Toward IMRT 2D dose modeling using artificial neural networks:A feasibility study

Georgios Kalantzisa)

Radiation Oncology Department, University of Texas, Health Science Center San Antonio, Texas 78229 andRadiation Oncology Department, Stanford University School of Medicine, Stanford, California 94305

Luis A. Vasquez-Quino and Travis ZalmanRadiation Oncology Department, University of Texas, Health Science Center San Antonio, Texas 78229

Guillem PratxRadiation Oncology Department, Stanford University School of Medicine, Stanford, California 94305

Yu LeiRadiation Oncology Department, University of Texas, Health Science Center San Antonio, Texas 78229

(Received 23 February 2011; revised 26 August 2011; accepted for publication 28 August 2011;

published 27 September 2011)

Purpose: To investigate the feasibility of artificial neural networks (ANN) to reconstruct dose

maps for intensity modulated radiation treatment (IMRT) fields compared with those of the treat-

ment planning system (TPS).

Methods: An artificial feed forward neural network and the back-propagation learning algorithm

have been used to replicate dose calculations of IMRT fields obtained from PINNACLE3 v9.0. The

ANN was trained with fluence and dose maps of IMRT fields for 6 MV x-rays, which were obtained

from the amorphous silicon (a-Si) electronic portal imaging device of Novalis TX. Those fluence

distributions were imported to the TPS and the dose maps were calculated on the horizontal mid-

point plane of a water equivalent homogeneous cylindrical virtual phantom. Each exported 2D dose

distribution from the TPS was classified into two clusters of high and low dose regions, respec-

tively, based on the K-means algorithm and the Euclidian metric in the fluence-dose domain. The

data of each cluster were divided into two sets for the training and validation phase of the ANN,

respectively. After the completion of the ANN training phase, 2D dose maps were reconstructed by

the ANN and isodose distributions were created. The dose maps reconstructed by ANN were eval-

uated and compared with the TPS, where the mean absolute deviation of the dose and the c-index

were used.

Results: A good agreement between the doses calculated from the TPS and the trained ANN was

achieved. In particular, an average relative dosimetric difference of 4.6% and an average c-index

passing rate of 93% were obtained for low dose regions, and a dosimetric difference of 2.3% and an

average c-index passing rate of 97% for high dose region.

Conclusions: An artificial neural network has been developed to convert fluence maps to corre-

sponding dose maps. The feasibility and potential of an artificial neural network to replicate com-

plex convolution kernels in the TPS for IMRT dose calculations have been demonstrated. VC 2011American Association of Physicists in Medicine. [DOI: 10.1118/1.3639998]

Key words: artificial neural network, IMRT, dose modeling, back-propagation, EPID

I. INTRODUCTION

Neural computation is inspired by the knowledge from neuro-

science, though it does not try to be biologically realistic in

detail. In the most general terms, an artificial neural network

(ANN) is a system composed of many simple interconnected

processing elements operating in parallel, whose function is

determined by the network structure, the connection strengths,

and the computation performed at the processing elements. An

ANN approach has some inherent capabilities in which other

programming techniques lack. They are naturally parallel and

thus hold the promise of being able to solve intricate problems,

which require very large amounts of conventional, serial com-

putational power. The ANN also learns either in a supervised

mode, where the network is provided with the correct response,

or in an unsupervised mode, where the network self-organizes

and extracts patterns from the data presented to it. Once trained,

the network generalizes to produce a correct response to input

combinations for which it has not been trained. Finally, a three-

layer network can perform any continuous nonlinear mapping

from inputs to outputs or emulate any deterministic classifier,

and, thus for, some problems neural networks are easier to

implement than conventional pattern matching or statistical

methods.1 Several studies have demonstrated the capability of

the neural networks to be universal approximators.2–4 From the

learning point of view, the approximation of a function is

equivalent to the learning problem of a neural network.

