### D_{m} plan originally created for treatment

Ten NPC cases in stage T3 or T4, 10 lung cancer cases and 10 bone target cases (7 cases of lumbar vertebra metastasis, 3 cases of thoracic vertebra metastasis) treated at Sun Yat-sen University Cancer Center were retrospectively chosen in this study. The gross tumor volumes (GTVs) and clinical tumor volume (CTV) were contoured by experienced radiation oncologists according to definitions in the ICRU 50 and ICRU 62 reports [11, 12], and the planning target volume (PTV) were generated following a set of physician prescribed margins that were consistent with departmental protocols specific to the disease sites. Monaco TPS (Version 5.0, Elekta) was used to create the treatment plans for step-and-shoot IMRT with an Elekta Synergy linac, and MC calculated D_{m} was chosen for dose reporting. Nine equally spaced fields were used for NPC cases. The prescription of NPC cases and Lung cancer cases were 70 Gy (32 or 33 fractions, 5 days/week) and 65 Gy (26 fractions, 5 days/week) respectively. The main planning objectives for NPC are PTV V_{100%} > 98% and PTV V_{110%} < 10% (V_{x%}, is the percentage volume of reign of interest (ROI) that receives at least x% prescription dose), spinal cord D_{2%} < 45Gy, brain stem D_{2%} < 54Gy, parotid gland D_{50%} < 30Gy, optical nerve D_{2%} < 54Gy, and the dose to lens as low as possible. For lung IMRT cases 5–7 fields were used. The planning objectives are PTV V_{100%} > 95% and PTV V_{110%} < 2%, spinal cord D_{2%} < 45Gy, normal lung V_{20 Gy} < 35% (V_{D Gy}, is the percentage volume of ROI that receives at least absorbed dose D) and normal lung mean dose <19Gy, heart V_{30 Gy} < 40%, and the maximum esophagus dose <65Gy. For bone target cases, 5–7 fields were used. The prescription of bone target cases was 25 Gy (5Gy/fractions, 5 days/week). The main planning objectives are for PTV, V_{100%} > 95% and V_{110%} < 10%, for spinal cord D_{max} < 26 Gy, for lung V_{10Gy} < 15%, and the maximum esophagus dose < 26 Gy.

### D_{w} calculation

The MC algorithm in the Monaco TPS used for this study, called XVMC, calculates dose based upon mass density. A technical issue of dose calculation with MC in treatment planning is how to obtain the density and chemical composition data for the patient model from the CT. An approximation is made by assigning a voxel to certain type of tissue in the human body based on its Hounsfield unit (HU) in a certain range, and the mass density and composition data can be looked up in the International Commission on Radiation Units & Measurements Reports No. 46 [13]. XVMC algorithm converts CT numbers to ED numbers using the user-defined CT-to-ED calibration table and takes with a fit function that maps continuously the electron density to mass density for matching a tissue with approximating cross section and attenuation coefficient data [14].

The conversion to D_{w} can be calculated based on the distribution of D_{m} plan according to the Bragg-Gray cavity theory:

$$ {\mathrm{D}}_{\mathrm{w}}={\mathrm{D}}_{\mathrm{m}}\ {s}_{w, med} $$

(1)

where *s*_{w,med} is the mean unconstrained mass stop power ratio of water to media of primary electron spectrum, and D_{w} is understood as the dose to the voxel replacement of water embedded to the actual media. Theoretically mass stop power ratio can be calculated by the following formula [8]:

$$ {s}_{w, med}={\int}_0^{E_{max}}{\left({\Phi}_E\right)}_m{\left(S/\rho \right)}_w dE/{\int}_0^{E_{max}}{\left({\Phi}_E\right)}_m{\left(S/\rho \right)}_{med} dE $$

(2)

where (*S*/*ρ*)_{w} and (*S*/*ρ*)_{med} are the unconstrained mass stop power of water and media, respectively. (Φ_{E})_{m} is the primary electron fluence in the medium and *E*_{max} is the maximum energy in the (Φ_{E})_{m} distribution. The stopping power ratio in Moncao was pre-calculated by approximation for tissue-like media.

The conversion from D_{m} to D_{w} in Monaco with a clinically accepted plan involved a simple recalculation with exactly the same set of plan parameters (all the geometric parameters and monitor units (MU)) retained. The stopping power ratios dependent of mass density were applied voxel by voxel. The matrix of dose calculation grid was 0.3 cm × 0.3 cm × 0.3 cm, and the Monte Carlo statistical uncertainty was set at 3% per control point.

### D_{m} and D_{w} dose verification

All the plans were measured with MapCHECK2 (Sun Nuclear, Florida, USA) to verify the dose distribution. MacpCHECK2 was mounted in a water-equivalent phantom (MapPHAN) with a 5 cm equivalent depth from the surface to the detectors. The TPS planed dose was calculated on the real phantom CT images without overriding the density. The measured dose distributions of composite fields were compared with the corresponding planned dose distributions (D_{m} or D_{w}), and the local dose normalization gamma (*γ*) passing rates were calculated at the setting dose difference (DD) and distance to agreement (DTA). In order to eliminate dose in the out-of-field region where a large relative dose difference can be calculated and hence skew the*γ* result, a lower dose threshold (10%) was set and below the threshold the*γ* result was ignored. Using 3%&3 mm, 2%&2 mm and 1%&1 mm tolerances, the gamma passing rates were calculated to find how the pass rates change with reduction of dose difference and DTA limits.

### Data analysis

According to the ICRU 83 report, the volume-dose is recommended to describe the dose information in the ROIs, as D_{x%} to note the dose that X% of volume of ROI receives [15]. For example, D_{98%} means 98% of volume received the dose at specified value such as 65Gy. These DVH parameters were used for statistical analysis of D_{w} and D_{m} dose distributions. The bin width of the DVHs was 1 cGy, and the resolution for DVH sampling was 0.1 cm. The difference between the D_{w} and D_{m} was calculated by:

$$ \mathrm{Diff}\ \left(\%\right)=\left({\left({\mathrm{D}}_{\mathrm{x}\%}\right)}_{\mathrm{w}}-{\left({\mathrm{D}}_{\mathrm{x}\%}\right)}_{\mathrm{m}}\right)/{\left({\mathrm{D}}_{\mathrm{x}\%}\right)}_{\mathrm{w}}\times 100 $$

(3)

The plan subtraction method was used to evaluate the spatial dose difference distribution of D_{w} and D_{m}.

Paired t-tests were performed using the SPSS software (Version 19, SPSS, Inc., USA) to determine the statistical significance of the difference between D_{w} and D_{m}, with a *p*-value < 0.05 as the threshold for consideration as statistically significant.