can simulation measurements be used to predict the irradiated lung volume in the tangential fields...

In1 J Rndmmn Oncology Biol Phys Vol. I& pp. I8 I - I87 0360.3016/90 $3.00 + .oO Printed in the U.S.A. All rights reserved. Copyright 0 1990 Pergamon Press plc

??Brief Communication

CAN SIMULATION MEASUREMENTS BE USED TO PREDICT THE IRRADIATED LUNG VOLUME IN THE TANGENTIAL FIELDS IN PATIENTS

TREATED FOR BREAST CANCER?

BRUCE A. BORNSTEIN, M.D.,’ CHEE WAI CHENG, PH.D.,’ LOIS M. RHODES, R.T.T.,’

HARUNOR RASHID, PH.D.,’ PAUL C. STOMPER, M.D.,2

ROBERT L. SIDDON, PH.D.’ AND JAY R. HARRIS, M.D.’

‘Joint Center for Radiation Therapy, Department of Radiation Therapy; 2Department of Radiology, Dana-Farber Cancer Institute and Brigham and Women’s Hospital; Harvard Medical School, Boston, MA 02 115

A simple method of estimating the amount of lung irradiated in patients with breast cancer would be of use in minimizing lung complications. To determine whether simple measurements taken at the time of simulation can be used to predict the lung volume in the radiation field, we performed CT scans as part of treatment planning in 40 cases undergoing radiotherapy for breast cancer. Parameters measured from simulator films included: (a) the perpendicular distance from the posterior tangential field edge to the posterior part of the anterior chest wall at the center of the field (CLD); (h) the maximum perpendicular distance from the posterior tangential field edge to the posterior part of the anterior chest wall (MLD); and (c) the length of lung (L) as measured at the posterior tangential field edge on the simulator film. CT scans of the chest were performed with the patient in the treatment position with 1 cm slice intervals, covering lung apex to base. The ipsilateral total lung area and the lung area included within the treatment port were calculated for each CT scan slice, multiplied by the slice thickness, and then integrated over all CT scan slices to give the volumes. The best predictor of the percent of ipsilateral lung volume treated by the tangential fields was the CLD. Employing linear regression analysis, a coefficient of determination r* = 0.799 was calculated between CLD and percent treated ipsilateral lung volume on CT scan. In comparison, the coefficients for the other parameters were r* = 0.784 for the MLD, r* = 0.071 for L, and r* = 0.690 for CLD X L. A CLD of 1.5 cm predicted that about 6% of the ipsilateral lung would be included in the tangential field, a CLD of 2.5 cm about 16%, and a CLD of 3.5 cm about 26% of the ipsilateral lung, with a mean 90% prediction interval of L7.1% of ipsilateral lung volume. We conclude that the CLD measured at the time of simulation provides a reasonable estimate of the percent of the ipsilateral lung treated by the tangential fields. This information may be of value in evaluating the likelihood of pulmonary complications from such treatment and in minimizing toxicity.

Breast neoplasms, Radiotherapy, Computed tomography, Radiotherapy treatment planning.

INTRODUCTION

Conservative surgery (CS) and radiotherapy (RT) has be- come an accepted alternative to mastectomy for the treatment of patients with early breast cancer. The use of CS and RT is based on studies demonstrating local control and survival comparable to those achieved with mastectomy (3, 11). The principal advantage of CS and RT is the improvement in the cosmetic outcome. Follow-up studies on patients treated with CS and RT have shown good-to-excellent cosmetic results for the majority of patients (2, 7).

In addition to providing high levels of local tumor control and satisfactory cosmetic results, the use of CS and RT must also be associated with a low risk of complications. One complication of concern is radiation pneumonitis, which can occur in up to 16% of patients when large amounts of lung are irradiated (4,9). For this reason, a simple method of estimating the amount of lung irradiated would be of use to the radiotherapist. To determine if simple measurements taken at the time of simulation can be used to predict the amount of lung irradiated by tangential fields, we performed CT scans as part of treatment planning in 40 cases and then related measurements

Presented in part at the Annual Meeting of the American Society for Therapeutic Radiology and Oncology, New Orleans, October 1988.

