1. Introduction

2. Previous Review Studies on Bone Drilling

3. A Brief Review of Medical Training System and Robotic Drilling

4. An Application of Vibration and Machine Learning Methods for Bone Drilling

4.2. Applied Machine Learning Methods

An application of the machine learning method for optimum bone drilling parameters prediction is presented in [37]. A genetic algorithm (GA) is used to find a minimum thrust force value from the combination of the bone drilling parameters during bone drilling. A mathematical model of the thrust force as a function of feed rate and spindle speed is calculated using response surface methodology (RSM). In the study, the optimal value of the spindle speed and the feed rate to achieve the minimum thrust force during bone drilling is developed using the GA method. A developed RSM of thrust force is used as an objective function in the GA method. The GA optimization result shows that a feed rate of 30 mm/min and a spindle speed of 1000 rpm are the optimal parameters for the minimum thrust force value. The GA predicted result is also compared to the experiment result for a similar feed rate and spindle speed value of 710.

Pandey et al. [38] presented a combined method to obtain an optimized grey fuzzy reasoning grade (GFRG) from all quality characteristics of bone drilling. The combined method consists of grey relation analysis (GRA) and fuzzy logic. The GFRG is used to determine the optimal combination of bone drilling parameters that minimize temperature, force, and surface roughness. The highest GFRG is obtained for the feed rate of 40 mm/min and the speed of 500 rpm.

A study that reported the use of radial basis function neural network (RBFNN) for drill wear classification in bone drilling is available [39]. The RBFNN is utilized to develop a drill wear classification model based on a multi-sensor approach. The features for the RBFNN classification model were extracted from signals such as cutting forces, servomotor drive currents, and acoustic emission.

Various machine learning models such as support vector regression (SVR), k-nearest neighbors (KNN), decision tree (DT), and random forest (RF) were used for predicting temperature elevation rotary ultrasonic bone drilling (RUBD) [40]. The machine learning models were compared with the standard response surface methodology (RSM) analysis. The result shows that SVR is the most outperformed model for this application compared to other machine learning methods.

The monitoring and prediction of temperature elevation during real-time in vivo medical surgery is a challenging task. A study that presents the Ridge regression for prediction of the temperature rise during orthopedic bone drilling is presented by Agarwal et al. [41]. The Ridge regression model is compared with other machine learning models such as multilayer perceptron, lasso regression, and multi-linear regression. According to the performance metrics such as mean absolute error (MAE), root mean square error (RMSE), and mean square error (MSE), the error metrics of the Ridge regression than other ML models indicated that the proposed method outperformed other models. In another the study presented by Agarwal et al. [42], the Ridge regression was compared with other ML models such as lassor regression, support vector regression (SVR), multi-linear regression, and artificial neural network (ANN). Ridge regression and other ML methods are to predict the surface roughness and cutting force during rotary ultrasonic bone drilling. According to the statistical analysis of the predictive results, it was observed that Ridge regression has the least error metrics compared to other ML methods in terms of surface roughness prediction. In the case of the cutting force prediction, SVR was the most accurate model compared to other ML models.

K-nearest neighbors (KNN) and ensemble classifiers were utilized in [43] for breakthrough detection in robotic orthopedic surgery. A feature set containing closed-loop control signals and force sensor data were the training datasets to develop the prediction models. It is found that the ML models accurately detect the breakthrough during bone drilling operations. The best accuracy of breakthrough detection is 98.1±0.2% for sheep femur bone.

A successful approach to categorizing bone drilling levels (bone layers) using a customized convolutional neural network (CNN) is presented in [44]. The CNN classification used vibration signals from a three-axial accelerometer attached to the cow femur bone. The CNN accurately classified raw vibration signals from the three-axial accelerometer into three distinct bone layers i.e. periosteum (the outermost layer), first cortical (the next layer beneath the periosteum), and spongy (the innermost layer).

Table 2. Summary of the application of machine learning methods on bone drilling.

Table 2. Summary of the application of machine learning methods on bone drilling.

