demonstrate patient variations in post-PVR outcome using the proposed active contraction band options. Results from this seven-patient study were consistent with previous findings: RV ejection fraction values of all seven patients increased after the surgery with active contraction band insertion. The mean ± SD RV EF value from the seven patients with plan E was 4.19 ± 1.11%, which is a significant improvement. Meanwhile, among all seven studied TOF patients, only two of them had increased EF values after pulmonary valve surgery (P1 and P6). The clinical mean ± SD EF was -4.97 ± 7.44% based on actual patient pre-and post-PVR data. This is the proof of the concept that PVR with active contraction band insertion may have the potential to improve post-PVR RV cardiac function measured by ejection fraction for repaired ToF patients.

Availability of Active Contracting Band
The idea of active band is completely theoretical currently. Our simulation provided the possible outcome of the surgery if such active contraction band could be made available. There are potential techniques that could be applied to manufacture active contracting band in the future including (a) using stem cells to cultivate muscle or (b) artificial mechanical muscle (Chou and Hannaford, 1996;Baar et al., 2005;Proulx et al., 2011;Sugimoto et al., 2017;Thomalla and Van deVen, 2018). Baar et al. (2005) used neonatal rat cardiomyogenic cells to construct a cylinder formed by cardiomyocytes which could be electrically induced to contract and showed positive inotropy and chronotropy (Baar et al., 2005). Proulx et al. (2011)   surrounded by non-extensible threads weaved into an external mesh shell (Chou and Hannaford, 1996;Sugimoto et al., 2017;Thomalla and Van deVen, 2018). Such actuators were already widely used in robot technology. Takuma et al. designed a robot with McKibben actuators which could operate periodic motions including walking (Sugimoto et al., 2017). Maximum active contraction ratio of McKibben actuator could reach about 30% (Chou and Hannaford, 1996;Thomalla and Van deVen, 2018), which would be enough to meet the contracting requirement of our active contraction band used in PVR surgeries.

Use of Ejection Fraction as a Measure of Surgical Outcome
RV EF was used as the measure of RV function in this paper because it is commonly used in practice and by many investigators, and it serves our demonstration purpose well. The concept is simple and calculation is easy. Outcome comparisons of different band options using a single indicator (EF) are straightforward and easy to understand. However, since it is only one number, it is lacking detailed local information for more careful evaluation of RV functions. 3D stress/strain distributions could compensate RV EV when detailed analysis is desired. RV kinetic energy due to its deformation in systole can be calculated as needed for a more detailed analysis. Since we currently have structure-only models, we would not be able to calculate the energy from the flow side and perform the analysis for that part. We are currently working on the corresponding fluid-structure interaction models. Full analysis from both structure and flow side will be reported when results become available. Those details will be helpful in band design and development of related tissue regeneration techniques .
It is true that EF is a crude measure of ventricular function (LV and RV), does not reliably reflect the functional status of the myocardium, and is sensitive to preload and afterload (so-called loading conditions). Despite these well-known limitations, EF has remained n inexplicably strong predictor of clinical outcomes in numerous diseases that affect the RV (e.g., repaired TOF) and the LV (e.g., aortic stenosis, hypertension, ischemic heart disease). These observation have been confirmed by numerous large studies. However, why EF is such a strong predictor of clinical outcomes is not fully understood. So, if the goal is to detect subtle abnormalities of heart muscle function, there are more sensitive tools. If the goal is to use it as a predictor of clinical outcomes (which is what ultimately matters), EF is an excellent marker.

Validations
Validation is always ideal for computational modeling effort. It should be noted that the parameter determination process is a self-validation process in some sense. Our pre-PVR models were self-validated since patient-specific tissue material parameter values were carefully adjusted to match MRI-measured ventricle volume data. Since the ventricles remained to be the same post-PVR, using the same parameter values was natural for our post-PVR band models. Without actual clinical post-PVR data, using pre-PVR material properties gave us the best-effort approximations for our band models. Accuracies of simulation results including calculation of ventricle volumes and ejection fractions should be interpreted with that understanding.
Since materials with active-contraction properties are not currently available, direct validations using either patients or animal models are not possible at present time. Researchers have been working on myocardium regeneration for many years and encouraging progresses have been made. Clinical application of the active contraction band is what we would like to achieve in the future.

Potential Clinical Applications
Possible potential clinical implementation of PVR with active contracting bands primarily depends on the availability of the availability of the active contracting bands. This modeling study is the proof of the concept that PVR with active contraction band insertion may improve post-PVR RV cardiac function measured by ejection fraction for repaired ToF patients. The mean ± SD RV EF value from the seven patients with plan E was 4.19 ± 1.11% (all patients had improved EF), which is a significant improvement over the actual PVR surgery data EF = −4.97 ± 7.44%. Meanwhile, among all seven studied TOF patients, only two of them had improved EF values after PVR (P1 and P6). A 9.16% average increase in RVEF compares favorably with published drug trials to treat heart failure where an improvement in LVEF of 3-4% resulted in a significant improvement in functional capacity (Aleksova et al., 2012).

Limitations
This paper used structure-only models to save model construction manpower and computing time (147 3D models). Fluid-structure interaction did not include algorithm that allows a more realistic simulation. Clearly, FSI models will provide a more complete structural and flow information. However, for our purpose, EF was used to measure surgical outcome for the surgical strategies under investigation. The model parameters in both structure-only and FSI will be adjusted to match MRImeasured ventricle volume data. Therefore, structure-only or FSI models will give the same EF. Another reason that structure-only model could be used as a good approximation to calculate EF is that ventricle volume is mainly determined by the flow pressure acting on the ventricle inner surface. The flow stress activating on ventricle inner surface could be decomposed into pressure (normal component) and flow shear stress (shear component). The magnitude of flow shear stress is nearly negligible compared with pressure. That was the reason we used structure-only models to save time. FSI models will take far more time to construct and will be needed when we investigate flow behaviors, valve functions, ventricle remodeling, etc.
Lack of validation is definitely a limitation. This was discussed in section "Use of Ejection Fraction as a Measure of Surgical Outcome." Several other limitations exist in our modeling study: (a) patient-specific TOF RV/LV myofibril orientations should be included if available in the future; (b) localized tissue material properties were not available; and (c) flow behaviors and valve dynamics were not included in this study. We are working hard to obtain better ventricle data and improve our models.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

ETHICS STATEMENT
The studies involving human participants were reviewed and approved by the Boston Children's Hospital Committee on Clinical Investigation. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

AUTHOR CONTRIBUTIONS
TG, RR, and PN collected the CMR and blood pressure data. KB did the biaxial test. HY, CY, XH, ZW, and DT did model construction. HY did statistical analysis. HY and DT wrote and revised the manuscript. All authors contributed to the article and approved the submitted version.