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British Journal of Radiology (2004) 77, 414-419
© 2004 British Institute of Radiology
doi: 10.1259/bjr/51786246
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Full Paper

Comparison of a lung fitting algorithm with CT data for tangential fields in radiotherapy of the breast

R J Wilks, BSc, PhD 1 P J Childs, BSc, MSc 2 and E M Donovan, BSc, MSc 2

1 Medical Physics Department, Torbay Hospital, Newton Road, Torquay, Devon TQ2 7AA and 2 Medical Physics Department, Royal Marsden NHS Trust, Downs Road, Sutton, Surrey SM2 5PT, UK

Correspondence: Dr R Wilks, Burraton Bungalow, Broadclyst, Exeter, Devon EX5 3DB, UK


   Abstract
Top
 Abstract
Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
A method of estimating the shape and position of the lung in tangential breast fields is presented for patients who have not been CT scanned. Using the Osiris system, the external contour is obtained optically, and an estimated lung structure superimposed on the transverse outlines based on the measured lung depth in the tangential fields and an analysis of the typical lung shapes obtained from CT images. The accuracy of this fit was determined by comparison with a set of 64 CT images imported into the Osiris system. Dose distributions were calculated by two treatment planning systems: ADAC Pinnacle and GE Target2. The computed dose distributions for 6 MV photons were compared against measured doses in a specialized breast phantom. For the worst case of lung fit compared with CT, the dosimetric error (based upon ADAC Pinnacle calculations) was 2.0% in the shadow of the lung. For the complete patient data set, the relative dose errors to these points were reduced from a mean value of 8.4% and standard deviation (SD)=1.8% (no lung correction) to a mean of 0.2% and SD=1.0% (lung correction using fitted lung). It was also found that for every 1 cm of lung path length the dose to the breast along that path length increased by approximately 1%. The results of these investigations indicated that the lung fit model was satisfactory for routine clinical use, so that good dosimetric results can be obtained using lung correction without the need for CT imaging.


   Introduction
Top
 Abstract
 Introduction
Materials and methods
 Results
 Discussion
 Conclusions
 References
 
When calculating the dose distribution within the breast for tangential radiotherapy fields, the presence of lung increases the radiation dose to the breast on either side of the lung due to increased transmission of radiation through the lung. For example, a dose calculation with no lung correction for a typical patient with 20 mm of lung protruding into the tangential fields will result in an underestimate of the maximum dose in the region of the medial–lateral edge by about 10%. This figure is of the same order as the maximum recommended variation of dose (–5% to +7%) planned throughout the breast volume [1, 2], and so the presence of lung is an important contribution to the dose variation obtained in practice.

If no direct correction is made for the presence of the lung, some allowance for the increased dose may be made by adjusting the field weightings and wedge angles in order to bias the dose distribution towards the breast apex. Preferably, however, an inhomogeneity correction to the plan is employed to give the actual dose distribution. A knowledge of the size, shape and density of the lung is required in order to perform the lung correction accurately, and this is usually performed using CT data, either from a CT scanner or a simulator-CT system.

The use of a CT scanner for the imaging of breast patients presents difficulties, however, because of the problem of maintaining the same treatment position within the limited CT aperture. The abducted arm (if used), and the effect of the slope of the inclined breast board both tend to move the patient towards or beyond the confines of the CT aperture, so that compromises on patient position may be required in practice [3–6]. Also many centres have limited access to a general-purpose CT scanner, for the large number of breast patients presenting for treatment. A simulator-CT is able to accommodate the treatment position satisfactorily, although the time to acquire the data is a consideration, e.g. delays due to the cooling of the X-ray tube.

The Osiris system (Qados Ltd, Sandhurst, UK) [7, 8] attempts to circumvent the use of a CT image entirely, by measuring the patient contours optically (either on a simulator or the treatment unit itself), and fitting the lung shape mathematically with the assistance of a portal image obtained using one of the tangential fields. The process is relatively quick and is easily repeatable on either the simulator or the treatment unit.

In our two centres (Torbay and Royal Marsden), the complete process of radiotherapy breast planning is normally carried out with the Osiris system. This includes the measurement of patient contours, geometrical field placement calculation, isodose production and monitor unit (MU) calculation. An inherent part of this is the estimation of lung position from the mathematical fitting algorithm.

