Deep learning for regression problem applied to radiotherapy pre-treatmentverification

Frédéric CHATRIE1,2,3, Xavier FRANCERIES2,3 and Marie-Véronique LE LANN1,21LAAS-CNRS, F-31000, Toulouse, France

e-mail: fchatrie@laas.fr2Inserm, UMR1037 CRCT, F-31000 Toulouse, France

e-mail: frederic.chatrie@inserm.fr3Université de Toulouse, INSA, UPS, F-31000 Toulouse, France

AbstractMachine Learning techniques have been increas-ingly used in medical applications, including can-cer treatment modalities, such as external beamradiation therapy (EBRT). The increased com-plexity of more advanced EBRT treatments re-quires thorough verification of the delivered ra-diation dose, either pre or during (in-vivo) pa-tient treatment. Electronic portal imaging de-vices (EPIDs) provide a means for this ver-ification (EPID-based dosimetry) where differ-ent approaches have been employed, but in-volving different complexity and approximations.In this work, an alternative method for EPID-based dosimetry, using Artificial Neural Net-work (ANN) algorithms is proposed. A su-pervised ANN algorithm consisting of a non-recurrent feed-forward multilayer model speciallydesigned for this application was developed topredict 2D reconstructed absorbed dose distribu-tions only based on EPID images, acquired dur-ing pre-treatment delivery on several machinesand for different treatment techniques. The algo-rithm was trained (learning phase) with EPID im-ages as input and absorbed dose distribution, pre-viously calculated during radiotherapy treatmentplanning, as output data sets. The setting and thebehavior of EPID dosimetry for pre-treatment ver-ification were correctly learned by the ANN algo-rithm creating a pattern by minimizing the erroron a maximum sample of data. Global gammapassing rates (2%/2mm) > 98% were obtainedfor the evaluated cases from Varian and Elekta in-stances, which showed the ANN capability to pre-dict the reconstructed absorbed dose distributionsfor distinct treatment verifications, based on EPIDinformation.

1 IntroductionArtificial intelligence is a broad domain, which consists ofusing non-deterministic algorithms able to model a complexsystem based on data and inspired by human brains. A sub-set of the latter is machine learning with its most popularalgorithms, the artificial neural networks (ANNs). In re-cent years, ANN has rapidly evolved due to the increasedcomputing capacity and the employment of graphics pro-cessing units (GPUs) and tensor processing units (TPUs).

These types of algorithm are versatile and have shown tobe suitable for complex problems and situations, such as formany pattern recognition problems in medical applications,including external beam radiation therapy (EBRT) used incancer treatment [1; 2; 3].

In EBRT, patient-specific treatment plans are designed bymeans of computerized treatment planning systems (TPSs),which optimize and calculate radiation absorbed dose distri-butions with the intent to maximize tumor control and min-imize normal tissue complications. The increased complex-ity of modern EBRT techniques, such as intensity modu-lated radiation therapy (IMRT), requires thorough treatmentverification procedures, before and/or during (in-vivo) treat-ment delivery, to check the accuracy of absorbed dose dis-tribution and detect clinically relevant errors in the radia-tion delivery. Solutions based on electronic portal imag-ing devices (EPIDs), which are flat panel MV X-ray de-tectors directly mounted on the treatment machine (lin-ear accelerator or linac-Figure1) have been employed fortreatment verification, allowing estimation of the delivereddose distributions (i.e. EPID-based dosimetry) [4]. Dif-ferent approaches have been used for EPID-based dosime-try, which implement calibration procedures to convertEPID signal to absorbed dose images in water employ-ing different corrections, and/or analytical algorithms toalso reconstruct 2D or 3D dose distributions in the patientfrom backprojected estimations of EPID primary fluence [5;6]. Others, are based on similar principles but use MonteCarlo simulations to provide more accurate models [7;8].

Figure 1: Illustration of linac (in blue) with EPID (in purple)image acquisition during patient treatment.

