Effect of coring conditions on temperature rise in bone

Abstract

Coring is a surgical procedure in bone biopsy retrieval and dental/orthopaedic procedures, which may cause thermal damage to bone tissues adjacent to the coring zone. This study was performed to determine the temperature rise in bone by coring using a semi-empirical thermocouple approach. Concurrently, a custom-made dynamometer was used to measure the cutting and thrust forces during coring bovine cortical bone samples. The experimental results indicated that the cutting force, cutting speed, and depth of cut significantly affect the temperature rise in the cutting zone during coring process. In addition, acute temperature rises in the cutting zone occurred when the cutting speed exceeded threshold levels. The limited capacity of heat dissipation during coring is most likely responsible for such a sharp temperature rise with increasing cutting speed. Moreover, it was observed that the maximum size of potential thermal damage zone could reach to 3.0 mm in depth from the surface of the coring hole, assuming that thermal damage would occur when the temperature is greater than 47°C. Thus, proper cutting conditions need to be selected to avoid the potential thermal damage to bone during the coring procedures.

Keywords

Bone coring thermal damage cutting temperature cutting force

1. Introduction

Bone cutting is one of the oldest surgical procedures in the history of medicine [1,2]. During the process, surgeons may encounter the problem of thermal necrosis due to the temperature rise [3,4], which has been reported in tibial reaming for intramedullary nail fixation [5] and drilling process [6]. In addition, cytosolic constituents (organelles) released during the cutting process may result in local inflammation, thus causing concurrent death of adjacent cells and consequently inflicting damage to the tissue [7–9].

Previous studies reported that thermal damage to bone occurred when cutting temperature was higher than 47–50°C [10,11] and that thermal necrosis started to take place after 50°C [12]. Thermal necrosis induced by surgeries is one of the most damaging factors for bone regeneration and osseointegration in cases of dental/orthopaedic implants, showing that the higher the degree of thermal necrosis, the slower the recovery of thermal damage affected areas [11]. Reduction of such damage is important for bone tissue regeneration, patient recovery, success of implant surgeries, and reduction of public health costs.

In the past, extensive studies have been focused mainly on drilling/reaming of bone. Limited information is available for coring. Since the cutting zone in coring process is much confined in a more enclosed region compared with other cutting processes, it is relatively hard for coolant to get into the cutting region, thus leading to higher temperature rises. Among the factors that affect temperature rise in cutting (e.g. cutting speed and depth of cut, geometry of cutting tool, coolant, and thermal properties of bone), cutting conditions (i.e. cutting speed and depth of cut) primarily determine the heat energy produced per unit time [13,14].

In this study, we intended to investigate the effect of cutting conditions on the temperature rise in bone during coring process. The specific objectives include: (1) to determine the effect of coring conditions on the temperature profile in the cutting zone using a custom-made dynamometer and a temperature sensor of thermocouples; and (2) to determine the size of potential thermal damage zone during the coring process as a function of cutting speed and depth of cut.

2. Materials & methods

Specimen preparation: In this study, a bovine femur from a two-year old cow at a local slaughter house was used. Bone cubes of roughly $6 mm \times 6 mm \times 6 mm$ were first dissected out from the mid diaphysis of the femur, then lapped and polished to the final size of $5.0 mm \times 5.0 mm \times 5.0 mm$ using sequential grits of sand papers. The cross section of the femur, which is vertical to the longitudinal direction of bone, was used for the coring tests. The bone cubes were wrapped in gauze soaked by a phosphate buffered solution (PBS), and preserved in freezer at −20°C prior to experiments.

Coring tests: The coring tests were conducted on a bench-top CNS milling machine (Prolight 1000 Machining Center, Light Machines Corporation, NM) under varying cutting speed ( $V_{c}$ ) and the depth of cut per tooth ( $d_{c}$ ), with eighteen combinations of six cutting speeds and three depths of cut (Table 1 ). For each cutting condition, the coring test was performed on four samples ( $N = 4$ ). In order to broaden the range of selectable cutting speeds, two different sizes (i.e. 2.2 mm and 2.7 mm) of trephine surgical coring bits (BASi Corporate, West Lafayette, IN) were used.

