With BMU control the challenge of understanding bone volume homeostasis is clearly daunting

The issue confronting us is how to make sense of available data on BMUs, and to turn this data into an integrated understanding of bone physiology that has explanatory power. This is typically the role of quantitative or theoretical models. There has been a fairly long history of mathematical and computational models of events in bone turnover. Earlier models, such as those summarized in Martin et al. tended to focus on questions of rates of bone turnover e.g. what rate of resorption, mineralization, or BMU activation. More recently, computational models have been developed to model the evolution of various bone cell lineages and the role of specific signaling molecules. Spatial aspects of cell organization within trabecular and Gomisin-D cortical BMUs have very recently also been considered. These past models tend to be based on systems of differential equations. A somewhat different approach to these past bone models is to look to ‘Albaspidin-AA control theory’ to provide some kind of framework for interpreting the available information on a BMU, as it deals with principles of control of dynamical systems. Indeed, that is what we will attempt to do in this paper and is the general conceptual approach that has been taken by others to understand bone regulation. By doing this we hope to ‘step back’ from specific processes/interactions in a bone remodeling event and instead focus on the general requirements to achieve bone balance as well as the constraints this then imposes on various interactions. This should help to provide an explanation for observations in terms of control of bone balance and to systematically predict other currently unknown control mechanisms. In contrast, previous bone models of specific processes/ interactions can be viewed as specific examples of these constraints known or assumed to occur. The classical design control issue is ensuring a system maintains a constant single output for a single input. This is typically achieved using negative feedback control, so that the input is adjusted to achieve a desired output. However, more complex systems with multiple processes also require control mechanisms to see that separate processes within the system are coordinated. Therefore within a BMU, we may expect to see negative feedback control and process coordination control. Both mechanisms need to be considered for the homeostatic control of bone volume by a single BMU. To make any progress, it is clear we first need to reduce the complexity described above. To do this, we would like the BMU to be operating in as simple a way as possible. So for the purposes of this study, we first assume that the BMU is established and steadily moving through the cortical bone. We further assume that signals from the ‘whole body’ level and from the ‘regional’ level to the BMU are in an averaged sense, time invariant. This enables us to focus on fundamental bone balance mechanisms operating within the BMU itself. This situation might be approximated in a young, healthy adult, with constant bone volume and normal bone turnover. Even with these simplifications, there remain many signaling systems operating within the BMU, and no one is sure how the actions of these signaling molecules are integrated to maintain bone balance. To tackle this problem one may first ask: what needs to happen in a BMU to ensure bone balance is maintained? What are the different possible general ways that bone balance may be achieved? Having answered these questions one may then ask: what signaling processes and mechanisms within the BMU are potentially part of the BMU control systems to maintain bone balance?

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