Dose-volume correlation in radiation-related late small-bowel complications: a clinical study

Radiotherapy Elsevier RADION

and Oncology,

18 (1990) 307-320

301

00758

Dose-volume

correlation in radiation-related late small-bowel complications : a clinical study

Joke G. J. Letschert, Radiotherapy Department,

Joos V. Lebesque, Roe1 W. de Boer, Augustinus Harry Bartelink

The Netherlands Cancer Institute (Antoni van Leeuwenhoek Huis), Plesmanlaan The Netherlands

A. M. Hart and 121,lOM

CX Amsterdam,

(Received 24 May 1989, revision received 30 March 1990, accepted 9 April 1990)

Key words: Small bowel, complications;

Dose-volume

correlation;

Radiation

tolerance

of small bowel

Summary The effects of the volume of irradiated small bowel on late small-bowel tolerance was studied, taking into account the equivalent total dose and type of pre-irradiation surgical procedure. A method was developed to estimate small-bowel volumes in the high-dose region of the radiation treatment using CT-scans in the treatment position. Using this method small-bowel volumes were measured for three-field and AP-PA pelvic treatments (165 cm3 and 400 cm3, respectively), extended AP-PA pelvic treatment (790 cm3), AP-PA treatment of para-aortic nodes (550 cm’) and AP-PA treatment of para-aortic and iliac nodes (1000 cm’). In a retrospective study of 111 patients irradiated after surgery for rectal or recta-sigmoid cancer to a dose of 45-50 Gy in 5 weeks, extended AP-PA pelvic treatment (n = 27) resulted in a high incidence of severe small-bowel complications (37%), whereas for limited (three-field) pelvic treatment (n = 84) the complication rate was 6%. These complication data together with data from the literature on postoperative radiation-related small-bowel complications were analysed using the maximum likelihood method to fit the data to the logistic form of the dose-response relation, taking the volume effect into account by a power law. The analysis indicated that the incidence of radiation-related small-bowel complications was higher after rectal surgery than after other types of surgery, which might be explained by the development of more adhesions. For both types of surgery a volume exponent of the power-law of 0.26 + 0.05 was established. This means that if the small-bowel volume is increased by a factor of 2, the total dose has to be reduced by 17% for the same incidence of small-bowel complications.

Address for correspondence:

1105 AZ Amsterdam, 0167-8140/90/$03.50

Joke G. J. Letschert, The Netherlands.

Radiotherapy

0 1990 Elsevier Science Publishers

Department,

B.V. (Biomedical

Academisch

Division)

Medisch

Centrum,

Meibergdreef

9,

308 Introduction The occurrence of late small-bowel damage is one of the most important dose-limiting factors in radiotherapy of the abdomen. The reported incidence of late small-bowel complications varies between 0.5 and 15% [22]. Serious complications, requiring surgery, occur in less than 5 % of patients [ 2,34 J, for a fractionation schedule of 45-50 Gy in 5 weeks. The main factors predisposing to late small-bowel complications are: previous surgery [2,7,31,34], the total radiation dose, dose per fraction [7,34] and the volume of small bowel irradiated [ 9,14,39]. Other factors which have been reported to determine small-bowel tolerance are pre-existent vascular disease and body habitus [ 311. The first quantitative analysis of clinical data was published by Cohen and Creditor [6] using the Cell Population Kinetic (CPK) model [4]. In this analysis the volume effect on the tolerated dose is represented as Zy where 2 is the length of the side of the equivalent square field. The “field-size” exponent y was found to be equal to 0.22 for late gut damage. As pointed out by Orton and Cohen [28] this “field size” exponent can be transformed to a volume exponent by dividing by 2, resulting in a volume exponent for late intestinal damage of 0.11. In the study on volume effects by Gallagher et al. [ 1 l] orthogonal radiographs were used to make a more realistic estimation of small-bowel volumes. Although they found a profound effect of the volume of irradiated small bowel on late toxicity, they did not perform a quantitative analysis of this volume effect. The purpose of the present study is to determine, quantitatively, the impact of the volumes of irradiated small bowel on the incidence of severe late small-bowel damage. A quantitative relationship between the dose-effect relation for late small-bowel complications and the irradiated volume (taking into account type and number of pre-irradiation surgical treatments) facilitates the estimation of late small-bowel morbidity and enables the radiotherapist to make individual

dose adjustments. Secondly, these clinical data are needed if one wants to optimize treatment techniques using modem 3-D radiation treatment planning systems, since the volume effect on the tolerated dose plays a crucial role in the assessment of expected complications using dosevolume histograms [23-251.

