A 50 mm × 25 mm × 25 mm cavitation chamber was constructed of clear, acrylic sheets for this study. Acrylic sheets were selected not only for durability but also for optical clarity to facilitate imaging of the shock-induced cavitation event (described in Section 2.2). A depiction of the experimental setup, including the cavitation chamber, shock tube, pressure transducers, and cameras, is shown in Figure 1. The wall of the cavitation chamber that is in front of the shock tube was the thinnest (1 mm). The side walls were 5 mm thick, and all the remaining walls were 10 mm thick.

The cavitation chamber was filled with 31 mL of deionized water by using a syringe. Deionized water was used to avoid the residual effect of any ions or electrical conductance on cavitation.

The deionized water was heated to the desired temperature by using a hot plate, and the temperature was recorded with a graduated tube thermometer and a digital thermometer function (Traceable Salinity Pen, model 4367). Five trials were used for each testing temperature, which ranged from 20°C to 60°C in 5°C increments.

The fluid temperature was recorded before and after filling the chamber and after shock exposure. In between shock exposures, the deionized water was removed from the chamber by using a syringe.

A three-dimensional (3-D) shock tube model was used to generate the shock waves, which induced cavitation in chambers filled with deionized water. The 76.2-mm oxyacetylene shock tube is divided into a driver (0.3 m) and a driven (4.6 m) section, separated by a 25.4-μm Mylar diaphragm. The oxyacetylene in the driver section was ignited, which ruptured the diaphragm and generated a shock wave that propagated down the driven section of the shock tube and toward the cavitation chamber. The fluid-filled cavitation chamber was placed 2 mm from the exit of the shock tube. Pressure transducers (PTs) record the speed and pressure–time profile of the shock wave. Piezoelectric pressure transducers 0 and 1 (PT0 and PT1, PCB Piezotronics, Model 102B15) are 1.5 m apart and are located on the driven section of the shock tube so that the shock wave speed and overpressure can be measured (see Figure 1). PT1 is 127 mm from the front wall of the cavitation chamber. The cavitation chamber was illuminated using two separate LED lights (Nila Zaila Deluxe Daylight) prior to igniting the oxyacetylene in the shock tube.

During each trial of the shock tube experiments, the images of the cavitation chamber were recorded at 100,000 frames per second using two high-speed monochrome digital cameras (Photron, FASTCAM SA-Z) with a 105-mm macro lens (Nikon, AF-S VR Micro-NIKKOR 105-mm f/2.8G IF-ED). In this study, a trial refers to one ignition of the oxyacetylene in the shock tube and the subsequent recording of the cavitation event (or lack thereof, if cavitation did not occur). A subset of 50 images, which covers 0.5 ms, was found to completely depict the cavitation event. This subset of 50 images was saved for each trial, resulting in a total of 2,250 images for the 45 trials conducted since there were five trials at each 5°C increment. These 2,250 images were processed using the bubble detection program described in Section 2.3.

A bubble detection program was written using the commercially available software MATLAB (version: 9.10.0.1602886 (R2023a)). The program detected the bubbles automatically within the entirety of the chamber’s interior, which was selected as the cavitation region of interest. The region of interest for the first image in the series was selected manually, and all subsequent images were batch-cropped to the same region. An example of image cropping, as well as bubble detection for the region of interest, is shown in Figure 2.

Each cropped image was then pre-processed to minimize noise by removing artifacts, such as light reflections from the chamber’s exterior or shock tube. The MATLAB function “imfindcircles” was used to detect the bubbles in each processed image. The center coordinates were recorded for all of the bubbles in each of the images. A count of the number of bubbles (i.e., bubble count) and bubble locations was recorded for each image. Each bubble was assigned an identification number based on its first appearance to facilitate tracking bubbles through the frames recorded by using high-speed cameras (Crocker, 1999). This allowed individual cavitation bubbles in the image series to be counted, without repeatedly counting bubbles which occur in multiple frames. At each 5°C increment, between 20°C and 60°C, the data from each image describing the total bubble counts and bubble locations were recorded. The grand total number of shock-induced cavitation bubbles and bubble locations used in each trial was obtained by aggregating the total bubble counts and bubble locations from all the images in an image series.

