Three-dimensional dose reconstruction of breast cancer treatment ...

Three-dimensional dose reconstruction of breast cancer treatment 

using portal imaging 

R. J. W. Louwe, E. M. F. Damen, M. van Herk, A. W. H. Minken, O. Törzsök, 

and B. J. Mijnheer a) 

The Netherlands Cancer Institute/Antoni van Leeuwenhoek Hospital, Department of Radiotherapy, 

Amsterdam, The Netherlands 

Received 30 August 2002; accepted for publication 12 May 2003; published 22 August 2003 

In this study, we present an algorithm for three-dimensional 3-D dose reconstruction using portal 

images obtained with an electronic portal imaging device EPID. For this purpose an algorithm for 

2-D dose reconstruction, which was previously developed in our institution, was adapted. The 

external contour of the patient was used to correct for absorption of primary photons, but the 

presence of inhomogeneities was not taken into account. The accuracy of the algorithm was determined 

by irradiating two anthropomorphic breast phantoms with 6 MV photons. The dose values 

derived from portal images were compared with results from 3-D dose calculations, which, in turn, 

were verified with data obtained with an ionization chamber and film dosimetry. It was found that 

the application of contour information significantly improves the accuracy of 2-D dose reconstruction. 

If the total dose at the isocenter plane resulting from all treatment beams is reconstructed, the 

average deviation from the planned dose is 0.1%1.7% 1 SD. If contour information is not 

available, the differences increase up to 20% for the individual beams. In that case, the dose can 

only be reconstructed with reasonable accuracy when nearly opposing beams are used. The 

average deviation of the 3-D reconstructed dose from the planned dose in the irradiated volume is 

1.4%5.4% 1 SD. If the irradiated volume is enclosed by planes less than 5 cm distant from the 

isocenter plane, then the average deviation is only 0.5%3.4% 1 SD. It can be concluded that the 

proposed algorithm for a 3-D dose reconstruction allows a determination of the dose at the isocenter 

plane and the dose–volume histogram with an accuracy acceptable for an independent verification 

of the treatment. © 2003 American Association of Physicists in Medicine. 

DOI: 10.1118/1.1589496 

Key words: Radiotherapy, breast cancer, dose verification, EPID, portal dosimetry 

I. INTRODUCTION 

Portal transit dosimetry, using electronic portal imaging devices 

EPIDs, is a technique where dose measurements 

made behind a patient are used to verify the dose delivered to 

that patient. Several classes of portal dosimetry methods 

have been developed, which can be divided in two main 

categories. The first group, which can be defined as class a 

solutions, uses planning CT data, the prescribed number of 

monitor units, and information concerning the beam setup to 

predict the dose at the level of the EPID, and compares the 

measured and predicted dose distributions. 1–4 By adapting 

the primary energy fluence in an iterative way, the dose distribution 

at the position of the EPID can then be recalculated 

until agreement with the measured dose distribution is 

obtained. 2,3 In this way the actual dose delivered to a patient 

can be reconstructed from EPID images. The second category 

consists of techniques that back-project the EPID dose 

distribution to the patient level, either at the exit plane, or at 

the midplane, or through the whole irradiated volume. The 

differences between these back-projection methods are 

mainly related to the amount of knowledge about the patient 

anatomy that is used during the back-projection stage. In our 

institution, methods have been developed that are based on 

rather simplifying assumptions about the patient anatomy 

class b, such as symmetry of the irradiated part of the 

body. 5,6 Other groups have used planning CT scans to derive 

the dose in a specific plane class c. 7,8 The most advanced 

approaches apply on-line acquired CT data to compute the 

actual treatment-time dose distribution using various sophisticated 

algorithms class d. 9,10 

The validity of these approaches mainly depends on the 

type of errors that may occur and should be traced by portal 

dosimetry, as well as on the availability of planning or online 

CT data. Because portal dosimetry is generally used as 

independent verification of the treatment similar to an independent 

monitor unit calculation, its accuracy does not need 

to be as high as the dose calculation performed by the clinically 

applied treatment planning system. The accuracy of the 

portal dosimetry procedure determines the magnitude of errors 

that can be detected. The following types of errors may 

potentially be detected by portal dosimetry: 1 machine output, 

field flatness, or intensity modulation errors; 2 errors in 

monitor unit calculations; 3 patient setup errors; 4 errors 

due to patient shape changes and organ motion. Machine 

output errors are detected by all methods. Methods in class 

a are insensitive to errors in the monitor unit calculations 

because the same number of MUs is used for the measurement 

and calculation of the portal dose images. 8 Methods in 

2376 Med. Phys. 30 „9…, September 2003 0094-2405Õ2003Õ30„9…Õ2376Õ14Õ$20.00 © 2003 Am. Assoc. Phys. Med. 2376

2377 Louwe et al.: 3-D dose reconstruction 2377 

FIG. 1. Beam setup and location of the radiographic films during irradiation of the anthropomorphic phantoms. Panel a: axial slice of phantom A films 

oriented in sagittal planes. Panel b: coronal slice of phantom B films oriented in transversal planes. For phantom B, at most, three films are applied 

simultaneously, placed at positions B1, B2, or B3, and B4. The positions of the radiological midplane 1, the isocenter plane 2, the isocenter 3, and lungs 

4 have been indicated. Panel c: construction of the total dose distribution broken line, 2 sum ) resulting from all treatment beams at the plane bisecting the 

isocenter planes of the medial and lateral beams solid lines, 2 med and 2 lat , respectively. 

classes a, b, and c are, in principle, insensitive to dosimetric 

errors caused by patient setup errors in the beam direction. 

Consequently, these methods should be combined 

with a geometrical verification protocol, preferentially based 

on an orthogonal set of EPID images, to minimize the influence 

of patient setup errors. Only the class d methods can 

detect organ motion and patient deformation and allow a 

complete dosimetric and geometric verification. With methods 

in classes a–c the source of a deviation between the 

planned and measured dose may not always be clear. For 

instance, weight loss of the patient may cause similar dosimetric 

deviations as a machine error. For this reason, clinical 

protocols need to be devised on how to handle observed 

errors, for instance, including a rescan of the patient. 

