A treatment planning system with new paradigms in the effectiveness and side-effect evaluation sections

Academic dissemination of the “SMp treatment planning system (TPS)” for external beam radiotherapy, which has been developed as a software function that could meet the denition of a device with an entirely new intended use. This system will have new paradigms in the effectiveness and side-effect (S-E) evaluation sections, where tumor control probability (TCP) is calculated with computational simulations instead of current analytical TCP models; and S-E is evaluated with the normal tissue non-complication probability (NTCP0) methodology instead of standard NTCP one.


Introduction
This work is aimed to disseminate the rst treatment planning system (TPS) that uses normal tissue noncomplication probability (NTCP0) as a new alternative of evaluating side-effects (S-Es) without requiring of the current organ at risk dose-volume histograms (OAR DVHs). Also, the "TCPsim" is the application of this TPS that calculates tumor control probability (TCP), and represents a signi cant advance in radiotherapy, where they only calculate TCP based on analytical models, while us do it based on computational simulations. The TCPsim methodology could replace the current ones employing analytical models.
Our application aims to develop a TCP\NTCP0 based TPS, where contrary to current systems using TCP and NTCP analytical models, ours employs computational simulation for determining TCP and NTCP0 as a new alternative of evaluating S-Es of the radiation treatments.
The "TCPsim" will represent a big contribution due to one potential innovation is that rather than evaluating TCP by analytically calculating, this is calculated based on its own probabilistic de nition; and can be considered an extension of the Monte Carlo, where outcomes of the radiation interactions with three possible types of tumor cells are analyzed, instead of the DNA damages.
Given inherent probabilistic aspects of a speci c stochastic process (SP) with more than outcome, like normal tissue complications in a radiation treatment given to a speci c population under speci c circumstances, this has own discrete probabilistic distribution (DPD). Then, a) Whatever speci c radiation oncology treatment has associated a NTCP(x i ) DPD; b) NTCP0 = NTCP(0), total NTCP (TNTCP = sum(NTCP(x i )) where x i is the i th complication, i = 1..nc, and nc: Number of complications); and c) As a SP, the normal complications have their deterministic and stochastic regions. The SMp NTCP0 parameters TDmin and TDmax are respectively the lower and upper limits of the stochastic region. "NTCP0cal" application calculates/estimates NTCP0 using three options. The rst of them is related with the wellknown phenomenological models, in particular SMp NTCP0(D) is a probabilistic-decreasing function, and appropriate for describing the mean radiobiological behavior of NTCP0 in function of D. The second option is based on the probabilistic relationship between NTCP0 and TNTCP like NTCP0 = 100%-TNTCP. Contrary to TCP calculations that can be done with computational simulations, for NTCP0 is very di cult or impossible due to numerous parameters and variables involved. The second and third option can be used for assuming the NTCP(x i ) DPDs. In the third, we employ the binomial distribution (BD) as an excellentmathematical generator of these distributions.
The "TCPsim" is a better computational simulator as compared to its previous version of (1) and calculates the TCP as a function of minimum dose per fraction (dmin) in the tumor region with the total minimum dose (Dmin) and number of fractions (n). The simulator is based on strong probabilistic-radiobiological foundations and knowledge/estimation of some radiobiological and tissue parameters, such as α, α/β, cell repair and cell sub-lethal damage. The "NTCP0cal" is a tool that calculates/estimates NTCP0, which is a new alternative of evaluating side-effects (S-Es).
