Pre‐intervention myocardial stress is a good predictor of aortic valvoluplasty outcome for fetal critical aortic stenosis and evolving HLHS

Fetal critical aortic stenosis with evolving hypoplastic left heart syndrome (CAS‐eHLHS) causes biomechanical and functional aberrations, leading to a high risk of progression to hypoplastic left heart syndrome (HLHS) at birth. Fetal aortic valvuloplasty (FAV) can resolve outflow obstruction and may reduce progression risk. However, it is currently difficult to accurately predict which patients will respond to the intervention and become functionally biventricular (BV) at birth, as opposed to becoming functionally univentricular (UV). This prediction is important for patient selection, parental counselling, and surgical planning. Therefore, we investigated whether biomechanics parameters from pre‐FAV image‐based computations could robustly distinguish between CAS‐eHLHS cases with BV or UV outcomes in a retrospective cohort. To do so we performed image‐based finite element biomechanics modelling of nine CAS‐eHLHS cases undergoing intervention and six healthy fetal control hearts, and found that a biomechanical parameter, peak systolic myofibre stress, showed a uniquely large difference between BV and UV cases, which had a larger magnitude effect than echocardiography parameters. A simplified equation was derived for quick and easy estimation of myofibre stress from echo measurements via principal component analysis. When tested on a retrospective cohort of 37 CAS‐eHLHS cases, the parameter outperformed other parameters in predicting UV versus BV outcomes, and thus has a high potential of improving outcome predictions, if incorporated into patient selection procedures. Physiologically, high myocardial stresses likely indicate a healthier myocardium that can withstand high stresses and resist pathological remodelling, which can explain why it is a good predictor of BV outcomes.


Introduction
In selected fetal hearts with critical aortic stenosis (CAS), natural history studies have shown there to be a 73% likelihood of progression to hypoplastic left heart 0 Laura Green is currently pursuing a PhD at Imperial College London within the Cardiovascular Biomechanics and Ultrasound Laboratory, under the guidance of Dr Choon Hwai Yap.Her research is dedicated to advancing understanding of fetal left ventricular biomechanics, with a particular focus on investigating the impact critical aortic stenosis with evolving hypoplastic left heart syndrome has on fetal cardiac functionality, both before and after fetal aortic valvuloplasty intervention.
syndrome (HLHS) by the time of birth, and for this reason, was named CAS with evolving HLHS (CAS-eHLHS) (Gardiner et al., 2016;Mäkikallio et al., 2006).Progression to HLHS was especially likely for cases with retrograde transverse aortic arch flow, left-to-right flow across the foramen ovale, and monophasic mitral inflow.The aortic obstruction in these cases leads to high left ventricular (LV) pressure, globular LV shapes, hypertrophy of LV walls, diminished LV contractile deformation, high aortic valve (AV) velocity, endocardial fibroelastosis and mitral valve regurgitation (MVr), which also causes high left atrial (LA) pressure and LA distension (Tulzer & Arzt, 2013).These abnormalities are likely detrimental to the growth of the LV and cause of subsequent hypoplastic development, which leads to a univentricular (UV) outcome.
In such cases, fetal aortic valvuloplasty (FAV) was found to be promising, by reducing the risk of progression to HLHS (Friedman et al., 2018;Gardiner et al., 2016;Mäkikallio et al., 2006;Tulzer, Arzt, Gitter et al., 2022).FAV is a catheter-based intervention which widens the aortic obstruction to improve several of the above abnormal features, which will likely restore LV growth to prevent a UV outcome.A recent cost-benefit analysis showed that FAV confers a modest medium-term (age 6) survival benefit from 72% to 82% (Pickard et al., 2020).However, high volume institutions have shown FAV to carry with it a 4-8% chance of fetal demise (Pickard et al., 2020;Tulzer, Arzt, Scharnreitner et al., 2022).
Current patient selection criteria for FAV includes the presence of LV systolic and diastolic dysfunction, retrograde bidirectional transverse aortic arch flow, a LV long axis Z score< −2, dilated LV, left-to-right shunting through the foramen ovale and MVr or aortic stenosis gradient >20 mmHg (Friedman et al., 2018;Tulzer & Arzt, 2013).However, a substantial proportion of fetuses selected for FAV did not avoid progression to a UV outcome, even with a successful intervention, suggesting a current inability to accurately predict outcomes, and that current selection criteria for the intervention can be refined to more accurately identify patients that will benefit from the intervention.More accurate prediction can better inform decisions on whether to proceed with the intervention, given that there are significant procedural risks to fetuses.It may also lead to the identification of cases that are likely to respond to the intervention, but that are outside of the current selection criteria.For this reason, there has been continued investigation into biomarkers that are indicative of outcomes (Beattie et al., 2020;Friedman et al., 2018;Prosnitz et al., 2018;Tulzer, Arzt, Gitter et al., 2022).
Biomechanics evaluation of the CAS-eHLHS fetal heart, or the investigation of its force dynamics in relation to its motion and deformation, is important.The CAS-eHLHS heart has drastically different biomechanical characteristics from the healthy heart, the FAV intervention is essentially a mechanical intervention in nature, and the heart is likely to be mechanosensitive in its growth, where abnormal biomechanics may play a significant role in the progression to malformation.Cardiac finite element (FE) computational modelling is a good approach for investigating myocardial biomechanics and has been very useful in improving our understanding of a multitude of heart diseases in the past (Dewan et al., 2017;Ong et al., 2020;Shavik et al., 2021;Wisneski et al., 2020).For example, we have previously used such a model to elucidate the effects of how various CAS-eHLHS characteristics impact cardiac function and biomechanics (Ong et al., 2020).Further, a previous FE model coupled with a myocardial growth mathematical model showed that reduced strain stimuli can potentially explain the gestational development of some HLHS cases (Dewan et al., 2017).FE modelling performs an assessment of the physics of the heart's function and can provide biomechanics parameters that are difficult to directly obtain from clinical measurements, such as myocardial stresses and the extent of active tension generation, which may be useful for predicting outcomes.
Here, we performed image-based, patient-specific FE modelling of CAS-eHLHS and healthy hearts to elucidate the biomechanical characteristics of the disease.We hypothesize that the biomechanics parameter of myocardial stress, obtained at a pre-interventional stage for CAS-eHLHS cases undergoing FAV, may show a better association with UV or BV outcomes compared with clinical measurements, and thus has the potential to be a better predictive biomarker.