Table 1
Cutting conditions used in this study by different combination of rpm and coring bit diameter

$V_{c}$ (m/min)

$d_{c}$ (mm) $V_{c 1} = 1.005$ $V_{c 2} = 1.257$ $V_{c 3} = 1.571$ $V_{c 4} = 1.963$ $V_{c 5} = 2.513$ $V_{c 6} = 3.931$

$d_{c 1} = 0.001$ A rpm = 200 A rpm = 200 B rpm = 200 B rpm = 200 A rpm = 200 B rpm = 200

$d_{c 2} = 0.002$ A rpm = 200 A rpm = 200 B rpm = 200 B rpm = 200 A rpm = 200 B rpm = 200

$d_{c 3} = 0.003$ A rpm = 200 A rpm = 200 B rpm = 200 B rpm = 200 A rpm = 200 B rpm = 200

	$V_{c}$ (m/min)
$d_{c 1} = 0.001$	A rpm = 200	A rpm = 200	B rpm = 200	B rpm = 200	A rpm = 200	B rpm = 200
$d_{c 2} = 0.002$	A rpm = 200	A rpm = 200	B rpm = 200	B rpm = 200	A rpm = 200	B rpm = 200
$d_{c 3} = 0.003$	A rpm = 200	A rpm = 200	B rpm = 200	B rpm = 200	A rpm = 200	B rpm = 200

Note: $V_{c}$ : Cutting speed; $d_{c}$ : depth of cut per tooth; rpm: revolution per minute, A: Type A coring bit with an average diameter of 1.76 mm, B: type B coring bit with an average diameter of 2.25 mm.

Cutting speed ( $V_{c}$ ): The cutting speed was adjusted by varying the rotational speed of spindle (80, 200, 250 and 500 rpm) and the diameter of the coring pit (2.2 mm and 2.7 mm). The cutting speed was calculated as follows: $\begin{matrix} (1) & V_{c} = π d n \end{matrix}$ where, $V_{c}$ is the cutting speed (m/min); d is the diameter of coring pit (m); n is the rotational speed of spindle (rpm).

Depth of cut per tooth ( $d_{c}$ ): The feed rate was maintained at 8, 16, or 24 mm/min during coring. The depth of each cutting tooth $(d_{c})$ was then determined by dividing the depth of coring feed per revolution $(d_{coring})$ by the number of cutting tooth $(N_{tooth})$ of the coring bit. $\begin{matrix} (2) & d_{c} = \frac{d_{coring}}{N_{tooth}} \end{matrix}$ where, $d_{coring}$ was estimated by subtracting the incremental deflection of the dynamometer beam per revolution from the feed rate.

Fig. 1.

Schematic representation of the custom-made beam-type dynamometer for measuring the torque (T) and vertical force (F) in the coring process: strain gages are placed at the locations where the maximum strains are expected with respect to the torque and vertical load.

Measurements of cutting forces: A custom-made beam-type dynamometer was used to measure the torque and vertical force during the coring tests. The beam of dynamometer was manufactured from Plexiglas with dimensions of $130 mm \times 3.8 mm \times 5.8 mm$ to ensure sufficient sensitivity of detecting torque/forces (Fig. 1 ). The beam was mounted on a Plexiglas support using super glue and the whole device was secured on the table of a CNC machine during coring tests. Totally, six (6) strain gauges were mounted on the beam to measure strains induced by torque and vertical load, respectively. A water chamber was secured on the top of the beam to submerge bone specimens in PBS during the coring tests (Fig. 1 ). Four strain gauges (Vishay Americas, CT) were placed in four maximum strain locations induced by torque to make a full-bridge circuit, whereas two strain gauges were placed in the maximum tension and compression strain locations induced by the vertical force in a half-bridge circuit (Fig. 1 ). The dynamometer was calibrated to measure the torque and vertical force during coring tests. The torque was then converted into the cutting force ( $F_{c}$ ) exerted to each cutting tooth of the coring bit. The analogue signals from dynamometer were amplified through a strain gauge input modules (NI 20160B, National Instruments, Austin, Texas) and then converted to digital signals by a data acquisition card (BNC-2010, National Instruments, Austin, Texas).

Fig. 2.