Methods and materials Measuring data

small-bowel

volume

using

CT-scan

To obtain quantitative data on the volume of small bowel in the high-dose region of the dose distribution a contrast medium has to be used to visualize the small bowel. Consequently, the measured volume will always represent the contrast-filled lumen of the small bowel. This (contrast) volume is representative for the volume of small-bowel tissue since the contrast volume is proportional to the volume of the small-bowel tissue itself as long as the contrast filling of the small bowel is rather uniform. A second problem in the determination of small-bowel volumes in the high-dose region of a radiation treatment is that a single estimation of this volume will always be an approximation since small bowel is a rather mobile organ as long as there is no fixation of small-bowel loops due to adhesions [ 111. A method using CT-scans was developed to measure small-bowel volumes in treatment position. The peritoneal cavity within the 90% isodose-line was delineated for all relevant CT-slices spaced 10 mm apart (Fig. 1). Bladder, prostate and uterus were visually excluded for each relevant CT-slice. The small-bowel volume from a histogram of CT-values could then be determined (Fig. 2), since contrast-filled small bowel with positive CT-values could be separated from fatty tissue having negative CT-values. The total contrast volume was calculated from the number of pixels with CT-values between 0 and 400. In this way, 3-D information was obtained on the volume of small bowel irradiated.

Fig. 1. CT-slice of a patient in treatment

position irradiated after surgery for rectal carcinoma. The 90 % isodose and peritoneal cavity are indicated by the white lines.

These results were compared to those obtained using the method described by Gallagher et al. [ 111. They used orthogonal small-bowel radiographs in the treatment position (Fig. 3), the small bowel being visualized using barium enema. A 1 cm spaced grid was superimposed on the PA and lateral radiographs and smallbowel volumes were measured by the summation of the products of the segmental lengths. Both techniques were used for 13 representative patients, irradiated after surgery for rectal carcinoma. A good correlation between the two methods was obtained (correlation coefficient 0.8), taking into account the mobility of the small bowel and the time interval between the two procedures (Fig. 4).

Patient material In the first part of the study the incidence of severe late small-bowel complications was reviewed after surgery and radiation of patients, treated for rectal and recta-sigmoid cancer in the Netherlands Cancer Institute during the period 1979-1985. Before 1983, 27 patients in the Institute were irradiated to large parahelopposed fields with the upper border of the fields extending up to L2-L3 (Fig. 5) to a total dose of 45 Gy (fraction size 1.8 Gy). After that period, the technique for treatment of these patients was changed to a three-field pelvic technique (a posterior and two lateral beams, Fig. 3) and in the period 1983-1985, 84 patients

310 P2ooo

were irradiated to a total dose of 50 Gy (fraction size 2 Gy) or to a total dose of 45 Gy (fraction size 1.8 Gy), depending on the amount of small bowel in the high-dose region of the dose distribution. All patients were advised to undergo

SI

E

Is00 -

WOO-

soo-

400.

-200

-loo

0

loo

200

300

400

500 CT value

Fig. 2. Histogram of CT-values of the peritoneal cavity derived from all CT-slices of a patient. The two peaks in the histogram correspond to fatty tissue (mean CT-value: - 70) and contrast filled small bowel (mean CT-value + 70). The total volume of contrast filled small bowel is calculated from the number of pixels with CT-values between 0 and 400.

Fig . 3. Orthogonal barium enema radiographs in a typical 3-field treatment position. The small bowel is visualized within the PA and lateral field edges (outer square) and a 1 cm spread grid is superimposed (taking into account the magnification factor). The: volume of small bowel in the high dose region of the dose distribution can be estimated by summing the products of the segmental lengths [ 111.

311 the treatment with a full bladder; no external compression devices were utilised. Late smallbowel complications were divided into four categories of severity (Table I) for both groups of patients. The small-bowel volumes for the two groups of patients were measured with the CT-scan method. From a sample of 28 patients who were irradiated after 1983 by a three-field technique, the small-bowel volume was measured to get a reliable estimate of the small-bowel volume for this technique. For the group of patients irradiated on large treatment fields before 1983, both CT-scans and orthogonal small-bowel radiographs were lacking. Therefore, estimates of the

small-bowel volume from CT-scans of a comparable group of patients, matched according to type of rectal surgery, sex, age and abdominal diameter were obtained. In the second part of the study mean smallbowel volumes were estimated for typical standard abdominal and pelvic treatments, for which data on fractionation schedules and complication rates have been published in the literature. These measurements were performed for three types of treatment techniques for patients who all underwent surgery prior to irradiation: - standard AP-PA pelvic treatment fields with the upper border at the promontorium.

312 srnall bowel volumes

0 100

0

200

300

401 Vcnpm’

Fig. 4. Scatterplot of small-bowel volume measurements for 13 patients irradiated after surgery for rectal carcinoma by the orthogonal method (VGal) according to Gallagher et al. [l l] and by the method based on CT-scan data analysis (V,).

- AP-PA fields for irradiation of para-aortic lymph nodes (from Th 11 to L5). - AP-PA treatment fields for irradiation of both para-aortic and iliac lymph nodes. Data analysis The linear-quadratic model was used to convert the different fractionation schedules from this study and from the literature into equivalent biologic dose schedules with a fraction size of 2 Gy.