A k-nearest neighbor (kNN) model and an adapted support vector machine model using error-correcting output codes (ECOC SVM) were constructed to predict shock-induced cavitation behavior as a function of temperature. The kNN and ECOC SVM machine learning models use fluid temperature as an input and the level of cavitation (i.e., cavitation level) as an output. The cavitation level refers to the grand total number of shock-induced cavitation bubbles produced at a specified fluid temperature, which is described further in Section 2.5. Fluid temperature refers to the bulk temperature of the deionized water that is inside the cavitation chamber.

Both kNN and SVM are supervised machine learning methods, meaning they use labeled points with known solutions to train the machine learning models. As a result, the machine learning models are first trained to predict the cavitation level using labeled training points, where each “point” represents one experimental trial. The training points are considered “labeled” because the kNN and ECOC SVM machine learning models have been provided with both the input (i.e., fluid temperature) and the output (i.e., level of cavitation) for each trial. After training the kNN and ECOC SVM models using the labeled training points, the machine learning models are able to classify cavitation levels using testing points. A testing point is an experimental trial at a given fluid temperature, which is given as an input for the machine learning model to predict the cavitation level. As such, the output from using a testing point in the kNN and ECOC SVM models is a prediction of the cavitation level given a fluid temperature. Thus, the machine learning model’s predictive accuracy can be measured by comparing the predicted level of cavitation for a given testing point (i.e., an experimental trial) with the actual cavitation level calculated using the bubble detection program from the experimental trial.

Figure 3 illustrates the coupled bubble detection and machine learning (i.e., kNN and ECOC SVM) processes.

Cavitation level is not something that has been previously defined, although prior studies have applied levels to cavitation damage (Fadaei Kermani et al., 2018). Thus, this manuscript defines the cavitation level as the number n of cavitation bubbles that appear after the cavitation chamber is exposed to a shock wave with an overpressure of 207 kPa from the pressure transducer PT0. The different levels of cavitation are described using four different “cavitation schemes.” These four schemes assess how precisely the kNN and ECOC SVM models could predict cavitation bubble numbers (e.g., delineating 5–10 bubbles from 15–20 bubbles) as a function of temperature.

Since a standard definition for the “cavitation scheme” does not exist, two different approaches were considered to determine the appropriate bin sizes at each cavitation level. The first approach is “data-driven” because bins are selected based on the distribution of the cavitation bubbles obtained from the shock tube experiments. The second approach is “distribution-driven” and focuses on the similarity of bin sizes, regardless of the actual distribution of the cavitation bubbles from the shock tube experiments. Two different cavitation schemes were explored for both the “data-driven” and “distribution-driven” approaches.

Table 1 shows the definition of each cavitation level for the two different approaches and four cavitation schemes. These cavitation level definitions apply to both the kNN and ECOC SVM models.

The two cavitation schemes (i.e., schemes 1 and 2) for the “data-driven” approach were selected to reflect the actual numbers of cavitation bubbles observed in each trial. This means that the levels were defined such that each level reflected the actual cavitation bubble number of at least one trial, and there were no levels that did not correspond to a real trial. For example, if the trials contained 1, 2, 2, 5, 8, 10, and 12 bubbles, then the cavitation levels might be 1–5 and 8–12. The cavitation levels are not necessarily equally sized and are selected such that each level will have training trials that fall within those cavitation levels.

The two cavitation schemes (i.e., schemes 3 and 4) for the “distribution-driven” approach were created using equally sized bins. These equally sized bins may contain cavitation levels that are not associated with a trial since the number of cavitation bubbles at that level may not have been observed during the shock tube experiments.

Figure 4 shows the pressure history for PT0 and PT1 during the shock tube experiments. The shock wave speed inside the shock tube was 484 m/s (Mach 1.4).

The overpressure recorded by PT0 and PT1 during the experiments was 207 kPa and 148 kPa, respectively.

The magnitude and duration of the overpressure decrease when the shock wave approaches the shock tube exit (i.e., the end of the driven section).

