# Analysis of radiation-induced liver disease using the Lyman NTCP model.

**ABSTRACT** To describe the dose-volume tolerance for radiation-induced liver disease (RILD) using the Lyman-Kutcher-Burman (LKB) normal tissue complication probability (NTCP) model.

A total of 203 patients treated with conformal liver radiotherapy and concurrent hepatic arterial chemotherapy were prospectively followed for RILD. Normal liver dose-volume histograms and RILD status for these patients were used as input data for determination of LKB model parameters. A complication was defined as Radiation Therapy Oncology Group Grade 3 or higher RILD < o r =4 months after completion of radiotherapy. A maximal likelihood analysis yielded best estimates for the LKB NTCP model parameters for the liver for the entire patient population. A multivariate analysis of the potential factors associated with RILD was also completed, and refined LKB model parameters were obtained for patient subgroups with different risks of RILD.

Of 203 patients treated with focal liver irradiation, 19 developed RILD. The LKB NTCP model fit the complication data for the entire group. The "n" parameter was larger than previously described, suggesting a strong volume effect for RILD and a correlation of NTCP with the mean liver dose. No cases of RILD were observed when the mean liver dose was <31 Gy. Multivariate analysis demonstrated that in addition to NTCP and the mean liver dose, a primary hepatobiliary cancer diagnosis (vs. liver metastases), bromodeoxyuridine hepatic artery chemotherapy (vs. fluorodeoxyuridine chemotherapy), and male gender were associated with RILD. For 169 patients treated with fluorodeoxyuridine, the refined LKB model parameters were n = 0.97, m = 0.12, tolerance dose for 50% complication risk for whole organ irradiated uniformly [TD50(1)] = 45.8 Gy for patients with liver metastases, and TD50(1) = 39.8 Gy for patients with primary hepatobiliary cancer.

These data demonstrate that the liver exhibits a large volume effect for RILD, suggesting that the mean liver dose may be useful in ranking radiation plans. The inclusion of clinical factors, especially the diagnosis of primary hepatobiliary cancer vs. liver metastases, improves the estimation of NTCP over that obtained solely by the use of dose-volume data. These findings should facilitate the application of focal liver irradiation in future clinical trials.

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Page 1

PII S0360-3016(02)02846-8

CLINICAL INVESTIGATIONNormal Tissue

ANALYSIS OF RADIATION-INDUCED LIVER DISEASE USING THE LYMAN

NTCP MODEL

LAURA A. DAWSON, M.D., DANIEL NORMOLLE, PH.D., JAMES M. BALTER, PH.D.,

CORNELIUS J. MCGINN, M.D., THEODORE S. LAWRENCE, M.D., PH.D., AND RANDALL K. TEN HAKEN, PH.D.

Department of Radiation Oncology, University of Michigan, Ann Arbor, MI

Purpose: To describe the dose–volume tolerance for radiation-induced liver disease (RILD) using the Lyman–

Kutcher–Burman (LKB) normal tissue complication probability (NTCP) model.

Methods and Materials: A total of 203 patients treated with conformal liver radiotherapy and concurrent hepatic

arterial chemotherapy were prospectively followed for RILD. Normal liver dose–volume histograms and RILD

status for these patients were used as input data for determination of LKB model parameters. A complication was

defined as Radiation Therapy Oncology Group Grade 3 or higher RILD <4 months after completion of radiotherapy.

A maximal likelihood analysis yielded best estimates for the LKB NTCP model parameters for the liver for the entire

patient population. A multivariate analysis of the potential factors associated with RILD was also completed, and

refined LKB model parameters were obtained for patient subgroups with different risks of RILD.

Results: Of 203 patients treated with focal liver irradiation, 19 developed RILD. The LKB NTCP model fit the

complication data for the entire group. The “n” parameter was larger than previously described, suggesting a

strong volume effect for RILD and a correlation of NTCP with the mean liver dose. No cases of RILD were

observed when the mean liver dose was <31 Gy. Multivariate analysis demonstrated that in addition to NTCP

and the mean liver dose, a primary hepatobiliary cancer diagnosis (vs. liver metastases), bromodeoxyuridine

hepatic artery chemotherapy (vs. fluorodeoxyuridine chemotherapy), and male gender were associated with

RILD. For 169 patients treated with fluorodeoxyuridine, the refined LKB model parameters were n ? 0.97,

m ? 0.12, tolerance dose for 50% complication risk for whole organ irradiated uniformly [TD50(1)] ? 45.8 Gy

for patients with liver metastases, and TD50(1) ? 39.8 Gy for patients with primary hepatobiliary cancer.

