Many people hold two common beliefs about bones: that calcium is necessary for strong bones and growth, and that bones remain unchanged after puberty. However, this is not the case. Bones are organs just like the kidney, heart, or skin, and they undergo constant change.
Bones go through a complex process of continuous remodeling to maintain their shape and density. This process is influenced by various factors, including nutrition, hormones, exercise, and age. Modeling all these factors and their interactions is very complex. However, understanding the basic process of bone remodeling can be more easily achieved.
The bone remodeling process can be described step by step as follows: osteoclasts initially appear on a previously inactive bone surface and then excavate a lacuna on the surface of cancellous bone or a resorption tunnel in cortical bone. Subsequently, osteoclasts are replaced by osteoblasts, which refill the resorption cavity and become osteocytes, the inactive form of osteoblasts.
Additionally, one of the hormones that regulates this process is calcitonin. Calcitonin is secreted by the thyroid gland to regulate blood calcium availability. This hormone plays a very important role in the process of creating new bone tissue. The amount of calcitonin in the blood controls the amount of calcium with which osteoblasts can work to form the calcium hydroxyapatite matrix.
Rattanakul, C & Rattanamongkonkul, S. (2011) proposed the following equations, where constant summarize some related factors that affect the production/activation or loss/deactivation of calcitonin, osteoblast, and osteoclasts.
Calcitonin equation
The first term represents the production of calcitonin formed by constansts c1, c2 and k1.
The second term is the loss of calcitonin
Osteoclasts equation
The first term represents the production of active osteoclasts
The second term is the loss of osteoclasts in the system
Osteoblasts equation
The first term being the creation of new osteoblasts by the action of the osteoclasts.
The second term is the loss of osteoblasts.
These differential equations express the effect of calcitonin on the bone remodeling process. The ODE45 Matlab function was used to solve this model through Runge-Kutta numerical approximation.
When analyzing the results for the Physiological, we can observe that the levels of calcitonin and osteoblasts in the bones exhibit a sinusoidal behavior over time, while osteoclasts behave in a cosinusoidal manner, as these cells counteract osteoblasts.
Comparing the physiological case graphs (above) with the pathological case graphs (below), where the initial population of osteoblasts is reduced to “allow more osteoclasts to resorb bone,” we can observe distinct patterns when viewed through the lens of Control Theory. In the physiological case, the system exhibits light damping as it maintains continuous oscillations, while the pathological case shows increased damping, resulting in a decrease of active osteoblasts until it reaches equilibrium.
Reducing the initial population of active osteoblasts causes the system to reach equilibrium much more slowly. Additionally, changes to the amount of calcitonin or osteoclasts do not impact the behavior as significantly as changes to osteoblasts.
Hence, variations in the blood concentration of calcitonin do not significantly influence bone remodeling. The system can function with minimal initial levels of calcitonin, hormonal signaling of osteoblast and osteoclasts quickly increase the presence of calcitonin.
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