Using the recorded images from the shock tube experiments, the bubble detection program produced the grand total number of shock-induced cavitation bubbles detected as well as an assigned identification number for each bubble based on its first appearance (and location) to facilitate tracking of bubbles through the frames. To ensure accurate performance of the bubble detection program, the bubble number was manually counted from a subset of 75 randomly selected images where shock-induced cavitation was present. A subset size of 75 was chosen to validate the bubble detection program, which corresponds to 10% of the images from trials containing shock-induced cavitation. The variance between the bubbles counted manually and those counted using the bubble detection program did not exceed five (5) bubbles, even at the highest cavitation levels.

The performance of the bubble detection program at different temperatures is depicted in Table 2.

In addition, the bubble detection program also saves an annotated image consisting of cavitation bubbles that are outlined using the color red. An example of this bubble detection annotation is shown in Figure 2B for the 60°C case.

The following subsections describe the performance of the kNN algorithm, which varied by the choice of k and cavitation scheme.

The ECOC SVM outperformed the kNN model for all the cavitation schemes considered. This may be due to the lack of a parameter, similar to the k choice for the kNN, that needs to be optimized for the ECOC SVM model. The ECOC SVM model does require a “cost” parameter C, which affects the weight (or cost) assigned by the algorithm to each misclassified training point (i.e., the labeled point containing the fluid temperature and the actual cavitation level information from the trial). However, C is automatically processed using soft-margin minimization by MATLAB, which assigns the cost of each misclassification of the cavitation level based on the distance between the misclassified point and the corresponding margin for the class. The soft-margin minimization process allows the ECOC SVM algorithm to differentiate between misclassified points that are close to being classified correctly and those that are far from being classified correctly. As a result, the ECOC SVM model is better than the kNN algorithm because it is less sensitive to noise in the data.

Since the C is automatically processed for the ECOC SVM model, the performance is only compared across cavitation schemes. The cross-validation accuracies for the ECOC SVM models, by the cavitation scheme, are depicted in Figure 10.

Individual ECOC SVM model accuracy was depicted using a graphical representation (i.e., Figure 11), where a prediction line is used to illustrate when the model predicted the testing points. Confusion matrices for the predictions by the ECOC SVM model are also provided (i.e., Figure 12).

Supplementary Tables S5, S6, which can be found in Supplementary Materials, show the number of training points and testing points for the ECOC SVM models.

The cavitation scheme had a smaller overall effect on ECOC SVM performance when compared with the kNN’s performance. The simplest cavitation scheme (i.e., scheme 1) produced the highest accuracy of 93.11%. The second cavitation scheme performed only 4% worse than scheme 1, with an accuracy of 89.56%. Schemes 3 and 4 also had good accuracies of 88.89% and 89.56%, respectively. In all cases, the ECOC SVM model did at least 3% better than the best-performing kNN models in the data-driven schemes, but did up to 13% better than kNN for the distribution-driven cavitation schemes. The comparison of the two best-performing schemes (1 and 2) for the ECOC SVM is shown in Figure 11 and Figure 12. Specifically, the predictive performance for schemes 1 and 2 is shown in Figure 11, and the corresponding confusion matrices are shown in Figure 12.

The ECOC SVM model was able to generate much more accurate predictions of the cavitation level than the kNN models, regardless of the number of k neighbors chosen or the cavitation scheme used. Using a simpler cavitation scheme (i.e., scheme 1), both the kNN and ECOC SVM models produced a cross-validation accuracy above 85%, with the ECOC SVM obtaining almost 95% accuracy. Using the more complex cavitation scheme (i.e., scheme 4), ECOC SVM still outperforms the best kNN model (i.e., k = 3) by 11%. A comparison of the machine learning algorithms by the cavitation schemes can be seen in Table 3.

