Automatic Radiobiological Comparison of Radiation Therapy Plans: An Application to Gastric Cancer

Simple Summary The radiotherapy plans are usually judged using physical quantities, including dose and dose-volume values. Biological indices may also be applied for plan evaluation. A new software was developed for the quick and automatic calculation of tumor control probability (TCP) and normal tissue control probability (NTCP) from any radiation therapy plan and any fractionation scheme. Limited information has been published about the radiobiological metrics associated with gastric cancer irradiation. The new software was applied to radiobiologically compare photon plans for gastric malignancies generated with three-dimensional conformal radiotherapy (3D-CRT), intensity-modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT). The IMRT and VMAT plans provided higher TCPs than 3D-CRT. They also reduced the NTCPs and the risk of late adverse effects in most of the surrounding healthy organs compared to 3D-CRT. The presented results are useful for the plan optimization and choice of the appropriate radiotherapy technique for gastric cancer. Abstract (1) Aim: This study was conducted to radiobiologically compare radiotherapy plans for gastric cancer with a newly developed software tool. (2) Methods: Treatment planning was performed on two computational phantoms simulating adult male and female patients. Three-dimensional conformal radiotherapy (3D-CRT), intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT) plans for gastric cancer were generated with three-photon beam energies. The equivalent uniform dose (EUD), tumor control probability (TCP) of the target and normal tissue control probability (NTCP) of eight different critical organs were calculated. A new software was employed for these calculations using the EUD-based model and dose-volume-histogram data. (3) Results: The IMRT and VMAT plan led to TCPs of 51.3–51.5%, whereas 3D-CRT gave values up to 50.2%. The intensity-modulated techniques resulted in NTCPs of (5.3 × 10−6–3.3 × 10−1)%. The corresponding NTCPs from 3D-CRT were (3.4 × 10−7–7.4 × 10−1)%. The above biological indices were automatically calculated in less than 40 s with the software. (4) Conclusions: The direct and quick radiobiological evaluation of radiotherapy plans is feasible using the new software tool. The IMRT and VMAT reduced the probability of the appearance of late effects in most of the surrounding critical organs and slightly increased the TCP compared to 3D-CRT.


Introduction
Gastric cancer is the fifth most common malignant disease worldwide, with more than one million new cases per year, according to recent statistics from 185 countries [1]. Gastric carcinoma is also the fourth leading cause of cancer mortality globally, following lung, colorectal and liver cancers [1]. Complete tumor and regional lymph node resection is the primary treatment approach for patients with stomach cancer [2]. The curative or palliative surgical resection may be applied in 50-60% of these subjects during the first disease stage [2]. Macdonald et al. [3] showed that postoperative chemoradiotherapy for gastric cancer significantly improves overall and relapse-free survival compared to those associated only with surgery.
Adjuvant radiation therapy administered with concurrent chemotherapy is currently recommended for patients suffering from gastric cancer [4]. Radiation-related toxicity remains a concern for these patients subjected to the above treatment option [3,4]. The target volume in gastric cancer usually has large dimensions [5], and it is surrounded by many healthy organs with high radiosensitivities, such as kidneys, liver, heart, bowel and lungs. Special consideration needs to be given in the selection of the proper radiation therapy plan, ensuring adequate tumor control with minimal adverse events. The radiobiological optimization of treatment plans using biologically related models should supersede the well-known plan evaluation based on physical dose quantities [6]. Limited data have been published about the radiobiological metrics associated with the therapeutic irradiation of gastric cancer. Mondlane et al. [7] found that proton therapy reduced the normal tissue control probability (NTCP) of the left kidney with respect to volumetric modulated arc therapy (VMAT) with 6 MV photons. Photon and proton irradiation led to similar NTCPs for all other organs-at-risk (OARs). Sharfo et al. [8] showed that the automated VMAT plans result in lower NTCPs of kidneys and liver compared to manual VMAT planning with 10 MV photons. To our knowledge, no attempts have been made to investigate the impact of radiation therapy technique and photon beam energy on the tumor control probability (TCP) and NTCP related to gastric cancer irradiation.
The objectives of this study were (a) to determine the TCP and NTCP from threedimensional conformal radiotherapy (3D-CRT), intensity modulated radiation therapy (IMRT) and VMAT for gastric cancer with different photon beam energies, and (b) to develop a new software package providing automatic calculation of the above radiobiological parameters derived from the treatment plans.

XCAT Male and Female Phantoms
This work was carried out using 4D extended cardiac-torso (XCAT) computational phantoms. Analytical whole-body anatomies of male and female adults were defined by Segars et al. [9] with non-uniform rational B-splines. The bones, muscles and vessels of the human body, together with all internal organs, were modeled in the XCAT phantoms [9]. The height and weight of the XCAT phantom simulating a male patient were 1761 mm and 81 kg, respectively. The corresponding dimensions for the female phantom were 1627 mm and 66 kg. The XCAT phantoms have already been used for treatment planning and dosimetric purposes in radiation therapy [10][11][12].