Ethical approval
Nine CAS-eHLHS datasets and one healthy dataset were obtained with informed consent in writing from the Kepler University Hospital, Austria, under Institutional Review Board protocol 1009/2017.The remaining healthy datasets were obtained, also with written informed consent, from National University Hospital Singapore under Domain Specific Review Board protocol 2014/00056.The studies conform to the latest revision of the Declaration of Helsinki, except for registration in a database.

Image acquisition
4D echocardiography images of nine fetal hearts with CAS-eHLHS undergoing FAV and six healthy hearts were acquired using the GE Voluson E10 (GE Healthcare, Chicago, IL, USA) ultrasound machine.Images were taken in the spatio-temporal image correlation mode, using the standard settings of sweeps of 10-15 s and capture rate of 70-90 frames per second.Of the nine CAS-eHLHS cases, five went on to achieve a functionally BV heart at birth, four went on to be functionally UV at birth.

L. Green and others
Y -yes, N -no, Dil -balloon dilatation of the AV, RK -Ross-Kono procedure, NW -Norwood Procedure, Conv -BV to UV conversion.N/A -no procedure as parents chose comfort care at an alternative centre; procedure planned for this patient was Ross-Konno surgery, with patient believed to progress to a BV outcome classification, therefore, for the purpose of this study the patient was classified as BV.
2D echocardiography and Doppler measurements for a further 28 CAS-eHLHS fetuses undergoing intervention, acquired with the Vivid E95, were also obtained from Linz Hospital, Austria, and were further used together with the first nine CAS-eHLHS cases for analysis on the predictive capabilities of various parameters.Since the original nine CAS-eHLHS cases were used to develop the empirical equation without referencing their BV versus UV outcomes, they were still eligible for use when testing for how well parameters can predict outcomes.

Patient characteristics
Healthy control cases were from ages of 21 + 2 weeks + days to 32 + 0 weeks + days gestation.At the time of study all CAS-eHLHS patients that had complete datasets with clear 4D volume images were used.The CAS-eHLHS patients were selected for FAV intervention at Linz Hospital, Austria, if they exhibited the following characteristics: dilated and poorly contracting LV, left-to-right shunting at atrial level, retrograde aortic arch flow, LV length Z score >0 or right ventricular (RV)/LV ratio >1.1 and no signs of AV atresia.The CAS-eHLHS patients ranged from 22 + 4 weeks + days to 32 + 0 weeks + days gestation.Age-matched healthy control cases for CAS-eHLHS patients were not available, so a range of healthy cases were selected that encapsulated the age range of CAS-eHLHS patients.
Characteristics of patients included in the study are given in Table 1, including age, disease features and postnatal outcomes and postnatal procedures.Throughout the study, the disease cases with a BV birth outcome were denoted by 'BV' in front of the ID number, while those with a UV outcome were denoted by 'UV' in front of the ID number.Healthy cases were denoted by an 'H' in front of the ID number.A BV circulation postnatal outcome was defined when the LV was the only source of systemic circulation and where there was an absence of pulmonary hypertension at 1 year of age.Diseased cases outside of this definition were designated to be a UV outcome.Analyses were performed to determine which pre-interventional features correlated with outcomes and have a potential to be used for outcome predictions.Postnatal procedures for cases with BV outcomes included AV dilatation or the Ross-Kono procedure, while that for cases with UV outcomes included the Norwood procedure or a Ross-Kono with subsequent BV-UV conversion.