Author (year)	Data used in the machine learning method	Machine learning method	Machine learning is used for?	The purpose of using machine learning method
Pandey et al. (2014) [37]	Temperature, force, and surface roughness	grey relation analysis and fuzzy logic	Optimization	To determine the optimal combination of bone drilling parameters that minimize temperature, force, and surface roughness.
Pandey et al. (2014) [38]	Temperature, force, and surface roughness	Grey fuzzy reasoning grade	Classification	To find an optimal value of feed rate (mm/min) and speed (rpm).
Staroveski et al. (2015) [39]	Cutting forces, servomotor drive currents, and acoustic emission	Radial basis function neural network	Classification	To develop a drill wear classification model based on a multi-sensor approach.
Torun et al. (2020) [43]	Closed-loop signal and force sensor data	K-nearest neighbors and ensemble classifier	Classification	To detect breakthroughs and to estimate the condition of the drill bit in robotic bone drilling.
Agarwal et al. (2022) [40]	Temperature	K-nearest neighborsSupport vector regressionDecision treesRandom forest	Regression	To introduce different machine learning methods for predicting temperature elevations in rotary ultrasonic bone drilling.
Agarwal et al. (2022) [41]	Temperature	Multilayer perceptronLasso regressionRidge regression	Regression	To predict temperature rise during bone drilling.
Agarwal et al. (2022) [42]	Surface roughness and cutting force	Ridge regression, lasso regression, support vector regression, multi-linear regression, artificial neural network	Regression	To predict the surface roughness and cutting force during rotary ultrasonic bone drilling.
Caesarendra et al. (2024)	Vibration signal	Convolutional neural network	classify	To classifiy three bone layers based on vibration signal.

5. Experimental Procedure of Bone Drilling

3.2. Bone Drilling Lab Experiment of the Present Study

A bone drilling lab experiment utilized a Dobot Magician robot, National Instrument (NI) data acquisition (DAQ) module NI-9345, Brüel & Kjær three-axis accelerometer type 4535-B, and standalone academic LabVIEW software. A Dobot Magician robot was connected to a PC with available software for robot programming. A schematic of the bone drilling lab experiment is presented in Figure 2.

The original end effector of the Dobot Magician robot was replaced with the customized drilling mechanism as presented in Figure 2. The objective of using the Dobot Magician robot is to control the drilling process and to provide an accurate depth penetration of each layer in the bone drilling experiment. Bone drilling vibration was performed intermittently from the periosteum layer (the outermost layer), first cortical layer (the layer beneath the periosteum layer), and spongy layer (the innermost layer). An illustration of the bone layer is also presented in Figure 2. The vibration signal was acquired with a sampling frequency of 5 kHz. During the experiment, the drill was operated with 0.002 to 0.006 in/min feed rate and 500 rpm. The drill geometry was chosen as a twisted drill bit with a 3.5 mm diameter.

One three-axial accelerometer was attached near the hand drilling and another one was attached to the bone that will undergo drilling to obtain vibration signals during the drilling process as presented in Figure 2. The drill bit was then placed at the anterior surface of the proximal femur and drilled in clockwise rotation continuously. A fresh frozen cow femur was used in this research because this type of bone has almost similar characteristics to human bone [16]. The sample was fixed with a laboratory clamp while the drilling process was performed. The bone drilling was repeated up to about 8 holes, however, only three holes were used in the machine learning method.

To be able to separate the recordings and assign them to respective labels, the breakthrough sequence form drilling was recorded through the second cortical layer of the femur until breaking through into the adjacent soft tissue. Overall, ten individual drill holes were captured, however, only 8 holes were successfully drilled (holes 2 and 7 were unsuccessful). All recordings processed within the vibration signal were recorded using LabVIEW software as presented in the LabVIEW tabs plot in Figure 2.

The vibration data of the bone drilling experiment for three different layers is presented in Figure 3, Figure 4 and Figure 5. Figure 3 presents the bone drilling vibration data (x-axis) for the duration of one second. Figure 3(a), Figure 3(b), and Figure 3(c) are the vibration signals from the periosteum layer, first cortical layer, and spongy layer, respectively. The raw vibration signals of different layers are difficult to distinguish. However, if the vibration signal was plotted only for 0.2 seconds (0.5 ~ 0.7 sec) for zooming purposes, it shows a different vibration signal shape as presented in Zoom in parts of Figures 3(a)-(c). Another information that can be revealed in Figure 3 is the vibration signal amplitude of each layer. The deeper the drill bit comes in, the higher the amplitude (in mV) of the vibration signal.

Figure 4 presents the bone drilling vibration data (y-axis) for the duration of one second. Figure 4(a), Figure 4(b), and Figure 4(c) are the vibration signals from the periosteum layer, first cortical layer, and spongy layer, respectively. Similar to Figure 3, the raw vibration signals of three different layers in Figure 4 are also difficult to distinguish visually. However, if the vibration signal was plotted only for 0.2 seconds (0.5 ~ 0.7 sec) for zoom-in purposes, it shows a different vibration signal shape and amplitude as presented in zoom-in parts of Figures 4(a)-(c).

Figure 5 presents the bone drilling vibration data (z-axis) for the duration of one second. Figure 5(a), Figure 5(b), and Figure 5(c) are the vibration signals from the periosteum layer, first cortical layer, and spongy layer, respectively. Similar to Figure 3 and Figure 4, the raw vibration signals of three different layers in Figure 5 are not distinguishable visually. If the vibration signal was zoomed in for 0.2 seconds (0.5 ~ 0.7 sec), it shows a different vibration signal shape and amplitude.