TABLE

Fig. 5. Typical AP-PA treatment field for radiation after surgery for rectal or recta-sigmoid cancer during the period 1979-1983 in the Netherlands Cancer Institute.

For late small-bowel damage a value for the a/p ratio of 3 Gy was applied. This low IX/~value was used since only such a low value could explain the large dose per fraction effect on

I

Late small-bowel Complication

complications

in patients irradiated

score

No complications Medication-responsive abdominal cramps and/or diarrhoea Small-bowel stenosis and/or adhesions requiring surgery Fatal small-bowel stenosis and/or perforation

after surgery for rectal carcinoma. I. Large AP-PA fields (%) (n = 27)

II. Three-field (n = 84)

41

65

22

29

30

6

7

0

technique

(%)

313 small bowel complications as observed by Cosset et al. [7]. The equivalent total dose (Deq) was then calculated from the total dose (D) and the dose per fraction (d) from the equation:

50% complication rate and k is the “steepness” parameter of the dose-response relation. The volume was taken into account by scaling the D,, (V) with a power law of the volume:

De, = D(a/P+ d)/(a/B+ 2) with a/P = 3 Gy.

(1)

The data on small-bowel complications were related to the equivalent total doses for several small-bowel volumes. Dose-complication curves were fitted through the data using the maximum likelihood method. The dose-response function used in the fit of the data was a logistic function according to: 1 p(D,J’) =

(2)

where I/rer is a reference small-bowel volume and n is the volume exponent. The data were also fitted to the cumulative Weibull distribution (see Appendix), a distribution which was used by Herbert [ 171 to describe and explain the volume effect for normal tissue damage. Using this distribution not only the power-law model but also the probabilistic model [see Appendix, Eqn. (A5)] for the volume effect can be tested.

1 + {D,, (k’)lD)k where p(D,V) is the complication rate for a small-bowel volume V and equivalent total dose D,D5,, (V) is the equivalent total dose at

Fig. 6. Severe late small-bowel complication data as a function of the equivalent total dose (D,,) and volume. The dashed curves and the open symbols correspond to the fitted dose-volume-response relation and data, respectively, after surgery for rectal or recta-sigmoid carcinoma. The drawn curves and the closed symbols correspond to the fitted dose-volume-response relation and data, respectively, after other abdominal/pelvic surgery. 0, Withers et al. [39]; 0, Gunderson et al. [15,16]; A, Tepper et al. [35]; 0, this study; ?? , Cosset et al. [7]; A, Goffinet et al. [13]; 0, Glanzmann [12].

Results The mean small-bowel volume of the patients treated before 1983 on large AP-PA treatment fields amounted to 790 f 78 cm3 (range: 450 to 1350 cm’). This volume was much greater (Table II) than the average volume of the 84 patients treated after 1983 with a three-field technique (165 k 16 cm’). Within the range of irradiated small-bowel volumes (45-390 cm”) for this last patient group, no significant volume effect could be established. The 56 patients who were treated with a total dose of 50 Gy, had a mean small-bowel volume of 133 k 16 cm3 (range: 45 to 149 cm’) as estimated from a sample of 16 patients. In the same period, 28 patients were treated to a lower total dose of 45 Gy and for this group of patients the mean small-bowel volume was greater (206 k 25 cm3, range: 94 to 390 cm3), as would be expected. The effect of prior surgery (abdominoperineal resection versus low anterior resection) on small-bowel volumes was only found in the patient group treated before 1983 with the AP-PA technique (mean small bowel volume 1027 cm3 and 621 cm3, respectively), but not in the group treated after 1983 with a three-field

314 TABLE

II

Treatment characteristics, carcinoma.

total dose and small-bowel

Upper border Equivalent total dose (fraction size 2 Gy) Mean small-bowel volume ( + SEM) Range of small-bowel volumes

volumes for two groups of patients

irradiated

after surgery for rectal

Large AP-PA fields (n = 27)

Three-field technique (n = 84)

L2-L3

Promontorium

43.2 Gy

43.2-50 Gy

790 f 78 cm3 450-1350 cm3

165 f 16 cm3 45-390 cm3

technique (mean small-bowel volumes 164 cm3 and 165 cm3, respectively). All patients had a minimal follow-up of 2 years. To compare the complication rates of the patients treated before and after 1983, the complications were divided into four categories (Table I). Of the 15 severe complications (requiring surgery or fatal) all but one occurred within one year after the start of the radiation treatment. A high incidence of small-bowel stenosis, perforation and fistulas requiring surgery (37%) was noticed in the group of patients irradiated to large parallel opposed treatment fields, compared to the group of patients irradiated with a three-field technique (6%). This difference was significant (p < 0.05). We also estimated mean small-bowel volumes for groups of operated patients for which reliable data on small-bowel complications are available from the literature (Table III). For AP-PA pelvic treatment (upper border at the promontorium) after surgery for rectal and gynaecological cancer a mean small-bowel volume of 400 k 50 cm3 could be deduced. Glanzmann [ 121 reported small-bowel complication data for pelvic treatments with AP-PA and three-fields techniques. The mean small-bowel volume for all his patient material was estimated to be 282 cm3 with an average of 400 cm3 and 165 cm3 for the AP-PA and three-field technique, respectively. A mean small-bowel volume of 550 k 60 cm3 was measured for patients treated on para-aortic lymph nodes