Treatment Planning for Gastric Cancer
The dicom XCAT images were compatible with Monaco treatment planning system (Elekta Instrument AB, Sweden). A series of 3-mm CT images depicting the anatomy of each XCAT phantom was used for contouring. The phantoms were in supine position. A radiation oncologist manually contoured the clinical target volume (CTV) and the planning target volume (PTV) for gastric cancer treatment. Manual delineation was performed for the following organs-at-risk (OARs): left and right lungs, heart, left and right kidneys, liver, bowel and spinal cord. The treatment plans were created by an experienced medical physicist for an Infinity linear accelerator (Elekta Instrument AB, Sweden) producing 6, 10 and 15 MV photons. The prescription dose was 45 Gy, given in 25 fractions.
Three-dimensional conformal radiotherapy (3D-CRT) plans were generated using the field-in-field technique. Three different plans consisting of four treatment fields at the gantry angles of 0 • , 90 • , 180 • and 270 • were generated using 6, 10 and 15 MV photon beams. No more than four segments were used for each field. The IMRT plans included a seven-field arrangement at the following angles: 0 • , 51 • , 102 • , 153 • , 204 • , 255 • and 306 • [13]. The VMAT plans were designed using two complete arcs in opposite directions. The above VMAT planning strategy is used for abdominopelvic tumors in our department [14,15]. Six and ten MV X-rays were used for IMRT and VMAT plans. For 3D-CRT plans, 95% of the PTV had to be covered by at least the 95% of the prescribed dose. The corresponding goal for plans with intensity-modulated beams was V 42 . 75Gy ≥ 99%. The previously reported dose constraints for lungs, heart, kidneys, liver, bowel and spinal cord were used for generation of the above treatment plans [4]. The constraints are shown in Table 1. The average dose (D av ) received by each OAR and the parameters V nGy denoting the organ volume exceeding n Gy were recorded from the dose-volume histograms (DVHs). The maximum dose (D max ) to spinal cord was also taken from the DVHs. For the PTV, the homogeneity index (HI) and the conformation number (CN) were determined. The HI was found with the following equation: where D 5% and D 95% are the radiation doses to 5% and 95% of the PTV. The CN was calculated as follows: where PTV PD is the target volume covered by the prescribed dose, PTV is the volume of the target and V PD is the whole volume of the phantom receiving the prescribed dose.

TCP and NTCP Calculations
The equivalent uniform dose (EUD) model was used for calculating the TCP NTCPs [16,17]. These calculations were performed for the seven different radiation therapy plans for gastric cancer generated on a phantom representing an average male or female patient. The EUD was found with the formula: where V i is the partial volume i absorbing a radiation dose equal to D i and α is a unitless factor associated with OAR or target. The V i and D i inserted in Equation (3) were obtained by the DVH of each structure of interest. For fraction doses other than 2 Gy, the biological equivalent physical dose (EQD i ) needs to be inserted in Equation (3). The EQD i was calculated as follows: where α ⁄β is the tissue-dependent linear quadratic parameter for the irradiated tissue and D f is the tumor dose per fraction.
The TCP was calculated as follows: where TCD 50 is the radiation dose to tumor, resulting in control of 50% of the cancer cells, and γ 50 is a model parameter related to each tumor type. The NTCP for lungs, heart, kidneys, liver, bowel and spinal cord was found with the following equation: where TD 50 is the dose tolerance leading to a 50% complication rate.