The purpose of this paper is to report on the comparison of the fit of the calculated lung shapes with those measured for the same patients on a CT scanner, together with the estimated and measured dosimetric consequences of the geometrical differences found. Data from the independent trials of each centre were combined for this study.


   Materials and methods
Top
 Abstract
 Introduction
 Materials and methods
Results
 Discussion
 Conclusions
 References
 
Outlining of external contours and lung fitting
A set of outlines and skin mark positions are first acquired using the outlining functions of the Osiris optical system. The system is then used to calculate the geometrical setup to be used for the treatment of the tangential fields, i.e. treatment focus-to-skin distance (FSD), to a reference mark, lateral shift and gantry angles for the selected field width. With the patient in the treatment position, a portal image (electronic device or film radiograph) is taken to establish the maximum amount of lung depth which protrudes into the tangential fields at each longitudinal outline position. The portal image may be produced, for example, using the medial field either with a simulator or with the treatment unit, and the value which results is just the extent of the lung in the tangential fields, and not the path length of the radiation through the lungs. The purpose of the lung fit algorithm described below is to make an estimate of the shape and size of the lung from a knowledge of the lung depth in the tangential fields, and how this depth is related to typical path lengths through the lung.

An initial lung model, which had been in use on the system for a number of years, was to fit the lung with an ellipse. From observation of a large number of CT scans, it was clear that this was a reasonable approach, provided the external shape of the patient was also used to determine the shape of the ellipse. Moreover, it was only necessary to provide a fit in the area within the tangential fields. However, as a result of the collaboration between our two centres, the results obtained when analysing the joint data were used to modify the methodology of the lung fitting. This somewhat simpler model required the fitting of an arc of a circle to the anterior portion of the lung.

Figure 1Go shows the position of the circle relative to the medial–lateral back edge (MN) of the tangential fields. When a portal image is taken, the position and angle of the back edge is known. The image is used to establish the amount of lung, p, in the field by means of a line which is a tangent to the shape of the lung, i.e. it touches the edge of the lung without intersecting with it (line FG in Figure 1Go). The beam divergence of line FG relative to MN is small and is ignored. For the fitted lung shape, the radius, a, of the circle was calculated directly from the measured value of p and the value of lung path length, L, by the relationship: a=p/2+L2/8p. The value of L was determined from a linear fit to the CT data, as described below (Figure 2Go). In practice, the values of the lung, p, for each longitudinal position of transverse outline may be read automatically from a digitized portal image, to reduce the operator workload when multiple transverse surface contours are taken.



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  		Figure 1. Illustration of circular lung fit criteria: tangent (FG) from portal image defines p, which generates lung path length, L. Arc centred at O varies in position along MN. Tissue thickness, t, is constrained not to be less than a pre-determined minimum over the whole of the arc anterior to MN. An example of tissue thickness, t, is shown for the horizontal extension used for joining the lung shape to the centre of the patient.

 


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  		Figure 2. Lung path, L, along medial–lateral line plotted against lung in tangential fields, p, as measured from CT images. Linear relationship: L=41+2.75p is used for lung fitting purposes. Points are contained within indicated lines 20 mm above and below the central line.

 
In addition to calculating the size of the fitted lung, a method of estimating its position along the back edge MN was required. A necessary constraint was that the lung must not get closer to the surface than a pre-defined minimum distance. This may occur occasionally if there is a relatively large amount of lung and not much tissue thickness (e.g. chest wall treatments). In practice, the position of the fitted lung along MN was modelled by a simple analytic expression determined from evaluation of the CT data, as explained below.

After the size and position of the fitted lung was calculated, a mathematical check was made on the minimum distance between the fitted lung and the surface contour. This was calculated automatically for each patient and when the lung was closer to the surface than the pre-defined minimum distance, the radius of the circle was decremented in 1 mm steps until the minimum distance was satisfactory or until the total radial decrement had reached 20 mm.

The tissue thickness, t, was given a nominal minimum value of 15 mm which was chosen from observation of the CT images. If there was a small amount of lung in the fields (i.e. a small value of p) the calculated value of t was greater than the nominal minimum value. As the value of p increases, so t decreases, and is normally limited to 15 mm. However, some "chest wall" patients have a large amount of lung and a thin chest wall. A slightly improved fit in the medial region was obtained for these patients by decreasing the value of t to a minimum of 10 mm. This calculation was performed automatically from the comparison of the surface contour and the fitted lung shape.

