Optimization of drilling parameters for thermal bone necrosis prevention

Abstract

BACKGROUND:

Bone drilling is a mandatory process in orthopedic surgery to fix the fractured bones. Excessive heat is generated due to the shear deformation of bone and friction energy during the drilling process.

OBJECTIVE:

This paper is carried out to optimize the bone drilling parameters to prevent thermal bone necrosis. The main contribution of this work is instead of only consider the influence of rotational speed and feed rate, the effect of tool diameter and drilling hole depth are also incorporated for optimization study.

METHODS:

Response surface methodology (RSM) was used to develop a temperature prediction model. Drilling experiments were performed using finite element software DEFORM-3D. Analysis of variance (ANOVA) was conducted to investigate the drilling parameters’ effect. Desirability function in RSM was used to determine the optimum combination of drilling parameters.

RESULTS:

Results indicated that one applicable combination of drilling parameters could increase the bone temperature by less than 0.03%. To avoid thermal bone necrosis, eight reasonable combinations of drilling parameters were proposed. 3.3 ${}^{\circ}$ C residuals between in-vitro experiments and predicted values were demonstrated.

CONCLUSIONS:

It is envisaged that finite element simulation with RSM can simplify tedious experimental works and useful in the clinical application to avoid bone necrosis.

Keywords

Drilling parameters osteonecrosis temperature response surface methodology optimization

1. Introduction

Bones are susceptible to fracture when exposed to excessive loads, accidents, and illnesses [1, 2]. Fractured bones are frequently treated with internal and external fixation to restore their original position and alignment. Drilling of bone is required before screws and fixations are installed to the fractured parts. Excessive heat is generated from shear deformation during the cutting process and from the friction between drill bit and bone [3]. Bone temperature elevation to 47 ${}^{\circ}$ C for 1 minute exposure time could cause thermal osteonecrosis or irreversible death to the bone cells [4]. For this reason, the installed screws and plates could be loosened, but it reduces the sustainability and strength of the fixations.

Many researchers focused on the study of machining parameters’ influences on heat generation during the bone-cutting process [5, 6]. However, all of these studies mainly highlighted on the influences of individual drilling parameters on bone temperature. The real bone drilling procedure consists of the effect from the synergy of all drilling parameters. There has been insufficient literature published on the optimization of bone drilling process. Pandey and Panda [7] utilized grey-based fuzzy algorithm to optimize the response (temperature, force, and surface roughness) in the drilling of bovine bone with different drill speed (500–2,500 rev/min) and feed rate (40–60 mm/min). Then, they considered the Taguchi methodology coupled with fuzzy-based desirability function to optimize the bone drilling process with the same drill speed and feed rate ranges [8]. Nevertheless, one problem of both works was that the complexity of these approaches could be increased due to the determination of the weight of responses, which were based on user competency. Singh et al. [9] employed the Taguchi method with modified membership function to optimize rotational speed (1,000–3,000 rev/min) and feed rate (50–150 mm/min) during drilling of bovine cortical bones. They revealed that low rotational speed and feed rate produce the best results in terms of force and surface roughness. Yet, all of these studies neglected the influences of tool diameter and drilling hole depth on bone temperature. Tool diameter and drilling hole depth have been reported to cause significant bone temperature rise in the previous literature [10, 11].

Therefore, in this study, we investigated the influences of multiple parameters (rotational speed, feed rate, tool diameter, and hole depth) on bone temperature elevation with the finite element (FEM) simulation approach. Analysis of variance (ANOVA) was performed to better understand the influence of drilling parameters. RSM was used to develop a temperature prediction model combining all parameters and the optimum combination of these parameters was examined for smallest bone temperature elevation during the drilling process. Confirmation tests were conducted in vitro with bovine bones to validate the FEM results.

Table 1
Biomechanical properties of human bone

Properties	Value	Source
Density (kg/m ${}^{3}$ )	2100	[17]
Young’s modulus (GPa)	17	[18]
Poisson’s ratio	0.40	[18]
Specific heat (J/(kg K))	1260	[17]
Thermal conductivity (W/(m K))	0.38	[17]
Heat expansion coefficient (mm/ ${}^{\circ}$ C)	27.5 $\times$ 10 ${}^{-6}$	[19]
Emissivity	0.97	[20]

2. Materials and methods

2.1 Finite element-based simulations

In this study, the drilling simulations were performed with a finite element analysis software, DEFORM-3D (version 11, Scientific Forming Technologies Corporation, Columbus, OH, USA). Drilling simulation in DEFORM-3D consists of two phases (pre-processor and post processor phase).