However, these approaches can present different draw-backs, since the latter can be very time consuming, and theformer also employ several approximations and require val-

idation under various different clinical situations. Addition-ally, all these approaches are dependent of each linac andEPID models, commonly requiring extra commissioningand calibration procedures before implementation. There-fore, alternative solutions using ANN approaches can be ofparticular interest, since it would be possible to model thecomplexity of treatment verification problem in a more ef-ficient way, and provide more extensible solutions, easilyadapted to consider different linac and EPID models. Fewworks have implemented ANN algorithms for treatment ver-ification [9; 10; 11]. Tang et al. and Nyflot et al. haveused a classification ANN approach based on EPID, whichconsisted of knowing if the verification could be consideredcorrect or defective, whereas Kalantzis et al. have developedan hybrid approach, classifying low and high dose pixels be-fore predicting their values, different data training was im-plemented and it was only applied for Varian linacs. In thiswork, we propose a novel method using ANN algorithms topredict 2D reconstructed absorbed dose distributions exclu-sively based on EPID images, acquired during pre-treatmentdelivery on several machines and for different radiotherapytreatment techniques verification.

2 Materials and Methods2.1 Artificial neural networksArtificial neurons have been inspired from the biologicalneurons but they only are an abstract mathematical repre-sentation far from the complexity of the real neurons. ANNis composed by a set of artificial neurons organized in sev-eral layers according to their determined architecture. Manytypes of architectures already exist and also new ones areexpected to be found.

Like humans, artificial neural networks work via twophases - learning and recognition. Learning can be done viaseveral ways. One is unsupervised learning, which consiststo organize the only provided inputs data and making a linkbetween them, in order to create a pattern depending on thearchitecture used. Another one is supervised learning (thetype of learning that is used throughout this work) whichentails the creation of an organized architecture of neuronsby linking input and output data. In the latter, the output databrings an additional information like a "teacher" to help thelearning, this information has to be given by an expert to besure that the learning is done with the truth values.

The output could be either a label for the classification,which is the commonly used one in the literature, or a floatvalue for the regression model. The latter, allows to modelcomplex or non-linear functions, and was implemented inthis work to model the treatment verification problem.

The supervised ANN learning phase consists on settingdifferent weights associated to the level of importance ofsignals coming from the underlying layer. The predictedsingle neural result is calculated by the following expres-sion:

yneural = f

((∑i∈N

wi ∗ xi

)+ b

)where wi are the weights corresponding to the signals xi,

b a bias and f an activation function.In order to set the weights, several optimization algo-

rithms can be used (e.g. gradient descent, stochastic gradi-ent descent, Adam, Levenberg-Marquardt) minimizing, iter-atively, the error between the predicted result and the target

value for all data set. The error here is defined by a lossfunction, also called cost function, which can take differentforms (e.g. mean squared error (MSE) or mean absolute er-ror, for regression problem and cross entropy or Hinge, forclassification).

One of the issues regarding the optimization algorithmsis the existence of local minimums. Indeed, for convexmathematical problems, the local minimum correspond tothe global minimum. However, ANN being a non-convexproblem, can exhibit several local minimums. In this case,it is important to find a local minimum with a weak valueof the loss function in order to be close to the global min-imum [12]. Although recovering the global minimum ofa model with a significant size showed great outcomes re-garding the learning phase, however, the model was not rep-resentative of the system [13] and can often leads to overfit-ing. Overfiting, also called overtraining, appears when thenetwork learns very well the training data sets including anon-desired noise with complicated model. Therefore, therecognition phase with a new data set will give wrong re-sults. In this case, the model loses its generalization capa-bility. A compromise has to be found between the general-ization of the model and a sufficiently low local minimum.

The learning phase can be time consuming but once theANN weights have been established, the use of the neuralnetwork during the recognition phase will be instantaneous.

For both, unsupervised and supervised techniques, therecognition phase consists of using new input data that hasnot been used as training to predict output data, thus differ-ent data from the one used during the learning phase.