Verification of lung fitting
Entry of patient geometry
At one centre (Royal Marsden), a series of 20 CT patients were entered into the Osiris system via tracing of suitable hardcopies (central slice only), with the depth of lung on the central axis being entered via the computer keyboard. A hardcopy was produced of the external contour and lung for comparison with the CT hardcopy. Three measurements were taken on the hardcopies of the CT and Osiris outlines: the depth of lung, the maximum width of lung intersecting the baseline of the tangential fields and the shift along the back edge of the centre of the Osiris-fitted lung shape with respect to the CT lung.

At the other centre involved in this study (Torbay), CT scans of chest patients were read into the Osiris system electronically and planned as if for breast tangential treatment. Several slices of each patient were used, leading to a total of 46 images for 17 patients.

Dosimetry
Two planning computers were used to assess the effect on the dosimetry of any inaccuracies of the lung fitting algorithm:

1. ADAC Pinnacle, Milpitas, CA, USA (Royal Marsden)

2. GE Target-2, Prism Microsystems Ltd, Bickington, UK (Torbay)

The CT outlines were planned and compared with those produced using the lung fitting method described above. For both planning computers, the breast tissue was assigned a bulk density of 1.0 and a lung tissue value of 0.3. The Pinnacle system used a collapsed cone algorithm, which corrects for the lack of lateral scatter at the anterior of the breast outline. The Target-2 computer planner makes no such correction, but the lack of scatter was partially compensated for by increasing the calculated monitor units by 2.0%, as determined experimentally. The lung corrections made were of the simple equivalent path length method [9].

For both sets of plans from each centre, representative points within the breast on either side of the lung were taken in order to assess the dosimetric effects of the presence of lung. These points were chosen to be at a distance of 7 mm from the medial–lateral line so as not to be within the penumbra of the tangential fields, and were mid-way between the patient surface and the lung contour. A nominal beam energy of 6 MV was used for all the planning calculations.


   Results
Top
 Abstract
 Introduction
 Materials and methods
 Results
Discussion
 Conclusions
 References
 
Geometry
The combined CT data from both centres was used to produce the graph shown in Figure 2Go, where the medial–lateral lung path length, L, was plotted against the lung depth, p. The range of values of p varied from 5 mm to 39 mm, so extending beyond the maximum limit of 20–25 mm of lung normally used for the tangential fields. A linear fit is feasible over this range, with an error of ±20 mm in path length containing almost all of the points. The linear fit was used in the lung fitting model to calculate the radius of an arc which would have the same values of p and L, as described above. The path length variation thus followed that shown in the graph, i.e. to within ±20 mm.

From analysis of the lung positions in the CT image data set, the fitted lung positions were modelled by the simple expression: v=0.4 x (MN+0.15) x (L–Lmin), where v was the distance of the centre of the lung along MN as measured from M, and Lmin was the extrapolated value of the fitted line of Figure 2Go on the vertical axis (nominally 40 mm). The maximum value of v calculated by this formula was limited to 0.5 x MN, so that the position of the centre of the lung was always between 40% (small lungs) and 50% (large lungs) of the length MN, as measured from the medial mark. The position of the centre of the fitted lung compared with that of the CT shape showed a mean difference of 0.2 mm away from the medial mark, and a standard deviation of 10.0 mm (52 data points).

A simplified beam model using differential calculus (not discussed here) was used to investigate the relationship between the path length error due to an inexact fit and its associated dosimetric error for a range of patient geometries. Figure 3Go summarizes the results found for a calculated dosimetric error of 2.0% in the breast either side of the lung for a given lung density of 0.30. Figure 3Go shows the error in lung path length, dL, which is required to produce a 2.0% error for a given lung path length, L, for a family of medial–lateral marks separations, s. The variation of dL with lung density is relatively insensitive (e.g. a lung density of 0.25 reduces the point for s=200 mm, L=100 mm from 23.8 mm to 22.3 mm, a slightly tighter restriction). Hence this analysis shows that, to a reasonable approximation, there is an increase in the dose to the breast either side of the lung of approximately 1% for each additional 1 cm of lung. This was confirmed by the results of measurements on the computer plans produced at each centre.