In the pre-processor phase, drilling parameters such as rotational speed, feed rate, tool diameter, and hole depth were inserted into the software to develop the drill bit and bone model’s machining conditions [12]. The bone model was constructed with a 20 mm diameter and 10 mm thickness, and the biomechanical properties of a human bone (Table 1) were manually inserted into the software. The initial bone temperature was assumed to be 37 ${}^{\circ}$ C to reflect the temperature of a normal human body. A stainless steel drill bit model with 118 ${}^{\circ}$ point angle and 28 ${}^{\circ}$ helix angle was developed as recommended in literature [13, 14]. The bone was considered plastic and the drill bit as rigid during the simulations [15]. A shear friction factor of 0.3 was utilized for the interface between the drill bit and bone [16]. The velocity of the bone model was fixed along the $x$ , $y$ , and $z$ axis. The movement of the drill bit was fixed in the $x$ and $y$ direction. The ambient temperature was assumed to be 30 ${}^{\circ}$ C. For meshing of the models, tetrahedral element with size ratio of 1:4 was used for the drill bit and 1:7 for the bone model [12]. The default meshing method applied in DEFORM was the Lagrangian method because this method is capable of remeshing and restarting the simulation from the last point where the model stops. The database then was generated and proceeded for the simulation process. In the post processor phase, performance of the drilling simulation was analyzed and the data was extracted for statistical analysis. The complete drilling simulation process is presented in Fig. 1.

Figure 1.

Drilling simulations process in DEFORM-3D.

2.2 Response surface methodology

RSM is a collection of mathematical and statistical techniques, which is applicable in quantifying the influence of several input variables and the output response and is widely used in optimization of engineering problems [21, 22, 23]. The purpose of RSM is to optimize the response based on the investigated factors in the experiment plan.

Our study utilized the Design Expert Version 10.0 software to develop the experimental plan for RSM analysis. With this software, we performed analysis of the variance (ANOVA) on the recorded data to verify whether the proposed model is adequate to represent the relationship between all factors and response. A good model must possess an insignificant lack of fit, a significant value of Prob $>$ F (less than 0.05), and R ${}^{2}$ value close to 1. If the model is satisfactory, then the three-dimensional and contour plots could be proceeded with the interpretation.

Figure 2.

Flow chart for optimization study.

The bone drilling process was explored with a RSM design that is commonly used, which is called central composite design (CCD). Three levels were considered for the input parameters (rotational speed, feed rate, tool diameter, and hole depth) and represented as a code ( $-$ 1, 0, 1). The coded level (1) represents the highest original value, ( $-$ 1) represents the lowest original value, and (0) represents the average value of these two. The response for this study was the maximum bone temperature elevation during the drilling process. Based on the CCD approach, the total number of experiments to approximate the five drilling parameters with three levels for each parameter was 26 runs. Analysis of variance (ANOVA) was performed to analyze the significant parameters and the confidence interval was set at 95%. Then, the response data (maximum bone temperature) was fitted with the empirical model. The linear function is the simplest RSM model as shown in Eq. (1):

$\displaystyle Y=\beta_{0}+\sum_{i}^{k}\beta_{i}X_{i}+\varepsilon$ (1)

The second-order model in Eq. (2) would be considered if the model demonstrates any curvature:

$\displaystyle Y=\beta_{0}+\sum_{i}^{k}\beta_{i}X_{i}+\sum_{i<j}^{k}\beta_{ij}X% _{i}X_{j}+\varepsilon$ (2)

Generally, RSM expresses the relationship between input factor and output response with a second-degree polynomial equation as shown in Eq. (3):

$\displaystyle Y=\beta_{0}+\sum_{i}^{k}\beta_{i}X_{i}+\sum_{i}^{k}\beta_{ii}X_{% i}^{2}+\sum_{i<j}^{k}\sum\beta_{ij}X_{i}X_{j}+\varepsilon$ (3)

Here, $Y$ is the maximum bone temperature, $\beta_{0}$ is a constant, $\beta_{i}$ is the first degree coded input parameter, $\beta_{ii}$ is the second degree input parameter, and $\beta_{ij}$ is the interaction between parameters. The flow chart for this optimization study is illustrated in Fig. 2. Firstly, the input variables (drilling parameters) and their levels were decided to develop the design study. Drilling simulations were performed according to the study design and completely randomized. The response data (maximum bone temperature) then was extracted from the finite element software and statistical analysis was conducted to find the optimum drilling combinations. Finally, the in vitro validation experiments were performed on a conventional milling machine with bovine bones as the human bone substitute.

Table 2

Factors and levels for experimental study

Factor	Low level ( $-$ 1)	Center level (0)	High level ( $+$ 1)
A-rotational speed (rev/min)	1000	2000	3000
B-feed rate (mm/rev)	0.04	0.12	0.20
C-tool diameter (mm)	2	4	6
D-hole depth (mm)	1	3	5