The radiation oncology treatments have their own NTCP(xi) discrete probabilistic distributions (DPDs), where NTCP0 = NTCP(0). For this reason, NTCP0 is not a creation, such as the complication-free cure (P+) and uncomplicated TCP (UTCP); but an inherent concept of the stochastic processes. Our NTCP0 studies do not disregard the last 10-15 years of research; but NTCP0 was not considered in the radiation treatments during those last 10-15 years.
Our SMp TPS is based on new probabilistic knowledge about BD and Poisson distribution, like the incoherently derived Poisson-based TCP model, all described in (2).
According to the section VI of (4) "Vision of TG-166 for future development of biologically based treatment planning (BBTP)", the nal evolution stage (No. 3) for the Plan Optimization/Evaluation Strategy are the Absolute values of TCP/NTCP/UTCP. While for our research team, the nal evolution stage will be associated with the absolute values of TCP and NTCP0 determined with our proposed TPS. In the following table we establish comparisons among the current BBTPs and ours. Some variables used in this module S1: The linear-quadratic cell survival (S) for one fraction with dose dmin; the LQ S1(dmin), where K1 = 1-S1. The proposed TPS will let to the radiation oncologists to decide the selection of the determined treatment parameters: dmin and n as part of the optimization/evaluation processes.
The selected DVH tumor must satisfy the condition: Dim/n = dmin. Our TCP methodology only involves Dmin.
When a living tissue tumor is irradiated in a fractionated treatment, the nal result of this irradiation may be:1) All tumor cells are wholly killed; or 2) There is an amount of survived tumor cells. Due to these two possibilities, the effectiveness (Point 1) of the radiation oncology treatments is evaluated with TCP, which evaluates how likely a tumor control is to occur.
As is shown in the diagram of the Fig. 1, for simulating a fractioned treatment, one should consider: The rst fraction generates a mean nkc killed cells, nslc sub-lethally damaged cells, and nudc undamaged cells.
For the second and successive fractions, the three kinds of cells are analyzed in their possible nal outcomes in each fraction.
The Matlab function rand is used for generating a random number gnum < = 1. The probability of meeting a killed cell (PMKC) is calculated as nkc/NTC, then if gnum < PMKC, the analyzed cell is died, but this is survived.
For a killed cell, the simulator will analyze a new cell; but for a survived cell, there are two possibilities: the cell is undamaged or sub-lethally damaged. The probability of meeting a sub-lethally damaged cell is de ned with a new gnum > nslc/(nslc + nudc).
For an undamaged cell, if a new gnum < probability for K, this cell will die, but if gnum < = K + probability for SL, this is become in a sub-lethally damaged.
For a sub-lethally damaged cell (SLDC) there is a range of damage degree. Two new random numbers gnum1 and gnum2 are generated, and let us de ning KSL = max(gnum1;1-gnum1). If gnum2 < = KSL, the cell will die, but is kept as a sub-lethally damaged. The previous condition is associated to a major probability of killing the SLDC.
While the number of fractions increases, nkc increases, and nudc decreases. The nslc increases after the rst fractions, and can increase or decrease and nally decreases after the second or successive fractions.
The cell repair is a temporal-cellular process; and the number of repaired cells is determined after each fraction as: nrc = nslcj-nslcj*CR.
If nkc ≥ NTC after n fractions, there is tumor control. The TCP is calculated as: TCP = TCOK/nvs.
As responsible of the radiation treatments, the radiation oncologists with collaboration of the medical radiation physicists will choose or estimate the values of the radiobiological and tissue parameters. The current radiosensitivity studies are described with S, which probabilistically is related with K, cell sublethal damage (SL) and cell undamaged (U) as K + SL + U = 1 (100%), where S = SL + U. Due to little available information of the SL, in many cases the SL values should be assumed taking into account that SL ≤ S. The TCPsim reports the LQ S(dmin) for being compared with the assumed value of the SL, which should be ≤ S.
The Table 2 and Table 3 show TCP reported in some references, and obtained with the TCPsim.