Pattern recognition may be one of the best practical uses

of neural networks. The network is trained with known data

5807 Med. Phys. 38 (10), October 2011 0094-2405/2011/38(10)/5807/11/$30.00 VC 2011 Am. Assoc. Phys. Med. 5807

and learns to classify the input into a prespecified number of

categories. The inputs and outputs are dependent on the spe-

cific problem and can be binary or continuous. In the past,

ANN and machine learning algorithms have been used

widely for many pattern recognition problems in clinical

applications, including evaluation of prostate intensity

modulated radiation treatment (IMRT) plans,5 identification

of subjects with obstructive sleep apnea,6 screening of smear

cells,7 diagnosis of anterior infraction of myocardial,8

improvement of radiologist performance for diagnosis of

cerebral tumor,9 diagnosis of radiation-induced pneumoni-

tis,10 and evaluation of anesthetic medicine.11 Additionally,

ANNs have been employed for the computation of dose dis-

tributions and percentage depth dose,12–15 whereas alterna-

tive approaches incorporate Monte Carlo algorithms, look up

tables or analytical fits to data.16,17

Due to the characteristics of amorphous silicon (a-Si)

based electronic portal imaging devices (EPIDs), there has

been considerable interest in their use as two-dimensional

dosimeters. These characteristics include high spatial resolu-

tion, large imaging area, stability, dynamic range, and real-

time acquisition of images. The use of any EPID for dosi-

metric IMRT applications requires implementation of a suit-

able procedure to establish the relationship between pixel

intensity and either energy fluence maps or dose distribu-

tions. The relationship between dose and EPID response is

complicated since the various layers of material that consti-

tute the EPID differ significantly from those of a single water

phantom. Therefore, for accurate quantitative dosimetry,

complex calibration is required. Convolution methods and

scatter kernels have been suggested in the past for the con-

version of the EPID response to dose. To do this, the convo-

lution method converts a 2D EPID pixel distribution to a

dose distribution in a homogeneous phantom. The mathe-

matical form of these scatter kernels are derived either by

Monte Carlo modeling18 or empirically by adjusting the ker-

nels to obtain the best possible agreement between EPID

doses using the convolution method and measurements from

the ionization chambers or films19

In this study, we demonstrate for the first time, to our best

knowledge, the potential of neural networks to reconstruct

two-dimensional dose distributions of IMRT fields. Our

effort was to extend the work of previously published litera-

ture on ANN by including dose calculations in the context of

IMRT plans. The feasibility and potential of ANN to repli-

cate treatment planning system (TPS) calculated dose maps

are demonstrated, and the results are comparable with those

of the TPS. IMRT dosimetry, calculations have become

more demanding as complex convolution kernels, is often

used for dose calculation. For adequate quality assurance

(QA) programs, a 2-dimension (2D) dosimetry with fixed ge-

ometry is common practice. Pretreatment verification of the

IMRT dose calculation is a daily routine which often

requires expensive equipment accompanied with proper soft-

ware and careful setup. A future clinical application of our

study is the development of a method for EPID-based dose

validation of IMRT fields using ANN. The main advantage

of using ANN is its small requirements of memory storage,

its speed once the network is trained and the ease of its

implementation given the availability of freeware software

and tool kits for modeling using neural networks.

II. METHODS

II.A. Training and validation of the ANN

The method employed is summarized in Fig. 1 and con-

sists of two phases: the training phase and testing phase.

During the training phase, the opening density matrixes

(ODM) of the IMRT fields for the training data set were

acquired with amorphous silicon (Varian a-Si1000) EPID.

ANN has been incorporated in the past with portal images

for treatment verification of lung radiotherapy,20 tangential

breast irradiation design,21 and dose image comparison.16

Additionally, a-Si EPIDs have been used successfully in the

past for the acquisition of fluence maps.23–25

These fluence maps were imported to the TPS to calculate

the 2D dose maps of the horizontal isocenter plane of a

homogeneous virtual cylindrical phantom. Applying a

K-means algorithm and the Euclidian metric in the fluence-

dose domain, the data were divided into two clusters of high

and low doses. During the training phase for the high dose

region, the fluence maps from the EPID were used as the

input for the ANN and the PINNACLE calculated doses as the

desired output. After completing the training phase inde-

pendently for the two clusters of the data sets, the ANN has

learned to generalize the information and map 2D fluence

distribution to 2D dose map. The final step is the validation

of the ANN performance. For that purpose, a different set of

IMRT fields was used, rather than those of the training

phase. The same methodology was applied independently

for the low dose region as well. The ANN dose maps of the

IMRT fields were generated separately for the two regions of

high and low dose, and a composite dose distribution

was constructed and compared with that of PINNACLE3.