Table 3

Experiments design layout

		Factor				Space type
Std	Run	A (rev/min)	B (mm/rev)	C (mm)	D (mm)
17	1	1000	0.12	4	3	Axial
7	2	1000	0.20	6	1	Factorial
1	3	1000	0.04	2	1	Factorial
4	4	3000	0.20	2	1	Factorial
16	5	3000	0.20	6	5	Factorial
21	6	2000	0.12	2	3	Axial
6	7	3000	0.04	6	1	Factorial
11	8	1000	0.20	2	5	Factorial
14	9	3000	0.04	6	5	Factorial
20	10	2000	0.20	4	3	Axial
3	11	1000	0.20	2	1	Factorial
19	12	2000	0.04	4	3	Axial
15	13	1000	0.20	6	5	Factorial
13	14	1000	0.04	6	5	Factorial
2	15	3000	0.04	2	1	Factorial
9	16	1000	0.04	2	5	Factorial
5	17	1000	0.04	6	1	Factorial
24	18	2000	0.12	4	5	Axial
8	19	3000	0.20	6	1	Factorial
18	20	3000	0.12	4	3	Axial
26	21	2000	0.12	4	3	Center
25	22	2000	0.12	4	3	Center
10	23	3000	0.04	2	5	Factorial
22	24	2000	0.12	6	3	Axial
12	25	3000	0.20	2	5	Factorial
23	26	2000	0.12	4	1	Axial

2.3 Experimental plan

In this work, four factors were investigated and their low and high levels are presented in Table 2. Rotational speeds in the range of 1,000 to 3,000 rev/min were considered and are parallel with the previous studies [24, 25]. Feed rate levels of 0.04 to 0.2 mm/rev have been frequently investigated in the literature [26, 27]. Tool diameters of 2 to 6 mm were used to reflect the standard size drill bit for bone drilling procedures [28]. Drilling hole depths of 1 to 5 mm were selected after considering the thickness of human cortical bone reported by Treece et al. [29].

Table 3 presents the experimental layout with the corresponding space type.

Table 4
Maximum bone temperature for drilling simulations study

Std	Run	Maximum bone temperature ( ${}^{\circ}$ C)
17	1	47.1
7	2	38.6
1	3	37.6
4	4	38.7
16	5	49.6
21	6	46.8
6	7	45.4
11	8	37.6
14	9	61.8
20	10	44.9
3	11	37.2
19	12	54.1
15	13	43.8
13	14	50.5
2	15	43.0
9	16	37.4
5	17	43.8
24	18	53.6
8	19	39.4
18	20	48.7
26	21	48.8
25	22	47.9
10	23	37.8
22	24	50.9
12	25	44.5
23	26	37.5

3. Results and discussion

The results from the bone drilling simulations are shown in Table 4. Statistical analysis was performed using the Design Expert software to analyze the influences of drilling parameters on bone temperature rise. From the Fit Summary output of maximum bone temperature, it was unveiled that the quadratic model is statistically significant ( $p$ value $=$ 0.0005) and as the highest order of polynomials, which is not aliased. Hence, it is used for further analysis.

Table 5
ANOVA table (partial sum of squares) for response surface quadratic model (response: maximum bone temperature)

Source	Sum of squares	dF	Mean square	F value	Prob. $>$ F
Model	715.97	14	51.14	14.12	$<$ 0.0001	Significant
A-Rotational speed	72.00	1	72.00	19.87	0.0010
B-Feed rate	79.38	1	79.38	21.91	0.0007
C-Tool diameter	153.12	1	153.12	42.27	$<$ 0.0001
D-Hole depth	139.44	1	139.44	38.49	$<$ 0.0001
AB	1.21	1	1.21	0.33	0.5750
AC	1.82	1	1.82	0.50	0.4929
AD	15.60	1	15.60	4.31	0.0622
BC	29.16	1	29.16	8.05	0.0162
BD	0.64	1	0.64	0.18	0.6824
CD	45.56	1	45.56	12.58	0.0046
A ${}^{2}$	2.53	1	2.53	0.70	0.4207
B ${}^{2}$	0.94	1	0.94	0.26	0.6209
C ${}^{2}$	5.13E-003	1	5.13E-003	1.42E-003	0.9707
D ${}^{2}$	73.16	1	73.16	20.19	0.0009
Residual	39.85	11	3.62
Lack of fit	39.45	10	3.94	9.74	0.2448	Not significant
Pure error	0.40	1	0.40
Cor total	755.82	25
S.D	1.90		R ${}^{2}$	0.9473
Mean	44.76		Adj. R ${}^{2}$	0.8802
CV	4.25		Pred. R ${}^{2}$	0.7090
PRESS	219.93		Adeq. precision	13.5570

Table 6

Resulting ANOVA table (partial sum of squares) for reduced quadratic model (response: maximum bone temperature)

Source	Sum of squares	dF	Mean square	F value	Prob. $>$ F
Model	709.34	8	88.67	32.43	$<$ 0.0001	Significant
A-Rotational speed	72.00	1	72.00	26.33	$<$ 0.0001
B-Feed rate	79.38	1	79.38	29.03	$<$ 0.0001
C-Tool diameter	153.12	1	153.12	56.00	$<$ 0.0001
D-Hole depth	139.44	1	139.44	51.00	$<$ 0.0001
AD	15.60	1	15.60	5.71	0.0288
BC	29.16	1	29.16	10.66	0.0046
CD	45.56	1	45.56	16.66	0.0008
D ${}^{2}$	175.07	1	175.07	64.03	$<$ 0.0001
Residual	46.48	17	2.73
Lack of fit	46.08	16	2.88	7.11	0.2874	Not significant
Pure error	0.40	1	0.40
Cor total	755.82	25
Std. Dev.	1.65		R ${}^{2}$	0.9385
Mean	44.76		Adj R ${}^{2}$	0.9096
C.V. %	3.69		Pred R ${}^{2}$	0.8705
PRESS	97.91		Adeq precision	20.3950

3.1 ANOVA analysis

To obtain a good model, the test for significance of the regression model and individual model coefficients as well as test for lack-of-fit must be conducted. The results of these tests were summarized in ANOVA table as shown in Table 5.