A root mean square (RMS) of the bone drilling vibration amplitude is presented in Table 4. It is shown that the RMS amplitude increases as the drill bit goes through deeper. It indicates that the bone structure of each layer is different and when the bone structure has contact with the drill bit and triggers the vibration signal. In detail, an increase in RPM values from the periosteum to the first cortical layer is not as high as an increase in RPM values from the first cortical to the spongy layer. It indicates that the spongy layer has less stiffness than the other two layers (periosteum and first cortical).

Table 2. Vibration amplitude of different axes and different layers represented by RMS.

Table 2. Vibration amplitude of different axes and different layers represented by RMS.

Layer	RMS of x-axis vibration (mV)	RMS of y-axis vibration (mV)	RMS of z-axis vibration (mV)
Periosteum	0.044	0.044	0.044
First cortical	0.092	0.063	0.051
Spongy	4.044	5.505	5.853

4. Long Term-Short Memory (LSTM) Method

5. LSTM Results

5.1. LSTM Model

In this study, the LSTM algorithm that is available in TensorFlow Keras was used. To develop the LSTM model, 70 % vibration data was used for training, and 30% data was used for testing. The validation data was obtained from 20% of the training data. The LSTM architecture used in this project is presented in Table X and the summary is as follows: Input Layer -> LSTM Layer (return_sequences=True) -> LSTM Layer -> Flatten Layer -> Dense Layer (Output Layer). With this architecture, the model can accept the sequential vibration data from the x-, y-, and z-axis for each layer. The sequential vibration data was processed in two LSTM layers to obtain the prediction model for multiclass classification. The ‘softmax’ activation function was selected as the dense layer.

Table 2. LSTM architecture for multi-class classification.

Table 2. LSTM architecture for multi-class classification.

Layer (type)	Output shape	Param #
input_1 (InputLayer)	[(None, 3, 1)]	0
Astm (LSTM)	[(None, 3, 32)]	4352
lstm_1 (LSTM)	(None, 32)	8320
flatten (Flatten)	(None, 32)	0
dense (Dense)	(None, 3)	99
Total params: 12771 (49.89 KB)
Trainable params: 12771 (49.89 KB)
Non-trainable params: 0 (0.00 Byte)

5.3. LSTM Classification Results and Discussion

Once the model is developed, the next step is to compile and train the LSTM model. At the compilation stage, the LSTM model is configured with an ‘adam’ optimizer, a ‘categorical_crossentropy’ loss function because this is a multiclass classification problem. Some ‘callback’ functions such as EarlyStopping, ModelCheckpoint, and LearningRateScheduler are also used to control the training process. An ‘accuracy’ metric to evaluate the model’s performance is used during the training process. The model evaluation is presented in Figure 7 with has test loss of 0.013 and test accuracy of 0.993

Table 2 shows a classification report which provides detailed information regarding model performance for each target class. The evaluation results of layer 1 (periosteum) and layer 2 (first cortical) show that the model has 0.99 for precision, recall, and f1-score. In the case of layer 3 (spongy) layer, it produces perfect classification as shown in precision, recall, and f1-score of 1.00. Figure 8 shows the precision-recall curve that shows layer 3 has perfect results compared to the other two layers (periosteum and first cortical) which have small different.

Table 2. LSTM classification report.

Table 2. LSTM classification report.

	Precision	Recall	F1-score	Support
Periosteum (layer 1)	0.99	0.99	0.99	29993
First cortical (layer 2)	0.99	0.99	0.99	30087
Spongy (layer 3)	1	1	1	29920
Accuracy			0.99	90000
Macro avg	0.99	0.99	0.99	90000
Weighted avg	0.99	0.99	0.99	90000

A confusion matrix for the training and testing process of LSTM model development with 10 epochs is presented in Figure 9. It is shown the classification of the three bone layers is generally successful. However, there were a few misclassification results as presented in the confusion matrix of training and testing. In the training confusion matrix, the periosteum layer of about 716 out of 70006 data is classified in a first cortical layer which is about 1.02 % incorrect prediction. Another misclassification is also found in the first cortical layer with 677 out of 69913 data predicted in the periosteum layer which is about 0.97 % classification error. The perfect classification result was shown in the spongy layer where 100% data was classified correctly.

In the testing confusion matrix, the periosteum layer of about 284 out of 29993 data is classified in a first cortical layer which is about 0.95 % incorrect prediction. Another misclassification is also found in the first cortical layer with 323 out of 30084 data predicted in the periosteum layer which is about 1.07 % classification error. The perfect classification result was shown in the spongy layer where 100% data was classified correctly.

6. Conclusions

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