The Ntcp0cal Module
As is shown in the Fig. 3, the nal decision for a radiation treatment one should conjugate TCP and criteria of the S-Es.
This module provides three options, two of them employ the well-known aspects of a phenomenological model, or the relationship with TNTCP; and the third option determines NTCP0 from an assumed NTCP(x i ) DPD generated from the binomial distribution (BD), where one of its parameters is automatically de ned from a databased of the Disease locations Vs. Late complications. The Fig. 4 is the diagram of procedures of the NTCP0cal.
The steps for executing the NTCP0 calculation are: d) Select one of three panels pressing the "Use" button of the desired panel.
If the selection is "Using the SMp NTCP0 parameters".
If the selection is "Using an assuming NTCP(x) DPD".
Select the disease location.
Introduce the BD parameter p.
If the selection is "Using a known/assumed NTCPi DPD".
Introduce the VP for Other complications OCs. e) Press the "For calculating NTCP0" button for obtaining the result of NTCP0.
f) If the selection is "Using an assuming NTCP(x) DPD", one can de ne the legend of the numerical and graphical information. Each disease location has its number of possible cases (Xmax). Xmax is equal to BD parameter n. g) Pressing the "Finish" button of the selected panel you return to main screen.

The SMp NTCP0(D)
The SMp(x) function of (8)  The Lyman-Kutcher-Burman (LKB) NTCP (Deff) of (4) is widely used for evaluating S-Es in the radiation treatments. LKB is the normal cumulative distribution function (NCDF), where Deff: Effective dose. As a cumulative distribution function, the NCDF has a sigmoidal shape and should be used for calculating the probability P(Deff < = x) if Deff follows a ND. Given the NCDF is an increasing function, they have used this complex probabilistic function for correlating NTCP with Deff. The widely used LKB NTCP model is more mathematically complex than the SMp NTCP0, and is DVH-based.
The current NTCP models provide approaches of this metric; i.e. NTCP estimations. An experienced radiation team will be able to assume good NTCP (x i ) distributions. This implies good NTCP0 estimations too.

The NTCP(x i ) DPD assumed
While the TCP is obtained with simulated calculations analyzing an irradiated tumor volume, the simulations for obtaining the NTCP0 are di cult or almost impossible due to lot of variables and parameters involved. Contrary to the TCP calculations, nowadays, the determination of NTCP0 by means of mathematical and mechanistic models or computational simulation for treatments with few or none data is very complicated or almost impossible. Front of these di culties, there is an option of assuming NTCP(x i ) distributions using generators of DPDs, like BD. For choosing the BD parameter p, one should consider that: 1) if p < < 0.5, the NTCP0 is the event with maximum probability (EwMP) ; 2) if p < 0.5, one of the complications is the EwMP, and NTCP0 > > 0%; if p ≈ 0.5, one of the complications is the EwMP, and NTCP0 > 0%; and 3) if p > 0.5, one of the complications is the EwMP, and NTCP0 ≈ 0%.
For selecting NTCP(x i ) and its correspondent x i , the aspect described in the Table 4, sub-region of the disease and other clinical and physical factors should be considered.

Conclusions
The future researches related with our simulator should be aimed to obtaining better values or ranges of its parameters.
If we include a module for tumor DVH calculations, our system can be built stand-alone.
Our simulator will represent a big contribution due to one potential innovation is that rather than evaluating TCP by analytically calculating, this is calculated based on its own probabilistic de nition.
TCPsim is an extension of the MC that analyzes outcomes of the radiation interactions with three possible types of tumor cells, instead of the DNA damages.
Our NTCP0 work does not disregard the last 10-15 years of research, but we encourage the medical physicist communities to use the NTCP0 methodologies. Actually, NTCP0 was not considered during those last 10-15 years.
Concerning the mathematical correlations, the NTCP0(D) model is three-parameter phenomenological, and given its number of parameters and its type, it is very easy to t whatever real data NTCP0 Vs. D, whose radiobiological mean behaviors should be described with decreasing functions aimed to acceptable estimations of S-Es.
The NTCP0 methodologies of evaluating S-Es in the radiation treatments could be extended to whatever hazard activity.
The probabilistic aspects NTCP0cal application discussed in this work, and others of the [2] show why its validation is a priori; i.e., its foundations are based on knowledge considered to be true without being based on previous experience or observation.
The current NTCP models used for evaluating S-Es in the radiation treatments provide NTCP approaches.
An experienced radiation oncology team can assume a good NTCP(x i ) DPD based on database. Despite a NTCP DPD is generated, the team should be interested only for one value, NTCP0. The NTCP0 estimations will be corrected in the future when a major data will be available.

Declarations
Funding: Not applicable.
Con icts of interest/Competing interests: Not applicable.
Availability of data and material: Not applicable Code availability: Not applicable Authors' contributions: Not applicable