From Table 5, it can be seen that the model is significant because the “Prob. $>$ F” value is less than 0.05, which is desirable as it illustrates that the terms in the model have a significant influence on the response (maximum bone temperature). In a similar manner, the main effect of rotational speed (A), feed rate (B), tool diameter (C), and hole depth (D); and the two-level interaction of feed rate and tool diameter (BC), and tool diameter and hole depth (CD); as well as the second-order effect of hole depth (D ${}^{2}$ ) are significant model terms. The other model terms and lack-of-fit are insignificant, which is useful since the model needs to fit. These insignificant terms can be dismissed to improve the model.

The backward regression procedure was performed to eliminate the insignificant terms and the resulting ANOVA table for the reduced quadratic model for maximum bone temperature is presented in Table 6. It is apparent from Table 6 that the model, the main effect of drilling parameters (rotational speed (A), feed rate (B), tool diameter (C) and hole depth (D)), the two-level interaction of rotational speed and hole depth (AD), feed rate and tool diameter (BC), tool diameter and hole depth (CD), and second-order effect of hole depth (D ${}^{2}$ ) are the significant terms. From the “F value” in Table 6, it can be concluded that the second-order effect of hole depth (D ${}^{2}$ ) is the most significant factor for bone temperature. For the main effect, tool diameter (C) contributes the most to the bone temperature rise due to the increase of friction energy with larger tool diameter and hence, it increases the bone temperature elevation [10]. The lack-of-fit is still insignificant. The value of R ${}^{2}$ is close to 1, which is desirable. The difference between predicted R ${}^{2}$ and adjusted R ${}^{2}$ is less than 0.2 and in a reasonable agreement. The predicted R ${}^{2}$ value is useful to determine whether the model is too complex and the ability of the model to predict the observation (maximum bone temperature). The adjusted R ${}^{2}$ is used to compare the model with different predictors. The adequate precision displays the ratio of signal to noise, which in this study is 20.395. A ratio higher than 4 demonstrates that the model can be used to navigate the design space and predict the response.

The coded factors are used in design of experiments (DOE) to transform the scale of the investigated factors (drilling parameters) to $+$ 1 (high value) and $-$ 1 (low value). The final empirical model in terms of coded factors for maximum bone temperature is as shown in Eq. (4) deduced by the statistical software:

$\displaystyle\text{Maximum bone temperature}=48.65+2.0A-2.1B+2.92C+2.78D+0.99% AD-1.35BC+1.69CD-5.62D^{2}$ (4)

Figure 3.

Normal probability plot of residuals for maximum bone temperature data.

Figure 4.

Residuals and predicted response for maximum bone temperature.

The final empirical model in terms of actual factors for maximum bone temperature is as shown in Eq. (5) based on Eq. (3):

$\displaystyle\text{Maximum bone temperature}=29.117+5.187\times 10^{-4}\text{ % Rotational speed}+7.499\text{ Feed rate}+1.205\text{ Tool diameter}+7.149\text% { Hole depth}+4.938\times 10^{-4}\text{ Rotational speed}\times\text{Hole % depth}-8.437\text{ Feed rate}\times\text{Tool diameter}+0.422\text{ Tool % diameter}\times\text{Hole depth}-1.406\text{ Hole depth}^{2}$ (5)

This model can be utilized to predict the maximum bone temperature elevation in bone drilling process within the limits of this experiment. Figure 3 indicates the normal probability plots of the residuals for maximum bone temperature. A check on the plots in Fig. 3 unveiled that the residuals fall on a straight line, which means that the errors are distributed normally.

Figure 4 shows the plots of residuals versus the predicted response for maximum bone temperature. No obvious pattern was identified, which implies that the proposed models are adequate and there is no violation of the independence or constant variance assumption.

3.2 Surface plots analysis

The 3D surface plots are useful in analyzing the effects of experimental parameters and searching for the optimum combination of drilling parameters to produce minimal elevation of bone temperature during the drilling process. Figure 5 shows the 3D surface plots for maximum bone temperature with respect to the interaction effects of hole depth and rotational speed. A positive correlation was located between bone temperature and rotational speed. This is expected since the friction energy increases with rotational speed; hence, bone temperature is increased. Augustin et al. [10] and Lee et al. [3] made similar observations in their studies. An increase in drilling hole depth increases the bone temperature, which reached the peak value at 3 mm depth. A plausible explanation is that the increase in temperature is caused by the increase in drilling force and friction energy with hole depth. Most of the energy was converted into heat. Heat accumulation in the drilling hole could occur and consequently resulted in an increase in the temperature. Similar behavior was also observed by [30, 31]. The bone temperature decreased slightly when the depth was increased to 5 mm. At this depth, most of the bone debris was removed from the drilling hole. It is known that heat is convected away along with the bone debris and this produces a cooling effect to the bone. However, this cooling effect was not sufficient to completely remove the heat in the hole; hence, bone temperature only decreased slightly.