Development of the Software Tool
A new software package was developed to facilitate the radiobiological evaluation of treatment plans. Scripting was performed with python 3.8 programming language. The algorithm of the software incorporates Equations (3)-(6). The required parameters TD 50 , α, α/β and γ 50 for the NTCP calculation of twenty-three different critical organs were taken from the literature [17][18][19][20][21][22][23][24], and they were inserted into the software. The above parameters are summarized in Table 2. The respective parameters for twelve macroscopic tumors and eleven microscopic malignancies derived from Okunieff et al. [25] were also incorporated into the new tool for plan analysis. To minimize the preprocessing time, the algorithm was developed to retrieve V i and D i values automatically from differential DVH text files exported from the Monaco treatment planning system. The graphical user interface (GUI) was developed with the tkinter module [26].  Figure 1). By selecting the NTCP button, the NTCP's GUI appears and the user can select the OAR under investigation, define the tumor dose per fraction in Gy or cGy and insert the relevant DVH file ( Figure 2). By selecting the 'Estimate EUD and NTCP' button, the algorithm automatically retrieves the required calculation parameters, performs all necessary computations and then presents the EUD and NTCP values together with the relevant endpoint in a new window. Moreover, the software gives the option to export and save a text file which may include information about the patient name, radiotherapy technique, total tumor dose, organ-specific parameters employed for software calculation, as well as the resultant EUD and NTCP values ( Figure 2).  The TCP's GUI may be presented by selecting the TCP button in the initial window of Figure 3. The user has to select whether this calculation is about a microscopic or macroscopic malignant disease. Then, the user defines the tumor site under examination, tumor dose per fraction in Gy or cGy, disease stage and imports the DVH text file. Furthermore, the software allows the user to calculate the TCP for tumors not considered in our calculator. In this case, the user has to import the appropriate values for TCD 50 , α, α/β and γ 50 . The results of the TCP calculator can be easily exported in a similar way to that described for NTCP calculations.
The accuracy of the newly developed software tool was investigated in the current study. The TCP and NTCPs of eight different critical organs associated with a 6 MV IMRT plan for gastric cancer generated on a phantom simulating a female patient were calculated with the aid of the software. The obtained results were directly compared with the manual calculations of the aforementioned radiobiological parameters.

Dosimetric Comparison of Treatment Plans
The isodose curves associated with 3D-CRT, IMRT and VMAT plans for gastric cancer are presented in Figure 4. The dose parameters for the PTV and eight different OARs derived from treatment plans on XCAT phantoms representing an adult male and female are shown in Tables 3 and 4, respectively. The V42.75Gy for the PTV in 3D-CRT plans varied from 95.8% to 98.3% by the beam energy and the phantom used. The respective value for plans with intensity-modulated beams was at least 99.9%. IMRT plans led to HI and CN values of 1.03-1.04 and 0.84-0.87, respectively. The corresponding parameters from VMAT were similar and equal to 1.03-1.04 and 0.85-0.87. The 3D-CRT plans led to a HI of 1.08-1.10, whereas the CN was 0.35-0.61.

Dosimetric Comparison of Treatment Plans
The isodose curves associated with 3D-CRT, IMRT and VMAT plans for gastric cancer are presented in Figure 4. The dose parameters for the PTV and eight different OARs derived from treatment plans on XCAT phantoms representing an adult male and female are shown in Tables 3 and 4, respectively. The V 42 . 75Gy for the PTV in 3D-CRT plans varied from 95.8% to 98.3% by the beam energy and the phantom used. The respective value for plans with intensity-modulated beams was at least 99.9%. IMRT plans led to HI and CN values of 1.03-1.04 and 0.84-0.87, respectively. The corresponding parameters from VMAT were similar and equal to 1.03-1.04 and 0.85-0.87. The 3D-CRT plans led to a HI of 1.08-1.10, whereas the CN was 0.35-0.61.    PTV, planning target volume; OAR, organ-at-risk; 3D-CRT, three-dimensional conformal radiotherapy; IMRT, intensity modulated radiation therapy; VMAT, volumetric modulated arc therapy; D av , average dose; V nGy , organ volume receiving more than n Gy; D max , maximum dose.   respectively. The V 10Gy , V 20Gy and V 30Gy for both lungs from 3D-CRT were found to be smaller than those from IMRT and VMAT plans. The opposite result was found for the V i parameters of right and left kidneys, liver and bowel. The V 30Gy for the heart associated with conformal radiotherapy of a female patient with gastric cancer was lower than that from IMRT and VMAT. The above was not observed for treatment plans generated on the XCAT phantom representing an adult male.