Reprint requests to: Bruce A. Bomstein, M.D., Joint Center for Radiation Therapy, 50 Binney St., Boston, MA 02 115.

Acknowledgement-The authors would like to thank Barbara Silver for her editorial assistance in the preparation of the manu- script.

Accepted for publication 19 July 1989.

181

182 I. J. Radiation Oncology 0 Biology 0 Physics January 1990. Volume 18, Number I

Fig. 1. The magnified parameters CLD, MLD, and L as measured on the tangential simulator films. The quantities CLD, MLD, and L used in the analysis are demagnified lengths. The central lung distance (CLD) and maximum lung distance (MLD) are measured from the field edge to the posterior part of the anterior chest wall. CLD is at the center of the field. through the isocenter. MLD is at the maximum distance. Field length (L) is also indicated.

taken at simulation to the amount of lung irradiated as demonstrated by the CT scan. Our results indicate that the perpendicular distance from the posterior tangential field edge to the posterior part of the anterior chest wall at the center of the tangential field (CLD) provides an easily determined and reasonable estimate of the percent of ipsilateral lung irradiated.

METHODS AND MATERIALS

We studied 29 breast cancer patients with computerized tomography (CT) scans in conjunction with treatment planning. Twenty-five patients, one with bilateral carcinoma, were treated with excisional biopsy and definitive radiation therapy. Four additional patients received post- operative radiation therapy to the chest wall after mastectomy. Ten patients underwent simulation twice (see explanation below) for a total of 40 simulations analyzed.

Patients were simulated for treatment using tangential fields only ( 14 patients) or tangential fields with a matched anterior supraclavicular/high axillary field ( 16 patients) using a technique described elsewhere (10). The tangential fields were planned with the posterior field edges aligned in one plane. The superior margin was typically at the level of the second intercostal space. At simulation we placed localizing markers on the patients to reproduce the treatment position at the time of CT scan; this included markers at the inferior, superior, lateral, and medial field entrance lines.

Lung volumes were determined by chest CT scan following the simulation. CT scanning was done on a body scanner* with a scan time to 2 seconds and a gantry ap- erture of 50 cm. The unit was equipped with a flat couch and linear laser localizing lights. Treatment position was duplicated by the same technologist at the CT scanner, including arm position and chest wall angle. Teflon rods were placed on the beam entrance line. (Teflon is radi-

opaque and does not create artifacts during scanning.) CT scans were performed in quiet respiration in 1 cm slice intervals from lung apex to base.

Figure I shows the magnified parameters CLD, MLD, and L as measured on the tangential simulator films. The quantities CLD, MLD, and L used in the analysis are demagnified lengths. The central lung distance (CLD) is the perpendicular distance from the posterior tangential field edge to the posterior part of the anterior chest wall through the isocenter (at the center ofthe field). The maximum lung distance (MLD) is the maximum perpendicular distance from the posterior tangential field edge to the posterior part ofthe anterior chest wall. We calculated two lung areas from the simulator films: (a) the area of lung within the tangent treatment field (AA) and (b) the same area excluding the area of the diaphragm (and pos- sibly superimposed lung) seen within the lung region (Lung-Diaphragm Area or LDAA). Figure 2 shows the magnified parameters AA and LDAA as measured on the tangential simulator films. The quantities AA and LDAA used in the analysis are demagnified areas. The length of the simulated tangential field was designated L and had a range of 15.5 cm to 23.5 cm with a mean and median of 19.0 cm. An average of the medial and lateral field measurements was used for analysis.

Figure 3 denotes the parameters calculated from the CT scan. The greatest perpendicular distance (GPD) from the posterior tangential field edge to the parietal pleural surface was measured on the CT scan slice corresponding to the level of the tangential field isocenter. On the side of the treated breast we calculated the total area of lung and the area of lung within the treatment field, multiplied by the slice thickness, and integrated over all slices to compute the respective volumes.