for Hodgkin’s disease. This mean small-bowel volume is representative for patients treated in the EORTC studies in which the para-aortic nodes were treated with different fractionation schedules [ 71. Finally, the small-bowel volumes treated in irradiating both para-aortic and iliac nodes (mean small-bowel volume: 1000 k 92 cm’) are typical for the patients described by Goffinet [ 131. The data on small-bowel complications in relation to equivalent total doses and small-bowel volumes (Table III) were fitted to the logistic dose-response relation [Eqn. (2)] taking the volume into account by a power law [Eqn. (3)]. The small-bowel complications after surgery for rectal and recta-sigmoid cancer were significantly higher than the other data in Table III and consequently a lower D,, ( l/ref) had to be used for the “rectal data” than for the other data (Table IV). This difference in small-bowel radiation tolerance between patients after surgery for rectal and recta-sigmoid cancer and patients operated for other indications amounted to 21 Gy (2 Gy per fraction) at the 50x-incidence level for a reference small-bowel volume of 500 cm3 (Table IV). For the volume exponent n [see Eqn. (3)] we found a value of 0.26 f 0.05. No major deviations between the model and the data seem to be present as judged from Fig. 6 and from the likelihood ratio calculated using the logistic model. Using the cumulative Weibull distribution (see Appendix) both the power-law model and the

315 TABLE

III

Equivalent total dose, treatment technique, mean small-bowel volume ( f SEM) and complication rate for several irradiated volumes after surgery. ~V (cm’)

Severe complications

D,, (GY)

Treatment technique/upper border

48.4

165 f 16

lo/165 ( 6%)

48.4

4-Field technique/ midportion of L5 AP-PA technique/L5

400 + 50

3/34 ( 9%)

43.2-52.8

AP-PA technique/L2

790 k 78

4/12

43.2-50.0

3-Field technique/ promontorium AP-PA technique/ L2-L3

165 + 16

5/84 ( 6%)

Recta-sigmoid cancer

Tepper et al. [35] MGH series Gunderson et al. [15,16] LDS series Withers et al. [39] MDAH series This study

43.2 Bladder/uterus

Glanzmann

790 f 78

lo/27

(33%)

(37%)

cancer

[ 121

40-50 50-60

AP-PA and

technique

282 + 70 282 + 70 282 f 70

4/131( 3%) 9/240 (3.8%)

AP-PA technique; para-aorta1 nodes

550 k 60 550 + 60 550 + 60

l/119 (0.8%) l/39 (2.6%) 4/23 ( 17%)

AP-PA technique; para-aorta1 and iliac nodes

1000 + 92

3167 (4.4%)

60-70

3-field technique

6/47 (13%)

Hodgkin lymphoma

Cosset et al. [7]

40

44 50 Non-Hodgkin lymphoma

Goffinet [ 131

40

~-

probabilistic model for the volume effect could be tested. The power-law model [according to Eqn. (A4)] gave a better fit to the data than the probabilistic model [according to Eqn. (A6)], but the difference did not reach significance

(p = O.ll), test.

TABLE

The mean small-bowel volume of 165 cm3 measured for patients irradiated after surgery for a rectal or recta-sigmoid carcinoma using a three-field pelvic technique is in the same range as described by Gallagher et al. [ 111. In contrast to the results of Gallagher et al., no difference in mean small-bowel volume between abdominoperineal resection and low anterior resection could be determined in our patient material for a three-field pelvic technique. However, for large AP-PA treatment fields extended up to L2 the

IV

Best-fitting parameters for the logistic dose-response relation [including a volume exponent n; see Eqns. (2) and (3)] for severe late small-bowel complications. Parameter n

5.8 (500) rectal (Gy)

D,, (500) other (Gy) m,,

value (f SE)

0.26 + 0.05

k D,,

Parameter

(500) (GY)