Figure 5.

3D surface graph for interaction effect of hole depth and rotational speed.

Figure 6.

3D surface graph for interaction effect of tool diameter and feed rate.

The effects of tool diameter and feed rate on bone temperature when keeping the hole depth and rotational speed constant are exhibited in Fig. 6. Strong evidence of increase in bone temperature was distinguished when tool diameter was increased. Larger tool diameter produces bigger contact area between drill bit and bone and hence, increases the friction energy. Consequently, larger heat was generated and caused bone temperature elevation. There are similarities in bone temperature trend between this study and those described in [10, 26]. The data in Fig. 6 indicates the inversely proportional relation between feed rate and bone temperature. It may be the case that high feed rate produces an efficient cutting process and thus, shorten the drilling duration. Short drilling duration contributes to lesser heat accumulation and friction energy. As a result, bone temperature is reduced. Findings in the present study are consistent with the findings of [32, 33].

Table 7

Constraints for optimization of drilling parameters and response

Parameters and response	Goal	Lower limit	Upper limit	Lower weight	Importance
A: Rotational speed (rev/min)	Is in range	1000	3000	1	3
B: Feed rate (mm/rev)	Is in range	0.04	0.20	1	3
C: Tool diameter (mm)	Is in range	2	6	1	3
D: Hole depth (mm)	Is in range	1	5	1	3
Maximum bone temperature ( ${}^{\circ}$ C)	Minimize	37.2	56.8	1	3

Table 8

Solution of optimized drilling parameters for minimum bone temperature

Solution	Rotational speed	Feed rate	Tool diameter	Hole depth	Bone temperature	Desirability
	(rev/min)	(mm/rev)	(mm)	(mm)	( ${}^{\circ}$ C)
1	1002.099	0.198	5.155	1.001	37.153	1
2	1028.163	0.200	3.642	1.002	37.198	1
3	1004.072	0.200	3.224	1.002	37.193	1
4	1002.665	0.199	5.326	1.001	37.094	1
5	1016.591	0.199	4.951	1.006	37.181	1
6	1000.125	0.200	3.165	1.000	37.183	1
7	1004.827	0.197	5.682	1.004	37.181	1
8	1039.558	0.200	3.658	1.001	37.199	1
9	1018.197	0.200	3.701	1.001	37.177	1
10	1027.940	0.198	4.701	1.004	37.198	1
11	1001.968	0.200	4.053	1.009	37.195	1
12	1000.000	0.200	6.000	1.000	37.011	1
13	1003.065	0.200	2.971	1.000	37.199	1
14	1065.745	0.200	5.304	1.010	37.193	1
15	1081.534	0.199	5.836	1.005	37.169	1
16	1020.848	0.200	4.996	1.009	37.175	1
17	1028.660	0.200	3.702	1.002	37.193	1
18	1006.151	0.199	3.836	1.001	37.181	1
19	1017.739	0.199	5.166	1.013	37.195	1

3.3 Optimization

The main objective of this study is to determine the combinations of drilling parameters to minimize bone temperature elevation during the bone drilling process. The optimal combination could be determined by using a desirability function approach. Table 7 presents the criteria applied to minimize bone temperature rise with the-larger-the-better desirability function [21]. By setting the drilling parameters’ goal to “within range” and the maximum bone temperature’s goal to “minimize”, the optimization provides a minimum level of response (maximum bone temperature).

Table 8 demonstrates the analytical results of bone drilling optimization for the present work. Nineteen results were obtained, which the desirability value was 1. In this case, any of these solutions can be selected for minimum bone temperature elevation. However, the only applicable solution in real clinical bone drilling process is solution number 12 when drilling conditions were at 1,000 rev/min rotational speed, 0.2 mm/rev feed rate, 6 mm tool diameter size, and 1 mm drilling hole depth. The reason is other proposed solutions were really difficult to apply in real bone drilling setup due to complex setting of drilling parameters’ values (up to three decimal places).

All of the 19 solutions proposed in Table 8 were limited to hole depth of 1 mm. However, in real bone drilling process, sometimes the hole needs to be perforated deeper for stable installation of screws and fixations. The vital criterion is that maximum bone temperature must be limited to 47 ${}^{\circ}$ C, which is the critical level for bone necrosis. Therefore, the criteria was revised for maximum bone temperature and set to “in range” of 37 to 47 ${}^{\circ}$ C. The results produced one hundred possible solutions. Out of these solutions, only eight drilling parameter combinations were suitable for clinical applications. These solutions include drilling hole depth of up to 5 mm, which is deep enough for clinical applications.