It is our treatment policy to spare lung tissue as much as possible and, as a result, preliminary analysis of the first 19 patients (20 breasts) studied revealed few patients

* General Electric 9800, Milwaukee, Wisconsin.

Irradiated lung volume 0 B. A. BORNSTEIN ef al 183

Fig. 2. The magnified parameters AA and LDAA as measured on the tangential simulator films. The quantities AA and LDAA used in the analysis are demagnified areas. The total area of lung within the tangential treatment field (AA) and the total area excluding the area of the diaphragm (LDAA) are shown as the stippled regions.

with large lung volumes in the field. To gather additional data for large lung volumes, we did a “second simulation” on the last 10 patients in the study population. At the completion of the first treatment planning simulation, the treatment couch was raised l-2 cm to increase the amount of lung within the treatment port. A second set of simulator x-ray films were then taken and additional skin labels were added. At the CT scan session extra Teflon rods were used and two sets of calculations were made for each of these patients. Results for the second simulations in the raised table position are noted.

The degree of agreement between the volume of lung in the tangential field as measured by CT scan and the various parameters on the simulator films is given as a coefficient of determination (r’) calculated by linear regression analysis. The coefficient of determination

measures the variation in the second sample that is “ex- plained by” the relationship between the second sample and the first sample as expressed in the regression line. The higher the r2 value, the greater the correlation between the simulator measurements and the lung volume on CT scan. Linear regression analysis only provides a prediction and it is necessary to put some bounds or limits on this estimate to take into account variability. Therefore, the 90% prediction intervals above and below the value predicted by the regression line were also calculated.

RESULTS

The first column of Table 1 shows the agreement between measurements taken at the time of simulation and the percent of ipsilateral lung within the tangential fields

Fig. 3. CT scan obtained in the treatment position shows the Teflon rods representing the medial and lateral entrance points of the beams (1 and 2). An additional Teflon rod was placed in the midline of the patient’s chest (unlabeled). The stippled area is the region of lung within the tangential treatment field. The greatest perpendicular distance (GPD) from the field edge to the pleural surface is marked.

184 I. J. Radiation Oncology 0 Biology 0 Physics

Table 1. Agreement between measurements taken at the simulator and the percent volume and absolute volume

of ipsilateral lung treated by the tangential fields

Simulator film parameter

Simulator lung-diaphragm area

Percent volume

r* *

Absolute volume

r* *

(LDAA) 0.826 0.657 Simulator lung area (AA) 0.820 0.648 Central lung distance (CLD) 0.799 0.628 Maximum lung distance (MLD) 0.784 0.596 CLD X L 0.690 0.415 MLDXL 0.649 0.369 Simulator tangential field length (L) 0.07 1 0.000

* Coefficient of determination of linear regression analysis.

as determined by CT scan. The degree of agreement between the two measurements is given as a coefficient of determination of the linear regression analysis. The second column of Table 1 shows the relation between measurements taken at the time of simulation and the absolute lung volume included with tangential fields. Comparing columns 1 and 2, each of the measurements taken at simulation shows better agreement with the percent than with the absolute volume of lung within the tangential fields.

Given that the percent lung volume is more accurately predicted, and probably more clinically useful, than the absolute volume, we attempted to determine which simulator film parameter predicted this best. The lung area measurements determined from simulation films (AA or LDAA) had the best correlation with the percent of ipsilateral lung incorporated by the tangential fields but these are difficult to calculate. Among the simple measurements available at simulation, central lung distance (CLD) showed the best agreement.

Figure 4 shows the plot of the CLD versus the percent of ipsilateral lung volume within the tangential field for the 40 cases studied. Linear regression analysis indicated the relationship: % LUNG VOLUME = 9.9(CLD) - 9.0, in the clinical range of CLD (l-4 cm). For example, a CLD of 1.5 cm predicts that approximately 6% of the ipsilateral lung will be included in the tangential field; a CLD of 2.5 cm, approximately 16%; and a CLD of 3.5 cm, approximately 26%. However, for each patient the mean 90% prediction interval (dashed lines) is f7.1% of the ipsilateral lung volume. The absolute value of the difference between the CLD of the medial tangent film and that of the lateral tangent film was calculated. The average difference was 0.15 cm with a standard deviation of 0.12 cm for these 40 cases (range O-O.5 cm). Thus, there was little variation in the CLD between the two simulator films.

