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Bone heating due to drilling

Bone fracture treatment and other orthopedic procedures often require the bone drilling. QuickField example demonstrates transient temperature fields in the bone material due to the heat generated during the drilling process.

Problem type:
Axisymmetrical problem of the Transient Heat Transfer.

Geometry:
Bone fragment is considered as a cylinder with 3 cm radius and 3 cm height. Drilling is performed with 3 mm radius bit.

Given:
Thermal conductivity of bone λ = 0.54 W/K·m)
Density of the bone ρ = 1500 Kg/m3
Specific heat of bone C = 440 J/(Kg·K)
Initial temperature of bone is 37 °C (310 K).
Boundary conditions are simplified as convection with ambient temperature 37°C and convection coefficient 40 W/(K·m2).
Heat is generated at the tip of the drill bit, which has 3 mm length. Volume power of the generated heat is 1e7 W/m3.
Drilling speed is 5 cm/min, drilling time is 20 sec.

Task:
Find the transient temperature field in the bone. Calculate the temperature in the point A (6 mm from surface, 3 3m from axis) during 20 sec drilling process

Solution:
Moving drill bit may be replaced by a moving heat source in the QuickField block "channel" using following QuickField Data Editor formula:
1e7*impulse(x,0.05/60*t,0.05/60*t+0.003)
Initial conditions are specified by the Static Heat Transfer problem, linked to the Transient Heat Transfer problem.
Boundary conditions for the bone fragment are simplified as convection.

Results:

Temperature distribution in the bone.

Temperature plot for point A.

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