Image processing of fetal echocardiography
From the fetal echo images, morphometric measurements of the heart chambers, including LV and RV longitudinal length, posterior wall thickness (PWT), LV inner diameter at diastole (LVID), and relative wall thickness (RWT) were performed in accordance with previous approaches (Tulzer, Arzt, Gitter et al., 2022), by two independent observers, repeated twice per person, and averaged.RWT is calculated as: and aspect ratio was calculated as: Patient-specific reconstructions of 3D computational models of fetal hearts were obtained using methods previously described (Ong et al., 2020).In brief, stacked 2D images were extracted from the 4D scans, at 0.5 mm intervals, at a specific time point.A Lazy Snap algorithm (Li et al., 2004) was then used to trace the endocardial and epicardial boundaries and the traced slices were reconstructed using a Vascular Modelling Toolkit.Any irregularities in the reconstructed geometry were smoothed in Geomagic (Geomagic Inc., Morrisville, USA). Figure 1 depicts all patient-specific geometries modelled in this study.
A validated cardiac motion estimation algorithm (Wiputra et al., 2020) was then used to extract cardiac motions, which was used to animate the heart chambers over the cardiac cycle and obtain reconstructions and chamber volumes, for all other time points (Fig. 2).Briefly, the cardiac motion was modelled as a cyclic and spatially consistent b-spline of Fourier whole-field motion model and was curve-fitted to the displacement fields from pair-wise image registration of images from all consecutive time frames (Wiputra et al., 2020).Using the estimated cardiac motion, the reconstructed LV geometry at end-diastolic volume (EDV) was animated over the cardiac cycle.For CAS-eHLHS diseased LVs, motion was diminished, and therefore this process was sufficient when extracting accurate motions from images.For healthy LVs, greater cardiac motions and deformations occurred, and reconstruction at end systole was needed to enhance motion estimation, by including the registration results of the end-diastole to end-systole time points to the curve fitting, as previously described (Wiputra et al., 2020).
LV myocardial engineering strains (eqn 3) were computed from the images in both the longitudinal and circumferential directions along a mid-wall line, identified by averaging the epicardial and endocardial boundaries, from the 4-chamber or transverse echo view, using previously documented techniques (Ren et al., 2023).The mid-wall line was discretized into 100 elements, its motion was tracked, and changes in lengths of elements from end diastole to end systole were computed and spatially averaged, The engineering strains measured will be reported as circumferential and longitudinal strains throughout the remainder of the study.

Computational modelling methods
Image-based, patient-specific FE modelling of fetal LV myocardial biomechanics was performed in accordance with our previous methodologies (Green et al., 2022;Ong et al., 2020).The FE model was connected to a lumped parameter model to enable ventricular-vascular coupling.
LV myocardium models reconstructed from echo images were used for FE modelling and were meshed L. Green and others J Physiol 602.4 into a minimum of 2500 quadratic tetrahedral elements (Fig. 3A), which was sufficient for mesh convergence as shown in our previous study (Ong et al., 2020).A transversely isotropic Fung-type passive stiffness model informed by experimental measurements (Guccione et al., 1991), and the Guccione model of active tension generation (Guccione et al., 1993) were adopted for the model.
The Fung-type transversely isotropic passive stiffness model (Guccione et al., 1991), is described by the following strain energy function (W): where C is the passive stiffness coefficient, E was the Green-Lagrange Strain, with subscripts f, s and n denoting the fibre, sheet and sheet-normal directions, respectively, and b is the stiffness exponent in specific directions specified by its subscript.Stiffness parameters described in Guccione et al.'s study was simply adopted (Guccione et al., 1991), parameter values are disclosed in Table 2.
Stiffness parameters were assumed to be the same across all our cases, as case-specific recovery of individualized stiffness parameters was not possible.Our previous studies demonstrated that minor scaling of the material stiffness parameters does not significantly affect the biomechanics and function of the heart, since stiffness was typically an order of magnitude smaller than the active tension generated by the heart (Ong et al., 2020).
Active tension (P act ) generation of myocardium was modelled using Guccione et al.'s calcium activation model (Guccione et al., 1993), where P act is expressed as: where T 0,LV describes the maximum fibre tension, which is a representation of the overall contractility and was back-computed in the patient-specific modelling protocol.
The value of Ca 0 is described in Table 2 and ECa 2 50 and the sarcomere length dependent calcium sensitivity (ECa 50 ) are calculated as follows: where B is a constant, which described the shape of peak isometric tension-sarcomere length relation, l is sarcomere length and l 0 is the sarcomere length at no tension generation.C t in eqn 5 is the temporal variation of the calcium activation model: where ω was dependent on the cycle time, with the variation: where t 0 was the time to peak tension, calculated using the model-specific cardiac cycle length and Mulieri et al.'s measured relationship between cardiac cycle and time to peak tension (Mulieri et al., 1992).t r was the relaxation time and was calculated using the following equation: where m is the gradient of linear relaxation duration and b is the time intercept of linear relaxation duration, dependent on the degree of myocyte stretch.For all models, the myocardium helix angle (HA) was assumed to vary linearly from the epicardium to endocardium, from −52°to +71°, respectively (example in Fig. 3B), which was the average HA configuration reported in three previous fetal LV tissue studies (Garcia-Canadilla et al., 2018;Nishitani et al., 2020;Ohayon et al., 1999).Before computations, the unloaded state of the LV, or  the theoretical geometry of the heart at zero LV cavity pressure, was calculated and assumed to be the stress-free condition.This was achieved via Finsberg et al.'s backward displacement method (Finsberg et al., 2018): the pressure loading from the load-free state to the end-diastolic state was iteratively simulated until the targeted end-diastolic pressure and volume was achieved, and at every iteration, the load-free state was adjusted by changing the pressure for an inverse of the loading deformation.The targeted end-diastolic pressure was set as 5 mmHg for healthy hearts (Johnson et al., 2000), but this was adjusted incrementally upwards in 1 mmHg intervals if negative pressures were encountered during early diastole.For diseased cases, end-diastolic pressure was assigned by the end-diastolic LA pressure, obtained by assuming a linear relationship between LA size and pressure (LA compliance) (Matsuda et al., 1990).This models the abnormal LA pressurization in diseased cases.The formal FE simulation was performed by minimizing the weak formulation of Lagrangian functions described by Shavik et al. (2018), which enforces tissue stress equilibrium, incompressibility, and a specific cavity volume to yield cavity pressure, using the Newton Solver in the FEniCS software.The boundary conditions were like those previously reported (Shavik et al., 2018), with the basal plane of the LV constrained in the longitudinal direction and a weak 90 Pa spring applied to the entire epicardium at the load-free state, to simulate interactions with surrounding tissues and to constrain translational motion of the model.
A lumped parameter model (Fig. 3C) was used for 0D modelling of fetal circulation and was coupled to the LV FE model.The lumped parameter model was based on Pennati et al.'s work (Pennati et al., 1997;Pennati. & Fumero., 2000), but underwent minor recalibration to more recent measurements of human fetal intracardiac pressure (Johnson et al., 2000), and descending aorta pulse pressure (Versmold et al., 1981), as explained in our previous modelling study (Green et al., 2022), where all model parameters are given.The model is scalable to a range of gestational ages, through a series of allometric equations.The model was executed for 30 cycles, to ensure steady state was achieved.