Table 9
Comparison of bovine and human bone [9, 17, 18]

Properties	Human bone	Bovine bone
Tensile strength (MPa)	130–200	140–250
Compressive strength (MPa)	40–145	45–150
Young’s modulus (GPa)	10–17	10–22
Shear modulus (MPa)	3	3
Density (kg/m ${}^{3}$ )	1800–2100	1950–2100
Poisson’s ratio	0.38–0.4	0.33
Specific heat (J/kg K)	1260–1330	1300
Thermal conductivity (W/m K)	0.1–0.43	0.1–0.3

Figure 7.

Experimental bone drilling setup and measurement.

3.4 In-vitro bone drilling confirmation test

Confirmation tests were performed experimentally to verify the adequacy of the optimized solutions from the numerical study. The work piece selected for this study was bovine femur due to its close resemblance in properties to human bones [8, 24, 34, 35, 36, 37]. The comparison of mechanical properties between bovine and human bones in Table 9 proved that bovine bones possess high similarity with human bone. Therefore, bovine bone is suitable replacement for human bone in the bone drilling validation process.

Fresh bovine bones were obtained from the same local butchery and were used within a few hours after slaughter to prevent change of the bone properties. No animals were harmed specifically for this study and the animals were slaughtered for the local food industry. The end part of femur (epiphysis) was cut with a hacksaw and the middle part of femur (mid diaphysis) was used for the drilling study. Soft outer layer tissues (periosteum) were removed to avoid clogging of the drill bit flute. Figure 7 shows the experimental setup for the drilling study. The experiments were performed using the 3 axis conventional milling machine GATE PBM 2000 (UK) with variable rotational speed, feed rate, and drilling depth. The bone temperatures were measured with a K-type thermocouple ( $-$ 200–1372 ${}^{\circ}$ C) with data logger OMRON ZR-RX25 (Japan). The thermocouples were placed 0.5 mm from the drilling hole at the depth of 5 mm [3, 10]. HSS drill bits with point angle of 118 ${}^{\circ}$ and helix angle of 30 ${}^{\circ}$ were used for drilling of the bone.

Table 10
Confirmation tests

Solution	A (rev/min)	B (mm/rev)	C (mm)	D (mm)	Temperature elevation ( ${}^{\circ}$ C)
					Predicted	Actual	Residual	95% PI low	95% PI high
3	2000	0.12	4	5	8.8	6.9	$-$ 1.9	5.1	12.5
5	1000	0.04	2	5	1.9	0.5	$-$ 1.4	$-$ 2.2	6.2
21	3000	0.04	2	5	7.9	4.6	$-$ 3.3	3.7	12.2

The predicted and actual in-vitro bone drilling temperature elevation values were compared and the residuals and the percentage errors were calculated (Table 9). The residuals between the actual and the predicted values for bone temperature elevation were $\sim$ $-$ 3.3 to $-$ 1.4. Therefore, it can be concluded that the empirical models developed were reasonably accurate and the solutions for optimization of drilling parameters were within 95% prediction intervals. Prediction interval is the range where any individual value falls into 95% of the time during the bone drilling process within the investigated drilling parameters.

4. Conclusions

The present study was designed to determine the optimum drilling parameters’ combinations which produce minimum bone temperature elevation to prevent thermal bone necrosis. The statistical analysis revealed that the main effect of tool diameter was the most to significant factor to the bone temperature rise, followed by hole depth, feed rate and rotational speed. The most critical finding from this study is that the combination of rotational speed of 1,000 rev/min, feed rate of 0.2 mm/rev, tool diameter of 6 mm and drilling hole depth of 1 mm produced the minimum bone temperature rise (0.1 ${}^{\circ}$ C). The second major findings was that thermal bone necrosis can be prevented with eight different combinations of drilling parameters with the highest approximated maximum bone temperature is below 46.7 ${}^{\circ}$ C. The empirical model for bone temperature prediction was developed using statistical analysis and the in vitro bone drilling results were in reasonable agreement with the FEM drilling simulation’s results. This research is envisaged to serve as a base for future optimization studies of bone drilling process involving other excluded parameters’ influences such as drill bit initial temperature and bone mineral density. It is recommended that further research to be undertaken in the following areas: drill bit geometries and cooling systems.

Footnotes

Acknowledgments

The authors are grateful to Universiti Malaysia Pahang (UMP) for the financial support under grant number RDU 170372.

Conflict of interest

None to report.

References

Greco

Pisani

Conversano

Soloperto

Renna

Muratore

, et al. Ultrasound fragility score: An innovative approach for the assessment of bone fragility. Measurement [Internet] 2016; 101: 236-42. Available from: https://dx-doi-org.web.bisu.edu.cn/10.1016/j.measurement.2016.01.033.

Pisani

Greco

Conversano

Renna

Casciaro

Quarta

, et al. A quantitative ultrasound approach to estimate bone fragility: A first comparison with dual X-ray absorptiometry. Measurement [Internet] 2017; 101: 243-9. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0263224116303918.

Lee

Chavez

Park

. Parameters affecting mechanical and thermal responses in bone drilling: A review. J Biomech [Internet] 2018 Apr; 71: 4-21. Available from: https://doi.org/10.1016/j.jbiomech.2018.02.025.

