An inverse technique to identify participant-specific bone adaptation from serial CT measurements

Simulated bone adaptation is framed as an interface evolution problem. The interface is extracted from a high-resolution computed tomography (CT) image of trabecular bone microarchitecture and modified by the level set equation. A model and its parameters determine the bone adaptation rate and thus the bone structure at any future time. This study develops an inverse problem and solver to identify model parameters from multiple high-resolution CT images of bone within the level set framework. We demonstrate the technique on a model of advection and mean curvature flow, termed curvature-driven adaptation. The inverse solver uses two CT scans to estimate model parameters, which map the bone surface from one image to the next. The solver was tested with synthetic images of bone changing according to the curvature-driven model with known model parameters. The algorithm recovered known model parameters excellently (R² > .99, p < .001). A grid search indicated that the estimated model parameters were insensitive to hyper-parameter selection for learning rate 1e^-5$\le \eta \le$ 5e^-5 and gradient scaling factor 5e^-5$\le \gamma \le$ 5e^-4 . Finally, we tested the algorithm's sensitivity to salt-and-pepper noise of probability $P$ , where .0 $\le P\le$ .9. Model parameter accuracy did not change for $P$ < .7, corresponding to Dice coefficients greater than .7. The inverse problem estimates bone adaptation parameters from multiple CT images of changing bone microarchitecture. In the future, this technique could be used to determine participant-specific bone adaptation parameters in vivo, validate bone adaptation models, and predict bone health.