In this study there were 17 right- and 13 left-sided treated breasts and there was no difference in results between these two groups of patients (Fig. 4). Also, the results for the four patients who received chest wall irradiation after mastectomy were similar to those for the patients

January 1990, Volume 18, Number 1

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:: 0 Standard

& 35- 0 Raised Table

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&0.799

0 2 3 4 Central kg Distance, CLD (cm) [simulation]

5

Fig. 4. Central lung distance (CLD) determined at simulation versus the percent of ipsilateral lung included in the treatment field as determined by CT scan. Linear regression analysis produced the equation: % LUNG VOLUME = 9.9(CLD) - 9.0, as shown in the solid line. The 90% prediction intervals are also indicated (dashed lines), with a mean value of ?7.1%.

treated with definitive irradiation. There was also no difference between the percentage of lung irradiated by the tangent portion of the three-field technique and that irradiated by the tangential fields alone. Furthermore, when the data were analyzed with and without the addition of the 10 data points for the patients who underwent a second simulation, there was no significant difference in the outcome.

Figure 5 shows the percent lung volume in the tangential field as determined by CT scan in relation to the greatest perpendicular distance (GPD) measured on the CT scan at the central axis slice for the 40 cases studies. Linear regression yielded a coefficient of determination r2 = 0.934 and a mean 90% prediction interval (dashed lines) of +4.1%. The line has a slope of 9.5 and Y-intercept of -7.9. Of note, this slope and Y-intercept are close to

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Greatest Perpendicular Distance, GPD (cm) [CT scan]

Fig. 5. Percent lung volume predicted by the greatest perpendicular distance (GPD) at the CT scan slice corresponding to the treatment field isocenter. Linear regression analysis produced the equation: % LUNG VOLUME = 9.5(GPD) - 7.9, as shown in the solid line. The 90% prediction intervals are also indicated (dashed lines), with a mean value of +4.1%.

Irradiated lung volume 0 B. A. BORNSTEIN et al. 185

those obtained when CLD was related to the percent lung volume (namely, 9.9 and -9.0, respectively). This would be expected as GPD and CLD measure similar distances. In fact, a linear regression analysis between GPD and CLD shows a line having a slope of 1.02 and a Y-intercept of -0.1 with a coefficient of determination (r2) of 0.820.

We examined the relationship between GPD and absolute lung volume. Linear regression analysis produced the equation: LUNG VOLUME (cc) = 122(GPD) - 94.5, with a mean 90% prediction interval of +109 cc. The coefficient of determination was r2 = 0.768, which is con- siderably lower than the r2 = 0.934 observed for GPD and percent lung volume, indicating that both CLD and GPD have better agreement with percent lung volume than with absolute lung volume.

Although linear regression analysis determines a linear (and therefore simple) relationship between two sets of data, by using a higher order equation the percent lung volume treated may be more accurately predicted for a given CLD. Figure 6 shows a plot of CLD versus percent lung volume with a cubic polynomial curve determined by regression analysis. (The appendix explains the rationale behind the choice of a cubic polynomial.) The equation for the curve is % LUNG VOLUME = 0.02 CLD + 3. I1 CLD’ - 0.28 CLD3 and the coefficient of determination is r2 = 0.8 12, which is not very different from the coefficient of r2 = 0.799 for the linear fit shown in Figure 4. Of note, in the range of clinically useful values, the cubic polynomial and the linear function very nearly coincide.