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  		Figure 3. Error, dL, in lung path length, L, required to produce an error of 2% in the dose to the breast either side of the lung. s is the separation (mm) of the medial and lateral marks, and {rho} is the density of lung relative to breast tissue.

 
The errors of ±20 mm in the lung path length produced with a linear fit with lung depth shown in Figure 2Go thus translate into an approximate ±2% error in breast dose from the data shown in Figure 3Go. The dose variation would be expected to reduce as a point moves away from the medial–lateral edge (i.e. beyond the penumbra, as for the chosen reference points), as the geometrical lung path length errors tend to become smaller.

Representative examples of the fit obtained in practice are given in Figures 4 and 5GoGo, where Figure 4Go shows a good fit, and Figure 5Go is the worst fit of lung shape obtained in the combined series of 64 CT slices. Figure 4Go uses CT image data directly, whereas the outlines have been traced in from hardcopies of CT scans for Figure 5Go, as explained in the section on Entry of patient geometry.



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  		Figure 4. Example of lung fit using arc of circle superimposed on original CT image. Only the fit above the medial–lateral line is relevant.

 


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  		Figure 5. Worst lung fit patient in dataset from both centres, caused by flattened lung shape. The fitted lung is shown as a dotted line. The dose either side of the lung is underestimated by about 2% using the fitted lung, and by about 8% if no lung correction is used. The medial–lateral line is given by ML.

 
Phantom study
Tissue-equivalent breast phantom
For this phantom [10], which has 20 mm of lung in the tangential fields, the calculated doses to the breast either side of the lung were compared with measured values. At Torbay, the calculated values were within 0.5% of those measured (using a 2% increase of MU to partially correct for lack of scatter). With no lung correction, the breast dose would have been underestimated by approximately 7.0%, as determined by applying no lung correction to the computer-generated plan. The corresponding measured doses at the Royal Marsden Hospital were within 0.6% of those predicted by the computer plan.

As a result of this check using a realistic breast and lung phantom, it was concluded that the dosimetric calculations on the combined sets of patient data would be sufficiently accurate for all patients when comparing the effects of lung correction, both for fitted and for CT-derived lung shapes.

Patient planning data
Each patient was planned using the standard breast planning technique of each centre: isocentric and with the back edges of the tangential fields aligned. The reference points described in the section on Dosimetry above were used to assess the dosimetric effects of the fitted lung shapes compared with the lung shapes defined by the CT images.

Figure 6Go shows a histogram of dose errors to the reference points both with and without lung correction. When no lung correction was made, the errors were all negative (planned doses were less than actual doses) and range from about –4%, for very little lung in the fields, to –12% when a large amount of lung was present. When lung correction was performed using the fitted lung, the errors were shown to be within about ±2%, as expected from Figure 2Go. The means and standard deviations of the two populations were –8.4% ±1.8% and –0.2%±1.0%, respectively. It is encouraging that the corrected histogram was relatively symmetrical around zero, indicating that there was no significant systematic error in the correction for the population as a whole.



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  		Figure 6. Histograms of dose errors to the breast either side of the lung (7 mm from back edge): no lung correction (black), Torbay data (mean=–8.4%, SD=1.8%, N=46); using fitted lung (white), combined data from both centres (mean=–0.2%, SD=1.0%, N=64). In both cases, the comparison is with lungs defined by CT data.

 

   Discussion
Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
Conclusions
 References
 
Various sources of error are inherent in the system, as follows:

a) The lung shape may deviate from an arc

CT scans have shown relatively small deviations for the majority of patients. An exception is shown in Figure 5Go, where the lung shape is flattened to produce a longer lung path length than that calculated by the model. However, even in this case, the understimate of breast dose of 2.0% may be compared with an underdosage of approximately 8% if no lung correction had been made.

b) The fitted lung may be at a different position along the medial–lateral edge

The dose to both the lung and the breast from summation of the two opposing tangential fields is not a sensitive function of the lung position—the path length through the lung is of more relevance.

c) Patient rotation between outlining and taking the check film may over- or under-estimate the amount of lung in the tangential fields

Comparisons of the portal images for lung distances, p, and air gaps outside the breast may be made with the original outlines to correct for this source of error. For example, a significantly larger air gap than expected from the surface contour implies the possibility of patient movement in a direction which would underestimate the amount of lung. A simple correction using the measured and expected air gap is used routinely at Torbay to reduce this problem.

d) No allowance is made for the presence of other structures (e.g. cardiac apex)

Caution on applying any correction in radiotherapy also applies in this case, and inspection of the portal image will indicate whether a particular transverse plane will be over- or under-corrected if the lung is taken into account for dose calculation. A larger value of lung density (e.g. 0.5) may be selected in these cases, if desired. Work is in progress to include a fitted shape for the cardiac apex inside the tangential fields.