FIG. 1. Flowchart of the ANN training and validation approach.

5808 Kalantzis et al.: IMRT 2D dose modeling using artificial neural networks 5808

Medical Physics, Vol. 38, No. 10, October 2011

The maximum output value of the ANN is 1. In order to

compare the ANN reconstructed relative dose map with that

from the TPS, we normalized the ANN dose map to its maxi-

mum dose DANNmax . Similarly, the dose map from the TPS was

normalized to the maximum dose DTPSmax by using two metrics:

the mean absolute deviation of the relative dose (MADRD)

and the c-index.26 The MADRD is given from the following

equation:

MADRD ¼ 1

N

XN

i¼1

DANNi � DP

i

�� ��DP

i

; (1)

where DANNi and DP

i are the normalized relative dose, of

voxel i, to the DANNmax and DTPS

max, respectively, and N is the total

number of voxels of the two-dimensional map.

II.B. Setup and acquisition of fluence maps from EPID

The first step in our method was the calculation of fluence

maps from the data collected using EPID. For all the meas-

urements, the a-Si based aSi1000 EPID (PortalVision, Var-

ian Medical Systems) mounted on a Novalis Tx was used to

obtain the fluence maps of the IMRT fields. The Linac is

equipped with the 2.5 mm 120HDVR

MLC. The aSi100 EPID

has an active imaging area of 40� 30 cm2 at Source to EPID

distance (SED) of 105 cm. The image matrix is created from

an array of 1024� 768 pixels and the maximum frame

acquisition rate is 9.574 frames=s.

All the measurements were performed at SED of 110 cm

without additional buildup. To calibrate the EPID, the dark

calibration was performed, which characterizes the EPID

response in the absence of radiation. The flood field calibra-

tion was also conducted to normalize each individual pixel’s

value and achieve uniform spatial response of the EPID.

A step-wedge irradiation was used to calibrate the relation

between the signal intensity and the delivered fluence [Fig.

2(a)]. Images were acquired and saved in DICOM format,

and image analysis algorithms were developed using MATLAB

v7.7 (MathWorks, Natick, MA). A linear relationship

between signal intensity (EPID pixel value normalized to the

maximum value) and fluence (number of MU) shown in Fig.

2(b) was confirmed consistently with the previous studies.27,28

Then the IMRT fields used in this study were delivered, and

the obtained EPID-based fluence maps were backprojected to

100 cm source to point distance (SPD) from the raw data

acquired by EPID with in house developed software.

The IMRT fluence maps were imported into the TPS

(PINNACLE3 V 9.0), and the 2D dose map was calculated on

the horizontal midpoint plane of a cylindrical phantom with

a 15 cm radius and 18 cm length made of virtual water

(TomotherapyVR

). The grid size, for both the fluence and dose

maps, was 0.25 cm and the fast convolution algorithm

(PINNACLEVR

) in TPS was used to calculate the 2D dose

distribution.

II.C. Architecture of the artificial neural network

A feed-forward multilayer ANN was used to convert flu-

ence map to dose map. Figure 3 shows the architecture of

the neural network. It consists of an input layer with 30

nodes and a hidden layer with 5 nodes, with each layer fully

connected to the succeeding layer.

There is no theoretical limit on the number of hidden

layers, but typically only one or two is enough, depending

on the complexity of the problem. With more hidden layers

added, both the complexity of the algorithm and the required

time for convergence increase. Additionally, using two hid-

den layers exacerbates the problem of local minima. Besides

the number of hidden layers, there is empirical evidence that

generalization to novel input patterns is improved by using

hidden layers with a small number of nodes.29,30 In these

cases, generalization from the training set to novel inputs

was better when the number of hidden nodes was relatively

small. The reason for improved generalization is that a small

hidden layer forces the input patterns to be mapped through

a low-dimensional space, enforcing proximities among

hidden-layer representations that were not necessarily pres-

ent in the input-pattern representations. However, we need to

mention that there are also cases for which reducing the

number of hidden nodes did not improve generalization.31

To test the impact of hidden layer numbers on the perform-

ance of ANN, spot checks were made manually to obtain a

reasonable fit to the data. Figure 4 shows the performance of

three different architectures of ANN we tested for the train-

ing phase. The first one has one input layer with 10 nodes

FIG. 2. (a) Step-wedge irradiation used for the EPID calibration and (b) linear relation between EPID response and number of MU delivered. Data acquired at