Eriksson

Albrektsson

. Temperature threshold levels for heat-induced bone tissue injury: A vital-microscopic study in the rabbit. J Prosthet Dent [Internet] 1983 Jul [cited 2016 Sep 6]; 50(1): 101-7. Available from: http://linkinghub.elsevier.com/retrieve/pii/0022391383901749.

Al-Abdullah

Abdi

Lim

Yassin

. Force and temperature modelling of bone milling using artificial neural networks. Meas J Int Meas Confed [Internet] 2018 116 (November 2017): 25-37. Available from: https://doi.org/10.1016/j.measurement.2017.10.051.

Bulutsuz

Tanyel

Katiboğlu

. Measurement of temperature change during the implant site preparation to determine influence of tool characteristics. Meas J Int Meas Confed [Internet] 2016 Feb; 79: 354-9. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0263224115003115.

Pandey

Panda

. Optimization of bone drilling parameters using grey-based fuzzy algorithm. Meas J Int Meas Confed [Internet] 2014; Available from: https://www-mendeley-com.web.bisu.edu.cn/research/optimization-bone-drilling-parameters-using-greybased-fuzzy-algorithm.

Pandey

Panda

. Optimization of bone drilling using Taguchi methodology coupled with fuzzy based desirability function approach. J Intell Manuf [Internet] 2015; 26(6): 1121-9. Available from: https://dx-doi-org.web.bisu.edu.cn/10.1007/s10845-013-0844-9.

Singh

Jain

Gupta

. Multi-objective performance investigation of orthopaedic bone drilling using Taguchi membership function. Proc Inst Mech Eng Part H J Eng Med [Internet] 2017; 095441191773512. Available from: http://journals.sagepub.com/doi/10.1177/0954411917735129.

10.

Augustin

Davila

Mihoci

Udiljak

Vedrina

Antabak

. Thermal osteonecrosis and bone drilling parameters revisited. Arch Orthop Trauma Surg [Internet] 2007 Oct 30 [cited 2016 Sep 6]; 128(1): 71-7. Available from: http://link.springer.com/10.1007/s00402-007-0427-3.

11.

Bogovič

Svete

Bajsić

. Effects of a drill diameter on the temperature rise in a bone during implant site preparation under clinical conditions. Proc Inst Mech Eng Part H J Eng Med [Internet] 2016 Oct 1; 230(10): 907-17. Available from: http://pih.sagepub.com/lookup/doi/10.1177/0954411916660737.

12.

DEFORM 3D Version 11.0, User’s Manual. Version 11. Vol. 0. Scientific Forming Technologies Corporation, 2545 Farmers Drive, Suite 200 Columbus, Ohio; 2014. p. 4274.

13.

Narasimha

Osman

MOM

Chandrashekhar

Frazao

. An investigation into the influence of helix angle on the torque-thrust coupling effect in twist drills. Int J Adv Manuf Technol 1987; 2(4): 91-105.

14.

Wiggins

Malkin

. Drilling of bone. J Biomech 1976; 9(9): 553-9.

15.

Wang

Meng

. 3D finite element modeling and analysis of dynamic force in bone drilling for orthopedic surgery. Int J Numer Method Biomed Eng [Internet] 2014 Sep; 30(9): 845-56. Available from: http://onlinelibrary.wiley.com/doi/10.1002/cnm.1494/full.

16.

Alam

Mitrofanov

Silberschmidt

. Finite element analysis of forces of plane cutting of cortical bone. Comput Mater Sci [Internet] 2009; 46(3): 738-43. Available from: https://dx-doi-org.web.bisu.edu.cn/10.1016/j.commatsci.2009.04.035.

17.

Huiskes

. Some fundamental aspects of human joint replacement: Analyses of stresses and heat conduction in bone-prosthesis structures. Acta Orthop Scand [Internet] 1980; 51(185): 3-208. Available from: http://www.tandfonline.com/doi/full/10.3109/ort.1980.51.suppl-185.01.

18.

Kohles

. Applications of an anisotropic parameter to cortical bone. J Mater Sci Mater Med [Internet] 2000; 11(4): 261-5. Available from: http://link.springer.com/10.1023/A:1008940914693.

19.

Ranu

. The thermal properties of human cortical bone: An in vitro study. Eng Med 1987; 16(3): 175-6.

20.

Feldmann

Zysset

. Experimental determination of the emissivity of bone. Med Eng Phys 2016 Oct; 38(10): 1136-8.

21.

Bagaber

Yusoff

. Multi-objective optimization of cutting parameters to minimize power consumption in dry turning of stainless steel 316. J Clean Prod [Internet] 2017; 157: 30-46. Available from: https://dx-doi-org.web.bisu.edu.cn/10.1016/j.jclepro.2017.03.231.

22.

Asiltürk

Neşeli

İnce

. Optimisation of parameters affecting surface roughness of Co28Cr6Mo medical material during CNC lathe machining by using the Taguchi and RSM methods. Measurement [Internet] 2016 Jan; 78: 120-8. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0263224115005217.

23.

