A Microstructure-Based Mechanistic Model for Bone Sawing: Part 2—Acoustic Energy Rate Predictions

Part 2 of this paper is focused on modeling the acoustic emission (AE) energy rate as a function of the specific cortical bone microstructures (viz., osteon, interstitial matrix, lamellar bone, and woven bone) and the depth-of-cut encountered by the bone sawtooth. First, the AE signal characteristics from the sawing experiments (in Part 1) are related to the pure haversian and pure plexiform regions of the cut. Using the cutting force predictions from Part 1 as input, the AE energy rate is then modeled in terms of the energies dissipated in the shearing and plowing zones encountered by the rounded cutting edge. For this calculation, the rounded edge geometry of the sawtooth is modeled as a combination of (i) shear-based cutting from a negative rake cutting tool and (ii) plowing deformation from a round-nose indenter. The spread seen in the AE energy rate is captured by modeling the variations in sawed surface height profile, tool cutting-edge geometry, and porosity of the bone. The five AE model coefficients are calibrated over a range of clinically relevant depth-of-cuts using pure haversian regions (comprising of osteon and interstitial matrix) and pure plexiform regions (comprising of lamellar bone and woven bone). The calibrated model is then used to make predictions in the transition region between the haversian and plexiform bone, which is characterized by gradient structures involving varying percentages of osteon, interstitial matrix, lamellar bone, and woven bone. The model predictions show a good correlation with the experimentally measured values. The validated AE model is useful for process monitoring both in terms of its ability to predict AE energy rate trends and cutting force variations, based on the differences in the underlying bone microstructures.