59 80 21

+

1.4

+ 21 f 32 f 11

according

to the likelihood

ratio

Discussion

316 influence of the type of rectal surgery could be demonstrated in this study (mean small-bowel volume 1027 cm3 after abdominoperineal resection as compared to 621 cm3 after low anterior resection). In the present study of patients irradiated after surgery for a rectal or recta-sigmoid carcinoma the complication rate was about 6% using a three-field treatment technique including lateral fields and a total dose of 45-50 Gy in 25 fractions. A similar incidence was reported by Tepper et al. [35] from the Massachusetts General Hospital (MGH) series using a four-field pelvic technique. Gunderson et al. [ 15,161 and Withers et al. [40] quoted an incidence of 10% from the M.D. Anderson (MDA) series and the Salt Lake City (LDS) series using a AP-PA pelvic technique. Only the LDS series could be used for statistical analysis since absolute numbers of patients were quoted. In the present study, within the range of irradiated small-bowel volumes (45-390 cm’) using a three-field treatment technique, no significant volume effect could be established. It should be noted that the incidence of severe small-bowel damage after surgery alone has been reported to be as high as 6% [ 16,35,40]. However, for greater irradiated small-bowel volumes (790 cm’) using an AP-PA technique, a volume effect was demonstrated by the unacceptable high incidence of severe small-bowel complications (37%). This high incidence was also found by Withers and Romsdahl [ 391 who used parallel opposed fields of about the same large size. Also in the Stanford series extended field radiation therapy (55 Gy) of prostatic cancer, after extensive intraperitoneal lymph node staging, resulted in a similar incidence of 38 y0 (8/2 1) for severe small-bowel obstruction [1,30]. In this first Stanford series, using two four-field techniques, only two fields a day were treated. The volume of small bowel in this series is difficult to assess, but was probably larger than in the MDA series, since the fields extended up to Th 12. In the second Stanford series, the technique of surgical staging, the irradiation technique and the total dose (50 Gy) were changed and the

incidence of severe small-bowel complications dropped to 8% (l/12). For other large abdominal fields using AP-PA techniques for the treatment of para-aortic lymph nodes or both para-aortic and iliac lymph nodes, we measured also quite large small-bowel volumes: 550 and 1000 cm3, respectively. The reported incidence of late small-bowel damage of 0.8-17x (Table III) was, however, well below the 30-40 y0 incidence found from the present clinical data, by Withers et al. [39] and Pistenma et al. [ 301 for large fields after extensive intraperitoneal surgery. This finding was confirmed by statistical analysis of the data. The D,, at a reference volume of 500 cm3 was found to be (21 k 11) Gy lower after rectal surgery in comparison to the D,, after a staging laparotomy or surgery for bladder or uterus carcinoma. This difference highlights the impact of the type and extent of intraperitoneal surgery on the smallbowel tolerance to subsequent irradiation. An explanation for a lower small-bowel tolerance to irradiation after extensive intraperitoneal surgery could be that this type of surgery results in a high level of physical injury of gut serosa or in a subclinical microbial invasion. Both phenomena could possibly lead to greatly enhanced radiationinduced adhesion formation, as has been suggested by recently published results of animal experiments [ 26,271. A second contributing factor could be found in the role of the intestinal microvasculature [ 81 in the development of late radiation enteropathy. It is quite possible that the vasculature of small-bowel loops in the sacral cavity after surgery for rectal or recta-sigmoid carcinoma is already impaired. Finally, unsuccessful reperitonealisation after pelvic surgery for rectal or recta-sigmoid cancer might result in more adhesions to the pelvic floor and consequently more immobile small-bowel loops than after other types of abdominal surgery. Although the question of the importance of the type of surgery on the incidence of radiation related small-bowel complications has not yet been completely answered, we found both after rectal surgery and after other types of surgery a

317 volume exponent n [see Eqn. (3)] of 0.26 ? 0.05. This means that if the volume of irradiated small bowel increases by a factor of 2, the equivalent total dose (total dose in fractions of 2 Gy) has to be decreased by 17% to obtain the same complication rate for both volumes. The volume exponent estimated from our analysis is a factor 2.4 times larger than the value reported by Orton and Cohen [28] as deduced from an earlier publication by Cohen and Creditor [6]. Also, Lyman [24] quoted a volume exponent for small bowel of 0.1, probably based on the same analysis as Cohen and Creditor [ 61. These last authors used the so-called CPK model to analyse clinical data on gut damage in general. They included in their analysis data on late rectal, sigmoid, colon and small-bowel damage, without taking into consideration the number and type of pre-irradiation surgical procedures. In our analysis we restricted ourselves to smallbowel complication incidence data after surgery and consequently the volume exponent of 0.26 found in our study seems to be a more reliable estimate for small-bowel damage after surgery. A second limitation of the analysis of Cohen and Creditor is their use of the length of the side of the equivalent square field as an indicator for the irradiated small-bowel volume. This procedure can lead to an over- or underestimation of the volume exponent, since both small pelvic fields and large total abdominal fields encompass other organs as well. The existence, interpretation and theoretical basis of the volume effect of normal tissue damage in general has been and still is the subject of a number of partly conflicting papers. For skin, for example, the acute tolerance to irradiation in the clinic was claimed by a number of authors [3,9,21,29,37,38] to be dependent on the area of skin exposed to radiation. However, Hopewell and Young [ 181 demonstrated by careful experiments on pig skin that the severity of the reaction was not influenced by the area of skin irradiated. As pointed out by these last authors the difference between the clinical experience

