**1. NAME AND TITLE**

TIMED: Calculation of Cumulated Activity of a Radionuclide in the Organs of the Human
Body at a Given Time After Deposition.

**2. CONTRIBUTOR**

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV and Assembler language; IBM 360/370.

**4. NATURE OF PROBLEM SOLVED**

TIMED is designed to calculate cumulated activity in various source organs at a specified time,
t, after deposition. TIMED embodies a system of differential equations which describes activity
transfer in the body. Activity transfer is based on the concept of a system of compartments with
constant rates of transfer to other compartments of the body. The pathways of transfer and transfer
constants for the lungs and gastrointestinal tract are those described in ICRP Publication 19 and
Publication 2. The models for activity transfer to other organs of the body must be supplied by the
user. The code is sufficiently general to allow for radioactive daughters born in the body and also
handles branching of decay schemes.

**5. METHOD OF SOLUTION**

The solution of the ordinary differential equation (ODE) is calculated using a subroutine
package which is based on a program written by C. W. Gear for the solution of initial value
problems for a system of ODE's. A prime feature of the GEAR package is the ability to solve stiff
ODE problems. The basic method used is a linear multistep method. The method is implemented
in a manner which allows both the step size and the order to vary in a dynamic way throughout the
problem.

**6. RESTRICTIONS OR LIMITATIONS**

The code is limited to 12,000 differential equations, i.e., compartments in the model. The maximum number of nonzero entries in a row of the coefficient matrix is 52. The maximum number of radionuclides in a chain is 10.

The user may include up to 10 source organs other than lungs and gastrointestinal tract. Each
source organ may include up to 10 compartments.

**7. TYPICAL RUNNING TIME**

For compilation, the FORTRAN routines require about 7.5 seconds; the Assembler language
routines 0.7 seconds. Execution time depends upon many factors: the number of differential
equations, the number of nonzero entries in the coefficient matrix, the length of the time period of
integration, etc. The execution time for a complicated chain of four radionuclides involving 116
differential equations is about 5.8 seconds.

**8. COMPUTER HARDWARE REQUIREMENTS**

The code is operable on the IBM 360/370 and requires about 310 K for execution.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A FORTRAN IV and Assembler compiler is required.

**10. REFERENCES**

S. B. Watson, W. S. Snyder, and M. R. Ford, "TIMED: A Computer Program for Calculating Cumulated Activity of a Radionuclide in the Organs of the Human Body at a Given Time, t, After Deposition," ORNL/CSD/TM-17 (December 1976).

J. M. Langsted, "Investigations of Several Task Group Lung Model Modifications to More
Accurately Describe Pulmonary Clearance of In Vivo Produced Daughter Products," M. S. Thesis,
U. Washington (1977).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one (1.2MB) DOS diskette which contains the source
code and sample problem input and output.

**12. DATE OF ABSTRACT**

December 1981.

**KEYWORDS: ** RADIONUCLIDES; INTERNAL DOSE; GAMMA-RAY SOURCE