

ORIGINAL ARTICLE 

Year : 2022  Volume
: 18
 Issue : 6  Page : 16971705 

Development and validation of an indigenous, radiobiological modelbased tumor control probability and normal tissue complication probability estimation software for routine plan evaluation in clinics
Ganeshkumar Patel^{1}, Abhijit Mandal^{1}, Avinav Bharati^{2}, Sunil Choudhary^{1}, Ritusha Mishra^{1}, Ankur Mourya^{1}
^{1} Department of Radiotherapy and Radiation Medicine, Institute of Medical Sciences, Banaras Hindu University, Varanasi, Uttar Pradesh, India ^{2} Department of Radiotherapy, RMLIMS, Lucknow, Uttar Pradesh, India
Date of Submission  17Mar2020 
Date of Decision  18Jun2020 
Date of Acceptance  17Sep2020 
Date of Web Publication  05Aug2021 
Correspondence Address: Abhijit Mandal Department of Radiotherapy and Radiation Medicine, Institute of Medical Sciences, Banaras Hindu University, Varanasi, Uttar Pradesh India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jcrt.JCRT_330_20
Purpose: Development and validation of a simple and convenient computational program in MATLAB environment for estimating the tumor control probability (TCP) and the normal tissue complication probability (NTCP), as a decision support system for routine plan evaluation. Materials and Methods: We developed an inhouse software using MATLAB 2016b (Mathworks) for estimating TCP and NTCP named as RBMODELV1. The program contains Niemierko free equivalent uniform dose (EUD) program code provided in authors research article. For rest of radiobiological (RB) models in the software separate coding is performed. The program accepts cumulative dose–volume histogram file in (.txt) format containing two columns dose and volume. A set of two RB parameters were prepared, default and userdependent in excel sheet named as RBDATA. We crossvalidated results of RBMODELV1 software with BioSuite software for Poisson's TCP model and LymanKutcherBurman (LKB) model. A set of total 20 patient's data of head and neck site took under study and respective TCP and NTCP calculated by all the RB models and compared. Results: This is the first study in which we tried to establish correlation between the mean doses (EUD) received by parallel structure (parotid gland and oral cavity) and predicted percentage of NTCP values. It is found that mean dose in the range of 35–40 Gy for parotid gland can result in more than 50% NTCP predicted by all four RB models. Similarly oral cavity receiving mean dose in the range of 53–58 Gy can results in more than 35% NTCP predicted by all the four models. There is <3% variation observed between TCP calculated by BioSuite and RBMODELV1 software and <4% variation observed between predicted NTCP for parotid gland and oral cavity OAR from LKB model by both the software. Conclusion: We created simple software RBMODELV1 which can be used as a research tool as well as decision support system.
Keywords: Dose–volume histogram, normal tissue complication probability, radiobiological model, tumor control probability
How to cite this article: Patel G, Mandal A, Bharati A, Choudhary S, Mishra R, Mourya A. Development and validation of an indigenous, radiobiological modelbased tumor control probability and normal tissue complication probability estimation software for routine plan evaluation in clinics. J Can Res Ther 2022;18:1697705 
How to cite this URL: Patel G, Mandal A, Bharati A, Choudhary S, Mishra R, Mourya A. Development and validation of an indigenous, radiobiological modelbased tumor control probability and normal tissue complication probability estimation software for routine plan evaluation in clinics. J Can Res Ther [serial online] 2022 [cited 2022 Dec 3];18:1697705. Available from: https://www.cancerjournal.net/text.asp?2022/18/6/0/323171 
> Introduction   
In radiotherapy, there is ongoing practice of plan evaluation is based on dose–volume histogram (DVH). DVH is a two dimensional representation of three dimensional dose distribution. However, design of treatment plan outcome based on biological objective functions has the potential to improve clinical outcomes. The biological objective functions are usually expressed in the form of tumor control probability (TCP) and normal tissue complication probability (NTCP). To obtain more reliable outcome, it require the knowledge of parameter values of TCP/NTCP models. There are sufficient number of radiobiological (RB) models exists in literature and most of them failed to get recognition because lack of reliability and clinical validation of models for accurate TCP/NTCP prediction. Therefore, most of researchers in their study always take into account multiple models to get output in terms of TCP/NTCP. There are various studies which compared multiple models and showed limitations and benefits over each other.^{[1],[2],[3],[4]} Uncertainties in parameter estimation while using particular RB model in clinical practice had applied brake on transition of dosebased treatment planning (DVH) to biologically based treatment planning. Still some planning system like Eclipse, Pinnacle and Raystation provided option of biologically based treatment plan optimization and evaluation with warning of precaution while applying results in actual clinical practice.^{[5]}
We are well aware that there are several software (CERR, DRESS, DORES, RADBIOMOD, BioSuite, TCP_NTCP_CALC) designed with similar intention. Some of this software is not freely available and some of them which are in open access are complex in their application.^{[6],[7],[8],[9],[10]} The abovementioned software used critical models which demand so many parameters. Our developed software employed simple models intended to build confidence amongst users those are little scared of RB models application. It is freely available by contacting the authors.