Planning CT data are not always available, and on-line 

CT data is currently only available to a few centers. We 

therefore adapted our class b portal dosimetry method to 

achieve a semiclass c or class d application by including 

only external patient contour data, which may be acquired 

during simulation class c or during treatment class d. 

Such an adapted algorithm can also be applied if CT data are 

available. The advantage of including more patient data is 

that treatment verification becomes more reliable in those 

cases that the dose calculation algorithm was inaccurate 

large contour variations, inhomogeneities. Clearly, the 

drawback of including pretreatment patient contour data in 

the verification system is that the sensitivity for dosimetric 

deviations due to contour changes is reduced and the advantages 

and disadvantages should therefore be carefully 

weighted. 

In breast radiotherapy, portal dosimetry is applied either 

to improve dose homogeneity in the irradiated volume 11–17 

or to verify the dose delivery. 18,19 Improvement of dose homogeneity 

may be achieved by applying portal dosimetry to 

design either compensators or intensity-modulated radiotherapy 

IMRT fields for individual patients. In our institution, 

the application of IMRT is planned for breast cancer 

patients with the main goal the reduction of the dose to the 

heart. 20,21 Criteria for selecting patients, who would benefit 

most from IMRT, are currently being developed in treatment 

planning studies. 21,22 Portal dosimetry may then be used to 

estimate the dose delivered to the heart. However, a comparison 

of patient dose distributions or its derivatives, e.g., 

dose–volume histograms, which have been reconstructed 

from portal images, with those obtained from the treatment 

planning system, is not straightforward. 

In many institutions, the dose distribution is calculated 

only in a single plane during treatment planning of breast 

cancer patients. The patient contour is measured during the 

simulator session in a plane through the isocenter perpendicular 

to the long axis of the patient. Subsequently, the dose 

distribution in that plane is calculated using a treatment planning 

system, maximizing the uniformity of the dose distribution 

by beam weight optimization, and determining the number 

of monitor units of the treatment beams. 

For these breast cancer patients, the planes used for the 

dose reconstruction from portal images do not correspond 

with the plane used for treatment planning. In portal dosimetry, 

the dose is generally reconstructed in the isocenter 

plane, i.e., the plane through the isocenter perpendicular to 

the direction of the treatment beam. 5,23–25 However, if the 

patient contour and/or the electron density distribution 

within the patient are not symmetric with respect to the isocenter 

plane, the dose will be reconstructed in the radiological 

midplane. The radiological midplane is, in fact, a surface 

that connects those points of the rays emerging from the 

radiation source in the direction of the portal imager that 

have an equal transmission within the patient at either side of 

that ray. For breast cancer patients in particular, the isocenter 

plane and radiological midplane do not coincide, as is shown 

Medical Physics, Vol. 30, No. 9, September 2003


schematically in Fig. 1a; the radiological midplane is 

curved and does not always include the isocenter. 

Our first aim in this study was to modify the original 

reconstruction algorithm to enable dose reconstruction at the 

isocenter plane by incorporating patient contour data. Next, 

the accuracy of the dose reconstruction using the modified 

algorithm was assessed by a comparison with film and a 

treatment planning system see Sec. II F. The accuracy of 

the original algorithm has been previously investigated for 

various geometries. 5,6,23–25 In particular, for configurations 

representative for pelvic treatments, the dose could be determined 

from EPID images with a maximum deviation of 

about 2% from the actual dose. The accuracy decreases when 

the tissue density distribution is inhomogeneous and/or 

asymmetrically distributed, especially if CT data is not used. 

The accuracy of dose reconstruction was also not yet assessed 

for breast cancer treatment. In addition to complicating 

factors such as the asymmetry of the patient contour and 

the presence of lungs, the accuracy of dose reconstruction for 

this patient group may be further decreased due to the relatively 

small distance between the patient and the portal imager. 

This air gap must be relatively small to allow imaging 

of the largest treatment fields. Consequently, the contribution 

of scatter from the patient to the portal imager will be larger 

and less homogeneous than accounted for in the original algorithm. 

Therefore, a more accurate correction for the scatter 

contribution from the patient to the portal imager has to be 

considered as well. 

Pretreatment verification using phantoms is currently the 

only way to verify dose delivery using 3-D conformal or 

IMRT techniques. It will, however, be very reassuring if also 

the actual dose delivered by these sophisticated techniques to 

patients could be verified. In addition to a more general and 

more accurate 2-D dose delivery validation, 3-D verification 

of the patient dose using portal images would be very useful. 

Especially in the absence of CT data, and for those patients 

whose dose is only calculated in one plane during treatment 

planning, 3-D dose reconstruction may prove to be a valuable 

tool to assess the dose delivery. Our second purpose of 

this study was therefore to extend the existing 2-D dose reconstruction 

algorithm and to test the accuracy of 3-D dose 

reconstruction. 

II. MATERIALS AND METHODS 

A. 2-D dose reconstruction 

We modified the original algorithm 6 to include contour 

information, but also other modifications have been made. 

The steps of the modified reconstruction algorithm are described 

below. The portal images of the treatment beams 

acquired with and without patient the latter will be called 

‘‘open images’’ are used as input for the reconstruction algorithm. 

In the first step, the measured pixel values I exp of 

both images are multiplied with a sensitivity matrix S ij to 

correct for the differences in gain and offset values of the 

individual pixels. In this equation also the calibration applied 

to the raw pixel values is described: 26 

I corr ij S ij I exp ij S ij I raw ij D ij 

F ij D ij F ijD ij ij , 1 

in which F and D are the flood- and dark-field calibration 

images that are applied for normal clinical use of the EPID, 

respectively, and ij denotes an average over all pixels 

within an image. In the second step, the corrected pixel values 

are converted to dose rate values. A power law doseresponse 

curve is used for this purpose with two fit parameters: 

called ‘‘a’’ and ‘‘b.’’ Subsequently, the applied number 

of monitor units MU and the monitor signal MS of the accelerator 

simultaneously digitized during the acquisition of 

the portal images, are used to convert the dose rate values 

into a dose image D EPID : 

D EPID ij Ḋ EPID ij MU/MS I corr 1/b 

ij 

MU/MS. 2 

a 

The third step consists of a deconvolution of D EPID with a 

2-D scatter kernel K EPID to correct for the lateral scatter 

within the plane of the imager: 

D EPID,corr EPID 

ij D ij 1 K EPID ij , 

in which 

K EPID ij C 1 e •r /r 2 , 

3 

where C 1 is a calibration constant, r is the distance to the 

origin, and is the linear attenuation coefficient of water. In 

the fourth step, the transmission T, through the patient, is 

estimated by the ratio of the patient and open portal dose 

values. Those pixels where the transmission is less than one 

for practical reasons, we use less than 0.9 correspond with 

tissue in the patient, and are set to 1 in image ; all other 

pixels are set to 0. The product of and the portal dose is 

then convolved with a 2-D scatter kernel K pat to estimate the 

contribution of patient scatter to the portal dose image, 

S pat→EPID : 

S pat→EPID D EPID,corr ij K pat ij , 

in which 

K pat ij const. 

