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Mathematical Models for Bone Formation and Metabolism

By Karthika Swamy Cohen

At the SIAM Conference on the Life Sciences being held in Boston this week, Alicia Prieto Langarica (Youngstown State University) gave an overview of modeling bone cell formation, analyzing interactions of osteocytes, osteoclasts and osteoblasts.

“Up until a few years ago, I used to think of bones as static,” she said. “But it's really highly dynamic and highly regulated.” She proceeded to explain how by describing a “patented lab in a chip” that studies interactions between  “bone cells, cells that create bone (osteocytes), cells that destroy bone (osteoclasts) and cells that monitor the bone matrix (osteoblasts).”

Bone remodeling. Image credit: Alicia Prieto Langarica, LS16 presentation.

In the simulation, osteocytes are put in a chamber and stressed much the same way as the stress that bones experience when we run. Pre-osteoblasts from mouse skull are used for the modeling experiment. Cells in culture are then induced. Once induced, they differentiate. They are fed every three days and their bone formation quantified.

A very small area is modeled. The main requirements for the model are flexibility and the need for extremely stochastic dynamics A cellular automate model is used to measure the different chemicals inducing bone. The cellular automate model is then upscaled into a PDE system. The model was then validated with experimental data obtained from osteoblastic bone cells induced to mineralize.

Karthika Swamy Cohen is the managing editor of SIAM News.