The bootstrap mean accuracy, standard deviation, and 95% confidence intervals for each model and cavitation scheme are presented in Supplementary Materials (Sections 1.5 and 2.6). Overall, the bootstrapped mean accuracy was within 4% of the cross-validation accuracy, and several of the cross-validation accuracies fall into the bootstrapped confidence intervals. The bootstrapped mean accuracies for schemes 1, 3, and 4 were within 2% of the cross-validation accuracies. There was a larger difference (8.7%, on average) between the cross-validation and bootstrapped accuracies for cavitation scheme 2. The overall trends that cavitation scheme 1 produced the highest accuracy and that the ECOC SVM models had higher accuracy than the kNN models were consistent using both the cross-validation and bootstrap mean accuracy methods. Since cavitation schemes 1, 3, and 4 had more consistent results between both the cross-validation and bootstrap mean accuracy methods, this could be an indication that these schemes are more robust. Comparing cross-validation and bootstrapped accuracies could be a useful tool in determining the ideal cavitation scheme for a model. The benefits and limitations to each method for assessing accuracy are further evaluated in Section 4.

The machine learning models in this study only considered one feature (i.e., fluid temperature), which has a strong and positive correlation with the number of cavitation bubbles. The results consistently showed that the ECOC SVM outperforms the kNN when predicting the cavitation level based on fluid temperature. Using other data structures (e.g., non-linear data or data points that have multiple labels), the kNN may be preferred over the ECOC SVM because the ECOC SVM generally does not handle the other data structures well. Additionally, the kNN may also perform better than the ECOC SVM when the amount of training data relative to model features (i.e., data inputted into the machine learning model) is increased (Singh et al., 2016; Chahar and Kaur, 2020).

The ECOC SVM is generally considered simpler and more interpretable than the kNN but can only identify a smaller set of patterns when compared with the kNN (Singh et al., 2016; Chahar and Kaur, 2020). Thus, it follows that the ECOC SVM would perform well on the one feature data set because the pattern is simple. The ECOC SVM model also tends to perform better than the kNN when there are a large number of inputs relative to sample size (Yan and Yang, 2014; Gaye et al., 2021). As a result, it would be advantageous to include additional inputs like salinity, pH, geometry, viscosity, and ion concentration in an ECOC SVM model since this action would likely improve predictions of shock-induced cavitation behavior to investigate cavitation as a bTBI mechanism.

Both kNN and SVM are shallow and supervised learning methods. Shallow versus deep learning refers to the architecture of a model and the number of layers of representations these models contain (Zhong et al., 2019). Supervised versus unsupervised learning refers to whether or not the model is trained using labeled (by humans) training data or is allowed to define its own groups and clusters based on the model’s own detected features in unlabeled data (Rajoub, 2020). Both supervised and shallow learning methods are appropriate for labeled datasets with simple patterns and provide high accuracy when making predictions (Malach and Shalev-Shwartz, 2019; Robles Herrera et al., 2022). The pros and cons of a deep learning approach for future work with these types of data are discussed in Section 4.4.

In future, the machine learning model will be expanded by increasing the number of input parameters and datasets. The performance of the modified machine learning model, containing the expanded input and data, will be tested using other commonly used supervised learning algorithms (e.g., decision trees, random forest, and XGBoost) and compared with the results from the kNN and ECOC SVM. Decision trees are often used in healthcare research and can handle versatile data structures, which would be useful to consider in a version of the model that applies a wider set of inputs (Charbuty and Abdulazeez, 2021). Decision trees were not selected for the current work due to the model design (a single input and output with different numbers of levels). This is attributed to decision trees being biased toward more levels, which could have impaired the identification of the optimal cavitation scheme in this work. Random forest algorithms create a set of decision trees that are trained using different subsets of the training points. Random forest models can be more robust to overfitting than a single decision tree and can handle larger datasets. As a result, random forest models may be useful for a bTBI prediction model that considers a larger number of input parameters for cavitation and other medical data. The capability to handle larger datasets was not necessary in this work, particularly when weighted against the decreased interpretability of the results and the increased number of hyperparameters (e.g., number of trees, tree depth, and number of features) of a random forest algorithm when compared with the kNN or ECOC SVM model (Ao et al., 2019). XGBoost is a boosting method that trains multiple models sequentially to help improve each new decision tree. While the speed and versatility of XGBoost make it an appealing option for a model having multiple input parameters, the literature has shown that the XGBoost technique is a sub-optimal model for small datasets and was therefore not considered in this work (Azmi and Baliga, 2020).

