Research On The Heat Transfer And Its Inverse Problem For Bone Grinding Process

Neurosurgery has entered the period of minimally invasive operation. Endoscopicendonasal approach, could avoid the damage to the normal tissues during the invasiveprocedures, thus has received extensively attention due to the less damage to humanbody and the fast recovery after operation. Bone grinding is common procedure in theneursurgery. The heat generated during the grinding process could bring thermaldamage to the key tissues, such as the bone and the adjacent cranial nerves, and thevascular structure. Till now, there are few researches concerning the thermal problem ofgrinding the neurosurgery bones.In this work, experimental and numerical simulation methods are combined tostudy the heat transfer in bone grinding using miniature spherical grinding tool. Thethermal model was established for the bone grinding process, and the transienttemperature field during this process was simulated. Using the experimental data ofbone grinding, the inverse problems were investigated on the transient heat fluxintensity and its spatial distribution. On the basis, the3-D transient temperature fieldduring bone grinding was reconstructed. The relationship between the duty cycle ratioof motor and the amount of heat flowing into bone during grinding was also studied,and a real-time model was preliminarily built to predict the grinding heat, whichestablished the foundation for the real-time monitoring of the temperature of boneduring the grinding. The heat transfer during grinding with the addition of cooling liquidwas investigated as well. The more detailed description of the research contents and theconclusions is as follows,(1) The heat flux distribution coefficient on the interface between bone andgrinding tool was determined based on mechanical grinding theory, and a3-D transientfinite element model was constructed for analyzing the temperature distribution duringbone grinding process using miniature spherical grinding tool. The effects of grindingconditions, such as motion direction of grinding tool (X direction and Y direction), thecontact angle (0°,15°and30°) between the grinding tool and the bone, and the cuttingdepth (0.10mm,0.25mm, and0.40mm), on the heat distribution in ground zone wasdiscussed with numerical simulation. Additionally, the3-D transient temperature fieldsof bone under different grinding conditions were analyzed as well.(2) The grinding experiments using fresh bovine cortical were carried out when no cooling is applied, and the measured temperature information was obtained for8grinding conditions. Then the optimization method of ‘Active set’ was utilized toinversely estimate the thermal conductivity of bone and the amount of heat entering tothe bone under different grinding conditions, and the3-D transient temperature fieldwas established. The results show that the instantaneous maximum temperature of thebone could reach up to210°C when the contact angle of tool is30°, the cutting depthand the feed rate are0.4mm and20mm/min, respectively. If50°C was set to be thecritical value for thermal damage of body tissue, the thermal damage could reach thearea of3mm from the surface of the grinding slot.(3) The relationship between the duty cycle ratio and the grinding heat wasexplored, on the basis of the PWM signal obtained from the grinding experiment andthe grinding heat entering the bones that calculated via the inversion method. A goodliner relationship was demonstrated between the duty cycle ratio and the grinding heat.It was found that the linear slope was slightly lower when the grinding tool moves alongthe x direction than that along the z direction. For the three selected grinding conditions,the linear function was used to predict the grinding heat, and the aforementionedtransient finite element thermal analysis model was utilized to get the transienttemperature field. By comparison with the temperature response obtained in experiment,the effectiveness of the linear function model was validated. All these results couldcontribute to the realization of the real-time monitoring of the grinding temperature.(4) The heat generation during bone grinding was considered as transient heattransfer problem with unknown distributed moving heat source, according to the existedproblems in the model of heat flux distribution within the interface between bone andgrinding tool, which was derived from the mechanical grinding theory. The transientdistribution function of heat flux in the grinding zone was constructed by combing thespatial and the time functions. Moreover, inversion was implemented for the transientaverage heat flux and the transient distribution function of heat flux on the interfacebetween bone and grinding tool using the sequential function specification method(SFSM) and the sequential quadratic programming method (SQP). The validity of theabove method was verified through numerical simulation. In addition, the transientdistribution of heat flux on the contact surface was inverted by integrating the real-timetemperature information obtained in the grinding experiments. The transienttemperature field during the measurement was inverted as well.(5) According to the disadvantages of room temperature irrigation technology commonly used in clinic, a cryogenic mist cooling experiment system was developedfor bone grinding. During experiment, transient bone temperature was measured at thelocation0.5,1.0, and1.5mm underneath the ground groove. The experimental resultsshow that when the grinding tool moves backward, the cryogenic (3°C) mist cooling at120ml/h flow rate has obvious pre-cooling effect, and the maximum averagetemperature measured at the location0.5mm beneath ground groove was about21.0°C; when the grinding tool moves forward, the position of the nozzle relative to thegrinding tool limits the coolant flowing to the ground zone, which results in poorcooling effect that the maximum average temperature measured at the location0.5mmbeneath ground groove was about70.0°C. Futher, with experimentally measuredtemperautre, the FEA thermal analysis model with convection heat transfer boundaryand inverse heat transfer method are applied to reconstruct the bone temperature fieldunder mist cooling. The numerical results indicate that with backward grinding motion,the cryogenic mist cooling technique can significantly surpress the43°C thermal injuryboundary propogating under the ground surface.