and the biological experiment can be explained by the definition of clinical tolerance. Some biological effects as skin desquamation are clinically well tolerated if they affect a small-skin area only, but they become clinically unacceptable if the affected area is large. Hence, for these effects clinical tolerance of large radiation fields is reached when the biologically scored level of normal-tissue damage is relatively low; for small fields, however, tolerance is reached when the biologically scored level of damage is high. Consequently, theoretical radiobiological models [5,33] using the above-mentioned volume (or area) dependent skin-tolerance data should be regarded with caution. In our analysis of late small-bowel damage data we used a power-law model [see Eqn. (3)], as has been used recently by a number of authors [23-251. These authors used the integrated normal (or probit) model to define the shape of the dose-response function. We used the logistic model [see Eqn. (2)] and the cumulative Weibull distribution (see Appendix). However, the differences of these functions are clinically indistinguishable as has been pointed out by Schultheiss et al. [32] and Herbert [ 171. Recently, a number of authors [5,32,42,44] introduced a probabilistic model (see Appendix) to explain and describe the volume effect of normal-tissue damage both in radiotherapy and radiobiology. In this model the probabilities of the occurrence of a normal-tissue complication in different subvolumes of the normal tissue are supposed to be fully independent of each other. Consequently, this approach excludes intra-organ or inter-individual variation of radiation sensitivities and intra-organ interactions. A second result of the probabilistic approach is that the magnitude of the volume effect is directly dependent on the steepness of the dose-response relation. If the dose-response relation is shallow, an increase in volume results in a large shift of the dose-response relation to lower doses, whereas a very steep dose-response relation will hardly be shifted to lower doses by an increase of volume. For the power-law model the volume effect is

318

1

described by the independent parameter II [ Eqn. (3)] and consequently the shift of the doseresponse relation to lower doses by an increase of volume is independent of the steepness of the dose-response relation. Due to these inherent assumptions of the probabilistic model, enough biological and clinical data should support the model before it can be applied clinically. Particularly volume-effect data on small bowel and spinal cord are important to validate the model and its underlying assumptions, since the probabilistic approach should be relevant to these linearly organised tissues. For spinal cord animal data on the volume effect [ 19,361 have been claimed to support the probabilistic point of view by Withers et al. [41] and by Yaes et al. [ 451. Hopewell and Van der Kogel [ 201, however, explained their own spinal-cord data by a factor (cell migration) which is in contradiction with the idea of independent subvolumes, an essential assumption of the probabilistic model. For small bowel, the volume effect on the clinical tolerance was clearly demonstrated in this and other studies. The power-law model gave a better fit to the data than a probabilistic model, but the difference did not reach significance. Clearly, more clinical data on small-bowel radiation tolerance in combination with smallbowel volume measurements are needed to assess the validity of the probabilistic model for small bowel.

4

5

6

7

8

9 10

11

12

13

References 14 1 Bagshaw, M. A., Pistenma, D.A., Ray, G. R., Freiha, F. S. and Kempson, R. L. Evaluation of extended field radiotherapy for prostatic neoplasms: 1976 progress report. Cancer Treat. Rep. 61: 297-306, 1977. 2 Bourne, R. G., Kearsley, J. H., Grove, W. D. and Roberts, S. J. The relationship between early and late gastrointestinal complications of radiation therapy for carcinoma of the cervix. Int. J. Radiat. Oncol. Biol. Phys. 9: 1445-1450, 1983. 3 Chen, F. D. and Hendry, J. H. Effects of field size on the incidence of skin healing and the survival of epidermal

