Is Machine Learning Able to Detect and Classify Failure in Piezoresistive Bone Cement Based on Electrical Signals?

As described in our previous work [9], piezoresistive bone cement (pBC) was formulated by mixing different amounts of chopped CF with aspect ratio of 430 (3 mm length and $7~{}\mu$m diameter; TEJIN Carbon America Inc., Rockwood, TN, USA) in dental PMMA cement (Bosworth Fastray). CFs were first tip sonicated in ethanol at 30 W and 20 kHz for an hour to disperse the fibers. The solution was then left to dry slowly to a powder on a heater plate at 65^∘C for 3 days. The CFs were then added to the dry PMMA, which included benzoyl peroxide as a radical initiator, and gently mixed using mortar and pestle. Methyl methacrylate (MMA) monomer was added to the dry mixture (800 ml MMA/gr of PMMA) which crosslinked with the powder to form a polymerized solid material. Cylindrical CF/PMMA specimens were molded with 10 different volume fractions of CF-to-PMMA ranging from 0.1% to 3.0%. In order to measure conductivity, the bottom and top faces of the cylindrical specimens were polished, cleaned with ethanol, painted with silver conductive paint, and covered with copper tape to reduce contact resistance, Fig. 2. Our study showed that percolation and maximum gradient occur near 1.25 vol.% CF and 1.5 vol.% CF respectively, Fig. 2. The same recipe with 1.5 vol.% CF was used to build the samples for this work.

An EIT phantom consisted of a cylindrical tank filled with deionized water and 16 electrodes spaced evenly around the exterior of the domain, Fig. 3(b,c) [11, 9, 36]. Test specimens consisting of a conical female component, which emulated the cavity within long bones (e.g. a femur), and a conical male component coated with silver paint, which simulated the surface of metal prosthesis (e.g. a femoral stem), were 3D printed, Fig. 3(a,c). A layer of pBC was sandwiched between the male and female components, Fig. 3(b). The male component was then subjected to compressive loads using a MTS machine Fig. 3(b,c) while EIT measurements were collected from a 16-electrode array encircling the phantom. Loads were increased incrementally from 45 N to 4000 N. EIT measurements were then post-processed via an in-house EIT routine developed by Tallman et al. to reconstruct the conductivity maps [34].

Herein, we utilized existing machine learning (ML) algorithms onto two different data set types. In the first approach, we applied machine learning directly to the raw voltage signals, which included all available data, but risked overfitting due to a large number of features. In the second approach, we first applied principal component analysis (PCA) on the voltage signals to reduce the number of features, and subsequently applied machine learning on only the first few principal components that captured more than 95% of the data variability. Matlab machine learning and neural network tool boxes were used to train different machine learning algorithms on the experimental data and create confusion matrices. As part of this study, we compared machine learning methods such as support vector machine (SVM), K-Nearest Neighbor (KNN), trees, and ensemble methods, to a two-layer feed-forward neural network for both classification and regression problems based on EIT measurements, in order to identify the most efficacious methods for these problems and for the low level of data available relative to what machine learning methods typically require for optimal performance.

In the first set of experiments, we placed a conical specimen (Fig. 3(a)) in different locations within the EIT phantom tank. The radial coordinates, $r$ and $\theta$, of the specimen center were tracked, Fig. 4. Specimens were placed at $r=$ 0 cm, 2 cm and 4 cm and at $\theta=0^{\circ}:30^{\circ}:330^{\circ}$. At each location, EIT measurements were performed on four different conical specimens and with 100 recordings at each measurement for averaging. We used the data from three specimens for the training whereas one specimen was used solely for testing. For this set of tests, analytical EIT solutions for reconstructing the phantom conductivity map were able to track the location of the specimen, Fig. 4.

We compared different machine learning algorithms to predict radial coordinates components $r$ and $\theta$, Fig. 4. Here, 60% of the data was used for training, 15% for validation and 25% for testing. Using an SVM algorithm directly on the EIT measurements resulted in 100% training and validation and 92% training accuracy for classifying the radial position of the sample. For the angular component, $\theta$ in Fig. 4, SVM resulted in 100% training accuracy and validation and 83% testing. However, due to the small number of tests compared to the large number of features, there is a high risk of overfitting.

Using the data pretreatment, the first four principal components described 95.5% of the data variability. Even though the training and validation of the regular machine learning algorithms resulted in 93% accuracy for the SVM algorithm, the testing of the trained model was very low at 39%. Other linear and nonlinear algorithms, such as decision trees and KNN, also worked well for training but not for testing. These results were similar for learning the angular component of position, $\theta$.

