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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.
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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
5810 Kalantzis et al.: IMRT 2D dose modeling using artificial neural networks 5810
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.
5811 Kalantzis et al.: IMRT 2D dose modeling using artificial neural networks 5811
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.
5812 Kalantzis et al.: IMRT 2D dose modeling using artificial neural networks 5812
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.
5813 Kalantzis et al.: IMRT 2D dose modeling using artificial neural networks 5813
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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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