4 

This scatter contribution is subtracted from the portal dose 

image to determine the primary dose at the portal imager and 

the transmission through the patient is subsequently recalculated 

as the ratio of the primary and open portal dose. In the 

next step, the primary dose at the midplane of the patient is 

calculated using the inverse square law and a correction for 

the attenuation of the photon beam see further below. To 

calculate the contribution of scattered radiation to the total 

midplane patient dose, the primary dose at the midplane is 

weighted with the normalized scatter-to-primary ratio, 

NSPR, which is a polynomial fit function depending on the 

recalculated transmission T 6 and subsequently convolved 

with another 2-D scatter kernel. Finally, the estimated scatter 

is added to the primary dose to yield the total patient midplane 

dose: 

D mid P mid S mid P mid K mid NSPRTP mid , 



in which 

K mid ij C 1 e C 2 •r /r C 3. 

5 

The sensitivity matrix, the calibration constants, and the 

fit parameters for the NSPR and scatter kernels are determined 

for each EPID-treatment beam combination for all 

clinically relevant field sizes from a series of experiments 

in which a set of polystyrene slabs with various thickness 

is applied. 

In the original algorithm, the midplane dose was determined 

indirectly, by first calculating the exit dose, which was 

subsequently converted to the midplane dose. 6 For this conversion, 

the inverse square law ISQL and a correction for 

the attenuation between the exit point and the midplane were 

applied to calculate the primary dose at the midplane. For the 

latter correction, it was assumed that the radiological midplane 

coincides with the isocenter plane. However, the ISQL 

and attenuation correction may refer to different planes: the 

isocenter plane and radiological midplane, respectively. For 

prostate treatments, these planes will, more or less, coincide, 

but for breast patients a significant error may be introduced, 

as shown in Fig. 1a. Furthermore, the conversion of exit to 

midplane dose introduces additional data and corresponding 

uncertainties and is redundant, since the fit parameters in the 

reconstruction algorithm can be optimized for direct midplane 

dose reconstruction. For these reasons, the original algorithm 

was adapted to explicitly distinguish between dose 

reconstruction in the isocenter plane i.e., with attenuation 

correction or in the radiological midplane i.e., without attenuation 

correction. 

For simple configurations e.g., if the radiological midplane 

and isocenter plane coincide, the dose at the isocenter 

plane can be reconstructed without the application of additional 

data. In that case, the primary portal dose image is 

scaled using the ISQL and T to calculate the primary dose 

at the isocenter plane. If this calculation would be used for 

asymmetric configurations, the primary dose would be approximately 

reconstructed at the radiological midplane. To 

calculate the primary dose at the isocenter plane, 3-D contour 

data are required to correct for the difference in attenuation 

of the treatment beam in the volume proximal to and distal 

from the isocenter plane. The scaling factor T is then replaced 

by a single exponential function: exp(•x), where 

and x represent the linear mass attenuation coefficient of water 

for a specific beam quality and the geometrical path 

length along a ray through the patient from the isocenter 

plane up to the exit surface, respectively. To compare the 

accuracy of both reconstruction algorithms, the patient dose 

was reconstructed both with and without the attenuation correction. 

At this stage of our study, the presence of lung tissue 

and bony anatomy is not taken into account, and is the topic 

of future work to extend the application of the algorithm to 

sites including these tissues. 

B. 3-D dose reconstruction 

An important new application of the modified algorithm is 

its ability to reconstruct the dose in three dimensions. To test 

the feasibility of this technique with the existing software, 

the patient dose was reconstructed in various planes. For the 

calculation of the primary dose at each reconstruction plane, 

the appropriate ISQL and attenuation correction, based on 

the external patient contour, are applied. Currently, the scatter 

kernel is taken independently of the depth of the reconstruction 

plane to limit the number of experiments required 

for the determination of the fit parameters. Because the lateral 

and medial beams are not exactly opposing, the planes at 

which the patient dose is reconstructed do not coincide. 

Therefore, the reconstructed dose distributions of the 

individual beams are geometrically projected on the plane 

bisecting the individual planes Fig. 1c. Subsequently, 

these dose distributions are added to calculate the total 

dose. In this way the error, which would be introduced if 

two noncoplanar dose distributions were directly added, 

is circumvented. A small error still may persist since the 

dose distributions are assumed to be invariant under 

projection. 27 

C. Portal imaging 

A Varian-MARK I-type detector Varian Inc., Palo Alto, 

CA was applied for portal imaging in this study. This detector 

has a sensitive area of 3232 cm 2 and an image is acquired 

in 5.2 s. A polystyrene build-up layer of 8 mm was 

placed on top of the EPID to obtain electron equilibrium at 

the position of the liquid of the ionization chambers in the 

experiments using 6 MV photon beams. The source–detector 

distance is equal to 145 cm, a distance at which for most 

breast treatments the complete treatment field could be 

imaged. For each beam, open images and images made with 

an anthropomorphic phantom were acquired. The dose 

distribution in the phantom was reconstructed from these 

images using the algorithm described in the previous 

sections. 24,25 

D. Beam setup and dose determination 

for the anthropomorphic phantoms 

Two anthropomorphic phantoms were irradiated using 6 

MV photon beams generated with an Elekta SL15 linear accelerator 

applying the standard treatment technique used for 

breast cancer patients in our clinic. This technique encompasses 

two nearly opposing tangential treatment fields, each 

consisting of an open and a wedged beam using a 60° motorized 

wedge. The individual beams are designated as 

medial-open, medial-wedged, lateral-open, and lateralwedged, 

respectively. The anthropomorphic phantoms have a 

geometry based on patient CT data as previously described 28 

and consist of polystyrene and cork, the latter being used as 

replacement for the lungs. Depending on the type of phantom, 

radiographic films can be positioned in sagittal phantom 

A or transversal phantom B planes Fig. 1. The lateral 

displacement from the isocenter of the radiographic 

films in phantom A was 4.5, 1.5, and 1 cm, respectively 

Fig. 1a. In phantom B, the radiographic films were 

placed at 5.5, 0.5 or 0.5, and 4.5 cm from the iso- 



center, respectively Fig. 1b. The absolute dose at the isocenter 

of phantom B could be measured by positioning a 

calibrated Farmer-type ionization chamber NE Technology 

Limited, NE2571 in a hole drilled in a slab of polystyrene. 