Tuning model for patient-specific match
The lumped parameter coupled FE modelling was iteratively performed by altering valve flow dissipative coefficients and myocardial contractility, to best match each computational model with clinical measurements.Through this matching process, the patient specificity of the model could be maintained, and the biomechanics parameters could be back-computed.
For healthy fetal hearts, the lumped parameter model was first scaled to the specific gestational age.Iterative FE and lumped parameter simulations were then performed while varying myocardial contractility (T 0,LV in eqn 5), until the simulated stroke volume (SV) matched that measured from the image, thus back-computing the contractility.60 kPa was used as the initial guess of active tension magnitude, based on the upper limit of experimental measurements of 49.9 ± 9.3 kPa of fetal myocardium at 18+4 weeks + days gestation (Racca et al., 2016).
For CAS-eHLHS hearts, the lumped parameter model was again scaled to the specific gestational age.The patient-specific matching process, however, was more extensively performed.First, iterative simulations were performed while varying flow dissipative coefficients of the AV, mitral valve (MV) inflow and MVr, until simulations matched the expected valvular pressure gradients, which were calculated from each patient's clinical valvular Doppler velocities, using the simplified Bernoulli's equation.Next, iterative simulations were performed while adjusting myocardial contractility, until the simulated SV matched that measured from images.A loop over the two types of iterative simulations was performed, until both valvular pressure gradients and SV matched measurements from echo images.This thus allowed the back-computation of myocardial contractility.
A simple gradient descent algorithm was used to reach convergence for all iterative simulations, and parameter matches were optimized to minimize errors as much as possible, to less than 10% error.Where a satisfactory match could not be obtained, the age scaling of the lumped parameter was adjusted and the optimization process was repeated, until a match could be achieved.

Calculation of biomechanics characteristics
A series of biomechanics characteristics were output to evaluate the functionality of the healthy and diseased models.LV work done or the work done by the LV on ejected fluid was calculated as the area within the pressure volume (PV) loop.Peak systolic myofibre stress was calculated by taking the component of the stress tensor in the direction of the HA, and then performing spatial averaging over the entire myocardial volume, at the time point where pressure was maximum, as shown in eqn 10: where V is the volume of the myocardium, f d is unit vector in the myocardial direction, and σ is the stress tensor at peak systole.

Principal component and regression analysis
Firstly, correlation analysis was performed between peak systolic volume-averaged myocardial stress to various echo parameters.A simple linear mathematical equation was then developed for rapid computation of peak systolic volume-averaged myocardial stress from clinically measurable echo parameters that demonstrated with strong correlation to myocardial stress.The parameters that had a good correlation and/or were theoretically relevant to myofibre stress were AV velocity, MVr velocity, LV longitudinal length, RV longitudinal length, LVID, RWT, EDV and SV (Note: EDV and SV were calculated by applying the half prolate ellipsoid equation to describe LV volume at EDV and end systolic volume (ESV)), as listed in eqn 11a.Principal component analysis was then used to seek modes or linear combinations of the echo parameters that best described the variability between diseased fetal cases.The resulting top three modes from the analysis described 93.05% of the cumulative proportion and are shown in eqn 11b.Then regression was performed to determine the coefficient for these modes (eqn 11c), so that a weighted sum of these modes could be used to estimate peak systolic myofibre stress.The final formulation of the principal component and regression analysis is outlined in eqn 11d.

