A Mathematical Model for Production and Inventory Management of Time-sensitive Pharmaceutical in a Molecular Imaging Center

The chemical attributes of Technetium-99m have made it popular for most medical imaging procedures. However, in recent years, the decay product of molybdenum-99, i.e., technetium-99m, has become expensive, and its routine availability can no longer be taken for granted. We proposed scenarios to maximize the throughput of Technetium-99m which is used to produce radiopharmaceuticals in a medical imaging center.

We proved a recursive function to imitate the decay dynamics of Technetium-99m, which is used in 80 percent of medical imaging. Then, we proved necessary and sufficient optimality analysis for this function.

We found optimal scenarios for distributing the radiopharmaceuticals into elusion periods according to clinical considerations.

 We developed a rigorous mathematical model based to maximize the throughput of radiopharmaceuticals in a molecular imaging center.