Schematic representation of the experimental setup and the heat transfer model used in this study for determining the temperature profile around the cutting zone: (A) placement of thermocouples and (B) moving-point-heat-source model. The temperature profile from the cutting zone to the depth of bone was estimated by extrapolation of temperature at point B measured by the thermocouples using the heat transfer model. Based on the temperature profile, the size of thermal damage zone size was determined as the distance ( $d_{damage}$ ) from the cutting zone where the estimated temperature exceeds 47°C.

Measurement of cutting temperature: The cutting temperature profile around the cutting zone of coring pit was measured using a semi-empirical approach. Briefly, the temperature rise ( $Δ T$ ) at a location adjacent to the cutting zone was first measured using a pair of K-type thermocouples (Fluke Networks, WA). The thermocouples were inserted in a previously drilled hole to a distance 0.05 mm–0.15 mm away from the anticipated coring hole to measure the temperature rise in the vicinity of cutting zone (Fig. 2 (A)). A data logger (MODEL 51 Thermometer, Fluke Networks, WA) was used to record the temperature data. By continuously recording temperature changes, the temperature profile around the cutting zone was then estimated by extrapolating the experimental data using the analytical model of moving-point-heat-source (Fig. 2 (B)). Since the cutting energy is mainly converted into heat energy within the cutting zone, the heat accumulation during coring process could be deemed as a heat source moving on the bone surface at a speed of feed rate. The general differential equation for this problem is given as $\begin{matrix} (3) & \frac{\partial^{2} T}{\partial x^{2}} + \frac{\partial^{2} T}{\partial y^{2}} + \frac{\partial^{2} T}{\partial z^{2}} + \frac{\dot{W}}{k} = \frac{1}{α} \frac{\partial T}{\partial t} \end{matrix}$ where, T is temperature, ( $x, y, z$ ) are the Cartesian coordinates, $α (= \frac{k}{ρ c})$ is the thermal diffusivity, t is time and $\dot{W}$ is the rate of heat generated within the solid per unit volume (i.e. W/m³), k is the thermal conductivity ( $W / m \cdot K$ ), and $ρ c$ is the volumetric specific heat (J/m³K). Solving for the temperature rise at the cutting zone using the boundary conditions shown in Fig. 2 , the following equation was obtained [15]: $\begin{matrix} (4) & Δ T = \frac{Q}{4 π r k} exp [- \frac{f (ρ + x)}{2 α}] \end{matrix}$ where, $ρ = {(x^{2} + y^{2} + z^{2})}^{1 / 2}$ ; f is the feed rate of the coring bit; and Q is the magnitude of heat source. By plugging in the measured temperature rise ( $Δ T$ ) adjacent to the cutting zone ( $x = 0.05 - 0.15 mm$ ), Q could be readily determined. Then, Equation (4) was used to determine the temperature profile at any point ( $x, y, z$ ) around the cutting zone. The thermal properties of cortical bone were selected using the data reported in the literature [16]. That is, the range of thermal conductivity was 0.38 to $2.3 W / m \cdot K$ , with an average of $1.29 W / m \cdot K$ ; the bone density ranged from $1.86 \times 103$ to $2.9 \times 103 kg / m^{3}$ , with an average of $2.2 \times 103 kg / m^{3}$ ; and the range of specific heat was $1.15 \times 103$ to $1.73 \times 10^{3} J / kg \cdot K$ , with an average of $1.26 \times 10^{3} J / kg \cdot K$ . In this study, the average values were used.

Work done in coring process and cutting energy: It was assumed that the rate of heat energy generated in coring was approximately equal to the total work done per unit time ( $\dot{W}$ ) as: $\begin{matrix} (5) & \dot{W} = F_{c} V_{c} \end{matrix}$ where, $F_{c}$ is cutting force and $V_{c}$ is cutting speed. In addition, the specific cutting energy ( $u_{c}$ ), which is defined as the energy consumed in removal of per unit volume of bone by each tooth, was estimated using the following equation: $\begin{matrix} (6) & u_{c} = \frac{F_{c}}{w_{t} d_{c}} \end{matrix}$ where, r is radius of coring bit, $w_{t}$ is width of the cutting tooth of the coring bit, and $d_{c}$ is depth of cut.

