Bone Adaptation as Level Set Motion
Bone microarchitecture is constantly adapting to environmental and mechanical factors. Changes in bone density and structure can lead to an increase in fracture risk. Computational modeling of bone adaptation may provide insight into mitigating aging and preventing disease. In this paper, the adaptation of bone is modeled as a curve evolution problem. Curves can be evolved according to the level set method. The level set method models basic bone physiology by adapting bone according to appositional growth following a trajectory in time with a natural definition of homeostasis. A novel curvature based bone adaptation algorithm is presented for modeling bone atrophy. The algorithm is shown to be weakly equivalent to simulated bone atrophy. These results generalize surface-driven and strain-driven models of bone adaptation using a surface remodeling force. Physiological signals (hormones, mechanical strain, etc.) can be directly integrated into this surface remodeling force. Remodeling can be naturally restricted around foreign bodies (such as modeling adaptation around a surgical screw). Future work aims to identify the surface remodeling force from longitudinal image data.
KeywordsLevel set method Bone adaptation Cancellous bone Finite difference method
B.A. Besler acknowledges support from Alberta Innovates Health Solutions and NSERC CGS-D.
- 11.Schulte, F., Lambers, F., Kuhn, G., Müller, R.: In vivo micro-computed tomography allows direct three-dimensional quantification of both bone formation and bone resorption parameters using time-lapsed imaging. Bone 48(3), 433–442 (2011). https://doi.org/10.1016/j.bone.2010.10.007CrossRefGoogle Scholar
- 21.Lorensen, W., Cline, H.: Marching cubes: a high resolution 3D surface construction algorithm. In: Proceedings of 14th Annual Conference on Computer Graphics and Interactive Techniques - SIGGRAPH 1987, pp. 163–169. ACM (1987). https://doi.org/10.1145/37401.37422
- 25.Yang, I., Tomlin, C.: Identification of surface tension in mean curvature flow. In: Proceedings of 2013 American Control Conference, pp. 3284–3289. IEEE (2013). https://doi.org/10.1109/ACC.2013.6580338
- 26.Yang, I., Tomlin, C.: Regularization-based identification for level set equations. In: Proceedings of 52nd Annual Conference on Decision and Control - CDC 2013, pp. 1058–1064. IEEE (2013). https://doi.org/10.1109/CDC.2013.6760022