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

• An inverse method is developed to estimate the temporal and spatial distributions of bone grinding heat flux.
• This method couples sequential function specification method (SFSM) and sequential quadratic programming (SQP).
• Numerical study is performed to evaluate the robustness and identify the limitations.
• The heat flux reconstructed by this method is similar to the prior work with grinding thermal model.

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.