For treatments using radiation fields other than tangential fields with the back edges aligned (e.g. directly opposing fields) a suitable correction to the amount of measured lung in the portal image may be applied. The resulting lung and breast doses calculated using the fitted lung will then be expected to be of the same accuracy as described in this paper. However, for fields using different gantry angles, for example smaller "top-up" fields, suitable portal images may be used to establish the amount of lung in these fields, if any. The typical displacements found in this study of the fitted lung along the medial–lateral line, when compared with the CT image, will have a negligible effect in practice on the doses to the lung and breast for the tangential fields, but may result in an incorrect estimate of the amount of lung within such "top-up" fields. Hence, this lung fitting method should be applied with caution to field arrangements other than simple tangential fields.

In addition, no matter how accurate the lung shape, either measured by CT, ultrasound or modelled in some other way, the patient will breathe during treatment, so that a variable amount of lung will be treated throughout each exposure. If the lung moves through a vertical distance b, the change in lung path length is approximately 2b (obtained form the linear fit of Figure 2Go, and assuming a typical gantry angle of 45° from the horizontal). Measured breathing movements may reach 10 mm in a nervous patient, although 5 mm is more typical. Hence breathing may account for about 10 mm in lung path length error, or 1% error in the breast dose. Errors due to patient movements and setup errors will increase the uncertainty, so that a working figure of an expected 2% dose error seems reasonable, and this is of the same order as the maximum dose error due to the lung fitting algorithm described. It thus may be argued that there seems little incentive in attempting to find increased lung-fitting accuracy beyond this simple model.


   Conclusions
Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
References
 
Although there are sources of error involved in any mathematical fit, it is apparent from Figure 6Go that the accuracy obtained using the lung fitting model produces a significantly improved dose distribution than when no lung correction is made. In most cases, the dose to the breast either side of the lung will be within 2% of the value obtained if planning had been obtained using CT images. Every 1 cm of lung (path length) increases the dose to the breast either side of the lung by approximately 1%, and by 2% to the lung.

Received for publication January 7, 2003. Revision received October 9, 2003. Accepted for publication November 12, 2003.


   References
Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 

  1. ICRU Report 50. Prescribing, recording and reporting photon beam therapy. Bethesda, MD: ICRU, 1993.
  2. ICRU Report 62. Prescribing, recording and reporting photon beam therapy (Supplement to ICRU Report 50). Bethesda, MD: ICRU, 1999.
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  4. Canney PA, Deehan C, Glegg M, Dickson J. Reducing cardiac dose in post-operative irradiation of breast cancer patients: the relative importance of patient positioning and CT scan planning. Br J Radiol 1999;72:986–93.[Abstract]
  5. Das IJ, Cheng EC, Freedman G, Fowble B. Lung and heart dose volume analyses with CT simulator in radiation treatment of breast cancer. Int J Radiother Oncol Biol Phys 1998;42:11–9.
  6. Aird EGA, Conway J. CT simulation for radiotherapy treatment planning. Br J Radiol 2002;75:937–49.[Abstract/Free Full Text]
  7. Wilks RJ. An optical system for measuring surface shapes for radiotherapy planning. Br J Radiol 1993;66:351–9.[Abstract/Free Full Text]
  8. Wilks RJ, Bliss P. The use of a compensator library to reduce dose inhomogeneity in tangential radiotherapy of the breast. Radiother Oncol 2002;62:147–57.[CrossRef][Medline]
  9. Milan J, Bentley RE. The storage and manipulation of radiation dose data in a small digital computer. Br J Radiol 1974;47:115–21.[Abstract/Free Full Text]
  10. Venables K, Winfield E, Deighton A, Aird E, Hoskin P. Breast radiotherapy phantom design for the START trial. Br J Radiol 2000;73:1313–6.[Abstract]



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