6 MV.

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Medical Physics, Vol. 38, No. 10, October 2011

(square), the second has 15 nodes in the input layer and 2

nodes in the hidden layer (circle), and the third one has 30

nodes in the input layer and 5 in the hidden layer (diamond).

It is clear that the addition of a hidden layer improves signifi-

cantly the performance of the ANN.

The learning rate is another important variable for the

performance of the network. A large learning rate may cause

the network to oscillate around a minimum, and a very small

rate will increase the computation time. The learning rate of

0.0015 was chosen empirically through a “trial and error”

procedure. By testing learning rates of different order of

magnitude and testing the performance of the ANN, we con-

cluded that the suggested learning rate was sufficient for the

particular problem32 (Table I).

In neural networks, one of the major pitfalls is overtrain-

ing. Overtraining occurs when a network has learned not

only the basic mapping associated with input and output data

but also the subtle nuances and even the errors specific to the

training set. If too much training occurs, the network overly

memorizes the training set and looses its generalization

capability with new data sets. The result is a network that

performs well on the training set but performs poorly on out-

of-sample test data. For that reason, we halted the ANN peri-

odically at predetermined intervals, and the network was

then run in recall mode on a test set to evaluate the network’s

performance based on the mean-square error. We noticed

that after 400 epochs, the performance of the ANN did not

improve significantly. Therefore, the ANN training was

stopped after 400 epochs to avoid overtraining and losing

generalization capability.

Also, it is important to use a number of random initializa-

tions or other methods for global optimization. Four inde-

pendent random initializations were used for the training

phase and the one with the best fit was chosen for the valida-

tion phase. In this study, 26779 voxels (6 step and shoot

fields of prostate, 4 of lungs and 4 of head and neck) were

used for the sequential mode training.

The choice of the proper input variables plays a crucial

role on the performance of the ANN. Different methodolo-

gies have been proposed33,34 with successful application on

the prediction of lung radiation-induced pneumonitis.10

However, neural networks are not concerned with physical

FIG. 3. Architecture of the feed forward Neural Network. The input X(i,j) is the fluence in the voxel (i,j) and Y(i,j) is the dose in the voxel (i,j). The Lk,m indi-

cates kth node of the mth layer.

FIG. 4. Performance of three ANN architectures for the same set of training

data. In the legend, (k m) represents the ANN architecture with k and mnodes in each one of the input and output layers; [k m n] represents the ANN

architecture with “k,” “n,” and “m” nodes in each of the input, hidden and

output layers, respectively

TABLE I. Parameters of the ANN model used in this study.

Number of inputs 7

Number of nodes input layer 30

Number of nodes hidden layer 5

Number of nodes output layer 1

Activation function input layer 2�

1þ e�2x� �

� 1

Activation function hidden layer 2�

1þ e�2x� �

� 1

Activation function output layer 1=1þ e�x

Learning rate 0.0015

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Medical Physics, Vol. 38, No. 10, October 2011

laws. Their task is to map a particular input pattern to an out-

put. In our case, the task of the ANN was to relate the flu-

ence of a point to its dose value. A reasonable approach

would be able to use as inputs the coordinates of that point

and its fluence. However, Vassuer et al.15 suggested that the

accuracy of the network may be improved by introducing

the neighboring voxels for dose calculations as additional

inputs to the network. In our tests, we validated this assump-

tion. A significant improvement of the ANN performance

was noticed, by adding the fluencies of the four neighboring

voxels. Beyond that point, by adding more voxel fluencies as

inputs, the required time for convergence increased without

achieving a better fit of the data. The variable “i” is related

with the depth, h, of the voxel (i, j) according to the follow-

ing equation:

h ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 � i2p

where R is the radius of the cylindrical phantom. Finally, the

variable j defines the position of the voxel on the longitudi-

nal axis of the phantom. If the j coordinate of the voxel is

FIG. 5. (a) Planar dose of an IMRT field. The red line depicts the boundaries of the ANN replicated dose compared to the TPS (b) Isodose profiles for the 2D

dose map from the TPS (solid line) and the ANN (dashed lines), respectively (c) Distribution of the MADRD between the ANN reconstructed dose and the