Receiver operating characteristic (ROC) analysis
To determine which pre-FAV image-based characteristic had the greatest capability in distinguishing BV versus UV outcomes, ROC analysis was performed on retrospective images (n = 37).The nine cases used to develop the mathematical equation to compute myocardial stress were used here as well, as part of the 37 samples.This was appropriate as the equation was developed only to approximate myocardial stress, and this was done without any reference to outcomes of the cases.Outcome data were only used in the ROC analysis.Samples with incomplete datasets were not included here.The analysis was performed on parameters within this study, and for RV/LV longitudinal length ratio and estimated peak LV pressure, which were identified by Tulzer et al. (2022) and Friedman et al. (2018) as promising pre-FAV parameters for indicating post-FAV outcomes.

Statistical analysis
Z scores for echo measurement parameters were computed using healthy population data from Luewan All results are reported as mean and standard deviation.The Mann-Whitney U test was performed on all data comparisons due to small sample sizes (except for the ROC analysis where the DeLong test was used).Statistical significance was assumed when P < 0.05.To estimate the effect size of differences in specific parameters between the BV and UV groups the Cohen's D value was calculated as where x, is the mean value of the parameter for the UV or BV group as indicated by the subscript, s p is the pooled standard deviation and corr = 0.7839 and is the correction factor for when n < 50.

Echocardiography anatomical and functional measurements
Echocardiography cardiac anatomical and functional measurements for pre-FAV and healthy control hearts are shown in Fig. 4. Pre-FAV peak valvular velocity measurements (Fig. 4A-C) showed no statistical significance between the BV and UV disease sub-groups, although both AV and MV antegrade velocities were substantially higher than healthy hearts.Both BV and UV disease sub-groups had elevated EDV Z scores from healthy controls, but the difference was only significant between BV and healthy groups, and not between BV and UV groups (Fig. 4D).Both BV and UV groups had significantly lower SV and ejection fraction Z scores than healthy groups but again, there was no significant difference between BV and UV groups (Fig. 4E-F).The BV group had significantly higher LV and RV longitudinal length than controls (Fig. 4G-H), and although BV LV longitudinal length was generally higher than the UV group, the difference was not significant.Similarly, the BV group generally had a higher LVID (Fig. 4J), lower RWT (Fig. 4M) and higher aspect ratio (Fig. 4K) than the UV group and healthy controls; but again significance was found only between the BV and control groups.No significance was observed across all groups in RV/LV length ratio (Fig. 4I) and PWT (Fig. 4L).For ascending aorta diameter Z score, healthy patient-specific data were not available for ascending aorta calculations and therefore the standard deviation of normative data has been included in Fig. 4N (Chen et al., 2022).No statistical significance was found between the BV and UV groups, but both BV and UV groups were significantly greater than healthy controls.In terms of strains, both BV and UV groups were significantly smaller than healthy controls, but again, no significance was observed between the BV and UV groups (Fig. 4O-P).
Overall, the data demonstrated that diseased hearts were larger than healthy hearts and had lower strains and SV.Between the BV and UV groups, BV hearts tended to have larger average dimensions and higher average strains than UV hearts.However, there were consistently significant overlaps in measurements between the two groups, suggesting that it may not be easy to distinguish between the two groups with echo measurements alone.

Image-based simulations of cardiac biomechanics
The iterative FE modelling optimization process produced percentage error between simulation parameters and image-measured parameters of 2.55 ± 3.56%, 6.43 ± 4.20% and 4.80 ± 3.94% for SV, AV pressure gradient and MVr pressure gradient, respectively.MV pressure gradients were minimized to within 0.7 mmHg of the image-based value.Detailed data demonstrating this are given in the supplementary data file at https://doi.org/10.6084/m9.figshare.24793494.
Figure 5 shows representative results from the image-based FE simulations, showing that the resulting PV loops and spatially averaged myofibre stress over the cardiac cycle were reasonably physiological.
Peak LV pressure was known to increase with gestational age according to previous invasive measurements (Johnson et al., 2000), shown in Fig. 6A.From the trends of computed results, LV work done (the area within the PV loop), and myocardial contractility of healthy models also increased with gestational age from regression analysis (Fig. 6B and D).To account for the age dependency of these biomechanics parameters, the parameters were normalized by the expected value of a healthy heart of the same age from the regression analysis, before comparisons between groups were performed.Literature data was used for normalization in Fig. 6A because it has more samples and is more robust, but our healthy cohort data were used for normalization in Fig. 6B and D because no such literature data exist.For peak systolic myocardial stress in the myofibre direction (Fig. 6C), it appeared to have little change over age, and as such, no normalization was done.
From the normalized quantifications, diseased hearts were found to have generally higher LV pressures compared with the healthy controls and the UV group, but no statistical significance was found (Fig. 6E).Diseased hearts had significantly lower work done than healthy hearts, and the BV hearts produced higher work than the UV hearts, but no significance was found between the BV and UV groups (Fig. 6F).In terms of peak systolic myofibre stress, UV hearts had very similar values to healthy hearts, and the BV hearts had a drastic elevation (more than twofold), which was significantly higher than both the UV and healthy groups, with no data overlap between the groups (Fig. 6G).For myocardial contractility, both diseased groups were significantly lower than healthy controls, and a significant difference was observed between BV and UV groups (Fig. 6H).However, there was some overlap between the UV and BV data.
Overall, the data demonstrated that diseased hearts had significantly altered biomechanics, including elevated cavity pressures and decreased circulatory work done and lower myocardial contractility compared with healthy hearts.Further, BV, but not UV, LVs experienced higher myocardial stresses than controls.Between the BV and UV groups, both contractility and peak systolic myofibre stress were significantly different.The difference in peak systolic myofibre stress between BV and UV hearts was especially large with no overlap between the two groups.This was thus potentially a good parameter for distinguishing the two groups to predict FAV outcomes.

