## 2 Materials and Methods
### Patient Radiation Dose Determination  
CT head scans were performed in the helical mode with fixed exposure parameters (tube potential (kVp) and tube current (mA)) and without an AEC system. Patient data were categorized into five age groups based on clinical protocol settings as follows: for ages 0 to 6 months, the settings were 80 kVp and 220 mA; for ages 6 months to 3 years, 80 kVp and 330 mA; for ages 3 to 6 years, 100 kVp and 240 mA; for ages 6 to 12 years, 120 kVp with a current range of 230 to 300 mA. The scanned region extended from the base of the skull to the vertex. The CTDI\({}_{\text{vol}}\) was determined using a 16 cm cylindrical phantom for all protocols.  
The CTDI\({}_{\text{vol}}\) displayed on the CT monitor was verified following the quality assurance guidelines in International Atomic Energy Agency (IAEA) Report No. 19 [19]. The CTDI\({}_{\text{vol}}\) was estimated by performing axial scans of a 16 cm diameter and 15 cm length PMMA phantom using a pencil-type ionization chamber (RaySafe Model X2, Unfors RaySafe AB, Havas, Stockholm, Sweden) at kVp settings ranging from 80 to 120. The ionization chamber was calibrated at the Secondary Standard Dosimetry Laboratory (SSDL) of Thailand. CT radiation dose parameters, including the CTDI\({}_{\text{vol}}\) (mGy) and DLP (mGy\(\cdot\)cm) obtained from the Radimetrics\({}^{\text{TM}}\) Enterprise Platform as well as organ doses (mGy) for the brain and eye lens, were determined using Monte Carlo simulation.  
The Dw was calculated using the axial cross-sectional CT image of the brain, selected as the middle slice of the scan length. Patient dimensions and regions of interest (ROIs) were manually drawn using digital calipers and freehand ROI tools within the Synapse software version 4.3.2.1. An ROI was drawn around the perimeter of each patient's head. The effective diameter (D\({}_{\text{Eff}}\)) is the diameter of a circle with an area equivalent to the cross-sectional area of the patient [9]. The D\({}_{\text{Eff}}\) was calculated as the square root of the product of the anteroposterior (AP) and lateral (LAT) dimensions. Figure 1 depicts the positioning of the central slice of the scan length in the CT scanogram, the contouring of the region of interest (ROI), and the measurement of anteroposterior (AP) and lateral (LAT) dimensions in the axial cross-sectional CT images for pediatric patients of various ages.  
The SSDE\({}_{\text{Dw}}\) was computed by multiplying the conversion factor (f\({}_{\text{Dw}}\)) by the CTDI\({}_{\text{vol}}\). The conversion factor, f\({}_{\text{Dw}}\), is derived based on the patient size (Dw) and the absorbed dose to tissue [14]. The SSDE\({}_{\text{Dw}}\) and f\({}_{\text{Dw}}\) were calculated using Equations (1) and (2), respectively.  
\[\text{SSDE}_{\text{Dw}}=\text{f}_{\text{Dw}}\times\text{CTDI}_{\text{vol}} \tag{1}\]  
\[\text{f}_{\text{Dw}}=\alpha\text{e}^{-\beta\text{D}_{\text{w}}} \tag{2}\]  
where \(\alpha\) represents the absorbed dose to tissue (mGy/CTDI\({}_{\text{vol,16}}\)), with a value of 1.9852 mGy, and \(\beta\) is the coefficient, with a value of 0.0486 cm\({}^{-1}\). Dw is the water-equivalent diameter (cm), as determined by Equation (3):  
\[\text{Dw}\equiv 2\times\sqrt{\left(\frac{\overline{\text{CT}(\text{x},\text{ y})_{\text{ROI}}}}{1000}+1\right)\times\text{A}_{\text{ROI}}/\pi} \tag{3}\]  
where \(\overline{\text{CT}(\text{x},\text{y})_{\text{ROI}}}\) represents the mean CT number (HU) within the ROI in the axial cross-sectional CT image of the head and A\({}_{\text{ROI}}\) is the total area of the ROI (cm\({}^{2}\)).