TPS calculated dose. The mean MADRD is 2.7%, (d) histogram of MADRD of the relative dose as shown in panel (c), (e) the 2D c-index distribution, and (f)

histogram of the c-index, and 96% of the c values are smaller than 1.

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Medical Physics, Vol. 38, No. 10, October 2011

close to the longitudinal end of the cylinder, the dose would

be different compared to a voxel in the middle area of the

phantom due to different scattering.

The activation function is a key factor as well, in the

ANN structure.35 Back-propagation neural networks support

a wide range of activation functions such as sigmoid, step,

and linear function. The choice of activation function can

change the behavior of the back-propagation neural network

considerably. There is no theoretical reason for selecting a

certain activation function. In most cases, the proper activa-

tion function for a certain problem is found through the

experimentation. From our available data, we noticed that

the highest performance of the ANN was achieved by using

the activation functions depicted in Table I.

Because the output values range from 0 to 1, the dose in

the training phase was normalized to the maximum dose

(DTPSmax). A gamma correction filter with C equals to seven

was applied to the normalized dose map according to the

equation,

D0ði; jÞ ¼ Dði; jÞ1=C:This filter is commonly used in image processing and works

mostly on the mid tone section of the data. In this way, we

improved the required time for convergence during the train-

ing phase.

III. RESULTS

III.A. Modeling of 2D dose maps

We tested the accuracy of our method with 25 step and

shoot IMRT treatment fields. They ranged from relatively

less modulated IMRT fields of prostate cases to highly

modulated fields for head and neck cases (12 fields of pros-

tate, 7 fields of lung, and 6 of head and neck). The ANN

design and data processing were implemented in MATLAB

(version 7.7, MathWorks, Natick, MA) and all computations

were conducted on a AMD Turion64 (1.59 GHz) with 1 GB

RAM.

It is worth noting that in the regions where the fluence

value is below 0.25, the variability of the dose among the

different fields increases. That was noticed in previous stud-

ies15 where larger errors occurred in low dose regions and

high gradient dose regions. For that reason, similarly to pre-

vious studies.36 a threshold of 30% of DTPSmax was used for the

evaluation phase of the ANN. Figure 5(a) illustrates a sample

dose distribution from the TPS on the isocenter plane of our

phantom normalized to DTPSmax. The red line is the boundary of

the area defined by our threshold of 0.3 of DTPSmax. As one can

see, the isodose line that was used, successfully captures the

irradiated area of the treatment field only, excluding those

areas which have received dose from the scattered radiation.

Figure 5(b) shows the isodose distributions for both the TPS

(solid lines) and the ANN (dashed lines) dose. Despite the

high irregularity of the particular field, we have achieved

good agreement between the TPS calculated dose and that

from ANN.

Figures 5(c) and 5(d) illustrate the MADRD [see Eq. (1)]

between the TPS and the neural network and its distribution,

respectively. As was expected, the largest error occurs for

the low dose areas on the periphery of the radiated field.

Similarly, in Figs. 5(e) and 5(f), the 2D c-index distribution

and its histogram for the corresponding IMRT field are

shown.

III.B. Evaluation of the neural network model for highdose regions

Our method was evaluated in two ways. First, the

MADRD was calculated for each IMRT field. In Fig. 6, the

mean deviation of each IMRT field used in the ANN valida-

tion is shown as solid circles, and the overall mean (solid

line) and the standard deviation (dashed line) of MADRD

were also indicated. The MADRD for each field was smaller

than 5%, while the overall mean MADRD was 3.6%.