> Materials and Methods   
We have developed a simple application using MATLAB licensed version 2016b (Mathworks) for estimating TCP and NTCP named as RBMODELV1. The program contains Niemierko free equivalent uniform dose (EUD) program code provided in authors research article.^{[11]} This program was initially validated as per guidelines of the author but we found error while running the code in MATLAB software which has been corrected. Author provided standard six inputs and six outputs for program validation, but it was found that three inputs were wrong and could not produce the right output. Hence, by hit and trial method, we corrected input for which output was matched. Corrected input given below.
 Given = (0 100; 200 0) corrected = (0 100; 120 0)
 Given = (0 100; 12000 0) corrected= (0 100; 120 0)
 Given = (0 100; 14000 0) corrected= (0 100; 140 0).
For rest of RB models in the software separate coding is performed. Software has user friendly graphical user interface (GUI). The program accepts cumulative DVH file in (.txt) format containing two columns, dose and volume with minimum bin size of 0.1 cGy. This application incorporated two most widely used TCP models of Poisson's and Niemierko and four NTCP models LymanKutcherBurman (LKB), Niemierko EUD model or logit, logistic model and Weibull distribution model. A set of two RB parameters dataset were prepared, default and recommended in excel sheet format named as RBDATA provided with software. User has freedom to choose any one of them for TCP and NTCP estimation and can modify or update. We crossvalidated results of our developed software with BioSuite software for Poisson's TCP model and LKB model.^{[10]} A set of total 20 patient's data of head and neck site took under study and respective TCP and NTCP calculated by all the RB models and compared variations against each other.
Radiobiological models
In this software simple RB models opted, as clinical dose response data have sufficient diversity; use of complex models with too many parameters typically results in significant parameter correlation and ambiguity in biological interpretation. The four models are briefly discussed in the following paragraphs, and the parameters used in each of the models are summarized in [Table 1] and [Table 2].  Table 1: containing biological parameters used for NTCP calculation by four radiobiological models for head and neck cancer site
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 Table 2: Containing biological parameters used for TCP calculation by four radiobiological models for head and neck cancer site
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Niemierko equivalent uniform dose or logit model
The EUD model is a simple model based on two equations (1) and (2). The unique thing is that same model can be used for both TCP and NTCP predictions.
Where, EUD is the equivalent uniform dose, which represents the dose that, if delivered uniformly to the entire organ, would produce the same effect as the given heterogeneous dose distribution.^{[12]} “a” is a unitless model parameter that is specific to the normal structure or tumor of interest, and V_{i} is unitless and represents the i^{th} partial volume receiving dose Di in Gy. Since the relative volume of the whole structure of interest corresponds to 1, the sum of all partial volumes V_{i} will equal to 1. The choice of parameter a will determine the behavior of the EUDbased model. Values of “a” represents volume effect which can be understand by the example. For normal tissues that exhibit a large volume effect (e. g., liver, parotids, and lungs), the dose response may be closer to the mean dose therefore “a” should be small positive number.
In normal tissues with a serial or “links in a chain” architecture like the spinal cord, breaking one of the links will likely rupture the functional tissue chain, therefore “a” will usually be a large positive number.
The local control of a tumor will likely depend on the volume that received the minimum dose; since this is where the tumor clonogen survival should be highest therefore “a” should be large negative number.
To calculate the EUDbased NTCP, Niemierko proposed parameterization of the dose response characteristics using the logistic function as shown below.
Where, TD_{50} is the tolerance dose for a 50% complication rate at a specific time interval.
ϒ_{50} is a unitless model parameter that is specific to the normal structure or tumor of interest and describes the slope of the doseresponse curve.
Similarly, to calculate the tumor control probability (TCP), the EUD is substituted in the following equation.