15

16

colony-forming cells after irradiation. Br. J. Cancer 53 (Supl. 7): 73-74, 1986. Cohen, L. A cell population kinetic model for fractionated radiation therapy. I. Normal tissue. Radiology 101: 419-427, 1971. Cohen, L. The tissue volume factor in radiation oncology. Int. J. Radiat. Oncol. Biol. Phys. 8: 1771-1774, 1982. Cohen, L. and Creditor, M. Iso-effect tables for tolerance of irradiated normal human tissues. Int. J. Radiat. Oncol. Biol. Phys. 9: 233-241, 1983. Cosset, J. M., Henry-Amar, M., Burgers, J. M. V., Noordijk, E. M., Van der Werf-Messing, B., Meerwaldt, J. H. and van der Schueren, E. Late radiation injuries of the gastrointestinal tract in the H2 and H5 EORTC Hodgkin’s disease trials: emphasis on the role of exploratory laparotomy and fractionation. Radiother. Oncol. 13: 61-69, 1988. Dewit, L. and Oussoren, Y. Late effects in the mouse small intestine after a clinically relevant multifractionated radiation treatment. Radiat. Res. 110: 372-384, 1987. Ellis, F. Tolerance dosage in radiotherapy in 200 kV X-rays. Br. J. Radiol. 15: 348-450, 1942. El Senoussi, M. A., Fletcher, G. H. and Borlase, B. C. Correlation of radiation and surgical parameters in complications in the extended field technique for carcinoma of the cervix. Int. J. Radiat. Oncol. Biol. Phys. 5: 927-934, 1979. Gallagher, M. J., Brereton, H. D., Restock, R. A., Zero, J. M., Zekoski, D. A., Poyss, L. F., Richter, M. P. and Kligerman, M. M. A prospective study of treatment techniques to minimize the volume of pelvic small bowel with reduction of acute and late effects associated with pelvic irradiation. Int. J. Radiat. Oncol. Biol. Phys. 12: 1565-1573, 1986. Glanzmann, Ch. Late effects after high-voltage irradiation therapy in the region of the minor pelvis: experience with more than 1000 patients between 1950 and 1977. Strahlentherapie 156: 678-683, 1980. Goffinet, D. R., Glatstein, E., Fuks, Z. and Kaplan, H. S. Abdominal irradiation in non-Hodgkin’s lymphomas. Cancer 37: 2797-2806, 1976. Green, N., Iba, G. and Smith, W. R. Measures to minimize small intestine injury in the irradiated pelvis. Cancer 35: 1633-1640, 1975. Gunderson, L. L. Radiation therapy of colorectal carcinoma. In: Digestive Cancer, Vol. 9, pp. 29-38, XII International Cancer Congress Proceedings. Editor: N. Thatcher. Pergamon Press, New York, 1979. Gunderson, L. L., Russel, A. H., Llewellyn, H. J., Doppke, K. P. and Tepper, J. E. Treatment planning for colorectal cancer: radiation and surgical techniques and value of small-bowel films. Int. J. Radiat. Oncol. Biol. Phys. 11: 1379-1393, 1985.

319 17 Herbert, D. E. An extreme value paradigm for the effect of size of target volume on end results in radiation oncology. Med. Phys. 10: 589-604, 1983. 18 Hopewell, J. W. and Young, C. M. A. The effect of field size on the reaction of pig skin to single doses of X-rays. Br. J. Radiol. 55: 356-361, 1982. 19 Hopewell, J. W., Morris, A. D. and Dixon-Brown, A. The influence of field size on the late tolerance of the rat spinal cord to single doses of X-rays. Br. J. Radiol. 60: 1099-l 108, 1987. 20 Hopewell, J. W. and van der Kogel, A. J. Letter to the editor. Br. J. Radiol. 61: 973-975, 1988. 21 Jolles, B. and Mitchell, R. G. Optimal skin tolerance dose levels. Br. J. Radio]. 20: 405-409, 1947. 22 Kinsella, T. J. and Bloomer, W. D. Tolerance of the intestine to radiation therapy. Surg. Gynaecol. Obstet. 151: 273-284, 1980. 23 Kutcher, G. J. and Burman, C. Comparative evaluations of 3-dimensional treatment plans using complication probability factors. Int. J. Radiat. Oncol. Biol. Phys. 13 (Suppl. 1): 200, 1987. 24 Lyman, J. T. Complication probability as assessed from dose-volume histograms. Radiat. Res. 104: S13-S19, 1985. 25 Lyman, J. T. and Wolbarst, A. B. Optimization of radiation therapy. III. A method of assessing complication probabilities from dose-volume histograms. Int. J. Radiat. Oncol. Biol. Phys. 13: 103-109, 1987. 26 McBride, W. H., Mason, K. A., Davis, C., Withers, H. R. and Smathers, J. B. Adhesion formation in experimental chronic radiation enteropathy. Int. J. Radiat. Oncol. Biol. Phys. 16: 737-743, 1989. 27 McBride, W. H., Mason, K. A., Withers, H. R. and Davis, C. Effect of interleukin 1, inflammation and surgery on the incidence of adhesion formation and death after abdominal irradiation in mice. Cancer. Res. 49: 169-173, 1989. 28 Orton, C. G. and Cohen, L. A unified approach to doseeffect relationships in radiotherapy. I. Modified TDF and linear quadratic equations. Int. J. Radiat. Oncol. Biol. Phys. 14: 549-556, 1988. 29 Paterson, R. The Treatment of Malignant Disease by Radium and X-Rays. Edward Arnold, London, 1948. 30 Pistenma, D. A., Bagshaw, M. A. and Freiha, F. S. Extended-field radiation therapy for prostatic adenocarcinoma: status report of a limited prospective trial. In: Cancer of the Genitourinary Tract, pp. 229-247. Editors: D. E. Johnson and M. L. Samuels. Raven Press, New York, 1979. 3 1 Potish, R. A. Importance of predisposing factors in the development of enteric damage. Am. J. Clin. Oncol. 5: 189-194, 1982. 32 Schultheiss, T. E., Orton, C. G. and Peck, R. A. Models