The charge was measured with a Keithley, K3 electrometer. 

Because phantom A has been glued together, we decided not 

to drill a hole for the placement of an ionization chamber. 

The beam configurations for the two phantoms were identical, 

but the isocenter position was slightly different in the 

two phantoms; more lung was irradiated in phantom A compared 

to phantom B, resulting in small differences in the 

dose distributions in the two phantoms. 

Treatment planning was performed using Pinnacle 

ADAC/Philips release 5.2g, applying the collapsed cone 

superposition/convolution algorithm. Radiographic films 

were positioned in the anthropomorphic phantoms during CT 

scanning to assure an identical phantom geometry as during 

irradiation. Since the elemental composition of cork is not 

known, the relative electron density of cork in the anthropomorphic 

phantom was set to 0.25. To trace inaccuracies in 

the reconstruction algorithm, which are specific for a particular 

treatment beam e.g., due to the application of wedges, 

the dose distributions of all beams were determined separately, 

both experimentally and with the TPS. 

E. Film dosimetry 

Sensitometric curves of the radiographic films KODAK 

X-OMAT V were obtained by irradiating seven films with 

varying exposures, ranging between 0–120 monitor units 

MUs, using a field size of 1010 cm 2 . These calibration 

films were placed at 10 cm depth in a phantom consisting of 

ten polystyrene slabs with a total thickness of 20 cm. The 

absolute dose at the position of these films was measured 

using a calibrated Farmer-type ionization chamber. Each 

measurement was repeated at least once to check the reproducibility 

of the calibration experiments, and for each box 

of radiographic films a new sensitometric curve was 

measured. All radiographic films were processed using a 

Kodak X-Omat ME-3 film processor and digitized using 

a Konica KFDR-S film reader. After fitting the individual 

sensitometric curves using a third-order polynomial, the 

pixel readings of the radiographic films were converted into 

dose values. 

The total number of MUs used for irradiating the anthropomorphic 

phantoms was adapted to exploit the dynamic 

range of the radiographic films as much as possible, while 

avoiding saturation effects. The experiments were repeated 

several times to assess the reproducibility, and to eliminate 

possible differences in the handling of the films i.e., positioning, 

irradiating, developing and digitizing the films 

and/or differences between various film batches. In total, 192 

films were irradiated at the seven film positions. The reproducibility 

was calculated for each film position and treatment 

beam by first determining the average film dose and standard 

deviation of individual pixels and subsequently determining 

the average of the standard deviations over all pixels. If the 

average deviation between the dose distribution of a specific 

film and the mean dose distribution at that film position was 

larger than 3 times the standard deviation, that particular film 

measurement was considered to be an outlier and excluded 

from further analysis ten films in total. The film dose distributions 

were normalized, applying a single normalization 

factor for all measured film dose distributions. To calculate 

this normalization factor, the ratio of the dose distributions 

obtained with film dosimetry and with Pinnacle was determined 

for all pixels and averaged for each film position. 

Subsequently, these averages obtained for all film positions 

were averaged for both phantoms, applying a weighing factor 

for the number of pixels at each film position. In this way, 

trends due to systematic errors originating from film dosimetry 

and/or the dose calculation algorithm may be identified 

see the Appendix. 

F. Comparison of dose distributions 

The exact orientation of the films in a particular plane of 

the anthropomorphic phantoms is different in each measurement. 

In addition, the experimental and reconstructed dose 

distributions correspond to different planes and volumes. 

Therefore, the various dose distributions were geometrically 

matched, averaged and compared using 3-D matching software 

developed in our institution. 29 All matching was performed 

manually and the quality of the match was judged by 

eye. Alignment of the films with respect to each other and 

with respect to the CT data could be achieved straightforwardly, 

because the external contour of the anthropomorphic 

phantoms could easily be distinguished on individual films 

and the film positions were clearly visible in the CT data. 

The error resulting from misaligning film and CT data is 

estimated to be 2 mm at maximum for the irradiated part of 

the radiographic films. 

The EPID and film dose distributions correspond to different 

planes, and can only be compared directly at the intersection 

of these planes. Therefore, we have first validated the 

calculations of the absolute and relative 3-D dose distribution 

with the results of ionization chamber and film dosimetry, 

respectively. The 3-D dose calculations were then used as 

reference values for evaluating the results of 2-D EPID dose 

determinations. In addition, the feasibility of 3-D portal dosimetry 

was tested, by comparing the reconstructed dose distributions 

in several planes with 3-D dose calculations obtained 

with Pinnacle. For comparing the reconstructed dose 

distributions with calculated 3-D dose distributions, the geometrical 

information of the planned setup of the treatment 

beams was used and the experimental error in aligning the 

phantoms was ignored. 

For the quantitative analysis of the results, the lung region 

and the region with distances less than 2 cm from the skin 

were excluded. 

III. RESULTS 

The planned and experimental total dose distributions resulting 

from all treatment beams Fig. 2 display dose gradients, 

which are commonly observed for the standard treatment 

technique for breast cancer patients. In the AP 



FIG. 2. Dose distributions obtained with film bottom 

and calculated with the TPS top at the sagittal film 

positions A1–A3 in phantom A, and the transversal film 

positions B1–B4 in phantom B. The color scale indicates 

deviations from the dose at the isocenter. 

direction, a more or less homogeneous dose distribution was 

obtained by the application of a wedge to compensate for the 

variation of the breast contour. At the cranial and caudal 

parts of the breast and at the proximity of the lungs, however, 

regions with dose differences up to 10% relative to the prescribed 

dose were observed. 