Where, TCD_{50} is the tumor dose to control 50% of the tumors when the tumor is homogeneously irradiated.
LymanKutcherBurman model
Lyman's formula models the sigmoid doseresponse (SDR) curve of NTCP as a function of dose (Di) to a uniformly irradiated fractional reference volume (Vref).^{[13]} The expression of this NTCP is given as below:
The SDR model has three parameters: n, m, and D_{50}; n determines the dosevolume dependence of a tissue and thus accounts for differences in tissue architecture; m controls the slope of the doseresponse curve (in the case of homogeneous irradiation); and D50 represents the dose at which there is a 50% chance of complication, and thus dictates the position of the doseresponse curve.
Tumor control probability model based on Poisson's statistics
TCP models generally rely on the assumption that tumor control requires the killing of all tumor clonogens.^{[1]} Poisson's statistics predict that the probability of this occurring presented as:
Where, N is the initial number of clonogens, and P(D) is the cell survival fraction after a dose D. If it is assumed that cell survival can be described by singlehit mechanics,
The expression in Eq. (6) can be rewritten in terms of the two parameters describing the dose and normalized slope at the point of 50% probability of control, ϒ_{50} and D_{50.}
Using the assumption of independent subvolumes, for the case of heterogeneous irradiation, the overall probability of tumor control is the product of the probabilities of killing all clonogens in each tumor subvolume described by the cumulative dose–volume histogram (CDVH):
Thus, for a given DDVH {Di, vi}, the TCP can be calculated using the following twoparameter TCP formula:
Weibull distribution model
The mathematical form of the model is given below:^{[2]}
Where, P(D) is a NTCP
Logistic model
The mathematical form of the model represented as:^{[14]}
D_{50} is the dose leading to 50% complication rate, D is the dose to organ and ϒ_{50} is the relative change in complication rate per unit change in dose rate at the 50% level.
Application architecture
The RBMODELV1 was developed in MATLAB 2016b version (Mathworks) programming environment and is designed for use on a windowsbased computer. RBMODELV1 is a menu driven user interface designed to use conveniently. The framework of the application is simple as shown in [Figure 1]. The user has to browse input file in. txt format which should be cumulative DVH as it is most preferably form of plan evaluation. The rest of model parameters need to enter manually from the database provided with software. TCP or NTCP calculations are performed based on these parameter values for different RB models embedded into the application. Further details of the application functionality explained below.
Input section
The program accepts CDVH file in (.txt) format with two columns in the form of [Di, Vi]. There is one browse option for PTV and separate browse option for OAR CDVH files, therefore simultaneously TCP and NTCP can be calculated. While extracting CDVH file from the treatment planning system, it should be noted that DVH plot should be in absolute dose (cGy) versus absolute volume (cubic centimetre).
Parameter database and parameter selection
One of the prime purposes of the RBMODELV1 is to provide a convenient means of accessing and archiving current and future RB knowledge as it pertains to treatment plan evaluation. The program package contains parameter databases for two TCP and four NTCP models described above. For each of these models two databases were maintained: A “default” one, which is recommended for user and a “user dependent” database, which gives flexibility to user to add or delete entries. This parameter database separately provided in the form of excel sheet named as “RBDATA” in addition with software package. The [Table 3] contains biological parameter values for TCP model from Okunieff et al. study for various tumors of head and neck site. The [Table 4] contains biological parameters values for NTCP model of different organ at risk of head and neck site with 95% confidence interval where available. RB parameters (a, ϒ_{50}, TCD_{50}, TD50, α/&#s946;, m, n) collected from metaanalysis studies as well as proposed model parameters based on cumulative experience at various institutions which assume to be more representative and readily incorporated into clinical use.^{[14],[15],[16],[17],[18],[19]}  Table 3: Radiobiological model parameters of head and neck site for TCP calculation from Okunieff et al.
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 Table 4: Radiobiological model parameters reported in literature for head and neck site organ at risk (OAR)
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Display and output
The GUIbased display is shown in [Figure 1], the display divided into main four panels, patient information panel, instructions and software version details, TCP section and NTCP section. There are clear option for erasing the input and output entries. User has to click on Target file and OAR file button to browse the respective CDVH file. Push button is provided in TCP and NTCP section to enable calculation. User can take an output in. txt file by pressing print button.
