Research Papers

A Model for the Prediction of Thermal Response of Bone in Surgical Drilling

[+] Author and Article Information
Nazanin Maani

Department of Mechanical Engineering and Energy Processes,
Southern Illinois University,
Carbondale, IL 62901
e-mail: n.u.maani@siu.edu

Kambiz Farhang

Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University,
Carbondale, IL 62901
e-mail: farhang@siu.edu

Mohammad Hodaei

Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University,
Carbondale, IL 62901
e-mail: mhodaei@siu.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received September 6, 2013; final manuscript received January 24, 2014; published online May 9, 2014. Assoc. Editor: Srinath V. Ekkad.

J. Thermal Sci. Eng. Appl 6(4), 041005 (May 09, 2014) (17 pages) Paper No: TSEA-13-1151; doi: 10.1115/1.4026625 History: Received September 06, 2013; Revised January 24, 2014

This paper develops a mathematical model for predicting the thermal response in the surgical drilling of bone. The model accounts for the bone, chip, and drill bit interactions by providing a detailed account of events within a cylindrical control volume enveloping the drill, the cut bone chip within the drill bit flute, and the solid bone. Lumped parameter approach divides the control volume into a number of cells, and cells within the subvolumes representing the drill solid, the bone chip, and the bone solid are allowed to interact. The contact mechanics of rough surfaces is used to model chip–flute and chip–bone frictional interaction. In this way, not only the quantification of friction due to sliding contact of chip–flute and chip–bone rough surface contact is treated but also the contact thermal resistances between the rubbing surfaces are included in the model. A mixed combination of constant and adaptive mesh is employed to permit the simulation of the heat transfer as the drill bit penetrates deeper into the bone during a drilling process. Using the model, the effect of various parameters on the temperature rise in bone, drill, and the chip is investigated. It is found that maximum temperature within the bone occurs at the location adjacent to the corner of the drill-tip and drill body. The results of the model are found to agree favorably with the experimental measurements reported within the existing literature on surgical drilling.

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Fig. 1

Drill bit nomenclature

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Fig. 2

Drill cross section

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Fig. 3

Cross section of bone with drill bit embedded in it, pressure in the flute

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Fig. 4

Various views of cutting

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Fig. 5

Force balance on a chip section

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Fig. 6

Forces on a differential volume within the chip segment

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Fig. 7

The lumped cells and zones

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Fig. 8

Heat balance for various cells: (a) a general cell, (b) the interface, and (c) chip with mass transfer

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Fig. 9

Thermal resistors and capacitors (a) the chip cells, (b) the cells connectivity, and (c) the general cell within the control volume

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Fig. 10

Temperature rise versus drill depth for the bone cells adjacent to the friction interface during drilling: (a) zone III, (b) zone IV, and cells within the drill: (c) drill tip in zone III and (d) drill body in zone IV

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Fig. 11

Temperature distribution at the completion of drilling (a) in the presence of chip–wall interface friction and (b) in the absence of chip–wall friction (drill bit diameter = 2.5 mm, feed rate = 2 mm/s, angular velocity = 3000 rpm, point angle = 90 deg, and helix angle = 20 deg)

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Fig. 12

(a) Temperature rise in the critical cell within zone IV as drill depth increases and (b) temperature distribution for bone cells adjacent to the chip along the drill bit at the time of completion of drilling (drill bit diameter = 2.5 mm, feed rate = 2 mm/s, angular velocity = 3000 rpm, point angle = 90 deg, and helix angle = 20 deg)

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Fig. 13

Temperature response: (a) temperature distribution in the drill bit at the completion of drilling and (b) bone critical cell temperature history during drilling (drill bit diameter = 2.5 mm, feed rate = 2 mm/s, angular velocity = 3000 rpm, point angle = 90 deg, and helix angle = 20 deg)

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Fig. 14

Variation of maximum temperature in the first three cells within the bone located at 1.0, 0.3, 0.5 mm radial distances from the hole with changing (a) feed rate, (b) helix angle, (c) spindle speed, (d) point angle, and (e) diameter

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Fig. 15

Maximum temperature of bone, chip and bit at different depths at the time of completion of drilling for (a) feed rate of 0.2 mm/s and (b) feed rate of 2 mm/s

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Fig. 16

Maximum bone temperature during drilling with varying (a) feed rate, (b) helix angle, (c) spindle speed, (d) point angle, and (e) diameter (all the calculations are done with constant parameters, stainless steel, 2.5 mm diameter, 90 deg point angle, 3000 rpm with drill bit and bone of 20 and 37 °C. When not changed, feed rate = 2 mm/s, helix angle = 20, and spindle speed = 3000 rpm).



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