Bone balance within a cortical BMU: local controls of bone resorption and formation

Maintaining bone volume during bone turnover by a BMU is known as bone balance. Balance is required to maintain structural integrity of the bone and is often dysregulated in disease. Consequently, understanding how a BMU controls bone balance is of considerable interest. This paper develops a methodology for identifying potential balance controls within a single cortical BMU. The theoretical framework developed offers the possibility of a directed search for biological processes compatible with the constraints of balance control. We first derive general control constraint equations and then introduce constitutive equations to identify potential control processes that link key variables that describe the state of the BMU. The paper describes specific local bone volume balance controls that may be associated with bone resorption and bone formation. Because bone resorption and formation both involve averaging over time, short-term fluctuations in the environment are removed, leaving the control systems to manage deviations in longer-term trends back towards their desired values. The length of time for averaging is much greater for bone formation than for bone resorption, which enables more filtering of variability in the bone formation environment. Remarkably, the duration for averaging of bone formation may also grow to control deviations in long-term trends of bone formation. Providing there is sufficient bone formation capacity by osteoblasts, this leads to an extraordinarily robust control mechanism that is independent of either osteoblast number or the cellular osteoid formation rate. A complex picture begins to emerge for the control of bone volume. Different control relationships may achieve the same objective, and the 'integration of information' occurring within a BMU may be interpreted as different sets of BMU control systems coming to the fore as different information is supplied to the BMU, which in turn leads to different observable BMU behaviors.