A microcomputer algorithm for solving compartmental models involving radionuclide transformations.

Area of Science:

• Pharmacokinetics and Environmental Modeling
• Computational Chemistry and Physics
• Radiochemistry

Background:

• Compartment models are widely used to simulate dynamic processes involving the distribution and transformation of substances.
• Solving these models, especially those with numerous compartments and transfer routes, can be computationally intensive.
• Existing methods may lack efficiency or require specialized software, limiting accessibility.

Purpose of the Study:

• To develop an efficient analytical algorithm for solving first-order non-recycling compartment models.
• To provide a method suitable for implementation on microcomputers.
• To enable accurate calculation of material remaining and integrated transformations over time.

Main Methods:

• Development of an analytical algorithm based on fundamental transfer rate constants and initial compartment amounts.
• Implementation on microcomputers, demonstrating feasibility with limited random access memory (64 kilobytes).
• Adaptation of the algorithm for common modeling requirements like continuous intake and radioactive progeny transformations.

Main Results:

• The algorithm accurately calculates the amount of radioactive material remaining at any time t.
• It also determines the integrated number of transformations up to time t.
• Models with up to 100 compartments and complex interconnections can be solved in seconds on a typical microcomputer.

Conclusions:

• The presented analytical algorithm offers an efficient and accessible solution for first-order non-recycling compartment models.
• Its suitability for microcomputers democratizes complex modeling capabilities.
• The algorithm can be adapted for various real-world scenarios, and even recycling models can often be approximated.