A. Birchall

A microcomputer algorithm for solving compartmental models involving radionuclide transformations

An algorithm for solving first-order non-recycling compartment models is described. Given the initial amounts of a radioactive material in each compartment and the fundamental transfer rate constants between each compartment, the algorithm gives both the amount of material remaining at any time t and the integrated number of transformations that would occur up to time t. The method is analytical, and consequently, is ideally suited for implementation on a microcomputer. For a typical microcomputer with 64 kilobytes of random access memory, a model containing up to 100 compartments, with any number of interconnecting translocation routes, can be solved in a few seconds; providing that no recycling occurs. An example computer program, written in 30 lines of Microsoft BASIC, is included in an appendix to demonstrate the use of the algorithm. A detailed description is included to show how the algorithm is modified to satisfy the requirements commonly encountered in compartment modelling, for example, continuous intake, partitioning of activity, and transformations from radioactive progeny. Although the algorithm does not solve models involving recycling, it is often possible to represent such cases by a non-recycling model which is mathematically equivalent.

A New Dosimetric Model for Bone Surface Seeking Radionuclides in the Skeleton

Values for the fraction of skeletal alpha and beta activity deposited in the bone surfaces and in the red bone marrow following intakes of bone surface seeking radionuclides by adults have been calculated using a multicompartment bone model. This model (Pr84 Th85), unlike the existing ICRP model, incorporates features which allow for the relocation of radionuclide in the skeleton that results from bone remodelling. In one compartment of this model, namely the growing surfaces of cortical bone, radionuclide is taken to be retained and not subject to resorption or recycling. In the corresponding trabecular compartment the radionuclide is taken to be subject to both burial and resorption. Resorbed radionuclide is assumed either to be redeposited onto bone surfaces or to be retained in the bone marrow. The calculations were made assuming that radionuclide is deposited in the skeleton during a fifty year period. The calculations made with this model (see Table) suggest the ICRP recommended values for the fraction of skeletal radionuclide energy deposited in the bone surfaces and red bone marrow following intakes of the more important bone surface seeking radionuclides are about 6 times and 2 times too large, respectively.