2.2 ANN application for EBRT pre-treatmentverification

EBRT data for ANNThe data required to develop the proposed ANN applica-tion was, in part, obtained from different linac/EPID mod-els, installed at distinct collaborative centers to extend therange of application. These were used to perform EPIDmeasurements during the deliver of different radiotherapytechniques, conformal radiation therapy (CRT) and inten-sity modulated radiation therapy (IMRT). All EPID imageswere taken at 150 cm and 160 cm Source Detector Dis-tance using 6 MV photon treatment beams, with dose ratesof 600 MU/min and 400MU/min, from an a-Si1000 EPIDmounted with Exact-arm on a Clinac 23iX (Varian) and aniViewGT EPID on an Elekta Synergy, respectively. Thedifferent characteristics of both, Varian and Elekta linacs,comprised their different EPID imagers were studied. TheEPIDs have active areas of 30 × 40 cm2 (Varian) and 41 ×41 cm2 (Elekta), and images were acquired using the half-resolution mode in the a-Si1000 EPID (spatial resolution isreduced to 384 × 512 pixels from 768 × 1024), and a res-olution of 1024 × 1024 pixels in the iViewGT EPID. Thequasi-raw EPID signals were used as input data sets by theANN algorithms, since only dark-field and flood-field cor-rections were included. The dark field image correction cor-responds to an average of several frames without any radi-ation to remove the eletronic noise. The flood field imageis acquired by irradiating the area of detection with a largerradiation field in order to correct for the pixel sensitivitydifferences. The integrated acquisition mode of the imageacquisition software IAS3 was used, where one image is re-constructed from the average of all frames acquired duringradiation delivery.

On the other hand, the output data corresponded to 2D im-ages from absorbed dose distributions calculated at the planeof maximum depth dose in a water phantom, in EclipseTMand PinnacleTM TPSs, respectively for Varian and Elekta in-stances.

A selected region of interest, after applying a thresholdof a 10% of the TPS absorbed dose, was considered. Thecreated mask was applied for both data sets, EPID and TPSimages, in order to only keep and evaluate the pixels con-taining relevant treatment information.

During the learning phase, corrected EPIDs and expectedabsorbed dose distributions from TPS were used as the neu-ral network’s input and output information, respectively.Once the learning is completed - a process that requiresmany images - future EPIDs can be used to predict the de-livered absorbed dose distribution, allowing its comparisonwith the planned treatment. Non-negligible difference be-tween the expected and delivered distributions can indicatepotential problems during the treatment delivery.

ANN architecture and parametersThe algorithms have been developed with MATLAB R©(Matlab R2018a, MathWorks), before moving onto the Ten-sorflow Google tools Development. The work presentedhere only concerns the Matlab Development using the Neu-ral Network toolbox version 11.1.

The ANNs base their modelling on the provided datavia the architecture weights fixed with the optimization al-gorithms, minimizing the error between predicted and ex-pected values on a maximum sample during the learningphase. The analysis of the data was necessary to transposethe physics problem to the ANN model form in order to ob-tain a coherent solution. The physics phenomena involvedwere also taken into account to establish a relevant correla-tion between output and input data sets allowing the ANNto be able to model a complex and non-linear mathematicalfunction representative of the considering system.

In order to implement a correct model of the system, in-stead of using every EPID and TPS images as the sampleof data, every pixels from each EPID and TPS image wasconsidered. This is because every pixel corresponds to anEPID signal (in gray scale values) that is physically relatedwith every pixel dose values from the TPS. Apart from a di-rect physical relationship that could be established betweeneach EPID and TPS dose map pixels, the information fromthe neighbours were also taken into account, which allowedto intrinsically model the scatter radiation from the patientand other components during treatment delivery. All thisinformation, as well as spatial localization of those pixels,were set for the inputs. Every EPID and TPS images fromlearning data sets were considered and scaled to make thismodel more relevant, in terms of data quantity, and to begeneralized for other cases.

