| | ||||||
| | | | | | |
| Tutorial 1.3 exponentially decreasing dose rates How to set up radiation exposure scenarios |
The intensity of the radiation emitted from a fixed quantity of a radioactive material (e.g., a brachytherapy seed) decreases exponentially with time. Mathematically, the activity of a quantity of some radioactive material is given by: A(t) = A(0)exp(-lt) where A(t) is the activity at time t and A(0) is the initial activity (at time t = 0). The parameter l is the decay constant that characterizes the rate at which unstable atoms disintegrate (decay) and emit radiation. The rate of radioactive decay is specific to the radioisotope. Often the decay rate is specified in terms of an alternate parameter called the half-life. The half-life T of a radioisotope is the amount of time required for half of the initial number of atoms to disintegrate, i.e., l = ln(2)/T ~ 0.693/T. The half-life for selected radioisotopes of interest in radiation therapy, nuclear medicine, and radiation protection is available elsewhere in the manual (see the Table of half-lives for selected radioisotopes). Examples 1 and 2 illustrate how to setup a radiation exposure scenario in which the dose rate decreases exponentially with time. For additional discussion related to exponentially decreasing dose rates, see Exponentially Decreasing Dose Rates in the Examples section of the manual. Some of the theoretical background related to the DCUT or TCUT parameters is also available elsewhere in the manual. Example 1 A dose rate function that decreases exponentially with time until the irradiation time reaches TCUT (exp1.inp, exp1.out)/*Half time of exponential decay of dose rate (RHL):1443.36h (half-life for 125I) The dose rate function is truncated at 2886.72 h (twice the value of RHL) Renormalizing of the baseline 1 Gy TAD (Total absorbed dose) scenario using SAD, i.e., the dose delivered in 2886.72 h equals 140, 145, or 150 Gy. The step tolerance (STOL) controls the accuracy of the exponential (Chosen small) so that the shape of the dose rate function is very similar to a "true" exponential. Values for STOL in the range from about 0.05 to 1E-03 should be adequate for most biological simulations. In this example TCUT terminates the simulation at 2886.72 hours.*/DECAY: TAD=1 RHL=1443.36 TCUT=2886.72 STOL=1.0D-02 SAD=RX1RX1= 140 145 150 / Comment: The input contains 3 baseline exposure scenarios Definition: In the International System of Units (SI), the activity of a sample of radioactive material is specified in units called the becquerel (Bq). A Bq denotes one nuclear transformation (disintegration) per second. The Curie (Ci) is an other common (but non-SI) unit of activity. One curie equals 3.7 ´ 1010 Bq. Example 2 A dose rate function that decreases exponentially until a desired fraction of the total possible dose is delivered or until TCUT is reached (exp2.inp, exp2.out) /* Half time of exponential decay of dose rate (RHL):1443.36h (half-life for 125I) TCUT is chosen as 14433.6 h (ten times the value of RHL) DCUT =0.4, so that the simulation ends after 0.6 of the total dose is delivered. Renormalizing of the baseline 1 Gy TAD (Total absorbed dose) scenario using SAD :The dose delivered in 2886.72 h equals 140, 145, or 150 Gy. The step tolerance (STOL) controls the accuracy of the exponential (Chosen small) so that the shape of the dose rate function is very similar to a "true" exponential. Values for STOL in the range from about 0.05 to 1E-03 should be adequate for most biological simulations. In this example DCUT terminates the simulation earlier than 14433.3 hours.*/DECAY: TAD=1 RHL=1443.36 TCUT=14433.6 DCUT=0.4 STOL=1.0D-02 SAD=RX1 BGDR=1!NOTE: the above must appear on a single line in the input file.RX1= 140 145 150 / Suggested Problems: For all of the sample problems, use RIO to process the input file into an output file. Verify that the RIO application generates the desired exposure scenario. Debug as necessary.
|
| School of Health Sciences Purdue University Disclaimer | Last updated: 10 June, 2011 |