In the RMR model (Tobias 1985), five key parameters determine the mutagenic and cell killing potential of ionizing radiation.  The five parameters are:

1. Initial DSB yield Gy^-1 cell^-1. Specify using the DSB={value} keyword.
2. Probability a DSB is repaired incorrectly.  Specify using the A0 (or B0) keyword.
3. Probability a misrepaired DSB is lethal (e.g., inactivates a key housekeeping gene).  Specify using the PHI keyword.  NOTE: (1-PHI) is the probability a misrepaired DSB is not lethal.
4. 1^st order DSB rejoining rate. Specify using the LAM={value} keyword or RHT={value} keyword. The LAM and RHT parameters are related by LAM = LN(2)/RHT.
5. Rate of pairwise damage interaction (2^nd order DSB rejoining rate). Specify using the ETA={value} keyword.

1. Paste the contents of LPL sample file #1 into a new ASCII input file called lpl1.inp. Run the simulation (if you have already completed Tutorial 2.1, you can skip this step).
2. Paste the contents of RMR sample file #2 into a new ASCII input file called rmr1.inp.  Open the rmr1.inp file and set the value of the RHT and ETA parameters so that they are the same as in the lpl1.inp file.  Then set A0=0 and determine the value of PHI such that a and a/b predicted by the RMR model (rmr2.out file) is the same as the one predicted by the LPL model (step 1, lpl1.out file).  Is the product (1-A0)·PHI·DSB smaller, larger or the same as the value of the FL parameter in lpl1.inp?
3. Repeat step 2 with A0=0.5 (i.e., find the value of PHI such that a and a/b are the same as the ones reported in the lpl1.out file).  Is the product (1-A0)·PHI·DSB smaller, larger or the same as the value of the FL parameter used in the lpl1.inp file?

• Develop a formula to relate the LQ parameter a to B0, PHI and DSB.
• What is the relationship (i.e., derive a formula) between the RMR parameters A0, PHI and DSB and the LPL parameter FL?
• If the DSB yield is increased by a factor of two (DSB parameter), will the LQ radiosensitivity parameter a increase or decrease by a factor of two?  Are the trends in a predicted by the LPL model the same as the trends predicted by the RMR model, i.e., does the LPL model predict that the a radiosensitivity parameter increases (or decreases) as the DSB yield increases?
• If the value of A0 is reduced and/or the value of PHI is increased, does the LQ radiosensitivity parameter b increase, decrease or stay the same?  For comparison, does the value of b increase, decrease or stay the same as the value of the LPL parameter FL increases?

1. Paste the contents of RMR sample file #1 into a new ASCII input file called rmr2.inp.
2. Setup an exposure scenario to deliver doses of 0, 0.5, 1, 2, 3, 4, 5, 7.5, 10, 15, 20, 25 Gy at dose rates of 0.1 Gy/h, 2 Gy/h and 1,000 Gy/h (total of 36 exposure scenarios).  See Tutorial 1.1 for help setting up the exposure scenario(s).
3. Run the RMR simulation(s).
4. Setup a MS Excel spreadsheet to directly compute the surviving fraction using the formula S = exp{-D(a + bGD)}, where G = [2*[x + exp(-x)-1]/(x·x), where x = LAM×{irradiation time}.  Use the spreadsheet to compute the surviving fraction for the same LQ radiosensitivity parameters reported in the rmr2.out file.
5. Create a plot showing the % difference between the LQ and RMR surviving fractions (y-axis, linear scale) as a function of dose (x-axis, linear scale).

• Is the LQ a better approximation for the RMR when the dose is small or large?  For a given dose, does the accuracy of the LQ approximation tend to increase or decrease as the dose rate increases?  Explain in words the mechanistic basis for these trends.  Hint: Does first-order repair (LAM or RHT parameter) or second-order repair (ETA parameter) tend to become more important as dose and dose rate increases?

1. Create a copy of the rmr2.inp file and rename it rmr3.inp
2. Open the rmr3.inp file and reduce the repair half-time (RHT parameter) by a factor of two and increase the pairwise damage interaction rate (ETA parameter) by a factor of four.  Run the simulation.  Is the a/b ratio higher or lower than the one reported in the rmr2.out file?
3. Extract the LQ radiosensitivity parameters a and b from the rmr3.out file and paste them into the Excel spreadsheet from exercise 2.  Also, set the DSB repair half-time (RHT parameter) in the Excel spreadsheet to correspond to the value used in the rmr3.inp file.
4. Create a plot showing the % difference between the LQ and RMR surviving fractions (y-axis, linear scale) as a function of dose (x-axis, linear scale).

• Compare the figure from exercise 2 to the figure from exercise 3.  Is the LQ a better approximation for the RMR as the a/b ratio increases or decreases?  Explain the mechanistic basis for this observation.
• Can the differences between the LQ and RMR predicted surviving fractions be reduced by adjusting the LQ parameters used in the spreadsheet?
• The LQ is also a low dose and dose rate approximation for the LPL model (in retrospect, does this statement give you some clues as to how you should answer questions from exercise 1 and 2?).  Based on your experiences with this tutorial and Tutorial 2.1,would you expect the LQ to be an equally good (or bad) approximation for the LPL model?