Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in...

Area of Science:

• Radiation Protection
• Computational Biology
• Biokinetics

Background:

• Biokinetic modeling for radiation protection uses coupled ordinary differential equations (ODEs) to represent biological retention and excretion.
• These ODE systems are often 'stiff' due to disparate transfer rates between compartments.
• Accurate and stable numerical solutions are crucial for reliable biokinetic modeling.

Purpose of the Study:

• To evaluate and compare various Python ODE solvers and methods for biokinetic modeling.
• To establish a framework for selecting optimal ODE solvers for multi-level analysis in biokinetics.
• To analyze solver stability and numerical accuracy against analytical methods.

Main Methods:

• Comparison of different Python ODE solvers and numerical methods.
• Analysis of solver stability for stiff ODE systems.
• Exploration of Python-based linear algebraic methods, including matrix exponential (expm).
• Application to International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM) scenarios (inhaled 60Co Type M, 131I Type F).

Main Results:

• Customized implicit ODE solvers demonstrated enhanced stability for HRTM biokinetic models.
• Solutions from customized implicit solvers were consistent with the Python matrix exponential method (expm).
• Observed differences between solvers were attributed to numerical precision and approximation order.

Conclusions:

• Customized implicit methods provide stable and reliable solutions for complex biokinetic models.
• The study offers a framework for selecting appropriate Python ODE solvers for internal radioactivity modeling.
• This research is the first to analyze Python ODE solvers specifically for ICRP HRTM biokinetic models.