Clinical evaluation for the difference of absorbed doses calculated to medium and calculated to water by Monte Carlo method

Absorbed dose is an important parameter in characterizing the effect of radiation therapy for the efficacy of tumor eradication and protection from unacceptable damage to normal organs [1]. For historical reasons, in terms of dose, D_w has been assumed for reporting the dose to various media. However, human body is not only composed of water. Many tissues in the body have different densities than water, especially the bones and lung. For radiation therapy the dose absorbed to water cannot accurately represent the actual dose absorbed in different tissues. In practice, traditional treatment planning system (TPS) typically takes the effect of different tissue densities with attenuation and scatter into considerations but reports the dose at each location as the dose to water. Monte Carlo (MC) algorithm is the most accurate algorithm for dose calculation in that it simulates the transport properties of various particles in various media in the region of interest and scores the dose contribution locally to the medium with its assigned chemical composition as well as density. The resulting dose distributions may be different from those calculated by traditional dose calculation algorithms, especially for tissues of heterogeneity [2‐4]. In recent years, MC has been increasingly adopted in clinical application [5‐7]. There are a number of reasons for using D_w for reporting of MC calculated doses. Two major ones are that it has been used in decades of clinical studies for outcome correlation with the dose, and that the calibration protocols are all referenced to water. A technical issue related to dose calibration is that an MC based TPS could model the chemical composition of various biological tissues by approximation as a function of Computed Tomography (CT) numbers based on data of the human body (reference International Commission on Radiation Units & Measurements reports 44 and 46). Such an approximation may not perform well for non-biological materials like in a quality assurance (QA) phantom. MC based dose calculations typically report absorbed dose to media (D_m). Therefore there is a need to convert between D_m and D_w, and, as Siebers JV et al. [8] argued, MC is capable of doing the conversion. Siebers et al. presented a method to calculate the difference between D_m and D_w by applying the Bragg-Gray cavity theory, and their results showed a difference exceeding 10% in cortical bones.

Currently there is no consensus regarding whether D_m or D_w should be used for an MC based TPS [9, 10]. When it comes to clinical application, the difference between D_w and D_m will affect interpretation of dose distribution and perhaps the value of prescription dose, leading to differences in plan evaluation, dose reporting, and dose verification. In this work, D_m and D_w were both calculated using Monaco TPS for 10 nasopharyngeal cancer (NPC) cases, 10 lung cancer cases and 10 bone target cases, in order to investigate the issue in two common clinical sites in which differences of dose distributions may be highlighted. Dose Volume Histogram (DVH) was used to analyze dose parameters in the target and organ at risk (OAR), and three dimensional dose difference distributions between D_m and D_w were calculated. Gamma passing rates (measurement results vs D_m/D_w plans) were calculated at different QA criteria to evaluate the dose accuracy.

With the application of MC algorithm for dose calculation in radiation therapy, whether the dose should be calculated to medium or to water has been an unsettled debate [9, 10, 16]. The arguments that support D_w include that beam data was measured in water, that the beam output was calibrated in water, and that most clinical experience were based on dose to water, etc. However, the compelling argument to support the use of D_m is that it represents the true dose at each location of specific medium. It is the unique advantage of Monte Carlo in that D_m can be calculated directly, but D_m to D_w using stopping power ratios may involve an uncertainty [17]. In reality, different TPS use different dose calculation algorithms to produce D_w, from direct calculation to applying conversion factors. According to the AAPM TG 105 report [18], when the element components are considered in dose calculation, both D_m and D_w should be available for evaluation. When comes to a specific clinical situation, the difference between D_m and D_w should be known. N Dogan et al. [19] showed that converting D_m to D_w in EGS4 MC-calculated IMRT treatment plans introduces a systematic error in target and critical structure DVHs, and this systematic error may reach up to 5.8% for H&N and 8.0% for prostate cases when the hard-bone-containing structures such as femoral heads are present.

From our work using Monaco for NPC and lung cancer, D_m was less than D_w. The mean deviation for soft tissues was within 2%. For T-M joints and mandibular, the mean deviation was greater than 5%, and in regions of unspecified normal bone the difference could reach 10%. Our results agreed nicely with the work by Siebers et al. [8]. It is interesting to find, based on our study, that there was hardly any difference between D_w and D_m in low density regions. Although the stopping power ratio for both cortical bone and air can be above 1.10, the stopping power ratio is close to 1 for low density tissues like lung. For this reason, the issue with using D_w or D_m may have a minimal effect for majority of clinical situations.

The dose difference between D_w and D_m in bony structures may become clinically significant if the OAR is receiving doses close to its tolerance dose limit which can influence selection or rejection of a particular plan. The dose calculated by MC may need to be carefully evaluated in certain situations, e.g. bone metastasis, bone tumor, or constraining a hot spot in bone that becomes a limiting factor in plan optimization. From the Fig. 3, for PTV of the bone target cases, though the target dose coverages (the target volume (%) received the prescription dose) of D_m and converted D_w plan were similar, the mean median dose of D_w plan increased by 3.5% comparing with that of D_m plan (Table 3). That means the dose prescription for bone target could be about 3.5% higher than that of using D_w dose, and their treatment response and outcome may need further study in the future.

Previous studies [16, 20] using EGS4/MCSIM Monte Carlo and AXB dose calculations proved that conventional model based algorithms predicted dose distributions in bone that were closer to D_m distributions than to D_w distributions. It is therefore better to use D_m for consistency with previous radiation therapy experience. Our measurements showed that at widely used reference standard, 3% dose difference and 3 mm DTA, the D_m and D_w plan gamma passing rates were very close, but when the gamma calculation standard became stricter, the D_w was closer to the result of measurement than the D_m. That’s because the MapCheck2 CT images without forcing density were used to calculate the planned dose distribution, where the MapCheck2 detectors are made of high density metallic elements and the detectors are always calibrated by D_w. The CT scanner used for acquisition of patient simulation images has the limitation of scanning high density material such as the diode and the TPS also has limitation while accepting CT images with high density material. In our practice, D_m is used for treatment planning, and physicians and physicists will be consulted in case conversion to D_w in bone may affect the decisions to choose the appropriate dose distribution for treatment.

Conversion to D_w may be necessary for dose verification in the quality assurance phantom. If a water phantom is used, the difference between D_m and D_w can be ignored. Kan MW et al. [20] showed that for a heterogeneous phantom with high density materials contained the difference between D_m and D_w has an effect on the passing rate of QA measurement. Our results (Table 4) showed there were obvious differences between the D_m and D_w plan gamma passing rates when the QA criteria became strict. A simple method to bypass the problem is to assign a uniform density to the phantom and calculate to either D_m or D_w in a consistent manner. The choice of an appropriate density needs to be validated by an independent method such as point dose measurement.

Overall, the dose differences between D_m and D_w calculated by MC algorithm in Monaco are small in regions that have densities close or low to water. Our results show that dose calculated to medium by Monaco can be used clinically. In high density regions like cortical bone, the difference was 5 to 10%, and this may have a clinical consequence and needs to be carefully considered in certain clinical situations.