Next, we used two layer feed-forward neural networks with five hidden neurons, and directly used pretreated data. For this, the MATLAB’s Neural Network Pattern Recognition toolbox was used. The first four PCAs were used to train the neural networks. We again used 60% of the data for training, 15 percent for validation of the training and 25% for testing. The confusion matrices for training, validation, and testing of the model for classifying the radial distance are shown in Fig. 5. Overall, the neural network resulted in 94.0% accuracy in training, 92.1% in validation, and 91.9% in testing. For the angular component, $\theta$, we used MATLAB’s neural network fit toolbox. Similar to the classification of the radial component, this resulted in acceptable results in training, validation and testing, with an average of $10^{\circ}$ error, see Fig. 6.

This analysis shows that machine learning algorithms, especially neural networks, are able to interpret the EIT measurements for tracking location of an object inside a domain; however, we did not see an improvment in accuracy of machine learning algorithms when principal component analysis was used for tracking the location of samples.

We designed a second set of experiments to investigate if machine learning is better able to interpret boundary voltage data than analytical optimization-based solutions in order to locate defects on a sample. In this experiment set, a 1 mm width vertical cut was made by a bandsaw on four conical specimen that were placed at the center of the phantom tank. The specimen were rotated from $0^{\circ}$ to $360^{\circ}$ by $30^{\circ}$ steps with a fixed location at the center of the phantom tank. At each angle, EIT measurements were performed with 100 readings of signals at each measurement for averaging. A reconstruction the conductivity map using analytical EIT solution failed to distinguish between crack orientations as shown by the representative set of EIT-generated conductivity maps in Fig. 7. The EIT maps in Fig. 7 shows the conductivity difference between crack facing an angle $\theta$ and baseline of $\theta=0$. Similar to location tracking, we used the data from three specimens for the training whereas one specimen was used solely for testing. Therefore, 60% of the data was used for training, 15% for validation, and 25% for testing the model. The linear SVM algorithm applied directly to the EIT measurements resulted in 100% training and validation and 83% testing accuracy. However, there is again a high risk of over fitting due to the large number of features compared to experiments.

We also investigated using principal components of the voltage signals instead of the raw voltages.The first four principal components showed 95.5% of the data variably and were used for developing the following machine learning algorithms. The Gaussian Process Regression available in the regression learner toolbox of MATLAB resulted in $5.6^{\circ}$ root mean square error during the training and $16.73^{\circ}$ during the testing. Next we used neural network regression fit available in MATLAB neural network toolbox. The first four principal components were used as the model features. Again, 60% of data was used for training, 15% for validation, and 25% testing the model. This resulted in root mean square errors of $6.1^{\circ}$ and $7.0^{\circ}$ for training and testing, respectively. Even with a small numbers of experiments, this suggests that machine learning is able to track the defect orientation thereby demonstrating the burgeoning potential of using machine learning to better interpret EIT measurements.

In the third set of experiments, we considered four cement health conditions: healthy, vertically cracked, horizontally cracked, and loose, Fig. 10(a). Three specimens were tested for each condition. The cracks were implemented as a bandsaw cut in both the surrogate and the cement layer. For looseness, we coated the male components of the conical specimens with Vaseline before curing the cement to allow conformal molding but prevent adhesion. Looseness was confirmed by manually pulling out the male component after the cement cured. All of the specimens were prepared with 1.5 vol.% CF pBC [9]. Each specimen was then subjected to compression loading from 300 to 2200 N as EIT measurements were simultaneously collected. The conductivity change measured by EIT showed consistent increase in the absolute conductivity change for all of the specimens, Fig. 10(b). Healthy specimens show the largest change followed by the loose specimens, vertically cracked specimens, and, lastly, horizontally cracked specimens.

Because of the low number of tests in this set of experiments relative to the number of health conditions, we immediately used EIT data pretreated with PCA. Contrary to the prior two cases, location tracking and crack orientation, the first four principal components found here described only 88% of the data variability. To cover 95% variability, seven principal components had to be considered; however, for consistency and to avoid potential overfitting we decided to use the first four principal components for this analysis. Fig. 10(c) shows the first two principal components for all specimens and all loading conditions. The results show four divided clusters for each health condition with the exception of a few similarities between vertically cracked and healthy samples. We then trained different machine learning algorithms with five-fold cross validation using only the first four principal components of the EIT measurement on 75% of the data, and reached 99.3% accuracy in training and 98% testing accuracy (25% of the data) for classifying failure types using the KNN algorithm. We also used MATLAB’s two layer feed-forward neural network with three hidden neurons. The neural network resulted in 100% accuracy in training and validation and 96.2% in testing accuracy, which was expected considering how the principal components showed four well-divided clusters for the health conditions. This result demonstrates the viability of using PCA with multiple machine learning methods to classify defect types in a piezoresistive bone cement, even given the limited number of experiments.