Conclusion: These data demonstrate that the liver exhibits a large volume effect for RILD, suggesting that the

mean liver dose may be useful in ranking radiation plans. The inclusion of clinical factors, especially the diagnosis

of primary hepatobiliary cancer vs. liver metastases, improves the estimation of NTCP over that obtained solely

by the use of dose–volume data. These findings should facilitate the application of focal liver irradiation in future

clinical trials.© 2002 Elsevier Science Inc.

Liver cancer, Conformal radiotherapy, Radiation toxicity, Radiation-induced liver disease, NTCP, Lyman

model.

INTRODUCTION

Radiation-induced liver disease (RILD) is a dose-limiting

complication of liver irradiation. RILD is a clinical syn-

drome of anicteric hepatomegaly, ascites, and elevated liver

enzymes (particularly serum alkaline phosphatase) occur-

ring typically 2 weeks to 4 months after completion of

hepatic irradiation. RILD resembles the suprahepatic vein

obstruction and hepatic toxicity seen after high-dose che-

motherapy (with or without total body irradiation) for bone

marrow transplantation. The pathologic lesion in RILD is

venoocclusive disease, characterized by areas of marked

venous congestion in the central portion of each lobule, with

sparing of the larger veins. Unfortunately, the treatment

options for RILD are limited, and, in severe cases, liver

failure and death can occur (1).

The tolerance of the whole liver to radiation is low, and

RILD is seen in 5–10% of patients treated with 30–35 Gy to

the whole liver. For this reason, radiation has traditionally

had a limited role in the treatment of intrahepatic cancers.

However, treatment of parts of the liver with higher radia-

tion doses is possible without adverse consequences as long

as an adequate volume of normal liver is not irradiated to

high doses (2–5). Patients with focal unresectable intrahe-

patic malignancies treated with higher radiation doses have

Reprint requests to: Laura A. Dawson, M.D., Department of

Radiation Oncology, University of Michigan, UH-B2C447, 1500

E. Medical Center Drive, Ann Arbor, MI 48109-0010. Tel: (734)

926-7810; Fax: (734) 763-7370; E-mail: dawson@umich.edu

Supported in part by NIH Grants P01 CA59827, R01 CA85684,

and M01-RR00042.

Presented in part at the American Society for Therapeutic Ra-

diology and Oncology (ASTRO) Annual Meeting, San Francisco,

California, November 2001.

Acknowledgments—The authors thank Steve Kronenberg for as-

sistance with figure preparation.

Received Dec 6, 2001, and in revised form Mar 13, 2002.

Accepted for publication Mar 19, 2002.

Int. J. Radiation Oncology Biol. Phys., Vol. 53, No. 4, pp. 810–821, 2002

Copyright © 2002 Elsevier Science Inc.

Printed in the USA. All rights reserved

0360-3016/02/$–see front matter

810

Page 2

better response rates, symptom improvement, and survival

rates than do patients treated with lower doses (6–8). Ad-

ditional knowledge of the partial liver tolerance to radiation

may permit safer dose escalation and lead to improvements

in clinical outcomes for patients with intrahepatic malignan-

cies. In addition, knowledge of partial organ tolerances to

radiation is required for successful implementation of novel

radiotherapy (RT) strategies such as automated optimization

for intensity-modulated RT.

A number of models estimating the volume dependence

of normal tissue toxicity have been used to compare the

relative merits of competing three-dimensional RT plans

(9–12). The Lyman model assumes a sigmoid relationship

between a dose of uniform radiation given to a volume of an

organ and the chance of a complication occurring (9) (see

“Methods and Materials” below). We have used the Lyman

model (13) clinically, because it is relatively simple (con-

taining 3 parameters) and, when implemented using the

Kutcher–Burman (KB) effective volume (Veff) dose–vol-

ume histogram (DVH) reduction scheme (14), it permits

comparisons between plans based on DVHs before assign-

ing the dose (15). Our previous effort (16) to reestimate the

parameters for the Lyman model was limited by a relatively

small number of patients, few cases of RILD, and a simpli-

fied statistical analysis. The purpose of this study was to

describe more quantitatively the dose–volume relationship

of the liver to RILD, based on dose–volume data from more

than twice as many patients as previously analyzed, using

the LKB normal tissue complication probability (NTCP)

model. When a multivariate analysis demonstrated that

RILD was associated with nondosimetric factors such as

diagnosis, the LKB model was used to describe the dose–

volume effects for patient subgroups with different risks of

RILD.

METHODS AND MATERIALS

Patients

All patients included in this analysis had unresectable

intrahepatic cancer (hepatocellular carcinoma, cholangio-

carcinoma, or colorectal carcinoma metastatic to the liver)

and were treated in prospective clinical trials (Table 1).

Ninety-three patients included in this analysis have been

previously described (16, 17).

