Determination of spatially dependent diffusion parameters in bovine bone using Kalman filter

Area of Science:

• Biomaterials Science
• Chemical Engineering
• Orthopedic Research

Background:

• Bone is an inhomogeneous material with varying porosity.
• Porosity is understood to decrease from inner to outer bone boundaries.
• Bone diffusivity is hypothesized to increase with porosity.

Purpose of the Study:

• To experimentally determine spatially dependent diffusion parameters in bone.
• To develop and validate a mathematical model for bone diffusion.
• To investigate the relationship between bone structure and ion transport.

Main Methods:

• Experimental setup using bovine bone samples saturated with potassium chloride (KCl).
• Measurement of water conductivity changes due to chloride ion diffusion.
• Application of a one-dimensional, spatially dependent mathematical diffusion model.
• Kalman filter technique for determining diffusion parameters.

Main Results:

• Spatially dependent diffusion parameters were determined for endosteal and periosteal surfaces.
• Endosteal surface diffusion parameter: (12.8 ± 4.7) × 10(-11) m(2)/s.
• Periosteal surface diffusion parameter: (5 ± 3.5) × 10(-11) m(2)/s.
• Mathematical model showed excellent agreement with experimental data (MSE: 0.06–0.183 × 10(-6) (μS/m)(2)).

Conclusions:

• Bone exhibits spatially dependent diffusion characteristics.
• Diffusivity is higher at the endosteal surface compared to the periosteal surface.
• The developed mathematical model accurately describes ion diffusion in inhomogeneous bone.