In this study we also measured the lung encompassed by the supraclavicular field for the 16 patients treated with a three-field technique. The amount of lung ranged from 10 cc to 294 cc, with a mean of 147 cc and median of 164 cc. This translated to between less than 1% and 24% of the ipsilateral lung volume, with a mean and median of 12%. We compared these values with the amount of

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Central Lung Distance, CLD (cm) [simulation]

Fig. 6. Central lung distance (CLD) determined at simulation versus the percent of ipsilateral lung included in the treatment field as determined by CT scan. A cubic polynomial regression curve is shown and revealed: % lung volume = 0.02 (CLD) + 3.11 (CLD)’ - 0.28 (CLD)3.

lung treated in the tangential fields. In the 30 breasts planned for treatment without raising the simulator table to include additional lung, the range of lung volume within the field ranged from 22 cc to 333 cc, with a mean of 129 cc and a median of 117 cc. The percent lung volume in the tangential fields ranged from 2% to 25%, with a mean of 10% and median of 8%.

DISCUSSION

This study found the central lung distance (CLD) to be the most useful predictor of ipsilateral lung volume encompassed by the tangential fields in the treatment of breast cancer with radiotherapy. Although other parameters predicted the ipsilateral lung volume slightly better when compared by linear regression analysis, the central lung distance was highly predictive, reproducible, and easy to measure at the time of simulation.

Results published by Danoff et al. (1) on breast cancer patients showed a trend toward increasing ipsilateral lung volume in the treatment field as determined by CT scan with increasing amounts of lung seen on the simulator film. The results of the Danoff series correlate well with the results published here. For the 22 patients treated with tangential fields only, they found the median percent lung volume in the field to be 15.5% for a CLD of 2.0-2.5 cm, 23% for a CLD of 2.6-3.0 cm and 24% for a CLD of 3. l- 3.5 cm. This compares with 13.3%, 18.7%, and 23.7%, respectively, for the current series when the mean CLD values from the Danoff groupings are applied to the curve published in this article (Fig. 4).

Although the present study shows a correlation between the CLD and the percent of ipsilateral lung volume in the treatment field, the mean 90% prediction interval of f7.1 percent indicates some degree of uncertainty. We attempted to identify potential sources of error to explain this degree of uncertainty. Patient movement associated with breathing, including the excursion of the diaphragm and movement of the lung and chest wall during simulation, accounts for at least some of the variation, however we attempted to minimize this by using an average of the medial and lateral tangential field ports. Another potential source of error is variation in the patient’s position between the simulator and the CT scanner. This can be caused by either incorrect patient set-up or movement of the patient’s body after being placed in the treatment position. To reduce the likelihood of this type of error, the same technologist positioned the patient at both proce- dures and CT scans were usually done the same day or not more than 24 hr after simulation. Given this, we believe that the variation in patient position is not likely to be a major source of error.

Anatomical variation between patients may also be a source of error, but Rothwell and colleagues (9) did not find significant variation in the shape of the anterior chest wall in the 20 patients they examined. The lack of anatomical variation may help explain the excellent corre-

186 I. J. Radiation Oncology 0 Biology 0 Physics January 1990. Volume 18, Number I

lation between the CT scan GPD and the percent lung volume within the treatment field, shown in Figure 5. However, a mean 90% prediction interval of *4.1% was noted even for this relationship in which set-up error and patient body movement were minimized. Therefore anatomical variation must be responsible at least in part for the uncertainty noted when GPD and CLD are correlated with percent lung volume in the treatment field. It seems likely that patient movement, variation in patient set-up and anatomic variation all contribute to the f7.1% prediction interval.

Note that the simulator parameters all correlated better with percent ipsilateral lung volume than with absolute lung volume in the treatment field. One explanation for this is that the percent lung volume is a “normalized” quantity that takes into account the patient’s chest wall anatomy. For example, for a patient with a large chest diameter one would expect a large absolute amount of lung to be included within the tangential fields. whereas for a patient with a small chest diameter the absolute amount might be less. The CLD in each case could be the same even if the radius of curvature of the chest wall is different. When the greater absolute volume of lung treated in the first case is divided or “normalized” by the total volume of ipsilateral lung. the percentage of lung treated may not be greater than the percentage calculated for the patient with the small chest wall diameter. Thus, two patients of different size can have similar CLD measures and similar corresponding percent lung volumes treated although the absolute amount of lung treated is quite different.