Damage zone determination: The depth of thermal damage zone ( $d_{damage}$ ) in bone from the surface of coring hole was estimated based on the temperature profile obtained using the semi-empirical approach as shown in Fig. 2 . $d_{damage}$ was considered zero if the temperature rise ( $Δ T$ ) in bone was less or equal to 10°C, which is equivalent to a temperature of 47°C in the body, considering the body temperature as 37°C. We selected this temperature (47°C) because previous studies have reported that thermal damage to bone may occur at the temperature [12]. If the temperature was greater than 47°C, thermal damage would be considered at the location and maximum distance of the thermal damage zone from the cutting zone was considered as $d_{damage}$ .

Data Analysis: The correlations among the parameters measured in this study ( $F_{c}, d_{c}, Δ T$ , $\dot{W}, u_{c}$ , and $V_{c}$ ) were analyzed to investigate the effect of coring conditions on the temperature rise in bone. Additionally, multiple linear regression analysis was performed to examine the contribution of cutting speed and depth of cut to the temperature rise. The statistical significance was considered only if $p < 0.05$ .

3. Results

Cutting forces vs. cutting speed and depth of cut : The cutting force ( $F_{c}$ ) was significantly correlated to the depth of cut and cutting speed ( $p < 0.05$ ), showing an increase almost linearly with increasing depth of cut, but a decrease with the cutting speed (Fig. 3 ). In addition, the vertical (or thrust) force ( $F_{v}$ ) indicated similar trends with increasing cutting speed and depth of cut ( $p < 0.05$ ).

Fig. 3.

Effects of depth of cut (A) & (B) and cutting speed (C) & (D) on the cutting and vertical forces. The cutting force ( $F_{c}$ ) was significantly correlated to the depth of cut and cutting speed ( $r > 0.9$ , $p < 0.05$ ), showing an increase almost linearly with increasing depth of cut, but a decrease with the cutting speed. In addition, the vertical (or thrust) force ( $F_{v}$ ) indicated similar trends with increasing cutting speed and depth of cut ( $r > 0.9$ , $p < 0.05$ ).

Temperature rise vs. cutting speed and depth of cut : The temperature rise ( $Δ T$ ) in the cutting zone varied with both the depth of cut and the cutting speed (Fig. 4 ). $Δ T$ decreased almost linearly with the depth of cut irrespective of cutting speeds, with the correlation coefficients of the regression being greater than 0.90 ( $p < 0.05$ ). However, the correlation between the cutting speed and temperature rise exhibited a different trend. First, $Δ T$ gradually increased almost linearly at slower cutting speeds ( $< 2.0 m / \min$ ). Then, $Δ T$ demonstrated an acute increase after the cutting speed reaching to about 2.0 m/min, and then leveled off at higher cutting speeds afterwards. This trend was very consistent irrespective of the depth of cut. Since the work done per unit time during the coring process increases with cutting speed, the amount of heat energy transformed from the work done would in turn increase per unit time, thus eventually resulting in an increase of cutting temperature at the cutting zone. The sensitivity analysis in the regression indicated that the first-order sensitivity indexes of depth of cut and cutting speed were 51.2% and 73.6% for temperature rise, respectively, showing a much higher effect inflicted by cutting speed on the temperature rise in the cutting zone compared to the depth of cut.

Fig. 4.

Effect of cutting speed (A) and depth of cut (B) on the temperature rise in the coring zone. A sharp increase ( $p < 0.05$ ) in temperature rise was observed from the cutting speed 2.0 m/min to 3.0 m/min, indicting an accelerated heat accumulation under the condition. In addition, the temperature rise was negatively proportional to the depth of cut ( $r > 0.9$ , $p < 0.05$ ).

Fig. 5.

Relationships between the work done per unit time during the coring process and the temperature rise in the cutting zone (A) and between the specific cutting energy and the temperature rise in the cutting zone (B). The sudden increases of temperature rise ( $p < 0.05$ ) before and after the threshold cutting work done per unit time suggest that heat dissipation cannot cope with the heat accumulation induced by the coring process (A). Linear relations ( $p < 0.05$ ) were observed to show a decreased energy with temperature rise in the cutting zone (B).

