Tolerance levels of mass density for CT number calibration in photon radiation therapy

Abstract Computed tomography (CT) data are required to calculate the dose distribution in a patient’s body. Generally, there are two CT number calibration methods for commercial radiotherapy treatment planning system (RTPS), namely CT number‐relative electron density calibration (CT‐RED calibration) and CT number‐mass density calibration (CT‐MD calibration). In a previous study, the tolerance levels of CT‐RED calibration were established for each tissue type. The tolerance levels were established when the relative dose error to local dose reached 2%. However, the tolerance levels of CT‐MD calibration are not established yet. We established the tolerance levels of CT‐MD calibration based on the tolerance levels of CT‐RED calibration. In order to convert mass density (MD) to relative electron density (RED), the conversion factors were determined with adult reference computational phantom data available in the International Commission on Radiological Protection publication 110 (ICRP‐110). In order to validate the practicability of the conversion factor, the relative dose error and the dose linearity were validated with multiple RTPSes and dose calculation algorithms for two groups, namely, CT‐RED calibration and CT‐MD calibration. The tolerance levels of CT‐MD calibration were determined from the tolerance levels of CT‐RED calibration with conversion factors. The converted RED from MD was compared with actual RED calculated from ICRP‐110. The conversion error was within ±0.01 for most standard organs. It was assumed that the conversion error was sufficiently small. The relative dose error difference for two groups was less than 0.3% for each tissue type. Therefore, the tolerance levels for CT‐MD calibration were determined from the tolerance levels of CT‐RED calibration with the conversion factors. The MD tolerance levels for lung, adipose/muscle, and cartilage/spongy‐bone corresponded to ±0.044, ±0.022, and ±0.045 g/cm3, respectively. The tolerance levels were useful in terms of approving the CT‐MD calibration table for clinical use.


| INTRODUCTION
Computed tomography (CT) data are imported to a radiotherapy treatment planning system (RTPS), and it is required to structure a target and calculate the dose distribution in a patient's body. In order to calculate a dose distribution in human body with RTPS, CT number calibration should be performed with several inserted tissue substitutes of a calibration phantom. 1 Generally, there are two CT number calibration methods for photon radiation therapy, namely the CT number-relative electron density calibration (CT-RED calibration) and CT number-mass density calibration (CT-MD calibration).
The CT number calibration methods are different based on each RTPS or dose calculation algorithm.
In a previous study, 2 relative electron density (RED) tolerance levels were established for each tissue type. In the study, an effective depth was calculated with RED to water, and RED tolerance levels were determined with the effective depth and tissue maximum ratio (TMR). The tolerance levels of CT-RED calibration are useful in terms of the quality assurance (QA) of the CT-RED calibration table of planning CT and cone beam CT. 3,4 The tolerance levels of CT-MD calibration are also useful for the QA because the CT-MD calibration is used in several commercial RTPSes or dose calculation algorithms.
However, the tolerance levels of CT-MD calibration are not established yet. The tolerance levels are useful in approving the CT-RED calibration table or CT-MD calibration table for clinical use. It is reasonable to determine the tolerance levels of CT-MD calibration from the tolerance levels of CT-RED calibration as opposed to determining the tolerance levels without any reference. The tolerance levels of CT-RED calibration were determined by classifying standard tissues to five tissue groups including lung, adipose/muscle, cartilage/ spongy-bone, cortical bone, and tooth tissue. 5 When the mass density (MD) is converted from RED within a tissue group, the conversion of pure organ is simple because MD and elemental composition are fixed.
However, the conversion of multiple organs is complex because there are differences in the MD and elemental compositions between organs.
The purpose of this study involves determining the conversion factors from RED to MD with a whole body phantom and verifying the practicability of the conversion method. Furthermore, the tolerance levels for CT-MD calibration are established in each tissue type.

2.A | Conversion factor between MD and RED in human body
The relationship between MD and electron density (ED) is given as follows: where ρ e denotes ED; ρ denotes MD; N A denotes the Avogadro's number (6.022 × 10 23 ); i denotes the element index; and w i , Z i and given as follows: where À ρ and À ρ e denote the averaged MD and averaged ED, respectively; j denotes the voxel index; ρ j , (ρ e ) j , and v j denote the MD, ED, and unit volume, respectively; of the j-th voxel, and V denotes the sum volume of the tissue group. The conversion factors to MD form RED are given as follows: where C denotes the conversion factor to MD form RED. ρ e ð Þ H2O denotes ED of water ( ρ e ð Þ H2O = 3.34 ×10 23 ). There are five conversion factors for five tissue groups. The conversion errors between actual RED of ICRP-110 phantom data and RED converted from MD with the conversion factor are verified for adipose/muscle and cartilage/spongy-bone.

2.B | Tolerance levels for CT-MD calibration
The RED tolerance level based on TMR and effective tissue thickness were shown in previous study. 2,5 The RED tolerance levels were established to cause 2% dose error at effective tissue thickness with a 10 cm × 10 cm field. The tolerance levels are determined by the minimum usable energy in a RTPS because the tolerance levels are more strict with lower beam energy. The MD tolerance levels for photon beam are converted from RED tolerance levels. The conversion factors to MD from RED are determined based on ICRP-110 phantom data for each tissue group. The MD tolerance levels are given as follows: where TL MD denotes the MD tolerance level, TL RED denotes the RED tolerance level, and C denotes the conversion factor.

2.C | Practicability of the conversion factor
In order to validate the practicability of the conversion factors for MD tolerance levels in terms of eq. (4), the relative dose errors are compared between TL MD and TL RED for lung, adipose/muscle, and cartilage/spongy-bone. Thus, the dose variation caused by MD variation is compared with that by RED variation. In other words, Furthermore the influence of the conversion factor on each tolerance level is validated as follows: where ΔD denotes the dose variation between CT-RED calibration and CT-MD calibration.        Figure 4 shows each normalized doses for four RTPSes or six dose calculation algorithms. Figure 5 shows the averaged normalized doses and 1 standard deviation (SD) for two groups, namely, the CT-MD calibration and the converted CT-RED calibration. The effective tissue thicknesses, D err, RED , D err, MD and ΔD for each tissue type are shown in Table 2.

| DISCUSSION
The goal of this study involved establishing MD tolerance levels of CT-MD calibration for each tissue group. In a previous study, 2,5 the tolerance levels of CT-RED calibration were determined by the effective tissue thicknesses and TMR data. However, the tolerance levels of CT-MD calibration were not determined since the relationship between MD and effective tissue thickness was not established.
In this study, tissue groups were determined by classifying with respect to MD, and conversion factors to MD from RED were created from standard whole body phantom data. The conversion error was within ±0.01 for most standard organs. The differences in several bone organs exceeded ±0.01 although it was assumed that the conversion error was sufficiently small because the thicknesses of the bone organs were thin and the conversion error was lower than the RED tolerance levels ( Table 2

| CONCLUSION
In this study, we established the conversion factor from RED to MD with ICRP-110 data. The RED and MD of organs were not proportional given the differences in the MD and element weights between organs. However, RED was converted to MD with a proportional conversion factor by classifying all organs into five tissues groups, and this study demonstrated the practicability of the conversion factors with four RTPSes and six dose calculation algorithms. Therefore, the tolerance levels for CT-MD calibration were determined with conversion factors from the tolerance levels of the CT-RED.

CONF LICT OF I NTEREST
The authors declare no conflict of interest.