ranged from 8% to 14%. Rothwell et al. (9) showed a 16% incidence of pneumonitis in patients receiving post-mastectomy chest wall radiation using a modal dose of 4000 cGy in 15 fraction over 3 weeks. Polansky et al. (6) treated 37 women with early breast cancer using 4500-5000 cGy and an additional lOOO- 1500 cGy boost. They found radiologic changes in 16 patients (43%) but no cases of symptomatic radiation pneumonitis. Ten of the 37 patients (27%) had radiologic changes corresponding to the tangential radiotherapy fields and 6 other women had apical lung changes, probably secondary to supraclavicular radiation. In our own experience using doses of 4500- 5000 cGy in 5 weeks plus a boost to the primary site and CLD’s in the range of 1 to 3 cm, the incidence of symptomatic pneumonitis is less than 2% (5). We are currently examining pneumonitis in our patients in greater detail including its relation to the CLD.

A significant portion of lung may also be included in the supraclavicular field. However, note that the nominal dose is not delivered to the entire volume because of dose fall-off. In addition, because the pulmonary blood flow is lowest in the apices. the radiation effect from the supraclavicular field is less important than that of the tangential fields in the development of symptomatic pulmonary complications. Rothwell ct ul. concluded that the major cause of pneumonitis is the tangential fields, based on the distribution of radiological changes. This was also noted by Polansky et (11. (6) and by Roswit and White (8) in a review of radiation injuries of the lung.

The etiology of radiation pneumonitis is not well un- derstood. It is likely related to both the effective radiation dose and the volume of lung in the treatment field. Gross (4) reviewed four series of breast cancer patients treated with megavoltage radiotherapy and found between 20% and 70% of the patients had radiologic changes corresponding to the volume of irradiation. However, the total number of patients in these studies with symptoms only

We conclude that the central lung distance (CLD) is reproducible, easy to measure at the time of simulation and highly predictive of the percent of lung volume in the tangential fields. However, in certain clinical settings, such as patients with compromised lung function, the mean 90% prediction interval of ?7.1% may be too large. In such situations a CT scan in the treatment position should be done. However, for most cases we believe that CLD provides a reasonable estimate of the percent of ipsilateral lung treated.

REFERENCES

1. Danoff, B. F.; Galvin, J. M.; Cheng, E.; Brookland, R. K.; Powlis, W. D.; Goodman, R. L. The clinical application of CT scanning in the treatment of primary breast cancer. In: Ames, F. C., Montague, E. D., eds. Current controversies in breast cancer. Austin, TX: University of Texas Press; 1984:391-397.

2. Dewar, J. A.; Benhamou, S.; Benhamou, E.; Arriagada, R.: Petit, J. Y.; Fontaine, F.; Sarrazin, D. Cosmetic results following lumpectomy, axillary dissection and radiotherapy for small breast cancers. Radiother. Oncol. 12:273-280; 1988.

3. Fisher, B.; Bauer, M.; Margolese, R.; Poisson, R.; Pilch, Y.; Redmond, C.; Fisher, E.; Wolmark, N.; Deutsch, M.; Mon- tague, E.; Saffer, E.; Wickerham, L.; Lerner, H.; Glass, A.; Shibata, H.; Deckers, P.; Ketcham, A.; Oishi, R.; Russell, I. Five year results of a randomized clinical trial comparing total mastectomy and segmental mastectomy with or with-

out radiation in the treatment of breast cancer. N. Eng. J. Med. 3 12:665-673; 1985.

4. Gross, N. J. Pulmonary effects of radiation therapy. Ann. Intern. Med. 86:81-92; 1977.

5. Kinne, D. W.; Harris, J. R.; Hellman, S. Primary Treatment of Breast Cancer. In: Harris, J. R., Hellman, S., Henderson, I. C., Kinne, D. W., eds. Breast diseases. Phil., PA: J. B. Lippincott Co.: 1987:259-358.

6. Polansky, S. M.; Ravin, C. E.; Prosnitz, L. R. Pulmonary changes after primary irradiation for early breast carcinoma. Am. J. Roentgenol. 134:lOl-105: 1980.

