Professor Rice University Houston, Texas, United States
Introduction:: Heart valves (HVs) play a critical role in the heart by directing the flow of oxygenated and de-oxygenated blood. However, diseases such as aortic valve stenosis eventually require valve replacement with prosthetic or biocompatible materials that can mimic the mechanics of their native counterparts. Therefore, mechanical characterization of native and artificial HVs is imperative. Although tensile mechanical testing of HVs is the standard for mechanical evaluation, it is limited due to high equipment costs, sample preparation, testing, post-processing time, and sample destruction. Alternatively, imaging and deep learning networks, such as convolutional neural networks (CNNs), are more readily available, cost-effective, and have been used in a variety of applications for the prediction of physical properties. We hypothesized that CNNs could predict the mechanical response of heart valves since the response is largely dictated by the collagen fiber network (CFN) which results in macroscopically visible folds on the aortic surface. Therefore, in this work, we first imaged, mechanically tested, and curated a dataset for heart valve leaflets which will be made open access. Pre-trained CNNs implemented through PyTorch, Alexnet, VGG11, and Resnet18, were then selected to probe the capacity of stress-strain response prediction from aortic surface imaging and initial tests show promising results.
Materials and Methods:: 51 heart valve leaflets were sectioned with the long axis parallel to the circumferential axis of the leaflets. Imaging of the aortic surface was done using a Leica Stereo Microscope and mechanical testing was done on an Electroforce LM1 TestBench using a 22 Newton load cell (Figure 1). Tensile testing along the circumferential axis consisted of preconditioning to 10% strain at 0.1mm/s for 10 cycles, then pull-to-failure at 0.1mm/s. Stress and strain were obtained by using leaflet dimensions: stress σ = F/A, where F is the force and A is the cross-sectional area, and strain ε = ΔD/lg, where ΔD is the displacement in the grip heads pulling the sample and lg is the gauge length. Reconstruction curves were then obtained by fitting a polynomial to the stress-strain curve to a specified strain value. We considered various terms and strain caps which resulted in many reconstruction curves. Then, we used a data augmentation technique in which “children” images are extracted from the original 51 “parent” images. The children images are extracted from the parent images by sliding a window of size 224x224 pixels at a stride of 25 pixels in both x and y axes. Children images were assumed to have the same reconstruction coefficients as their parents during training (Figure 2). However, for testing, a parent’s children’s reconstruction coefficients are predicted and then the mean of each coefficient is taken to be the predicted value for the parent. Our focus was on predicting up to physiological strain or 10%.
Results, Conclusions, and Discussions:: Reconstruction curves obtained through the coefficient parameters described above were first evaluated using the root-mean-square-error (RMSE). Reconstruction curves to the physiological strain were accurate but exhibited incorrect behavior past the yield point (Figure 3). For a three-term polynomial, predicting for the linear and quadratic term’s coefficients only resulted in better results due to the high variance observed in the cubic term’s coefficient values leading to a better reconstruction curve prediction overall (Figure 4). The strain cap also greatly affected the prediction results, where the higher the strain cap, the higher the mean absolute error (MAE). This was due to increasing nonlinear behavior in the data as the strain increased towards the yield-point. To physiological strain, the lowest MAE observed was 3.99, 3.66, and 3.81 from Alexnet, VGG11, and Resnet18, respectively. Preliminary work had shown that using only 51 samples for training and testing was not enough to achieve adequate results from any pretrained CNN, which motivated us to use the data augmentation technique above. Although it is clear that each child’s image should have different mechanics from its parent due to its microstructure, the observed mechanics for a parent represent the contribution that each child has at the macroscopic scale. Our current results indicate that we can predict the stress-strain response from a heart valve leaflet’s image well, which will be further validated through k-fold cross-validation for the case of using a three-term polynomial and a strain cap of 10%. Finally, the dataset that we have curated will be made open access to encourage its usage throughout the field.