Temperature rise vs. work done by coring : By plotting the temperature rise with respect to the work done per unit time by coring, it was observed that strong correlations existed between the work done by coring and temperature rise in bone, showing a sharp increase ( $p < 0.05$ ) in the temperature rise in the cutting zone at a threshold value of work done per unit time (Fig. 5 (A)). However, the threshold values increased as the depth of cut was raised. Moreover, the magnitude of such acute changes decreases as the depth of cut increased ( $p < 0.05$ ). These results suggested that the capacity of heat dissipation was improved as the depth of cut increased. However, acute heat accumulation might occur in coring process, thereby leading to a sharp increase in temperature rise in the cutting zone.

Specific cutting energy : By plotting the specific cutting energy with respect to the temperature rise, it was found that the specific cutting energy decreased linearly with an increase in temperature rise irrespective of the depth of cut (Fig. 5 (B)). To estimate the significance level of the effect of both cutting conditions on specific cutting energy, a direct multiple linear regression analysis was performed. In this analysis, it was assumed that effect of depth of cut and cutting speed was independent. Correlations were considered significant at $p < 0.01$ . The results indicated that the effect of the depth of cut and cutting speed on the specific cutting energy was significant with a R value of 0.963. This result suggested that bone became less resistant to removal as the cutting speed increased.

Thermal damage zone assessment : It was observed that thermal damage occurred at certain combinations of the depth of cut and cutting speed (Table 2 ), the maximum depth of the estimated thermal damage zone reached to 3.0 mm under the cutting conditions of in this study. Using the table, the surgeons could select proper coring condition to avoid potential thermal damage inflicted during the coring process.

4. Discussions

The ultimate goal of this study was to determine the effect of cutting conditions on the temperature rise in bone and its potential impact on the thermal damage to bone. it is well known that the temperature rise in the cutting zone is the consequence of heat accumulation during cutting process. A number of factors including cutting speed, feed rate, tool geometry, and cooling condition etc. may affect the magnitude of heat generation. Among them, the cutting speed and depth of cut are considered as the most effectual factors in the heat generation [17]. In this study, we focused on the effect of cutting speed and depth of cut on the coring forces, temperature profile around the cutting zone, and specific cutting energy, all of which were estimated using the experimental data obtained using a custom-made dynamometer and thermocouples.

First, the results of this study indicate that the effect of cutting conditions on the cutting force is very similar with those reported in the literature, showing that the cutting force increases with the depth of cut (Fig. 3 (A)), but decrease with increasing cutting speed (Fig. 3 (B)) [18–22]. It is not surprising because an increase in the depth of cut would lead to more materials to be removed in the cutting process, thus requiring more cutting force to achieve the goal. On the other hand, an increase in cutting speed would lead to an increase in cutting temperature, thus subsequently reducing the resistance of materials to the removal process and finally reducing the cutting force. Similarly, the vertical (or thrust) force follows a similar trend with respect to the cutting speed and depth of cut as reported in the literature in orthogonal cutting of bone [18]. Previous studies reveal that such an increase in the thrust force with the increasing depth of cut is related to the elevated shear area during the chip formation process [19]. On the other hand, the decrease of thrust force with increasing cutting speed may be due to the heat-induced softening effect induced by the rising cutting temperature [19,20].

Table 2
Estimated thermal damage distance^∗ (mm) under different cutting conditions

^∗The thermal damage distance was estimated as the size of the region around the cutting zone where the estimated temperature was higher or equal to 47°C, which was defined as the threshold temperature that may lead to thermal damage to bone.

The results of this study indeed indicate that the specific cutting energy decreases as cutting temperature increases (Fig. 5 (B)). In fact, the specific cutting energy is directly related to cutting speed and depth of cut as reported in the literature [18]. The effect of depth of cut is most likely due to the size effect [23], showing that the toughness of bone decreases as the removal volume increases during the cutting process. The effect of the cutting speed on the specific cutting energy observed in this study is consistent with those reported in previous studies [24]. The decreased specific cutting energy with temperature rise is most likely due to the heat induced deterioration of bone mechanical properties (e.g. strength and toughness).