Akhbar

MFA

Malik

Yusoff

. Effects of drilling parameters in numerical simulation to the bone temperature elevation. Advanced Nanotechnology in Engineering and Medical Sciences 2018; 020002. Available from: http://aip.scitation.org/doi/abs/10.1063/1.5030881.

24.

Pandey

Panda

. Modelling and optimization of temperature in orthopaedic drilling: An in vitro study. Acta Bioeng Biomech 2014; 16(1): 107-16.

25.

Pandey

Panda

. Optimization of multiple quality characteristics in bone drilling using grey relational analysis. J Orthop [Internet] 2014 [cited 2016 Nov 30]; 6122552037(1): 1-7. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0972978X14000543.

26.

Augustin

Davila

Udiljak

Staroveski

Brezak

Babic

. Temperature changes during cortical bone drilling with a newly designed step drill and an internally cooled drill. Int Orthop [Internet] 2012 Jul 31 [cited 2016 Dec 7]; 36(7): 1449-56. Available from: http://link.springer.com/10.1007/s00264-012-1491-z.

27.

Noordin

Jiawkok

Ndaruhadi

Kurniawan

. Machining of bone: Analysis of cutting force and surface roughness by turning process. Proc Inst Mech Eng Part H J Eng Med [Internet] 2015; 229(11): 761-8. Available from: http://pih.sagepub.com/lookup/doi/10.1177/0954411915606169.

28.

Bertollo

Walsh

. Drilling of bone: Practicality, limitations and complications associated with surgical drill-bits [Internet]. Klika

, editor. Biomechanics in Applications 2011; 249-274. Available from: http://www.intechopen.com/books/biomechanics-in-applications.

29.

Treece

Gee

Mayhew

Poole

KES

. High resolution cortical bone thickness measurement from clinical CT data. Med Image Anal [Internet] 2010 Jun; 14(3): 276-90. Available from: https://dx-doi-org.web.bisu.edu.cn/10.1016/j.media.2010.01.003.

30.

Strbac

Giannis

Unger

Mittlböck

Vasak

Watzek

, et al. Drilling- and withdrawing-related thermal changes during implant site osteotomies. Clin Implant Dent Relat Res [Internet] 2015 Feb; 17(1): 32-43. Available from: http://doi.wiley.com/10.1111/cid.12091.

31.

Lee

Gozen

Ozdoganlar

. Modeling and experimentation of bone drilling forces. J Biomech [Internet] 2012 Apr [cited 2016 Dec 7]; 45(6): 1076-83. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0021929011007809.

32.

Lee

Ozdoganlar

Rabin

. An experimental investigation on thermal exposure during bone drilling. Med Eng Phys [Internet] 2012 Dec [cited 2016 Dec 7]; 34(10): 1510-20. Available from: https://dx-doi-org.web.bisu.edu.cn/10.1016/j.medengphy.2012.03.002.

33.

Abouzgia

James

. Measurements of shaft speed while drilling through bone. J Oral Maxillofac Surg 1995; 53(11): 1308-15.

34.

Gupta

Pandey

Silberschmidt

. Rotary ultrasonic bone drilling: Improved pullout strength and reduced damage. Med Eng Phys [Internet] 2017; 41: 1-8. Available from: https://dx-doi-org.web.bisu.edu.cn/10.1016/j.medengphy.2016.11.004.

35.

Gupta

Pandey

Mridha

Gupta

. Effect of various parameters on the temperature distribution in conventional and diamond coated hollow tool bone drilling: A comparative study. Procedia Eng [Internet] 2017; 184: 90-8. Available from: http://linkinghub.elsevier.com/retrieve/pii/S1877705817315795.

36.

Pandey

Panda

. Evaluation of delamination in drilling of bone. Med Eng Phys [Internet] 2015 Jul [cited 2016 Dec 7]; 37(7): 657-64. Available from: http://linkinghub.elsevier.com/retrieve/pii/S1350453315001034.

37.

Gupta

Pandey

. Experimental investigation and statistical modeling of temperature rise in rotary ultrasonic bone drilling. Med Eng Phys [Internet] 2016 Nov; 38(11): 1330-8. Available from: http://linkinghub.elsevier.com/retrieve/pii/S1350453316301898.

Optimization of drilling parameters for thermal bone necrosis prevention

Abstract

BACKGROUND:

OBJECTIVE:

METHODS:

RESULTS:

CONCLUSIONS:

Keywords

1. Introduction

Table 1 Biomechanical properties of human bone

2.1 Finite element-based simulations

Table 4 Maximum bone temperature for drilling simulations study

Table 5 ANOVA table (partial sum of squares) for response surface quadratic model (response: maximum bone temperature)

Table 9 Comparison of bovine and human bone [9, 17, 18]

Table 10 Confirmation tests

Footnotes

Acknowledgments

Conflict of interest

References

Table 1
Biomechanical properties of human bone

Table 4
Maximum bone temperature for drilling simulations study

Table 5
ANOVA table (partial sum of squares) for response surface quadratic model (response: maximum bone temperature)

Table 9
Comparison of bovine and human bone [9, 17, 18]

Table 10
Confirmation tests