Phenomenological model of bone remodeling cycle containing osteocyte regulation loop

Area of Science:

• Biomaterials Science
• Computational Biology
• Orthopedic Engineering

Background:

• Optimized hard tissue scaffold design requires understanding biological parameters like bone resorption and formation.
• Modeling scaffold integration necessitates comprehending the complex native bone remodeling process.
• Existing models often simplify the intricate cellular interactions within bone.

Purpose of the Study:

• To develop a mathematical model predicting osteoactivity in bone scaffolds in vivo.
• To integrate osteocyte activity into existing bio-cybernetic models of basic multicellular unit (BMU) action.
• To explore the dynamic behavior and underlying principles of bone remodeling.

Main Methods:

• Developed a four-dimensional mathematical model based on a bio-cybernetic vision of BMU action.
• Incorporated an additional regulatory loop accounting for osteocyte activity.
• Analyzed the system's behavior, steady-state characteristics, and phase space dynamics.

Main Results:

• The model exhibits steady-quasi-cyclic behavior within biologically relevant constant ranges.
• Identified a torus-like steady-state in multidimensional phase space, indicating a first integral.
• Proposed a biological and physical interpretation of this integral as a conserved substrate-energy regenerative potential.

Conclusions:

• The model provides a credible representation of normal bone remodeling, including its regenerative capacity against damage.
• The conserved value suggests an inherent potential for bone repair and maintenance within the BMU.
• Further research is needed to explore a wider range of constants and validate findings across diverse conditions.