2.1 Compositional analysis

We used Brain SR-2 (Gammex Inc., Middleton, Wisconsin, USA) as the BDP. To construct the SCC model, we analyzed the physical density and elemental composition of Brain SR-2 as well as previously analyzed lung-equivalent material (tough lung) and bone-equivalent material (Tough Bone) (Kyoto Kagaku Co., Ltd., Japan) [16]. For the compositional analysis of hydrogen (H), carbon (C), and nitrogen (N), we employed a 2400 II CHNS/O elemental analyzer (PerkinElmer Inc., Waltham, Massachusetts, USA). X-ray fluorescence spectroscopy was employed for the semi-quantitative analysis of elements, including aluminum (Al), silicon (Si), phosphorus (P), sulfur (S), chlorine (Cl), calcium (Ca), titanium (Ti), and barium (Ba).

2.2 CT Number measurement of brain-tissue equivalent density plugs

CT scans were performed using a Gammex RMI 467 calibration phantom (Gammex Inc., Middleton, Wisconsin, USA) with various tissue-equivalent materials, including brain SR-2, tough lung, and tough bone, to obtain the actual CT numbers of the BDP. The scans were conducted using an Aquilion Prime Beyond CT scanner (Canon Medical Systems Corporation, Japan) under the following parameters: tube voltage: 120 kV; tube current: 300 mA; slice thickness: 2 mm; field of view (FOV): 500 mm; reconstruction kernel: FC03. At our institution, the FC03 reconstruction kernel is commonly applied in chest and abdominal imaging to ensure stable CT number measurements for homogeneous standard materials. Therefore, for the BDP measurements, we used FC03 to align with the CT-RED/MD table used in CT-RED/MD protocol. These conditions match those used to construct the CT-RED/MD table. For CT number measurements of each tissue-equivalent material, a circular region of interest (ROI) with a diameter of 1.53 cm was positioned at the center of each material slice. The CT numbers for all pixels within the ROI were recorded, with the mean CT number calculated as the average of all pixel values. The standard deviation (SD) within the ROI was also computed from a single measurement to evaluate the variability.

2.3 CT number measurement and analysis of actual brain using clinical data

We analyzed CT data from ten patients who had previously undergone whole-brain irradiation for brain lesions to obtain CT numbers for actual brain tissue. The patients were randomly selected, with the study protocol approved by our institution’s ethics review board. CT scans were performed to measure the attenuation properties of brain tissue under the following conditions: tube voltage: 120 kV; tube current: 300 mA; slice thickness: 2 mm; FOV: 400 mm; reconstruction kernel: FC26. For brain tissue measurements, we used FC26, a high-contrast reconstruction kernel frequently employed in clinical brain imaging. This selection was made to better replicate actual clinical conditions, ensuring that the measured CT numbers accurately reflect those obtained in patient imaging. The same CT scanner described in Sect. 2.2 was used for all scans. The brain parenchymal regions were extracted using the auto-contouring function in Eclipse ver. 16.1 (Varian Medical Systems). The “actual brain” was defined as the whole-brain parenchyma excluding the gross tumor volume (GTV). The mean CT numbers and SDs were calculated for these regions. We first performed an overall comparison of all 10 cases and then conducted a detailed CT number histogram analysis for one representative case to illustrate the differences more clearly. The histogram was generated using CT number measurements from a circular region of interest (ROI) with a diameter of 1.53 cm, positioned at the center of each material slice. For the final analysis, the overall mean CT number and standard deviation (SD) were calculated as the average of all 10 cases.

2.4 Comparison of effective atomic number

ICRP Publication 110 does not differentiate between white and gray matter in brain tissue, treating them as a single material despite their distinct compositions in practice. To maintain consistency with this reference data, our analysis focused on whole-brain tissue rather than separately analyzing white and gray matter.