The temperature rise in the cutting zone may lead to a reduction in coring forces (Fig. 3 (C) & (D)) and therefore consequently result in less work done in the cutting zone. Since the heat generated in the cutting zone is mainly from the work done by the coring process, the reduction in the cutting work would give rise to less heat accumulation (or temperature rise) in the coring zone. This suppressing effect on temperature rise in the cutting zone is most likely due to the deteriorated toughness of bone associated with the temperature rise. Therefore, the transitional behavior in temperature rise with cutting speed is actually an outcome of thermodynamic balance between cutting energy reduction due to reduced cutting forces and rise of heat energy induced by an elevated cutting speed during the coring process (Fig. 5 (A)).

Interestingly, an acute increase in the temperature rise is observed in this study as the cutting speed exceeds a threshold value. In general, cutting temperature increases with cutting speed, while decreases with the depth of cut (Fig. 4 ). In fact, the rise of temperature is directly related to the increased heat energy generated in the cutting zone during the coring process (Fig. 5 (A)), which reflects the combined effect of both the depth of cut and cutting speed as aforementioned. As heat accumulates in the coring zone, a temperature rise is anticipated as the more heat energy needs to be dissipated through the surrounding media of the cutting zone. Several scenarios could be considered for the heat dissipation: (1) heat dissipation in surrounding bone tissues, (2) heat carried away by the tissue debris removed by cutting and the coolant (water), and (3) heat dissipated via the coring bit. Since the heat conductivity of bone is only about one order of magnitude below those of steels (coring bits), heat may be easily built up in the cutting zone of bone. In addition, heat generation and heat transfer in bone are also dependent on another two factors: (a) the rate of heat generation that is mainly related to cutting speed, and (b) the duration of heating that decreases with increasing cutting speed at a fixed location [14]. All these factors may be involved in the accelerated heat buildup in bone when cutting speed exceeds a threshold level, thus causing the acute temperature rise in the cutting zone of bone.

Finally, the results of this study suggest that the coring process could potentially induce thermal damage to bone if the coring conditions (i.e. cutting speed and depth of cut per teeth) are not properly selected. Improper coring conditions may result in excessive temperature rise, thus consequently cause thermal damage to bone. Keeping this in mind, the proper selection of cutting speed and depth of cut becomes important for design of coring tools by engineers and optimal operation of coring process by surgeons.

Some limitations exist for this study. First, estimation of temperature rise was performed using a semi-empirical method, considering a moving-point-heat-source, which may not necessarily represent the exact situation. However, it is reasonable for approximately assessing the temperature in the cutting zone since the experimental measurement can accurately capture the temperature in the vicinity of cutting zone. Second, the depth of cut was calculated by compensating the feed of tool with the deflection of the dynamometer beam, which only gives an approximate assessment. Nonetheless, these data are still valid for relative comparisons between the test groups. Finally, the safe range of cutting conditions obtained in this study can only be used as a reference since it may change if the cutting conditions and cutting tool vary.

5. Conclusions

The results of this study indicate that potential thermal damage to bone can be induced in the coring process due to the temperature rise in the cutting zone. It is also found that a transitional behavior of temperature rise occurs when cutting speed exceeds a threshold. It is speculated that such acute increases in temperature rise is most likely caused by the heat buildup that cannot be effectively dissipated during the coring process. Finally, potential thermal damage zone could expand to 3.0 mm from the coring hole if the cutting condition is not properly selected.

Footnotes

Acknowledgements

The authors are grateful of Mr. Ray Hansburger for his help in designing and building the force/torque dynamometer and setting up the experimental system for the coring tests.

Conflict of interest

The authors have no conflict of interest to report.

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	$V_{c}$ (m/min)

$d_{c}$ (mm)	$V_{c 1} = 1.005$	$V_{c 2} = 1.257$	$V_{c 3} = 1.571$	$V_{c 4} = 1.963$	$V_{c 5} = 2.513$	$V_{c 6} = 3.931$
$d_{c 1} = 0.001$	A rpm = 200	A rpm = 200	B rpm = 200	B rpm = 200	A rpm = 200	B rpm = 200
$d_{c 2} = 0.002$	A rpm = 200	A rpm = 200	B rpm = 200	B rpm = 200	A rpm = 200	B rpm = 200
$d_{c 3} = 0.003$	A rpm = 200	A rpm = 200	B rpm = 200	B rpm = 200	A rpm = 200	B rpm = 200