Discussion
The quality of any particular radiotherapy plan and the subsequent comparison of plans usually relies on radiation dose and dose-volume parameters. The report of the therapy physics committee of the American Association of Physicists in Medicine previously suggested the use of biologically-based models for treatment planning [6]. The TCP and NTCP indices may reflect more closely the clinical outcome of radiation therapy compared to physical dose-volume quantities [6]. The above radiobiological indices have been widely employed for the analysis and evaluation of radiation therapy plans [27][28][29]. However, many treatment planning systems can not directly provide TCP and NTCP calculations. The determination of these quantities on the basis of the EUD model requires the extraction of DVHs from the planning systems and, then, the combination of histogram data with mathematical equations and model parameters. This procedure takes considerable time making its use to be rather difficult in everyday clinical practice.
This study introduced a new software tool for calculating the TCP and NTCP from radiation therapy plans. This tool was not limited to the needs of the present study related to gastric cancer and the surrounding OARs. It was designed to give calculations of radiobiological parameters for different tumor sites and different critical organs. Moreover, its design enabled the TCP and NTCP determination for any fractionation schedule. The DVH data of the target volume or any OAR, as obtained by the treatment planning system, was directly introduced into the software tool without any processing or modification. Organ-and tumor-specific parameters were introduced into the software environment to facilitate the EUD calculation and the subsequent determination of the TCP and/or NTCP. The user had to simply define the OAR or tumor site and the dose per fraction.
The accuracy of the software results was verified against manual calculations of the above biological indices. The proposed software tool may be routinely used as a clinical aid in the radiobiological comparison of any treatment plans. The user intervention in this process is minimal. The tool may directly give quick and automatic calculations of TCP and NTCP values. Further research is needed to investigate the application of the software tool to centers equipped with treatment planning systems different from that used in this work.
The newly developed software tool was applied for the radiobiological comparison of photon plans for gastric cancer. The target volume in radiotherapy for gastric malignancies has multi-concave shapes, and its size may vary widely from patient to patient. Jansen et al. [30] found a PTV range from 634 cm 3 to 1677 cm 3 . The analysis of treatment plans obtained by consecutive gastric cancer patients undergoing radiation therapy may not lead to representative dose results for the average subject. The previously reported guidelines of radiotherapy treatment planning [31] pointed out that some planning studies may benefit from the in-depth and profound examination of a few representative cases. The treatment plans of this study were created on two different computational XCAT phantoms simulating average adult male and female patients. The anatomies of the XCAT phantoms were properly adjusted to represent the 50th percentile of United States adult subjects aged 18-64 years [9]. Data from ICRP publication 89 [32] dealing with anatomical and physiological values of reference individuals were employed to determine the organ volumes of both phantoms.
Three dimensional-CRT plans were generated with 6, 10 and 15 MV X-rays on both XCAT phantoms. Photon beam energies of 6 MV and 10 MV were used for the IMRT and VMAT planning. The generated treatment plans were considered clinically acceptable, and they fulfilled the dose constraints for the examined OARs. The IMRT and VMAT plan led to almost the same TCP values, which were always higher than those related to 3D-CRT. The TCP difference between the intensity-modulated treatment techniques and conformal radiotherapy was found to be 4.0-6.0% for females treated for the gastric difference. The minimum difference for irradiated males was 2.2%. The calculated TCP values were consistent with those reported by Mehri-Kakavand et al. [19], who examined patients subjected to radiotherapy for gastro-esophageal junction cancer.
The NTCP values for the spinal cord and the critical abdominal organs, including left and right kidneys, liver and small bowel associated with IMRT and VMAT, were systematically lower than those from 3D-CRT for gastric cancer irrespective of the patient's gender and the beam energy employed. Conventional conformal radiation therapy on a phantom simulating an adult female resulted in smaller NTCPs for both lungs and heart with respect to advanced intensity modulated treatment methods. Similar results were found only for the left and right lungs based on the analysis of treatment plans created on a phantom representing a typical male. It should be noted that the NTCP values derived from all treatment plans for gastric cancer created on the two different XCAT phantoms were found to be small. The vast majority of these values were lower than 0.01%. One exception was the NTCP of the liver, which varied from 0.24% to 0.74%. The NTCP of the left kidney for males subjected to 3D-CRT was also more than 0.03%.
Comparing the biological indices from plans generated with different photon beam energies, useful conclusions were drawn about the optimal energy selection for radiotherapy for gastric cancer. The TCP and NTCP from 3D-CRT with 15 MV photons were lower than those associated with treatment plans created with both 6 and 10 MV X-rays. The photon beam energy had no effect on the TCP values derived from both IMRT and VMAT plans. However, the use of 10 MV instead of 6 MV photons for IMRT and VMAT for gastric cancer reduced the NTCP to five to six out of eight OARs examined in this work.

Conclusions
In conclusion, user-friendly software was developed for the calculation of TCP and NTCP values. The time efficiency and accuracy of the software make it a useful tool for the implementation of the radiobiological evaluation of radiotherapy treatment plans in everyday clinical practice. A radiobiological comparison of 3D-CRT, IMRT and VMAT plans for gastric cancer was performed with the new software. Both IMRT and VMAT resulted in slightly higher TCP values compared to 3D-CRT. The intensity-modulated treatment techniques were also superior to conventional irradiation in terms of dose homogeneity and conformity. The NTCPs of all the surrounding abdominal organs and spinal cord associated with IMRT and VMAT were lower than those from 3D-CRT plans. The above was not observed for the left and right lungs. The increase of the photon beam energy reduced the NTCP for most of the OARs under investigation, irrespective of the treatment technique and the patient's gender. The results from the radiobiological comparison of treatment plans provide useful information about the late effects of irradiation, and they can be used in the selection of the appropriate radiotherapy technique for gastric cancer patients.