An inverse method to reconstruct the heat flux produced by bone grinding tools

Abstract Surgical bone grinding using high-speed, small spherical abrasive tools could cause thermal damage to the surrounding neurovascular structures. Our prior work developed a thermal model based on the two-dimensional grinding theory to calculate the temperature distribution. To verify the grinding-theory-based model, this study used experimental data incorporated with an inverse heat transfer method to mathematically estimate the heat flux distribution. This inverse method also considered a time-varying system to reflect a temporal change of the heat flux. Specifically, a coupled approach combining sequential function specification method (SFSM) and sequential quadratic programming (SQP) was employed to calculate the temporal and spatial variables simultaneously. Numerical tests were performed to determine the effectiveness and the limitations of this method. Then, the experimental data of prior work was applied to reconstruct the heat flux. The results verified a nearly time-invariant heat flux and demonstrated a consistent trend in the spatial distribution.

[1]  B. Blackwell,et al.  Inverse Heat Conduction: Ill-Posed Problems , 1985 .

[2]  Bruce L. Tai,et al.  Thermal model to investigate the temperature in bone grinding for skull base neurosurgery. , 2013, Medical engineering & physics.

[3]  S. Karmani.  The thermal properties of bone and the effects of surgical intervention , 2006 .

[4]  A. Behbahani-nia,et al.  A dual reciprocity BE-based sequential function specification solution method for inverse heat conduction problems , 2004 .

[5]  G. Augustin,et al.  Cortical bone drilling and thermal osteonecrosis. , 2012, Clinical biomechanics.

[6]  M. T. Hillery,et al.  Temperature effects in the drilling of human and bovine bone , 1999 .

[7]  Jae-Seob Kwak,et al.  Heat flux distribution model by sequential algorithm of inverse heat transfer for determining workpiece temperature in creep feed grinding , 2006 .

[8]  Prediction of bone grinding temperature in skull base neurosurgery , 2012 .

[9]  Hédi Hamdi,et al.  Temperature measurement and heat flux characterization in grinding using thermography , 2008 .

[10]  Bunyamin Aksakal,et al.  Influence of drill parameters on bone temperature and necrosis: A FEM modelling and in vitro experiments , 2012 .

[11]  J. K. Chen,et al.  Inverse estimation of spatially and temporally varying heating boundary conditions of a two-dimensional object , 2010 .

[12]  Forooza Samadi,et al.  Estimation of heat flux imposed on the rake face of a cutting tool: A nonlinear, complex geometry inverse heat conduction case study , 2012 .

[13]  Bruce L. Tai,et al.  Mist cooling in neurosurgical bone grinding , 2013 .

[14]  Junxiang Shi,et al.  Inverse problem of estimating space and time dependent hot surface heat flux in transient transpiration cooling process , 2009 .

[15]  K. Hynynen,et al.  MRI investigation of the threshold for thermally induced blood–brain barrier disruption and brain tissue damage in the rabbit brain , 2004, Magnetic resonance in medicine.

[16]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[17]  Toma Udiljak,et al.  INVESTIGATION INTO BONE DRILLING AND THERMAL BONE NECROSIS , 2007 .

[18]  Stephen Malkin,et al.  Grinding Technology: Theory and Applications of Machining with Abrasives , 1989 .

[19]  Reginaldo Teixeira Coelho,et al.  An inverse method to estimate the moving heat source in machining process , 2012 .

[20]  K. Takakura,et al.  Thermological study of drilling bone tissue with a high-speed drill. , 2000, Neurosurgery.