The suggested k-value of 5, calculated using the square root of the training data, did not produce the highest cross-validation accuracy. Rather, the highest cross-validation accuracy (averaged over all cavitation schemes) was for a k-value of 3 (i.e., best k-value). There was a very small difference (less than 1%) between the average performance of the kNN model when using k nearest neighbor values of 2, 3, and 5. The k-values of 1 and 7 averaged 78% accuracy across all cavitation schemes, only 2%–2.5% less accurate than the other k-values. The results of the cross-validation highlight the importance of performing an analysis to determine the optimal choice of k. While the square root of the training data size is a good suggested starting point, the suggested k-value may not be the optimal k value for all data.

Although the ideal value of k may change in the data range (i.e., for each trial within a particular cavitation scheme), the best k-value was used in the analysis for simplicity (Garcia-Pedrajas et al., 2017). Thus, future work should consider the implementation of a data-driven k selection method where the optimal value of k is determined for each trial (Cheng et al., 2014). For instance, an adapted correlation matrix kNN could provide additional classification accuracy for the kNN model.

A universal method of quantifying the level of cavitation using the bubble number does not exist. As such, this paper explored several different definitions of the cavitation level using the term “cavitation scheme” to analyze the predictive ability of the kNN and ECOC SVM models. The choice of the cavitation scheme impacted the predictive accuracy of kNN models strongly and moderately affected ECOC SVM models. Two approaches to defining cavitation levels were explored. The first approach is the “data-driven” cavitation scheme, which bases the distribution and definition of the cavitation level on the actual data from the shock tube experiments. The data-driven schemes were selected so that each possible cavitation level was reflective of at least one trial from the dataset. The second approach is the “distribution-driven” cavitation scheme, where a similar number of bubbles are selected in each level or “bin.” In the “distribution-driven” schemes, there may not be trials in the training data for a given bin (i.e., it is possible to have a bin without any data describing the number of cavitation bubbles).

Overall, the data-driven approach performed better than the distribution-driven approach. The simplest scheme (i.e., scheme 1) was defined using the data-driven approach and achieved the highest accuracy. This result is as expected since the more data points fit within each classified level/bin, the more training points the machine learning algorithms had to “learn” at each level. However, the other cavitation schemes using either the data-driven or distribution-driven approach were still able to achieve high accuracy when predicting the level of cavitation. This demonstrates the need for an ideal cavitation scheme definition that maximizes both predictive accuracy and result specificity. For example, if both cavitation schemes 1 and 2 yield an accuracy above 90%, it may be more beneficial to select the more detailed cavitation scheme (i.e., scheme 2 for this study).

One limitation in the results presented in this paper is the small size of the dataset, which may result in the conclusions being a function of a random decision by the algorithms. However, despite the small size of the training dataset, the high accuracy obtained from the kNN and ECOC SVM algorithms supports continued efforts in applying machine learning to predict shock-induced cavitation. The present study demonstrates initial evidence that machine learning can be used to make predictions of cavitation behavior based on parameters related to blast injury and that these findings can be validated using a shock tube model.

This study only considered the kNN and ECOC SVM models since both have been considered in applications related to biology or cavitation. With more input parameters (e.g., ion concentration and viscosity), it is likely that ECOC SVM would continue to perform better than kNN. The current model is focused on predicting the cavitation bubble number (i.e., cavitation level). For other output parameters, like the strength of cavitation bubble collapse, it could also be useful to consider a different algorithm type (e.g., decision trees) that has been used in the literature (Wang et al., 2021). Additionally, as the data inputs increase in number and complexity, it could be useful to compare the performance of an unsupervised algorithm (i.e., k-means clustering) to the supervised ECOC SVM. As mentioned earlier, unsupervised machine learning describes algorithms that analyze unlabeled datasets without any human intervention (Rajoub, 2020). A key limitation to applying unsupervised learning to more complex data from clinical settings is interpretability. Since unsupervised algorithms may return categories that are not consistent with human-defined categories, the practical implications of the machine learning results can be difficult to interpret and pose challenges when evaluating their accuracy. Additionally, the kNN and ECOC SVM may be less prone to overfitting, when compared with unsupervised learning, since cross-validation methods can be used to help prevent overfitting in supervised learning (Koul et al., 2018). This is not easy in unsupervised learning due to the lack of labels associated with the data.

