Inside mathematical modeling: Building models in the context of wound healing in bone

As in many hierarchies of scientific models, the virtues of a simpler theory can, under the right circumstances, outweigh its vices. This comment concerning modeling, expressed by Raymond Lee and Alistair Fraser (see bibliography), is illustrated in the context of wound healing by means of a series of increasingly sophisticated analytical models. The motivation for these models is based on experimental studies of the critical size defect (CSD) in animal models which has been defined as the smallest intraosseous wound that does not heal by bone formation during the lifetime of the animal. For practical purposes this timescale can usually be taken as one year (later, the definition was further extended to a defect which has less than ten percent bony regeneration during the lifetime of the animal). CSDs can "heal" by fibrous connective tissue formation, but since this is not bone it does not have the properties (strength, etc.) that a completely healed defect would. A sequence of increasingly sophisticated models is developed and their biological implications are discussed in some detail.