Cema-based formalism for the determination of absorbed dose for high-energy photon beams

Investigations on the beam quality correction factor for ionization chambers in high-energy brachytherapy dosimetry

Objective. To enhance the investigations on MC calculated beam quality correction factors of thimble ionization chambers from high-energy brachytherapy sources and to develop reliable reference conditions in source and detector setups in water.Approach. The response of five different ionization chambers from PTW-Freiburg and Standard Imaging was investigated for irradiation by a high dose rate Ir-192 Flexisource in water. For a setup in a Beamscan water phantom, Monte Carlo simulations were performed to calculate correction factors for the chamber readings. After exact positioning of source and detector the absorbed dose rate at the TG-43 reference point at one centimeter nominal distance from the source was measured using these factors and compared to the specification of the calibration certificate. The Monte Carlo calculations were performed using the restricted cema formalism to gain further insight into the chamber response. Calculations were performed for the sensitive volume of the chambers, determined by the methods currently used in investigations of dosimetry in magnetic fields.Main results. Measured dose rates and values from the calibration certificate agreed within the combined uncertainty (k= 2) for all chambers except for one case in which the full air cavity was simulated. The chambers showed a distinct directional dependence. With the restricted cema formalism calculations it was possible to examine volume averaging and energy dependence of the perturbation factors contributing to the beam quality correction factor also differential in energy.Significance. This work determined beam quality correction factors to measure the absorbed dose rate from a brachytherapy source in terms of absorbed dose to water for a variety of ionization chambers. For the accurate dosimetry of brachytherapy sources with ionization chambers it is advisable to use correction factors based on the sensitive volume of the chambers and to take account for the directional dependence of chamber response.

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

PURPOSE

The Type A standard uncertainty in Monte Carlo (MC) dose calculations is usually determined using the "history by history" method. Its applicability is based on the assumption that the central limit theorem (CLT) can be applied such that the dispersion of repeated calculations can be modeled by a Normal distribution. The justification for this assumption, however, is not obvious. The concept of stochastic quantities used in the field of microdosimetry offers an alternative approach to assess uncertainty. This leads to a new and simple expression.

METHODS

The value of the MC determined absorbed dose is considered a random variable which is comparable to the stochastic quantity specific energy, z. This quantity plays an important role in microdosimetry and in the definition of the quantity absorbed dose, D. One of the main features of z is that it is itself the product of two other random variables, specifically of the mean dose contribution in a 'single event' and of the mean number of such events. The term 'single event' signifies the sum of energies imparted by all correlated particles to the matter in a given volume. The similarity between the MC calculated absorbed dose and the specific energy is used to establish the 'event by event' method for the determination of the uncertainty. MC dose calculations were performed to test and compare both methods.

RESULTS

It is shown that the dispersion of values obtained by MC dose calculations indeed depend on the product of the mean absorbed dose per event, and the number of events. Applying methods to obtain the variance of a product of two random variables, a simple formula for the assessment of uncertainties is obtained which is slightly different from the 'history by history' method. Interestingly, both formulas yield indistinguishable results. This finding is attributed to the large number of histories used in MC simulations. Due on the fact that the values of a MC calculated absorbed dose are the product of two approximately Normal distributions it can be demonstrated that the resulting product is also approximately normally distributed.

CONCLUSIONS

The event by event approach appears to be more suitable than the history by history approach because it takes into account the randomness of the number of events involved in MC dose calculations. Under the condition of large numbers of histories, however, both approaches lead to the same simple expression for the determination of uncertainty in MC dose calculations. It is suggested to replace the formula currently used by the new expression. Finally, it turned out that the concept and ideas that were developed in the field of microdosimetry already 50 years ago can be usefully applied also in MC calculations.

Enhancement of the EGSnrc code egs_chamber for fast fluence calculations of charged particles

PURPOSE

Simulation of absorbed dose deposition in a detector is one of the key tasks of Monte Carlo (MC) dosimetry methodology. Recent publications (Hartmann and Zink, 2018; Hartmann and Zink, 2019; Hartmann et al., 2021) have shown that knowledge of the charged particle fluence differential in energy contributing to absorbed dose is useful to provide enhanced insight on how response depends on detector properties. While some EGSnrc MC codes provide output of charged particle spectra, they are often restricted in setup options or limited in calculation efficiency. For detector simulations, a promising approach is to upgrade the EGSnrc code egs_chamber which so far does not offer charged particle calculations.

METHODS

Since the user code cavity offers charged particle fluence calculation, the underlying algorithm was embedded in egs_chamber. The modified code was tested against two EGSnrc applications and DOSXYZnrc which was modified accordingly by one of the authors. Furthermore, the gain in efficiency achieved by photon cross section enhancement was determined quantitatively.

RESULTS

Electron and positron fluence spectra and restricted cema calculated by egs_chamber agreed well with the compared applications thus demonstrating the feasibility of the new code. Additionally, variance reduction techniques are now applicable also for fluence calculations. Depending on the simulation setup, considerable gains in efficiency were obtained by photon cross section enhancement.

CONCLUSION

The enhanced egs_chamber code represents a valuable tool to investigate the response of detectors with respect to absorbed dose and fluence distribution and the perturbation caused by the detector in a reasonable computation time. By using intermediate phase space scoring, egs_chamber offers parallel calculation of charged particle fluence spectra for different detector configurations in one single run.