Besides the MADRD, for each IMRT field, the ANN-

reconstructed dose distribution was compared with the

planned dose distribution by means of a 2D c-index

FIG. 6. MADRD of the IMRT fields used for testing the neural network

(dots), the overall average of MADRD (solid line) and the corresponding

standard deviation. (dashed line).

FIG. 7. Fraction of pixels with c-index �1 and average c-index for each indi-

vidual IMRT field.

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Medical Physics, Vol. 38, No. 10, October 2011

evaluation method with distance to agreement (DTA) �5

mm and dose difference (DD) �5%, respectively. Figure 7

shows the percent of c-index smaller or equal to1 for each

field (blue bars) as well as the mean c-index (red bars). It is

worth noting that in most cases, the c-index is calculated for

the whole square field and not only for the radiated area as

was done in our case. Because of that, those areas which

have received low dose, due to the scatter radiation, may

contribute significantly in the percentage of the c-index val-

ues which are smaller than one. As was mentioned earlier

for the evaluation of our method for the high dose regions,

the irradiated area enclosed by the 30% isodose line of the

normalized dose was used.

III.C Performance of the ANN for low dose regions

The input=output training data are fundamental for super-

vised learning ANN as they convey the information, which

is necessary to discover the optimal operating point of the

ANN. Figure 8 illustrates the histogram of both the fuence

(a) and dose (b) of the training data.

Despite the large number of voxels with low fluence in

the data set used for the training phase, the ANN could not

successfully replicate low dose distributions. Additionally,

in clinical practice, low dose regions may be important. An

example of this can be seen with the radiation of lung

tumors. In that case, it is important to limit the total volume

which has received more than 20 Gy in order to reduce the

toxicity of the lung. It is common practice in the literature of

artificial intelligence to simplify the learning task by divid-

ing the initial problem into subsets of simpler problems.37

We applied a K-mean clustering algorithm to extract any in-

ternal characteristics of the training data based on their

Euclidian distance in the fluence-dose domain.

Silhouette is a common technique for internal validation

of data and can be used to evaluate the quality of a clustering

result.38 A high silhouette value indicates that an object lies

well within its assigned cluster, while a low silhouette value

means that the object should be assigned to the another clus-

ter. The average silhouette width could be applied for the

evaluation of clustering validity and also could be used to

decide how good the number of selected clusters is. The

largest overall average silhouette width indicates the best

clustering (number of clusters). Therefore, the number of

cluster with maximum overall average silhouette width is

taken as the optimal number of clusters. Figure 9 shows the

silhouettes plots of the classified data. The best clustering

was achieved by classifying the fluence into two sets with

ranges (0.05, 0.32) and (0.32, 1). Therefore, the same meth-

odology for the training and validation phase of the ANN

was repeated for areas (or voxels) in the fluence range of

(0.05, 0.32). Figure 10(a) shows the 5% isodose (green

dashed line) and 30% (red line). Figures 10 (b) and (c) illus-

trate the distribution of the 2D c-index and MADRD, respec-

tively. Combining the results of low and high dose regions, a

composite ANN-reconstructed dose distribution can be

FIG. 8. Histograms of (a) fluence and normalized dose and (b) of the training data.

FIG. 9. Silhouette plots of the training data. The average silhouette width is (a) 0.8525, (b) 0.8321, and (c) 0.8247 for 2, 3, and 4 clusters, respectively.

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created. The results of the calculated c-index of the compos-

ite reconstructed dose distribution are shown in Fig. 10(d).

Finally, we examined how the agreement between the

results from neural network and the TPS varies on areas

enclosed by different isodose levels for the same field. The

calculations for those areas of each treatment field, encom-

passed by the 5%, 30%, 40%, and 50% isodose lines were

performed, and the results were summarized in Table II. For

the 5% isodose line, a composite ANN-reconstructed dose

distribution was calculated. It can be seen that the percentage

of the c� 1 index averaged over all the IMRT fields

(i.e.,< c>� 1) increased by 4% and the average of the

mean deviation decreased by 2.3% when the isodose level

increased from 5% to 50%. We can conclude that the per-

formance of the neural network improves as we are moving

from regions of lower to higher dose.

