## Dynamics of rib bone regeneration in mice

Professor Francesca Mariani, a founding member of our company, is also a professor at the USC Keck school of medicine where she studies bone and cartilage repair and development. Investigations in her lab led to the discovery that ribs can regenerate relatively enormous lesions of up to 20-40% of their length under certain circumstances. This is remarkable considering that in humans even a 2-4% lesion in the femur heals very poorly and can cripple the patient's ability to walk. This regeneration of the rib was previously observed in humans by plastic surgeons harvesting rib bone for facial reconstruction, but was not previously documented in mice and no model organism development or systematic study of the process has been performed previously. Having developed the surgical skills and assays necessary to build the mouse model of this process, Dr. Mariani's lab has had an opportunity to examine some of the variables related to this rib regrowth.

As part of the early analysis, Micro CT scans of mouse rib regeneration were quantified using 3D imaging software and the regenerated tissue compared to the size of the unaltered rib. Statistical analysis was necessary to infer the unaltered size and to compensate for the difficulties in measurement.

Through the analysis of surgical results and the incorporation of biological understanding, a model arose as to the cause of this remarkable healing ability. A membrane surrounding the bone known as the periosteum or the cartilage (perichondrium) is thought to provide stem-cells that multiply in the membrane, invade the injured region, and rebuild the bone. In addition, bone building cells at the cut ends are expected to extend outward and affect healing near the ends. When the ends are nearly in contact, as occurs in a simple fracture, the extension process is dominant. However, when the lesion is long only healing from the surface sheath can accomplish the level of healing observed in the rib.

Through a mathematical analysis of the interplay of these two processes, we discovered that a critical ratio controls the healing rate: the surface area to volume ratio of the removed section. Through a constant parameter which has the units of velocity, a rate can be determined for a given lesion $r = \frac{vS}{V}$. This rate has units of $1/[\mathrm{time}]$ when $v$ has units of velocity and $S$ is a surface area and $V$ is the volume of the removed bone. Analyzing the data based on this simple ratio and a differential equation for regrowth led to a better understanding of why ribs have their remarkable regenerative capacity.