A. Validation of TPS calculations with ionization 

chamber and film dosimetry 

The calculated dose and the dose measured at the isocenter 

of phantom B using an ionization chamber were equal 

to 150.0 cGy and 150.60.3 cGy 1 SD, respectively. The 

difference between these values was less than the tolerated 

output fluctuation of the treatment machine. The difference 

in isocenter position of the two phantoms resulted in a lower 

calculated dose for phantom A of 140.1 cGy at the isocenter. 

The dose distributions calculated with the TPS corresponded 

very well with the normalized total film dose distributions 

for both phantoms Fig. 2. The difference between the calculated 

and measured film dose, averaged over all pixels, 

was 0.5%1.3% 1 SD and 0.2%2.1% 1 SD for phantoms 

A and B, respectively. In the Appendix it is shown that 

these deviations are consistent with the observed reproducibility 

of the film measurements. 

B. Accuracy of 2-D dose reconstruction 

If the attenuation correction was applied, the deviation 

between the reconstructed and planned total dose distributions 

resulting from all treatment beams is 0.3%1.6% 1 

SD and 0.3%1.8% 1 SD for phantoms A and B, re- 

TABLE I. Average deviation between the dose reconstructed at the isocenter 

plane from EPID measurements either with or without attenuation 

correction, and the dose calculated with the TPS. Results for the individual 

beams MO: medial open, MW: medial wedged, LO: lateral open, LW: 

lateral wedged as well as for multiple beams are shown. All values have 

been obtained by averaging the observed deviations over all pixels within 

the region of interest. The values in brackets represent the corresponding 

variations 1 SD. 

Phantom A 

Phantom B 

 

MO 3.6%2.0% 5.6%8.8% 0.2%1.5% 2.3%5.8% 

MW 2.3%1.7% 0.7%7.5% 3.6%1.6% 1.3%5.3% 

LO 0.9%2.0% 3.8%7.6% 1.2%3.0% 0.4%4.6% 

LW 2.8%2.1% 1.7%7.0% 2.3%2.5% 1.7%3.9% 

Sum open 2.2%1.7% 4.3%2.7% 0.3%1.8% 1.3%1.8% 

Sum wedge 2.5%1.5% 0.9%1.9% 3.0%1.7% 1.6%1.7% 

Total dose 0.3%1.6% 2.9%2.3% 0.3%1.8% 1.6%1.8% 



FIG. 3. Frequency distribution of the deviations between the reconstructed EPID isocenter plane dose relative to the dose calculated with the TPS: a total 

dose reconstructed with — and without --- the attenuation correction for phantom A; b the same as a but for phantom B; c dose reconstructed without 

the attenuation correction for the medial open beam —, the medial wedged beam ---, the lateral open beam –––, and the lateral wedged beam –-– for 

phantom A; d the same as c but dose reconstructed with the attenuation correction; e dose resulting from the two open beams — and the two wedged 

beams –––, reconstructed without the attenuation correction for phantom A; f the same as e but dose reconstructed with the attenuation correction. 



attenuation correction, while the error distributions were almost 

unchanged Table I, Figs. 3a, 3b, 3e, 3f. Ifthe 

attenuation correction was not applied for dose reconstruction 

of the individual beams, the average deviation for these 

beams ranged from 0% to 6%, with standard deviations up 

to 10% Table I, Fig. 3c. 

Several trends can be observed if the results obtained for 

the individual beams are inspected in Table I. The error in 

the dose reconstructed from the portal images was systematically 

higher more positive for phantom A than for phantom 

B, which had less lung tissue within the irradiated volume. 

Furthermore, a comparison of the results for open and 

wedged beams shows that dose reconstruction for beams 

with wedges probably results in too low dose values Figs. 

3e, 3f. However, the largest improvement in the accuracy 

of dose reconstruction was obtained if the attenuation correction 

was applied or if only the contribution of opposing 

beams was considered. This effect was considerably larger 

than the influence of inhomogeneities or wedges on the results 

for this treatment technique. 

FIG. 4. Error map of the reconstructed total dose distribution resulting from 

all treatment beams for phantom A. The black, hatched, gray, and white 

areas represent error levels of 0%–1%, 1%–2%, 2%–5%, and 5%, respectively. 

See also Fig. 5e. 

spectively Table I, Figs. 3a, 3b. At the isocenter, the 

deviation between the reconstructed and planned total dose 

was smaller than 1% for both phantoms. The spatial distribution 

of these deviations, as plotted in Fig. 4 for phantom 

A, shows that the difference was less than 2% at the major 

part of the isocenter plane. At the cranial and caudal side of 

the isocenter plane, the deviations were larger up to 2.5% 

as well as in a small region toward the outer contour up to 

1.5%. Only at the position of the lung and skin, the regions 

that have been excluded from quantitative analysis, 

this deviation increased up to 10%. The spatial distribution 

of deviations in phantom B displayed the same trend. The 

deviation between the reconstructed and planned total dose 

averaged over all pixels of the isocenter plane of both phantoms 

was 0.1%1.7% 1 SD. 

For the individual beams, the average deviation between 

the reconstructed and planned dose ranged from 3.6% 

to 3.6% with standard deviations of about 2% Table I, 

Fig. 3d. If the combined dose of opposing beams 

was considered, the deviations are slightly smaller Table I, 

Fig. 3f. 

If the attenuation correction was not applied, the accuracy 

of the dose reconstruction remained acceptable if the dose 

distributions of nearly opposing beam segments were combined. 

If the dose resulting from the sum of all individual 

beams, from the sum of the open, or from the sum of the 

wedged beams was reconstructed, the average deviations decreased 

by approximately 2% upon the application of the 

C. Accuracy of 3-D dose reconstruction 

In planes oriented parallel to the isocenter plane, the deviations 

between the reconstructed and planned dose were of 

the same order of magnitude, as observed for the isocenter 

plane Fig. 5. Also in these planes, the deviation between 

the planned and reconstructed dose was most pronounced in 

regions that are closest to the skin. In particular, in planes 

located 8 cm from the isocenter, the deviations were significantly 

larger. The average deviation over all reconstruction 

planes within the irradiated volume, excluding the lung 

region and the region less than 2 cm from the skin, was 

1.4%5.4% 1 SD. For planes within 5 cm of the isocenter 

plane, the deviation was 0.53.4% 1 SD. 