In this study, there was little value to applying unsupervised machine learning since a single, highly correlated input (i.e., fluid temperature) and output (i.e., cavitation level) were considered. Unsupervised learning has more potential benefit when there are complex patterns and interactions that a human might not be able to readily discern. In the context of bTBI, supervised learning would be beneficial to characterize singular, easily labeled outcomes (e.g., level of cavitation and presence or absence of coma). On the other hand, unsupervised learning methods could be more beneficial in detecting the underlying patterns in cavitation and intracranial pressure, which lead to moderate bTBI (Bröker et al., 2022).

The influence of chamber geometry on shock-induced cavitation was not assessed in this study, which is one limitation of this work. This limitation will be addressed in future work involving shock tube experiments using multiple chamber geometries to understand how the geometry will influence cavitation behavior. In this case, the machine learning algorithms would first be trained using the dimensions from multiple chamber geometries to see if cavitation can be predicted without the influence of geometry. If the prediction ability of the machine learning algorithms using the different geometries is poor, then the geometry would be added as a model input feature which will be experimentally validated.

While the kNN and ECOC SVM models presented in this study predicted shock-induced cavitation behavior based on the fluid property temperature, there may be an application where the machine learning model could predict the level of shock-induced cavitation that could lead to a bTBI. In this case, cavitation above a certain level would result in a model prediction of bTBI, while cavitation below that level would result in a prediction of no bTBI. To achieve something like this, machine learning could be coupled with experiments or simulations. The model would be given the blast and fluid conditions (overpressure, temperature, etc.) as inputs and would output whether a bTBI would be incurred or not, based on the predicted level of cavitation. This machine learning model may also be able to make predictive conclusions about the severity of the bTBI using the predicted level of cavitation. In the same way that Fadaei Kermani et al. (2018) assigned a cavitation index to a level of damage severity, the cavitation levels defined in this study could be assigned to levels of bTBI severity. For example, using cavitation scheme 1, level 1 could correlate to mild bTBI, level 2 is moderate, and level 3 is severe. These levels could be validated using real patient data, where the diagnosed bTBI severity is the output, and consider different input conditions such as age, presence of lesions in the brain, diagnostic scores, and magnitude of the overpressure (i.e., shock wave). Such a model could provide high clinical value due to the current ethical and practical challenges in quantifying brain injury severity and predicting injury outcomes. However, this model would require detailed knowledge of the injury conditions, and clinicians might be hesitant to discharge patients or recommend care plans based on the output from the algorithm. That being said, existing studies have already demonstrated the use of machine learning algorithms to predict patient outcomes or brain injury severity (Vergara et al., 2017; 2018; Hale et al., 2018). Despite the logistical obstacles posed by clinical implementation of machine learning algorithms, the low-risk nature of a potentially transformative reward supports investigation into this avenue. While ultimate medical recommendations should incorporate medical expertise and a variety of tests, machine learning is a potential option for clinicians to use patient data to help inform diagnostics and treatment plans. In the case of a heterogeneous condition like blast injury, models that can help accurately classify injury severity and predict outcomes can be a useful tool in the overall kit used to improve patient care.

This study further demonstrates the ability of machine learning to predict cavitation behavior in a fluid with good accuracy, which has implications for blast-injury models.

The machine learning algorithms presented in this study have the potential to quantify injury severity based on a mechanistic metric. If future machine learning models are adapted to predict injury severity based on the predicted cavitation level, then this would provide substantial support to the theory that cavitation is the main mechanism driving bTBI.

Consequently, the results of the present study emphasize the novel benefit that machine learning can offer for understanding the mechanisms of bTBI and predicting outcomes following this injury.