Note on uncertainty in Monte Carlo dose calculations and its relation to microdosimetry

Area of Science:

• Medical Physics
• Computational Physics
• Radiation Dosimetry

Background:

• Standard uncertainty in Monte Carlo (MC) dose calculations typically uses the "history by history" method, assuming the Central Limit Theorem (CLT) applies for Normal distribution.
• The justification for CLT applicability in MC dose calculations is not always clear.
• Microdosimetry concepts offer an alternative framework for uncertainty assessment.

Purpose of the Study:

• To investigate an alternative approach for determining Type A standard uncertainty in MC dose calculations.
• To introduce and validate a new uncertainty assessment method based on microdosimetry principles.
• To compare the proposed method with the conventional "history by history" approach.

Main Methods:

• The MC calculated absorbed dose is treated as a random variable, analogous to specific energy (z) in microdosimetry.
• The "event by event" method is developed, considering the absorbed dose as a product of two random variables: mean dose per event and number of events.
• MC simulations were conducted to compare the "event by event" and "history by history" uncertainty calculation methods.

Main Results:

• The dispersion of MC dose calculations is shown to depend on the product of mean absorbed dose per event and the number of events.
• A new, simple formula for uncertainty assessment is derived using the variance of a product of random variables.
• Both the "event by event" and "history by history" methods yield practically identical uncertainty results, especially with a large number of histories.

Conclusions:

• The "event by event" method is theoretically more appropriate as it accounts for the randomness in the number of events.
• Under conditions of numerous histories, both methods provide equivalent and simple expressions for MC uncertainty.
• The study suggests adopting the new expression for uncertainty determination in MC dose calculations, leveraging established microdosimetry concepts.