Effect size of parameter differences between UV and BV groups
To determine which of the parameters investigated had stronger ability to distinguish between UV and BV groups, we computed the Cohen's D standardized mean difference (Fig. 7) for all CAS-eHLHS cases modelled.The Cohen's D value quantified how different parameter values between the UV and BV groups were.Results showed that myofibre stress had the highest Cohen's D, which was much higher than Cohen's D for any other parameters.This was followed by echo-measured ventricular size parameters such as LV longitudinal length and LVID, which were close to the biomechanics parameters, normalized work done and contractility.

Relationship between echocardiographic parameters and biomechanics parameters
To understand the dependencies of the peak systolic myofibre stress, we performed correlation analysis between stress and echo parameters.We found that myocardial stress had a good positive correlation with LV size parameters (EDV, longitudinal length, SV and LVID) and MVr, and a good negative correlation with RWT (Table 8A).The correlations are logical from a theoretical standpoint.Myocardial stress was determined via a force balance between the cavity blood pressure and tensile forces in the myocardial walls, and was thus higher with greater systolic pressure, which was the driver of regurgitation.Myofibre stress thus correlated positively with MVr.Further, myocardial wall stresses could be approximated by myocardial wall forces divided by cross-sectional area, which was determined by wall thickness.Myofibre stress thus correlated negatively with RWT.The relationship between cavity pressure and wall tension was further governed by the shape of the LV chamber, as could be illustrated by the hoop stress theory, which stated that larger chambers had higher wall tension.Myofibre stress thus correlated positively with LV size.Finally, peak AV velocity was included, as from a theoretical perspective the value of peak AV velocity indicates the degree of aortic stenosis.These theories thus suggested that it is possible to derive a parameter that can be easily calculated with measurable echo parameters to theoretically represent peak systolic myofibre stress.This will enable fast and easy estimation of myofibre stress from echo scans without a need for time-consuming simulations, for the prediction of FAV outcomes.
These parameters were used to develop an empirical equation for rapid computation of stress from clinical measurements, via principal component and regression analyses.Combining all facets of the principal component analysis with regression coefficients generated eqn 13.The resulting equation for estimating peak systolic myofibre stress had a good correlation with the actual peak systolic myofibre stress from FE simulations, as demonstrated by Fig. 8B.(13) where V 1 to V 8 are echo parameters as given in eqn 11a.
Possible post-FAV outcome predictors, a retrospective analysis ROC analysis was performed to determine the ability of peak systolic myofibre stress, estimated via eqn 13, in classifying BV versus UV outcomes, to compare it with that of other known image-based pre-FAV predictors (Friedman et al., 2018;Tulzer, Arzt, Gitter et al., 2022), and with individual parameters within eqn 13.Detailed echo measurements used for computing myofibre stress via eqn 13 are provided in the supplementary data spreadsheet at https://doi.org/10.6084/m9.figshare.24793494.The results show estimated peak systolic myofibre stress to have the largest area under the curve (AUC) of 0.91 and therefore the greatest capability in distinguishing BV versus UV outcomes (Fig. 9).The next best performing parameters were LV longitudinal length Z score (AUC = 0.84) and EDV Z score (AUC = 0.83).
The approach of estimating peak myofibre stress was significantly better at distinguishing BV versus UV outcomes than RWT, MVr velocity, estimating pressure and AV velocity.