Advantages and disadvantages of the software
In this software we used very simple models demanding RB parameters which accept common input amongst the incorporated models. This surely reduces confusion for the enduser and once you entered all parameters you will find results of all models output simultaneously. In this study we crosscalibrated our results with BioSuite software for LKB model and Poisons TCP model. The most important thing which included in this software package is RB parameters generated after quantitative analysis of normal tissue effects in the clinic (QUANTEC) dose report summary.^{[20]} We also archived old parameter database for the enduser. The speed of TCP and NTCP calculation is very fast, even for input DVH file having 0.1 cGy dose binning.
Input file creation is a little time taking process as user has to export DVH file for individual OAR and PTV. This software is developed in MATLAB platform therefore user should have the MATLAB software and MATLAB is not a freely available software. Work is in progress to provide software in MATLAB compiler format or can say in application form so that no need for MATLAB installation will be required. The user has to simply download the application and run into his/her system. We are trying to develop software in Python platform, as Python is freely available software and now a day's popular in scientific community.
> Results   
We crossvalidated the results of predicted NTCP by LKB model and predicted TCP by Poisson's model with BioSuite software developed by Uzan et al. as these two models common in both the software.^{[10]}
The difference in TCP calculated for Niemierko or logit model and Poisson's model by RBMODELV1 program is found to be <3% as shown in [Figure 2]. There is <1% variation observed in calculated TCP for Poisson's model by BioSuite and RBMODV1 software as shown in [Figure 2]. The sigmoid dose response curve plotted for both the models as shown in [Figure 3.  Figure 2: Graph showing % variation of calculated TCP for two different models by two different programs
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 Figure 3: Statistical distribution used to describe the shape of dose response curve for two different TCP models
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Graph is plotted between predicted NTCP by four different models as a function of equivalent uniform dose (EUD) for parotid and oral cavity as shown in [Figure 4] and [Figure 8]. The difference in predicted NTCP of parotid gland and oral cavity from LKB model by two different programs is observe to be <4% as shown in [Figure 5] and [Figure 8]. The dose response curve plotted for both organs parotids and oral cavity which helps to understand variations of outcome of different NTCP models as shown in [Figure 6] and [Figure 9]. {Figure 1}  Figure 5: Graph indicating calculated NTCP values against equivalent uniform dose of parotid organ for LymanKutcherBurman model by two different programs
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 Figure 6: Statistical distribution used to describe the shape of dose response curve of parotid organ for four different NTCP models
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 Figure 7: Graph indicating calculated NTCP values by four different models as a function of equivalent uniform dose for oral cavity
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 Figure 8: Graph indicating calculated NTCP values against equivalent uniform dose of oral cavity for LymanKutcherBurman model by two different programs
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 Figure 9: Statistical distribution used to describe the shape of dose response curve of oral cavity organ for four different NTCP models
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The results of predicted TCP and NTCP by Niemerko EUD model is crossvalidated as per the author guidelines mentioned in his study which is found to be no variation with software calculated program. Weibull distribution model and logistic model results could not be crossvalidate as we do not have any reference software or program. The maximum percentage variation between Weibull distribution model and logistic model is <1% whereas there is <3% variation between Weibull, logistic and Niemerko EUD model for parotid gland and oral cavity as shown in [Figure 4] and [Figure 8]. [Figure 7] indicating the relationship between NTCP and EUD values calculated by four different models for oral cavity organ. The maximum percentage variation between predicted NTCP by all the models for the serial organ spinal cord is <1% as shown in [Table 5]. This shows that there is good correspondence in predicted NTCP values for serial structure as compare to parallel structure; this may be because volume effect is predominant in parallel structure.^{[20],[21]}  Table 5: Calculated NTCP values for spinal cord (serial organ) by RBMODELV1 and BIOSUITE software
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The NTCP predictions estimated by the four RB models for all twenty patients are inline with the QUANTEC guidelines for radiation induced myelopathy of spinal cord. Oral cavity excluded from comparison as it is not a part of the summary. In case of bilateral whole parotid gland, according to QUANTEC mean dose ≤25 Gy results in <20% rate of incidence of xerostomia. There are five patients who received mean doses <25 Gy and results of predicted NTCP by models are <20%, LKB prediction is on higher side as compare to rest three models.
This is the first study in which we tried to establish correlation between the mean doses received by parallel structure (parotid gland and oral cavity) and predicted percentage of NTCP values. It is found that mean dose in the range of 35–40 Gy for parotid gland can result in more than 50% NTCP predicted by all four RB models. Similarly oral cavity receiving mean dose in the range of 53–58 Gy can results in more than 35% NTCP predicted by all the four models.