The simplest ANN model has been chosen: a non-recurrent deep feed-forward ANN (Figure 2) was used withone input, one or more hidden layers and one output layer.Each node (called neuron) composing the input layer corre-sponds to each input signals. All input nodes were linked toall first floor of hidden nodes and last floor of hidden layerswhich were also linked to all output nodes. The number ofinput and output nodes is equal to respectively, the numberof inputs and outputs.

The number of hidden nodes is defined by the user andhas an importance. There is no theoretical way to fix it [14]

but this parameter can be correlated with the generalizationof the model. It must be correctly calibrated for the applica-tion, otherwise there is a risk of overtraining. Several caseshave been implemented regarding the number of nodes andthe architecture of hidden layers. When one hidden layerwas considered, the number of nodes was found to be 1.5times the number of inputs. When considering 5 hidden lay-ers with 0.2 times the number of inputs, the obtained timeconsumed during the learning phase was reduce since thenumber of epochs was considerably decreased for compara-ble outcomes.

EPID

TPS

...

......

I1

I2

I3

In

H1

Hn

O1

On

Input layer Hidden layer Ouput layer

Figure 2: Feed-forward architecture of neural network.

The optimization algorithm used for setting the weightswas Scaled Conjugate Gradient. The activation function,both hidden and output layers was sigmoïd and linear re-spectively. The initialization of every weights of the modelwas randomized. The loss function to be optimized was themean squared error which is the following :

L(o, y) = 1N

N∑i=1

(oi − yi)2

where o was a vector of target values (TPS outputs), ywas a vector of network prediction and N was the numberof samples of data sets.

3 Results

3.1 Verification of parameterized model

Once the model was parameterized based on the provideddata, it was important to verify if the obtained model wascorrectly set and scaled. For that, the performance and re-gression values obtained during the learning phase, wereevaluated for all cases (Varian and Elekta instances). Figure3 and 4, present the results corresponding to the verifica-tion of the model for the Varian instance, as example, whichpredicted results regarding the application of the model arepresent in Figure 5. All the other cases, for which predictedresults are also presented, followed the same shape regard-ing this evaluation.

Figure 3: ANN performance showing the evolution of theloss function during the learning phase.

As showed in the Figure 3, the learning phase has beenperformed with 652 epochs and the mean squared error(MSE) decreased most importantly after the first two hun-dred epochs. One epoch correspond to one step of the learn-ing considering all sample of training data. Nevertheless,regarding this example, the learning phase could have beendone with less epochs in order to earn time of learning. Allof the data sets, used for training(70%), testing(15%) andvalidation(15%) present a quasi-identical curve, indicatingthat the ANN model has been correctly scaled. In addition,this behaviour shows that the ANN model has been correctlygeneralized and new sample of data for this specific appli-cation can be used with confidence.

Figure 4: Regression line between target and output dataobtained during the learning phase.

Figure 4 shows the regression line between the tar-get (TPS dose distributions) and the output data (ANNpredicted dose distributions) obtained during the learning,which was also used to evaluate the quality of this phase.Here, all of data sets, training, testing and validation wasconsidered. The regression value was found to be 0.997 withroughly one billion sample of data. The regression value isexpected to be 1 for a perfect learning. In this case, thismean that all of predicted results by ANN is identical to thetarget values, considering the training data. These obtained

results highlight the coherence found between the input andoutput data sets, and show that the ANN model is highlyrepresentative of the system behaviour.

3.2 Results from Varian and Elekta machinesThe learning phase was performed using 8 and 11 in-put/output data sets, from CRT and IMRT treatments, re-spectively for Varian machine and 4 and 6 input/output datasets for CRT and IMRT Elekta case. All of the used data sets(both input corrected EPIDs and output TPS absorbed dosedistributions) consisted of 384 × 512 pixels for Varian and1024 × 1024 pixels for Elekta before applying the thresh-old, as described in the previous section. The EPID data thatwere used during the recognition phase were different.