IV. DISCUSSION

A feasibility study of artificial neural networks to model

dose calculation for IMRT fields has been described. For the

training of the ANN, fluence maps obtained from a-Si EPID

and dose maps calculated by the TPS were used. The fluence

data were separated into two clusters of low and high fluence

by using a K-mean clustering algorithm based on the Eucli-

dian distance in the fluence-dose domain. After the inde-

pendent completion of the training phase for the two clusters

of data, evaluation of the ANN performance was done by

using 25 IMRT fields. Despite the complexity of the task the

ANN had to accomplish, a good agreement between the dose

maps generated by ANN and TPS was achieved.

The main differences of our method compared with previ-

ous studies are the modeling of IMRT 2D dose distributions

instead of the percent depth dose (PDD) of square fields, the

acquisition and usage of EPID-based fluence maps instead of

the point dose derived from extensive Monte Carlo simula-

tions, the architecture of the ANN and the proper selection

of the input patterns, the proper preprocessing of the data

and the clustering of the training and validation data in order

to achieve results comparable to the TPS for both high and

low dose regions. An alternative approach is the use of the

EPID to create the fluence maps of the IMRT fields. These

fluences are compared with TPS-reconstructed fluences39

FIG. 10. (a) Low dose region as defined by the 5% isodose line (dashed line), (b) 2D c-index distribution for the low dose region with a 93.8% percentage of

c � 1, (c) distribution of MADRD between the ANN reconstructed dose and the TPS calculated dose. The mean value of the MADRD is 4.1%, and (d) 2D

c-index for a composite dose distribution.

TABLE II. Mean (<.>) and standard deviation (std.) of c �1 and MADRD

for four dose regions (5%, 30%, 40%, and 50%).

Dose region (%) � 1 Std. c <MADRD> Std. MADRD

�5 0.93 0.031 0.046 0.007

�30 0.95 0.016 0.036 0.005

�40 0.97 0.026 0.027 0.004

�50 0.97 0.029 0.023 0.005

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From our results, we can make the following observa-

tions. First, a single ANN could not predict accurately both

low and high dose regions simultaneously. A K-means algo-

rithm was applied to cluster the data into two sets of high

and low dose regions. In that way, we divided the initial

problem into two less complicated tasks. The training and

validation of the ANN were done independently for those

two dose regions and a significant improved performance

was achieved. Second, it was noticed that below the 5% iso-

dose line of Dmax, the predictions of the ANN were not accu-

rate. Figure 11(a) illustrates a sample plot of an IMRT field

after applying the gamma correction filter. It is clear that for

low fluence the deviation of the dose from the midline (Fig.

11(a) solid line) of the data points is larger. Figure 11(b)

shows the decrease of the standard deviation (std) of the nor-

malized dose as a function of the fluence. The reason of that

is the increased contribution of the scattered radiation rela-

tive to the primary one for areas with very low fluence. Since

the ANN is learning in a data-driven fashion, for those

regions with dose smaller than 5% of Dmax, the fluence-dose

relationship which the ANN had to extract was concealed by

the scatter radiation.

Another possible reason for the low performance of the

ANN is existence of multicolinearity of the input data when

the fluence is smaller than 5%. If multicolinearity exists

between the input variables in the model, it will cause the

ANN weight estimation to become large due to ill-

conditioning in the Hessian matrix leading to bad generaliza-

tion. To test if there exists multicolinearity in our data, the

partial variance inflation factor (VIF), which measures the

severity of multicolinearity, were calculated for fluence val-

ues lying in the range (0, 0.05), (0.3, 0.5) and (0.7, 0.9). In

Fig. 12, the partial VIFs for fluence smaller than 0.05 are sig-

nificantly high which indicate that multicolinearity exists in

the training data for that fluence region.