D. Accuracy of the dose–volume histogram 

Our algorithm provides both the 2-D dose reconstruction 

at the isocenter plane, and a 3-D dose reconstruction of the 

irradiated volume. It seemed therefore worthwhile to compare 

reconstructed 2-D dose distributions, given as dose– 

area histograms DAHs, with planned dose–volume histograms 

DVHs. It can be seen Figs. 6a–6c that the 

accuracy of assessing the uniformity of the delivered dose 

was limited if 2-D dosimetry was performed, especially if no 

attenuation correction was applied. In that case, the dose in 

the irradiated volume was overestimated by using the corresponding 

DAH, compared to the cumulative dose–volume 

histogram of the 3-D dose distribution obtained with the TPS 

Fig. 6a. Figure 6b shows that some improvement was 

obtained by including contour information during 2-D dose 

reconstruction. However, even if the TPS is used, assessing 

the uniformity of the delivered dose in the irradiated volume 

by applying the DAH from a 2-D dose distribution instead of 

the complete DVH is obviously limited Fig. 6c. Only if 



FIG. 5. Deviations between the reconstructed dose EPID and the calculated dose Pinnacle in various planes that are oriented parallel to the isocenter plane 

for phantom A. a, b,...,h, i correspond to planes oriented at 8 cm, 6 cm,...,6 cm,8 cm medially from the isocenter plane. The color scale indicates 

the magnitude of the observed deviations. 

the true DVH was calculated from the nine reconstructed 

dose distributions presented above, a high accuracy could be 

obtained Fig. 6d. 

IV. DISCUSSION 

A. Comparison of 3-D dose calculations and film 

dosimetry 

A large number of contradicting results have been reported 

concerning the response of radiographic film obtained 

under various experimental conditions. 28,30–40 Because the 

problems involved in applying film dosimetry for absolute 

dose determinations are beyond the scope of our present 

study, we decided to limit ourselves to relative film dosimetry. 

Under the application of an overall normalization factor, 

the observed deviations between the dose distributions obtained 

with film dosimetry and with the TPS did not show a 

trend with the orientation or depth of the radiographic films. 

Consequently, the effects of film orientation and/or the presence 

of air gaps as observed by Suchowerska et al. 40 have 

not introduced systematic errors in this study. However, the 

uncertainty in the positioning of the phantoms in combination 

with the steep change in film response with the angle of 

incidence of the photon beam at nearly parallel irradiation as 

observed by Suchowerska et al., 40 may have caused the 

somewhat reduced reproducibility of the results for phantom 

B. Because the 95% confidence interval of the measured film 

dose as calculated from the observed reproducibility see the 

Appendix, is larger than the magnitude of the observed deviations 

between the measured and planned dose distributions, 

we may conclude that the deviations between the film 

and planned dose mainly originate from film dosimetry. In 

addition, we found that the deviations between ionization 

chamber measurements and calculations performed with the 

TPS are smaller than the output fluctuations of the accelerator. 

Therefore, we estimate that the error in the 3-D dose 

calculations obtained with the TPS are less than 1% 1 SD 

over the volume of interest and that it is justified to use the 

3-D calculations obtained with the TPS as a reference for our 

EPID dosimetry work. 



FIG. 6. The comparison of various dose–volume histograms of the irradiated volume. The solid lines in a–d represent the DVH calculated with the TPS. 

The dotted lines are DVHs approximated by a a dose–area histogram of the dose reconstructed in the radiological midplane, b a dose–area histogram of 

the dose reconstructed in the isocenter plane, c a dose-area histogram of the dose in the isocenter plane calculated with the TPS, and d a DVH calculated 

from the 3-D dose reconstruction. 

B. Accuracy of 2-D dose reconstruction at the 

midplane 

One might argue that the dose reconstruction at the isocenter 

plane or radiological midplane i.e., with or without 

using contour information yields an equally valid representation 

of the patient dose and that the exact location of the 

reconstruction plane is not of clinical importance. However, 

the comparison of the reconstructed and planned dose can 

only be carried out if contour information is included and the 

two dose distributions correspond to the same plane. If the 

attenuation correction is applied, the average deviation between 

the reconstructed and planned total dose at the isocenter 

plane averaged over both phantoms is 0.1%1.7% 

1 SD. For the actual treatment of breast cancer patients, the 

amount of lung within the treatment beam, the external contour 

of each patient and the wedge angles will vary from 

patient to patient. To estimate the corresponding change in 

accuracy, the results for the individual beams as given in 

Table I can be analyzed. First, the average deviations 

observed for phantom A are approximately 3% higher more 

positive than those obtained for phantom B. In phantom 

B, the isocenter is located more to the apex of the breast, 

resulting in a negligible amount of lung tissue within 

the irradiated volume for phantom A. Therefore, the different 

results for phantoms A and B show that the contribution 

of scattered radiation to the dose in the target volume 

is overestimated by the reconstruction algorithm if lung 

tissue is present. Second, the deviations for the wedged 

beams are approximately 3% lower than those obtained 

for the open beams. Because the calibration constants and 



fit parameters for the dose reconstruction algorithm have 

been determined for open beams only, this effect is most 

likely related to beam hardening due to the application 

of wedges. Finally, the average deviations are approximately 

3% lower if the attenuation correction is applied, showing 

the influence of the asymmetric external contour. These different 

effects cannot simply be combined, but the results 

obtained for a reconstruction of the total dose show that the 

overall effect is small if the attenuation correction is applied. 

Therefore, the same accuracy for 2-D dose reconstruction 

may be expected during the treatment of patients as observed 

in this study. If contour information is not available, the accuracy 

of dose reconstruction is only sufficient for nearly 

opposing beams. One should note, however, that larger errors 

may be expected if contours of the breast obtained during 

treatment planning are used, rather than contours obtained 

during treatment. The effect of anatomical changes during a 

complete series of treatment fractions on the dose estimation 

is under study. 