> Discussion   
Out of four NTCP models and two TCP models, LKB model and Poisson's TCP model crossvalidated against BioSuite software. The BioSuite accepts differential DVH file in Microsoft excel format whereas RBMODV1 accept cumulative DVH file in txt format. It is found maximum variation of 1% in case of Poisson's model and maximum 5% variation in case of LKB model; this may be due to several reasons, e.g., dose binning error, use of different EQD2 formula, and variation in program coding. The variation in NTCP outcome between Logit or Neimierko, Logistic, and Weibull model is not significant because of small variation in mathematical formulation and all are using same input parameters. It is observed that there is significant difference in outcome of LKB model and the rest three NTCP models and this variation is direct function of dose.
The TCP/NTCP models incorporated in RBMODELV1 are based on assumptions of linear quadratic model. LQ model overestimated for higher dose per fraction (usually >3.2 Gy); hence, it is advised to the end user that results of the software are not reliable in such fractionation schedules. Besides this, the biological parameters (TD_{50}, ϒ50) which are derived from conventional fractionation should not be used directly for evaluation of higher dose per fraction treatment plans, which can results uncertainty. It has been suggested that in such cases, revised biological parameters should be applied for biological modelbased plan evaluation. The TCP/NTCP outcome is greatly affected by treatment gaps and accelerated fractionation treatment schedules specifically for early responding tissues (tumor, skin, and oral mucosa). This is because overall treatment time changes and abovediscussed models are not corrected for phenomenon of repopulation effect occurs in tumor tissue and normal tissue. It is well understood that radiotherapy outcomes may also be affected by multiple clinical and biological prognostic factors such as stage, volume, tissue sensitivity, tumor hypoxia, and concurrent chemotherapy.^{[22]} Hence, it is impossible to predict pattern of treatment failure or success. Bearing this into mind, we limited our approach of TCP calculation to two simple models for the sake of curiosity and research. Therefore, clinical validation of RB models for TCP calculation is difficult to establish.
RB models predicted NTCP cannot provide any direct relationship between complication grading (CTCAE, RTOG) and calculated percentage NTCP, hence toxicity assessment purely based on clinical experience. RB modelbased predictions are only as good as large data available. RB modelbased predictions are based on DVHs input. DVHs are not ideal representations of the 3D dose distribution as they discard all organspecific spatial information. Marks et al. well explained and discussed various limitations of NTCP models e.g., fractionation schedules, lack of spatial dose information in DVH, combined modality therapy etc.^{[20]} RB models are highly sensitive to parameters involved in the formulation and there is scarcity of studies which can quantify the variations while using them. Organ at risk delineation found to have differences which directly affect NTCP outcome therefore in our study we followed consensus guidelines for CTbased delineation of organ at risk for head and neck region.^{[23]} The NTCP models presents more reliability if large data is available and we can say that data driven decision support system becoming reality in modern day of radiation oncology.^{[14]}
Application RB models for particle therapy is quite interesting and opened a way to explore. There is a major difference in dose distributions achieved by photon therapy and proton therapy. Photon therapy deliver significant low dose to large volume of healthy normal tissue and organ whereas proton therapy restricts dose distribution to very short range. Blanchard et al. tested several NTCP models for proton treated patient plans and observed that performance of photon derived models is acceptable for estimating the risk of dysphagi, xerostomia and hypothyroidism, but not satisfactory for acute mucositis.^{[24]} Chaikh et al. performed comparison study between proton and photon based on EUD values.^{[25]} Author found that the available NTCP models may underestimate the real benefit from protonbased treatment plans. It is demanding that existing RB models needs to be modified by taking into account RBE and LET of particle therapy for better and accurate results.
Although the software is a research tool, if clinically validated NTCP models at the institutional level with updated biological model parameters, it can serve as a decision support system, designing new fractionation schedules as well as in clinical circumstances where risk versus benefit can be evaluate logically. The developed software RBMODELV1 is the first version of the software and next version will include new NTCP models with additional feature of dose response curve.
We created simple software RBMODELV1 which can be used as a research tool as well as decision support system. This software can assist in the treatment plan evaluation based on RB models. It also provides utility of common RB models by facilitating comparison of model predictions to actual clinical outcomes. This software provides platform to test sensitivity of model predictions to uncertainties associated with RB model parameters.
Acknowledgments
The authors wish to thanks Gaganpreet Singh for his suggestions which helped to troubleshoot the coding errors in the software.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