7. Rose, M. A.; Olivotto, I.; Cady, B.; Koufman, C.; Osteen, R.; Silver, B.; Recht, A.; Harris, J. R. The long-term cosmetic results of conservative surgery and radiation therapy for early breast cancer. Arch. Surg. 124(2): 153-157; 1989.

8. Roswit, B.; White, D. C. Severe radiation injuries of the lung. Am. J. Roentgenol. 129:127-136; 1977.

Irradiated lung volume 0 B. A. BORNSTEIN et a/. 187

9.

10.

Rothwell, R. I.; Kelly, S. A.: Joslin, C. A. F. Radiation pneumonitis in patients treated for breast cancer. Radiother. Oncol. 4:9-14; 1985. Siddon, R. L.; Buck, B. A.; Harris, J. R.; Svensson, G. K. Three-field technique for breast irradiation using tangential field corner blocks. Int. J. Radiat. Oncol. Biol. Phys. 9:583- 588; 1983.

1 1. Veronesi, U.; Saccozzi, R.; DelVecchio, M.; Banfi, A.; Clement, C.; DeLena, M.; Gallus, G.; Greco, M.; Luini, A.: Marubini, E.; Muscolino, G.; Rilke, F.; Salvador, B.; Zec- chini, A.; Zucali, R. Comparing radical mastectomy with quadrantectomy, axillary dissection, and radiotherapy in patients with small cancers of the breast. N. Eng. J. Med. 305:6-l 1; 1981.

APPENDIX

We developed a simple quantitative mode1 to provide a rationale for why the percentage of lung treated by the tangential fields is well predicted by the central lung distance (CLD). Figure 7 is a schematic drawing of the cross- section of a lung. The upper portion has been approximated as sphere-like in shape, with radius R and volume VI. The lower portion can assume any shape with a volume V2. The posterior border of the tangential field cuts through the sphere-like part and this defines an irradiated region VR and the CLD. The irradiated volume (VR) is related to the CLD and radius (R) by the following equation: VR = P(CLD)~(~R-CLD)/3. The total volume VT is the sum VI + V2. The percent of lung in the irradiated field (% LUNG VOLUME) is calculated by combining the above equations:

% LUNG VOLUME

=$X 100

(lOOaR) CLD2 + (- 100~) CLD3 =---

VT 3vr .

The equation has the form of a cubic-quadratic polynomial with no linear or constant terms.

Our data was fit to a cubic polynomial curve determined by regression analysis. The curve is plotted in Figure 7 and the equation is given below:

% LUNG VOLUME

= 0.02 CLD + 3.1 1 CLD2 - 0.28 CLD3.

The coefficient of determination (r2) is 0.812, which is not much different from the value obtained by linear regression analysis, shown in Figure 4, where r2 = 0.799. Note that: (a) The linear term (0.02) which is not in the model, is small. (b) The quadratic term (3.1 1) is positive, the same as the model. (c) The cubic term (-0.28) is neg-

LUNG VOLUME MODEL

Posterior border of fortgent field

\ lrregulor par 1

Fig. 7. Schematic drawing of lung volume model. The upper portion has been approximated as a sphere-like object of radius R and volume V, . The lower portion can assume any shape of volume Vz. The irradiated volume V, and the CLD are defined by the posterior border of the tangential field edge.

ative, the same as the model. To check our model and to see if the coefficients of the cubic polynomial regression curve are of the correct order of magnitude, we calculated VT and R by comparing the polynomial coefficients for the two expressions for percent lung volume given above. We found VT = 373 cm3 and R = 3.7 cm. Both values are smaller than expected but are of the correct order of magnitude. For most of the data CLD < R, which is the range for which the model is defined.

In conclusion, it appears that a cubic-quadratic curve best defines the relationship between percent lung volume and CLD. However, for the range of values seen clinically, a linear approximation is easier to use and is nearly as good as the more complex relationship. In other words, in the clinically useful range of CLD, the cubic-quadratic polynomial and the linear function very nearly coincide.

can simulation measurements be used to predict the irradiated lung volume in the tangential fields...

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