(a)

(b)

(c)

Figure 5: (a) EPID image, (b) ANN predicted absorbed doseand (c) planned absorbed dose for Varian instance.

Figure 5 and Figure 6 show the EPID image (a), the ab-sorbed dose distributions calculated by the neural network(b) and the distributions originally planned by the TPS (c),for IMRT cased from Varian and Elekta instances, respec-tively. It is important to mention that two different tech-niques of IMRT treatment have been used with each in-stance. For Varian instance an IMRT with dynamic mul-tileaf collimator (MLC) was used, while for Elekta instance

it was used an IMRT with static MLC during the irradiation.A common clinical metric, called, gamma index, γ, was

used to evaluate the difference between absorbed dose dis-tributions predicted by the ANN and planned by the TPS.The γ index could give the percentage of pixels that respecta given objective (gamma passing rate). In this case, as ob-jective for gamma evaluation, pixels should have a dose dif-ference ≤ 2% at a distance to agreement (DTA) ≤ 2mm.A global gamma index has been calculated only within theselected region of interest. Global gamma passing rates >98% were obtained for the evaluated cases from Varian andElekta instances, highlighting the neural network’s capabil-ity to predict the absorbed dose distribution based on EPIDimages.

(a)

(b)

(c)

Figure 6: (a) EPID image, (b) ANN predicted absorbed doseand (c) planned absorbed dose for Elekta instance.

In Figure 7, the capability to detect a failure during thetreatment is shown. So, with the same treatment seen inFigure 5, one leaf is kept on its initial position and its sim-ulated representation from EPID image appears on the Fig-ure 7(a). The obtained interesting outcome was that withoutprevious learning of this situation (leaf mis-positioning), theacquired reconstructed absorbed dose distribution is coher-

ent. Moreover, the Figure 7(b) seems to reproduce the un-derlying physics phenomena since the leaf contours are notas sharp as in the EPID image (Figure 7(a)).

The global gamma index, for this specific case, was foundto be 94%, 4% difference with the initially planned one,seen in Figure 5(c) corresponding to the weak spatial size ofthe leaf. This highlights the discrepancy between plannedand calculated absorbed dose distribution.

(a)

(b)

Figure 7: (a) EPID image, (b) ANN predicted absorbed dosefor simulated leaf mis-positioning.

4 DiscussionThese initial results showed that machine learning could beused to reconstruct the delivered absorbed dose distributionsbased on EPID images, independently of the used machine.The deep feed-forward ANN architecture has been used andhas been correctly set up in order to obtain a model of thesystem. Different machines and different techniques couldhave been modelised with the same method. For each case,only the considered data was different (specific to the equip-ment). It was shown that the model acquired good agree-ment as confirmed by the global gamma index metric. TheANN model has created a great pattern which was general-ized for this application. Moreover, a simulation of defec-tive situation has been tested with a leaf mis-positionned.The obtained results was coherent and showed that the leafmis-positioning was took into account.

These ANN algorithms have been developed for the pre-treatment verification step and it could be interesting todevelop the real-time treatment verification called in vivodosimetry. A lot of parameters remain to be consideredextending these algorithms for in vivo dosimetry. Indeed,modelling the influence of the patient geometry with ANNmethod can be challenging. Like for the previous work, theselection of the data which will bring sufficient and coherentinformation for the model will be required.

5 ConclusionIt was shown in this study, that pre-treatment verificationof CRT and IMRT based on EPID can be performed withneural network algorithms for different machines.

Currently, it is still challenging to know the absorbed dosethat is truly received by the patient during treatment ses-sions. The EPID imager can provide information relative tothe photon beam passing through the patient, which can po-tentially be used to produce real-time in vivo dosimetry viaANN methods.

Next works would be focused on extend the algorithmsfor reconstructing in-vivo absorbed dose distribution forCRT and IMRT techniques.

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