The effective atomic numbers (EANs) of BDP were calculated using the following formula based on elemental composition analysis and data from ICRP Publication 110:

$$_}=_\frac_Z}_}_}_^}_\frac__}_}}\right)}^\frac$$

(1)

ωi​ represents the mass fraction of the constituent elements i, while Zi and Ai​ denote the atomic number and atomic mass of each element, respectively. The exponent m, set to 3.3, reflects the balance between Compton scattering and the photoelectric effect within the effective energy range used in this study (50–60 keV). This choice is consistent with ICRU Report 46 data and shows excellent agreement with the reference \(_}\) values [17].

2.5 Theoretical CT number calculation for brain density plug (BDP) and actual brain tissue using stoichiometric CT number calibration model

Theoretical CT numbers were calculated using the SCC method based on a previously established model [11]. The initial model parameters for the SCC method were determined using the least squares method and the Nelder–Mead simplex algorithm implemented in Python (https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin.html).

These model parameters, optimized to reproduce the CT numbers of the tough lung, tough bone, and air, were input into the Gammex RMI 467 phantom. We calculated the theoretical CT numbers for both the BDP and actual brain tissue using the SCC method with optimized model parameters. The compositional analysis results of the brain tissue-equivalent density plug obtained in Sect. 2.1 and the physical density and elemental composition data for actual brain tissue derived from ICRP 110 were adopted in the SCC method [14].

2.6 Impact of CT-RED/MD conversion table modifications on dose calculations in brain cases

We performed dose calculations using modified CT-RED/MD tables to quantitatively assess the impact of CT number differences between the BDP and actual brain tissue on dose calculations. The calculations were conducted using Eclipse version 16.1, comparing the following three CT-RED/MD tables (Table 1):

1.

The standard CT-RED/MD table currently used in clinical practice, which includes a brain tissue-equivalent density plug (BDP) as a reference (Reference).

2.

A modified table excluding the BDP data points to assess how the absence of this density plug affects dose calculations (Modified (excluded BDP)).

3.

A modified table utilizing the CT number of actual brain tissue, derived from ICRP Publication 110 data, to evaluate the effect of using a more physiologically accurate representation of brain tissue (Modified (ICRP110 Brain)).

Table 1 Comparison of CT-RED/MD tables: original and modified versions

This comparison was designed to determine whether the presence of the BDP in the standard CT-RED/MD table introduces deviations in dose calculations and whether replacing it with a more accurate CT number from ICRP data would yield significant changes. By including these three conditions, we aimed to clarify how CT number differences in brain tissue modeling influence dose calculations in clinical settings.

For the dose calculations, we analyzed cases involving whole-brain irradiation (WBI) using a non-opposing four-field technique and brain stereotactic radiotherapy [SRS/SRT (stereotactic radiosurgery/stereotactic radiotherapy)]. The reason for selecting brain-related cases is to investigate the impact of the BDP on dose calculations. Furthermore, WBI and SRS/SRT were chosen to compare the effects on target volumes of different sizes, with WBI representing a large planning target volumes (PTV) and SRS/SRT representing a small PTV. The treatment plans for both SRS and SRT were generated using the dynamic conformal arc technique. The PTV for the three SRS and SRT cases were 7.13 cc, 11.27 cc, and 7.22 cc for Case 1, Case 2, and Case 3, respectively.

The dose calculation algorithms used were the anisotropic analytical algorithm (AAA) and Acuros XB (version 16.1.2), with a calculation grid size of 2.5 mm utilizing the physical material table in AcurosXB_13.5.We evaluated the dose–volume histogram (DVH) parameters D2%, D50%, and D98%. Here, Dx% represents the dose received by x% of the target volume. The Monitor Unit remained the same, with only the CT-RED/MD being changed for recalculation. All other parameters, including gantry angle, multi-leaf collimator positions, collimator angle, and jaw settings, were kept unchanged.

Using the dose calculation results obtained from the clinically utilized CT-RED/MD table as a reference, the relative dose differences between the reference and the other two tables were calculated using the following equation:

$$\Delta D= \frac_- _}_} \times 100 \left(\%\right)$$

(2)

where Dref is the dose calculated using the standard table (reference) and Dmod is the dose calculated using the modified table.