A Cellular Analysis

Understanding bone remodeling at the cellular level hopefully will allow us to make more accurate decisions regards remodeling of our horse's cannons at the macro level. At the cellular level, per my last post on Andres Tovar and his thesis, a mathematical model can be established regarding the interaction of bone cells--cell to cell-or cell unit to cell unit--regards response to stress.

Read through this closely--a little deep, I know, to get an understanding of the point:

"The state of any (bone) cell is determined through interaction with its neighbor through local rules. The state of each cell at the discrete location is defined by the mechanical stimulus Si(t), the error signal ei(t), and the mass fraction xi(t). This is:

Ai(t) = Si(t) ei(t)xi(t)"

Putting this formula into words:

In the existing equilibrium for any cell or group of cells, change = mechanical stimuls x error signals (something abnormal is happening) x mass fraction (the mass and size of the cell).

Thus to get a remodeling reaction an external stimulus causes signals withing the cell or cell group that affect the mass of the cell or group. The manner in which this occurs can be defined in terms of "rules" or, even more specific, "local" rules depending where in the total bone structure the events occur.

This "reaction" to "stimuli" hopefully may vary from optimal to various states of less than optimal depending on the various inputs in the mathematical formula--e.g. excessive stimuli might produce cell damage instead of cell optimization.

Tovar's thesis refers to human bone and it's long term adaptation to external stress. There is an actual "sensing" at the cellular level of where and how to remodel for long term functional adaptation of the bone structure in response to external stimuli. The "rules" control the net mass formation in order to maintain normal equilibrium. Error signaling refers to signals indicating things are out of balance.

There are four Tovar rules that control the process. Unnecessary to explain how the rules work except to note that the rules as they operate control such things in formation as positioning, density, proportion, memory as to prior states regarding average strain energy, and memory as to future states based on actual and previous states. Tovar names the four rules:

two-positional control
proportional control
integral control
derivative control

Tovar concludes that "overall global behavior can be computed by local rules imposed on cells that only know local conditions, which depend on the present states of the cell and its neighbors." "...by this, a topology of bone remodeling is created." Tovar ends this: "This has proved to be a promising new tool for future study of bone remodeling."

The horse perspective on all this, next post.

Training:
Sat. 2/14 Valentine's Day starts off at 20 degrees but by training time the ground had barely thawed to deep mud in the paddock track. Horses were driven riderless for about 8 minutes off and on in spurts for a conditioning workout. We've survived the week with every other day soft workouts to maintain condition into the coming good weather, and, although we lost the week in terms of galloping, given the time of year and what appears to lie ahead, I'm quite happy.