33

34

35

36

37

38

39

40

41 42

43

44

45

in radiotherapy: volume effects. Med. Phys. 10: 410-415, 1983. Skymko, R. M., Hauser, D. L. and Archambeau, J. 0. Field size dependence of radiation sensitivity and dose fractionation response in skin. Int. J. Radiat. Oncol. Biol. Phys. 11: 1143-l 148, 1985. H. F., Hancock, J. E. and Fletcher, Stockbine, G. H. Complications in 831 patients with squamous cell carcinoma of the intact uterine cervix treated with 3000 rad or more whole pelvic irradiation. Am. J. Roentgenol. 108: 293-304, 1970. Tepper, J. E., Cohen, A. M., Wood, W. C., Orlow, E. L. and Hedberg, S. E. Postoperative radiation therapy of rectal cancer. Int. J. Radiat. Oncol. Biol. Phys. 13: 5-10, 1987. Van der Kogel, A. J. Effect ofvolume and localisation on rat spinal cord tolerance. In: Proceedings of the 8th International Congress of Radiation Research, p. 352. Editors: E. M. Fielden, J. F. Fowler, J. H. Hendry and D. Scott. Taylor and Francis, London, 1987. Von Essen, C. F. Roentgen therapy of skin and lip carcinoma: factors influencing success or failure. Am. J. Roentgenol. 83: 556-570, 1960. Von Essen, C. F. A spatial model of time-dose-area relationships in radiation therapy. Radiology 8 1: 881-883, 1963. Withers, H. R. and Romsdahl, M. M. Postoperative radiotherapy for adenocarcinoma of the rectum and rectosigmoid. Int. J. Radiat. Oncol. Biol. Phys. 2: 1069-1074, 1977. Withers, H. R., Cuasay, L., Mason, K. A., Romsdahl, M. M. and Saxton, J. Elective radiation therapy in the curative treatment of cancer of the rectum and rectosigmoid colon. In: Gastro-intestinal Cancer, pp. 351-362. Editors: J. R. Stroehlin and M. M. Romsdahl. Raven Press, New York, 1981. Withers, H. R. and Taylor, J. M. G. Volume effect in spinal cord. Br. J. Radiol. 61: 973-975, 1988. Withers, H. R., Taylor, J. M. G. and Maciejewski, B. Treatment volume and tissue tolerance. Int. J. Radiat. Oncol. Biol. Phys. 14: 751-759, 1988. Wolbarts, A.B. Optimization of radiation therapy. II. The critical-voxel model. Int. J. Radiat. Oncol. Biol. Phys. 10: 741-745, 1984. Yaes, R. J. and Kalend, A. Local stem cell depletion model for radiation myelitis. Int. J. Radiat. Oncol. Biol. Phys. 14: 1247-1259, 1988. Yaes, R. J., Gorman, S., Berner, B., Kalend, A. and Maruyama, Y. Comment on the recent results of Hopewell, Morris and Dixon-Brown on radiation myelitis produced by irradiation of very short segments of rat spinal cord. Br. J. Radiol. 61: 967-969, 1988.

320 Appendix

A power-law results in:

The volume-factor and the cumulative Weibull distribution

PP,V

model for the volume effect [see Eqn. (3)]

= 1 - exp[ - {(Vv,J

The probabilistic The cumulative

Weibull distribution

can be expressed

D/D,, (J’AI44.

model for the volume effect according to

as

p(D,V)= 1 - [l -p(D,Vr,,)]vIvref F(x) = 1 - exp{ - (X/LX)@}

(Al)

tl and b are the scale and shape parameters, respectively. This distribution has the property that for any exponent i G(x) = 1 - [l - F(x)]’

is a Weibull parameter 2 approximated dose-response according to

(A2)

distribution again. For values of the shape < b< 6, the Weibull distribution is well by the normal distribution. The shape of a curve can be described by this distribution

p(D,V)= 1 - exp[ - {D/D,,(V)}%2].

(A4)

(A3)

(A5)

results in:

P(DY) = 1 -

exp[ -WV,,,)

Who (~r,f)~BW.

W)

Comparing Eqns. (A4) and (A6) shows that for n = l/p the power-law model coincides with the probabilistic model. For the Weibull distribution the probabilistic volume model is a special case of the more general power-law model. The power-law model is more general than the probabilistic model since the volume exponent n is independent of the steepness parameter j3. Also, for the logistic shape of the dose-response relation [see Eqn. (2)] the probabilistic model is a special case (n = l/k and p(D,V,,,) < 1) of the more general power-law model.