C. Accuracy of 3-D dose reconstruction 

The reconstruction of the dose in planes parallel to the 

isocenter plane yields surprisingly small deviations from the 

planned dose values, considering the fact that the same scatter 

kernel has been used to convolve the primary photon 

beam in each plane. Although the skin region itself has not 

been included in the analysis, the accuracy of dose reconstruction 

for breast patients with the algorithms presented in 

this work is mainly determined by the deviations occurring 

toward the skin. This is true, in particular, for 3-D dose reconstruction, 

since the region near the skin, which is included 

in the analysis, is relatively large. The experimental 

dataset, which is used to determine the parameters of the 

reconstruction algorithm, was obtained for phantoms with a 

thickness larger than 5 cm. Therefore, the PDD curve has 

most likely not been modeled properly for depths around the 

dose maximum. To improve the accuracy of dose reconstruction 

for these depths, a more dedicated fit parameter dataset 

is required. The applied model of the dependence of the reconstructed 

dose on phantom thickness i.e., the NSPR in 

the currently used algorithms is sufficiently flexible to manage 

an extended experimental dataset. An improved accuracy 

of the dose reconstruction at depths around the depth of dose 

maximum is part of our future work. 

Within a distance of 5 cm from the isocenter plane, the 

average deviation between the reconstructed and planned 

dose is 0.5%3.4% 1 SD. For a number of treatments 

other than the one considered in this study, the planning target 

volume lies within this volume. Also, the variation of the 

external contour is often much smaller and the target volume 

located farther away from the skin. Therefore, it is reasonable 

to expect that if contour variation or inhomogeneities 

are not important, the 3-D dose reconstruction will be more 

accurate than observed here. Still, a higher accuracy may be 

needed for future applications, e.g., for a 3-D dose verification 

of whole breast treatments. In those cases, appropriate 

scaling of the scatter kernels has to be applied. To obtain an 

extended dataset for scaling the scatter kernels, only a limited 

number of additional ionization chamber measurements 

in polystyrene slab phantoms would be involved for standard 

treatment configurations. 

Although the DVHs presented in this study are calculated 

using a relatively simple algorithm that may be further refined, 

a reasonably accurate estimate of the dose homogeneity 

in the irradiated volume is obtained if a 3-D dose reconstruction 

is applied Fig. 6d. 

D. Patient scatter to the image 

An assumption in the original dose reconstruction algorithm, 

which may not be completely justified for EPID dosimetry 

during breast cancer treatment, concerns the scatter 

from the patient reaching the EPID. It has been shown that 

this scatter contribution is small and homogeneously distributed 

if the distance between the patient and portal imager is 

large e.g., during prostate treatments. 5 In those cases, the 

contribution of patient scatter to the portal dose can be approximated 

using a simple proportionality between this scatter 

contribution and the uncorrected transmission of the irradiated 

volume. For the treatment of breast cancer patients, 

however, the distance between patient and portal imager has 

to be reduced to enable imaging of the large treatment fields. 

This reduced air gap may lead to a larger and nonuniform 

scatter contribution from the patient to the EPID and may 

deteriorate the accuracy of the dose reconstruction algorithm. 

Several investigators have studied this phenomenon and have 

proposed alternative methods to calculate the scatter contribution 

of the patient to the portal imager. 41–45 

In our approach, the scatter distribution at the position of 

the EPID is assumed to be uniform. Furthermore, for the 

phantom measurements we found that the scatter to primary 

ratio SPR is only 2.5%, which is in line with former values 

for this beam energy and field size. 41 Thus, the patient scatter 

correction effectively contributes 2.5% to the total dose at 

the isocenter plane if we ignore its influence on the NSPR at 

that plane. The latter approximation is valid because it is a 

second-order effect only. The error in the reconstructed 2-D 

dose reconstruction would therefore increase by 0.25%, at 

most, if the error in the calculation of the patient scatter 

would be as high as 10%. Given the applied beam qualities, 

the thickness of the irradiated volumes, and the size of the 

largest field sizes that may be applied clinically for breast 

cancer treatment, we estimate that the SPR at the position of 

the EPID will always be less than 10%. 41 Even if that would 

be the case and maintaining the previously assumed error 

level of 10%, the error in the reconstructed 2-D dose would 

only be 1% higher compared to the application of an exact 

calculation of the patient to EPID scatter contribution. Therefore, 

we conclude that the simple algorithm to estimate the 

patient scatter to the imager, as applied in our approach, 

suffices in practical applications. As an additional test, we 

implemented an extended algorithm, which improved the accuracy 

of the calculation of the scatter contribution by several 

percent for large field sizes. This extended algorithm 

includes an iterative loop similar to the routine described by 



Hansen et al., 41 although measured beam data were used as 

input in our approach. The results of dose reconstruction 

changed less than 0.5% for the experiments presented in this 

work, and the extended algorithm was not applied in the 

analysis. 

E. Comparison with other 3-D dose reconstruction 

methods 

Several authors have presented methods for a 3-D reconstruction 

of the patient dose using CT data, which are representative 

for the patient anatomy during treatment. In the 

concept originally presented by McNutt et al., 2,3 an iterative 

convolution/superposition method was used to determine the 

primary energy fluence and subsequently the patient dose 

applying predefined scatter kernels. Partridge et al. 10 also apply 

an iterative method to determine the primary energy fluence, 

but propose either the application of the original TPS 

or an independent algorithm e.g., Monte Carlo planning calculation 

to reconstruct the patient dose. Both methods require 

a more sophisticated algorithm to determine the primary 

fluence and patient dose, and/or a low-level access to 

the TPS, and rely on the validity of the CT data. On-line CT 

data are currently not available in many institutions, however, 

and will most likely only be available in a limited number 

of treatment centers and obtained for a limited number 

of patients in the near future. The relatively simple method 

we present in this study is therefore especially useful when 

CT data, whether on-line or not, are not available. 

F. Clinical factors influencing the accuracy of dose 

reconstruction 

During actual patient treatments, positioning errors may 

influence the accuracy of the dose reconstruction. When appropriate 

3-D setup verification and correction procedures 

are applied, patient-positioning errors can generally be minimized 

to a few mm, 46 in which case the accuracy of dose 

reconstruction will be within the previously specified range. 

Setup verification and correction of patient positioning is 

generally not performed for the treatment of breast cancer 

patients with the tangential field technique, however. Although 

the reconstructed patient dose will still represent the 

dose actually delivered to the irradiated volume if patient 

positioning errors occur, a determination of the coverage of 

the target volume and of the dose to organs at risk requires 

an independent analysis. 