The ANN was tested for a set of IMRT treatment fields

with different sizes and degrees of intensity modulation. The

c-index was employed to compare the agreement of the dose

maps produced from the ANN and TPS. In this study, the

5 mm DTA and 5% DD were chosen to calculate the c-

index, instead of the commonly used 3 mm DTA and 3%

DD.40,41 However, the dosimetric comparison depends on

several considerations:42 field size, degree of intensity modu-

lation, steepness of dose gradient, and field-by-field exposure

or single-gantry-angle composite exposure. Because of that,

the acceptance criteria vary from user to user.43–45 Alterna-

tive methods46,47 besides the c-index could be used for fur-

ther evaluation of our method. Additionally, optimization

techniques could be applied to improve the performance of

the ANN. Given the large variability of IMRT fields, a large

number of training data are required for fully training of the

ANN. One way to reduce the variability and consequently

the number of the sampling points which are required for the

training phase is the systematic categorization of the IMRT

fields based on the disease site or modulation level. The

training and validation procedure should be repeated for

each anatomical group and several number of data points

would be used. A database of IMRT or conventional

FIG. 11. (a) Plot of the normalized dose D=Dmax, generated by the TPS (black) and the ANN (white) for an IMRT field as a function of the fluence. The solid

line is the mean of the output and (b) standard deviation of the normalized dose as a function of the fluence.

FIG. 12. VIFs for three regions of fluence of the training data.

5815 Kalantzis et al.: IMRT 2D dose modeling using artificial neural networks 5815

Medical Physics, Vol. 38, No. 10, October 2011

treatment fields for the same anatomical region could serve

for the training and testing of the ANN. One candidate is the

mildly modulated treatment fields of the Prostate. In that

case, we would expect further improvement of the ANNs

performance since it will have to accomplish an easier task

with less degree of freedom.

In the current study, we model the dose distributions of

IMRT fields at 6 MV for a homogeneous cylindrical

phantom. Extension of our method would be the dose

modeling for different energies and in the presence of inho-

mogeneities. Vasseur et.al. have demonstrated the capability

of ANN to model dose in the presence of inhomogeneities.

Extension of our method could be the incorporation of

attenuation coefficients or CT numbers for each voxel in the

input layer of the ANN. One further extension of our method

would be the acquisition of the CT numbers from a CT scan

of the patient. In that case, the task the ANN has to accom-

plish is much more challenging and informative. Since the

geometry of the patient is not fixed, as it was with the phan-

tom, two additional possible variables we could use is the

distance from the entrance point to the dose calculation point

as well the distance from the dose calculation point to the

exit point of the beam.

For the training of the neural network, we have chosen

the most commonly used learning algorithm, the back-

propagation. Despite that fact, the back-propagation learning

algorithm has three intrinsic limitations: the step size prob-

lem, the moving target problem, and the attenuation and

dilution of error signal as it propagates backward through

the layers of the network. S. Fahlaman and C. Lebiere48

investigated optimization problems of back-propagation and

proposed the cascade-correlation method, a different archi-

tecture and learning algorithm that may further optimize our

results. Finally, besides the algorithmic part, there are alter-

native choices regarding the neural network architecture.

Another possible candidate network type is the convolution

neural networks,49,50 which have the capability of extracting

features in a hierarchical set of layers in a data-driven fash-

ion. Typically, convolutional layers are interspersed with

subsampling layers to reduce computation time and to gradu-

ally build up further spatial and configural invariance. This

type of neural network may be able to classify larger patterns

of fluence and produce more accurate results for the low

dose areas.

V. CONCLUSIONS

The dose calculation in the treatment planning is a com-

plicated task with many variables. Among them are the

usage of wedges, different photon or electron energies, SSDs

and geometry. Our results indicate the feasibility of ANN to

reconstruct dose calculations of IMRT fields at 6 MV com-

parable with those of the TPS for a homogeneous cylindrical

phantom. A similar method could be applied for dose calcu-

lations for non homogeneities and different energies as well.

Extension of the current work is the further optimization of

the neural network training algorithm as well as the investi-

gation of the performance of alternative ANN architectures.

Finally, a database of IMRT fields would be helpful to

further explore the potential of ANN in IMRT dose calcula-

tions for specific anatomical regions.

ACKNOWLEDGMENTS

The authors would like to thank Dr. N. Papanikolaou, Dr.

M. Swellius, and Dr. X. Chen who provided several useful

suggestions for improving this paper. The authors would

also want to acknowledge the Editor, Associate Editor, and

the Referees for their kind comments and suggestions

throughout the revision of the manuscript.

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