Discussion
We performed a retrospective analysis of CAS-eHLHS fetal hearts to identify pre-FAV parameters that have a high likelihood of having the ability to predict UV versus BV outcomes, after FAV intervention.To do this, we investigated differences in various parameters between UV and BV groups.Our study is different from previous such works in that we performed advanced patient-specific biomechanics simulations to obtain biomechanics parameters, to add on to echocardiographic parameters in our analysis.Our simulations enabled careful back-computation of the myocardial contractility and LV pressures, while adhering to echocardiographic image features and detailed biomechanics formulations, and it provided information on myocardial stresses, which are not measurable clinically.Importantly, our results showed that myocardial stress is uniquely large in the BV group and is potentially a better parameter for predicting UV versus BV outcomes than all currently proposed clinical parameters.Overall, our measurements agreed well with previous investigations on differences between UV and BV groups.Firstly, our data showed that BV groups had generally higher mean circumferential and longitudinal strains than UV groups, which were significantly lower than the control groups.Ishii et al. (2014) reported in a larger cohort study (n = 57) that there were similarly diminished strain magnitudes in diseased hearts, and found significant differences between UV and BV groups for circumferential strains in one out of six segments of the LV and for longitudinal strains in three out of six segments of the LV.In our study, however, as our sample sizes are smaller (n = 15), UV versus BV statistical significances were not found.
Secondly, our data showed that the BV group had higher EDVs (Fig. 4D), LV longitudinal lengths (Fig. 4G), RV longitudinal lengths (Fig. 4H) and LVIDs (Fig. 4J) than the UV group, but differences were not statistically significant.This aligns with previous studies, which analysed retrospective data and found cases that went on to be born as BV after intervention generally had larger LV long-axis Z scores (Friedman et al., 2018) and larger left heart structures (including, AV Z score, LV short-axis Z score and LV long-axis Z score) (McElhinney et al., 2009) at the pre-FAV time point.Again, our small sample size had likely prevented a statistical significance, but our data generally corroborated the literature on the direction of the UV versus BV differences.
Thirdly, our simulation results showed LV pressures were generally higher in BV hearts compared with UV hearts, but differences were not significant.Friedman et al. (2018) and McElhinney et al. (2009) estimated LV pressure from valve Doppler measurements and found that BV cases had significantly higher LV pressures compared with UV cases at the time of intervention, which corroborated our observations.Our data thus corroborated Friedman et al. and McElhinney et al.'s, and the lack of significance could again be attributable to our small sample size.However, we noted that Friedman et al. and McElhinnery et al. did not factor in pressure variation with gestational age (Johnson et al., 2000) when analysing LV pressure calculations, as we did.When we switched to an analysis of LV pressures without the age-normalization (supplementary data file at https://doi.org/10.6084/m9.figshare.24793494),we found that differences between UV and BV groups were larger than if normalization was done (lower P value).
Our main finding was that peak systolic myofibre stress was the best pre-FAV parameter to distinguish between UV and BV cases, and this outperformed all other parameters, including several that were found to have good predictive values in previous studies (Friedman et al., 2018;Ishii et al., 2014;Tulzer, Arzt, Gitter et al., 2022).For example, Tulzer et al. (2022) showed that RV-to-LV length ratio had strong predictive influence, Friedman et al. (2018) reported a high probability of a BV outcome in cases where peak LV pressure was >47 mmHg and ascending aorta Z score was ≥0.57while Ishii et al. (2014) reported higher LV longitudinal and circumferential strains in BV than UV cases.We made the comparison of these individual parameters to peak systolic myofibre stress and found that the latter still performed better.A limitation of our study is that sample sizes were smaller than previous reports.Nonetheless, given that the effect size of myofibre stress is much higher than other parameters Fig. 7, the results are likely to be repeatable with larger samples.Thus, myofibre stress has a good potential of enhancing predictions of UV versus BV outcomes.It can be used to enhance predictive frameworks such as the CART analysis proposed by Tulzer et al. (2022), which uses a combination of RV-to-LV length ratio, LV pressure (calculated from peak MVr velocity) and gestational age for prediction.
We believe that there are physiological explanations for why hearts with stronger contractility and higher stresses are likely to reach a BV outcome instead of a UV outcome.Stronger hearts are likely to support better contractile deformations after FAV intervention, providing better biomechanical stimuli for growth of the LV and thus supporting better growth and development before birth.Further, higher myocardial stresses in BV cases suggested that the myocardium in these cases resisted pathological hypertrophy and dilatation remodelling despite high tissue stresses, while retaining a strong functional ability to generate pumping pressures.This might suggest that the myocardium is healthier and could elicit better growth and remodelling responses after intervention.Generally, our results suggest that biomechanically 'stronger' LVs are more likely to respond positively to FAV, by progressing to a successful BV outcome at 1 year of age.
Our results suggest that biomechanical simulations of fetal hearts can improve predictive capabilities of outcomes, and this is likely useful for clinical decisions.However, presently, biomechanical simulations are computationally expensive, and involve multiple processing steps, including the computational reconstruction of the heart's structure and motion.We have thus proposed a simplified equation to quickly estimate the peak systolic myocardial stress from echo parameters with ease, as shown in eqn 13.Although this equation will not be as accurate as the FE simulations, we showed in Fig. 8B that it retained its ability to clearly distinguish BV and UV groups.The equation can be updated in future for accuracy when more data becomes available, or to reduce the number of dependent parameters to reduce error propagation.There is also potential for using physics-informed neural networks to achieve accurate, real-time estimations of myocardial stresses (Buoso et al., 2021).
When we performed validation on 37 CAS-eHLHS cases, we found that the estimated peak systolic myofibre stress parameter remained the best predictor of UV versus BV post-FAV outcomes, judging from its high AUC in the ROC analysis.Statistical significance, however, was observed only with some of the parameters compared, likely due to the small sample size.It is further likely that errors involved in estimating myocardial stresses via a simple linearized equation based on a small sample cohort had resulted in some reduction of predictive performance.In the future, eqn 13 should be refined, which could improve the statistical significance.Longer term biomechanics simulations may be possible in real-time via machine learning, particularly with physics-informed neural networks, which could resolve this issue altogether.We believe that such future work is warranted.From the ROC analysis, a potentially useful peak systolic myofibre threshold can be obtained for use in predictions.The threshold of myofibre stress = 17.4 kPa provides 100% sensitivity, and approximately 73% specificity (thus correctly predicting all BV cases), the threshold of myofibre stress = 26.1 kPa provides approximately 41% sensitivity and 100% specificity (thus correctly predicting all UV cases), while the threshold of myofibre stress = 17.4 kPa corresponds to the highest accuracy (average of sensitivity and selectivity weighted by prevalence), which correctly predicts 100% of BV cases and approximately 73% of UV cases.Presently, it is unclear which is the most clinically beneficial threshold to use, and further risk versus benefit analyses should be conducted.For example, recent thought about FAV is that even for UV outcomes, the FAV could have reduced disease severity and improved survival benefits, and such a notion warrants further study.
There are several limitations of this study.Firstly, our sample size is small, and future studies with larger sample sizes are likely to enhance the current analysis and produce positive refinement to our prediction model in eqn 13.Secondly, all CAS-eHLHS patients analysed in the study had already been selected for FAV intervention and the sample size was small due to limited data availability, which imposed bias.It would be recommended to widen the study to help mitigate this limitation.Thirdly, our biomechanics computations required idealizations, such as the assumption of the same HA spatial variability configuration, lumped parameter model values, and myocardial stiffness for all cases.Also, during the optimization loops, the best possible match with imaged parameters was obtained, but some match errors remained.Finally, it must be acknowledged that CAS-eHLHS data were only obtained from one institute and BV or UV outcome largely depends on the institutional experience and management algorithm, which is not standard between centres.