If contour information is used to reconstruct the dose, 

patient positioning errors along the axis of the treatment 

beam will yield an opposite effect for the medial and lateral 

beams and will cancel out in the total dose per fraction. 

Patient positioning errors, perpendicular to the beam axis, 

can first be corrected by matching the portal images to the 

available reference images simulator images or DRRs. 

Next, contours can be shifted accordingly prior to dose reconstruction. 

Although the accuracy of a 2-D correction on 

the 3-D setup error will be limited, we estimate that the 

influence of the remaining setup error on the accuracy of the 

dose reconstruction is negligible because it will be a secondorder 

effect only the attenuation correction is the first-order 

effect on the accuracy of dose reconstruction. 

Because the heart was not simulated in these phantoms, 

the accuracy of reconstructing the heart dose during breast 

cancer treatment could not be assessed. Considering the position 

of the heart within the lung region, the radiological 

midplane will be located more closely to the central plane of 

the heart than the isocenter plane. Therefore, it may be expected 

that reconstruction of the heart dose in the radiological 

midplane when contour information is not used will 

yield a more accurate representation of the heart dose than 

the dose in the isocenter plane. The use of the EPID for the 

verification of heart dose during patient treatment is the topic 

of further study. 

During the initial phase of this study, we observed that the 

EPID response varied considerably with time. By applying a 

thorough QA procedure, including regular recalibration of 

the EPID, the high accuracy of dose reconstruction as reported 

in this paper could be obtained. The study of the 

long-term stability of the EPID will be dealt with in a separate 

paper. 

V. CONCLUSIONS 

We have extended a previously developed algorithm to 

reconstruct the patient dose in the isocenter plane, specifically 

for the treatment of breast cancer patients. A simple 

attenuation correction is used based on the external contour 

of the patient. In addition to a more accurate 2-D dose reconstruction 

in the isocenter plane, we have shown that now 

also a reasonably accurate 3-D dose reconstruction is possible 

in planes within 5 cm from the isocenter plane using the 

extended dose reconstruction algorithm. The largest errors 

result from limitations of our algorithm in the presence of 

inhomogeneities lungs and at depths around the dose maximum 

skin. Furthermore, we have shown that 3-D dose reconstruction 

yields accurate values of the DVH of the irradiated 

volume, thus allowing the in vivo verification of the 

dose delivery to the irradiated volume. The uncertainty in the 

contribution of patient scatter to the imager has only a limited 

effect on the accuracy of dose reconstruction, and a 

crude estimate of this quantity is sufficient for most applications. 

ACKNOWLEDGMENT 

This work was financially supported by the Dutch Cancer 

Society Grant No. NKI 2000-2255. 

APPENDIX: ACCURACY OF TPS CALCULATIONS 

The contribution of random noise in the film dose determinations 

to the observed differences between the planned 

and film dose distributions was estimated from the observed 

reproducibility of film dose measurements. Because the 

variations in film dose were approximately normally distributed 

at all film positions data not shown, these variations 

were treated as random noise. For each film position, the 

total dose was calculated by averaging and adding the dose 

distributions of the individual beams. The final noise level 



TABLE II. The contribution of noise from film dosimetry to the observed 

deviations column 7 between the film and the planned dose distributions. 

The contribution of the individual beam segments to the noise level of 

the measured total film dose Mmedial, Llateral, Wwedge, Oopen is 

given as the average standard error of mean, SEM, for specific film positions 

columns 2–5. The estimated noise level SEM tot of the total dose distribution 

after averaging and summing the individual film dose measurements is 

given in column 6. Values in brackets represent the corresponding variations 

1 SD. Percentages marked with † have been obtained by excluding a single 

film outlier. 

Position SEM MW SEM MO SEM LW SEM LO SEM tot film,calc 

A1 0.5% † 0.6% 0.4% 0.8% 1.2% 0.2% 1.0% 

A2 0.4% 0.7% 0.7% 0.8% † 1.4% 0.2% 1.4% 

A3 0.5% 0.8% 1.0% 0.5% † 1.4% 1.3% 1.3% 

B1 1.1% 0.8% 1.0% 0.6% † 1.8% 0.6% 0.8% 

B2 1.0% † 2.1% 0.7% 0.9% † 2.6% 2.2% 1.2% 

B3 1.1% 0.9% † 1.0% 0.8% 1.9% 0.3% 1.0% 

B4 0.8% 0.9% † 0.9% † 1.5% † 2.2% 1.8% 0.6% 

for the total film dose distribution at a particular film position 

was calculated accordingly. First, the standard error of the 

mean, SEM ij , was calculated at each pixel position. These 

numbers were subsequently averaged for each film position P 

and for each treatment beam B to determine their contribution 

to the overall noise level of film dosimetry, SEM BP 

Table II: 

SEM BP SEM ij 

ij ij /N BP 

, A1 

n ij n ij 

in which ij , n ij , and N BP represent the standard deviation 

and the number of pixels at a specific film position, and the 

number of film measurements, respectively. The noise level 

of the total film dose was then calculated for each film position 

by quadratically summing the SEM of the individual 

beams: 

SEM P 

B 

SEM BP 2 . A2 

For phantom A, the overall noise level was 1.3% SEM. 

Three films out of 72 were marked as outlier and excluded 

from further analysis. For phantom B, an overall noise level 

of 2.1% SEM was obtained, while 7 films out of 120 were 

marked as an outlier. At each film position, the observed 

deviations between the planned and measured dose lie within 

the 95% confidence interval 1.96SEM of the total film 

dose Table II. Furthermore, the deviations in Table II as 

well as the deviations plotted in Figs. 2–3, do not show a 

systematic trend. Therefore, possible errors in the dose calculated 

with the TPS can be neglected. 

a Author to whom correspondence should be addressed: B. J. Mijnheer, The 

Netherlands, Cancer Institute/Antoni van Leeuwenhoek Hospital, Department 

of Radiotherapy, Plesmanlaan 121, 1066 CX Amsterdam, The Netherlands. 

Telephone: 3120-5122203; fax: 3120-6691101; electronic 

mail: bmijnh@nki.nl 

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