Conclusions
Biomechanics parameters, including peak systolic myofibre stress and back-computed myocardial contractility seemed to be promising metrics to differentiate between UV and BV cases.Importantly, peak systolic myofibre stress had a uniquely large difference between UV and BV cases, suggesting that it has the potential of being a better indicator of UV versus BV outcome than all other current clinical measurements.A simplified equation for estimating myocardial stress showed that this parameter has better predictive capabilities compared with echo measurements.We speculate that this parameter could be helpful in clinical evaluation for a more accurate patient selection for FAV.

Figure 1 .
Figure 1.All reconstructed cardiac geometries used in this studyTop row, models that went on to be functionally BV at birth.Middle row, models that went on to be functionally UV at birth.Bottom row, healthy models.Scale bar shown in the top left.

Figure 2 .
Figure 2. Example of reconstructed geometries with cardiac motion estimation and LV volume data Top row, example of patient-specific reconstructed LV geometries for one diseased case with BV outcome, with UV outcome and a healthy case.Geometries to scale, scale bar shown under H3.Middle row, reconstructed geometries superimposed onto associated echo image, green outline highlighting geometry proportion close to current image plane.Bottom row, volume over time variation of each geometry output from cardiac motion estimation methods.[Colour figure can be viewed at wileyonlinelibrary.com]

Figure 4 .
Figure 4. Imaged-based measurements overlayed onto mean and standard deviation bar plots, for the BV and UV diseased groups, with data for healthy controls included where appropriate Mann-Whitney U test performed on all data comparisons; statistical significance assumed when P < 0.05, indicated by ( * ) and (n.s.) denotes no significance.Sample sizes were n = 5 for BV, n = 4 for UV and n = 6 for healthy controls.For ascending aorta diameter, literature data were used (Chen et al., 2022) as measurements could not be clearly obtained from some of our images.[Colour figure can be viewed at wileyonlinelibrary.com]

Figure 5 .
Figure 5. Computational biomechanics outputs Pressure-volume loops and myofiber stress over the cardiac cycle for case 2 in the BV group (BV2), case 2 in the UV group (UV2) and case 3 in the healthy group (H3).[Colour figure can be viewed at wileyonlinelibrary.com]

Figure 6 .
Figure 6.Biomechanical parameters output from FE simulations for the BV (n = 5) and UV (n = 4) diseased groups and healthy controls (n = 6) A-D, parameters plotted with respect to gestational age.The expected normative values (dotted line) were obtained from measurements by Johnson et al. (2000) for A, and from regression of our healthy control data for B-D, B key also applicable to C and D. E-H, the same biomechanics parameters after normalization, by the expected normative values for the matching gestational age, expressed as data points superimposed on mean and standard deviation bar plots.Mann-Whitney's U test performed on all data comparisons; statistical significance assumed when P < 0.05, indicated by ( * ) and (n.s.) denotes no significance.[Colour figure can be viewed at wileyonlinelibrary.com]

Figure 7 .Figure 8 .
Figure 7. Cohen's D values of various parameters to describe the ability of parameters to predict intervention outcome Sample sizes were n = 5 for BV, n = 4 for UV and n = 6 for healthy controls.[Colour figure can be viewed at wileyonlinelibrary.com]

Figure 9 .
Figure 9. ROC curves computed from retrospective data (n = 37) for the individual classes of eqn 13, estimated peak systolic myofibre stress and literature-based pre-FAV predictors of post-FAV outcomes AUC values for each ROC included in key and the DeLong test was used to calculate the P value of each parameter with estimated peak systolic myofibre stress; statistical significance assumed when P < 0.05, indicated by ( * ) and (n.s.) denotes no significance.[Colour figure can be viewed at wileyonlinelibrary.com]