To be eligible for treatment with liver RT, patients had to

have an estimated life expectancy of ?12 weeks, be ?18

years old, and have had normal liver function (prothrombin

and partial thromboplastin time normal or correctable with

vitamin K), renal function, and bone marrow function. In-

formed consent was obtained in accordance with the proce-

dures of the Institutional Review Board of the University of

Michigan. Ineligible patients included those with prior up-

per abdominal irradiation, a history of bleeding from esoph-

ageal varices, or other serious intercurrent illnesses.

To be eligible for the present RILD analysis, patients had

to be assessable for RILD (minimal follow-up of 4 months,

with no evidence of hepatic progression). Approximately

three-quarters of all treated patients were eligible for RILD

evaluation.

Radiation-induced liver disease evaluation

All 203 patients were prospectively followed for RILD.

CT scans were routinely ordered at 2 and 4 months after RT,

and additional scans were ordered if clinically indicated.

Patients were followed for a minimum of 4 months. A

complication (yes vs. no) was defined as Radiation Therapy

Oncology Group Grade 3 or higher RILD (clinical RILD

requiring treatment). Alkaline phosphatase had to be ele-

vated by at least a factor of 2, together with nonmalignant

ascites, detected either clinically or by CT, in the absence of

documented disease progression. Patients who developed

hepatic tumor progression associated with ascites or im-

paired liver function within 4 months after RT and those

who were not seen in follow-up 4 months after RT were not

eligible for this analysis.

Radiotherapy

All patients were treated on consecutive liver radiation

dose-escalation protocols at the University of Michigan

Table 1. Treatment regimen

Patient

groupPatients (n)

Whole liver

dose (Gy)

Total tumor

dose (Gy)Chemotherapy

Patients with

RILD (n)

1

2

3

4

5

6

7

8

9

19

13

11

12

33

36

30

33

36

HA FUdR

HA FUdR

HA FUdR

HA FUdR

HA FUdR

HA FUdR

HA FUdR

HA BUdR

HA BUdR

HA FUdR

0

3

4

0

2

0

0

3

2

5

45 or 48

48 or 52.8

60 or 66

66 or 72.6

49.8–72.6

24–33

48–66

50–90

24–90

0

930

15

14

14

20

76

203

0

0

24–33

0

010

Total0–3619

Abbreviations: RILD ? radiation-induced liver disease; HA FUdR ? hepatic artery fluorodeoxyuridine; HA BUdR ? hepatic artery

bromodeoxyuridine.

811Dose–volume tolerance for radiation-induced liver disease ● L. A. DAWSON et al.

Page 3

from 1987 to 1999 (Table 1). Forty-one patients were

treated with whole liver irradiation; 20 patients were treated

with whole liver irradiation followed by a boost of radiation

to a partial liver volume, and 142 patients were treated with

partial liver irradiation alone. Radiation was delivered twice

daily in 11 fractions/wk, 1.5–1.65 Gy/fraction, with a min-

imal interfraction interval of 4–6 h. The median dose of

radiation delivered was 52.5 Gy (range 24–90). Concurrent

continuous infusion hepatic artery fluorodeoxyuridine

(FUdR) (n ? 169) or bromodeoxyuridine (BUdR) (n ? 34)

was used as a radiation sensitizer for the first 4 weeks of RT.

There was a 2-week break in RT after 2 weeks to minimize

the risk of complications related to the hepatic artery cath-

eter used for chemotherapy delivery.

All patients were treated using three-dimensional confor-

mal RT techniques (18). Target and normal liver volumes

were contoured on axial CT cuts, and the targets were

expanded to account for occult disease, setup uncertainty,

and breathing motion (13, 19). Treatment planning was

performed using the University of Michigan planning sys-

tem (20). The LKB NTCP model with revised parameters

(16) was used most recently in a dose-escalation trial, in

which each patient was subjected to a fixed predicted risk of

RILD and the Veffof liver treated ranged from 20% to 90%

(13, 15).

Normal liver (liver minus gross tumor) DVHs were ob-

tained for all 203 patients. The physical dose values in the

three-dimensional dose distributions for each treatment

course of all patients were converted to normalized iso-

biologic effective doses at 1.5 Gy/fraction using the linear

quadratic model (?/? ? 2 Gy) before computation of the

composite dose distributions from which the DVHs were

computed. Because uniform dose–volume distributions are

required in the Lyman NTCP model, the Kutcher and Bur-

man VeffDVH reduction scheme was used to convert the

nonuniform complex dose distributions into “equivalent”

uniform dose distributions. Veffis defined as the normal

liver volume, which, if irradiated uniformly to the reference

dose, would be associated with the same NTCP as the

nonuniform dose distribution actually delivered (14).

The mean dose to the normal liver was calculated by

summing the dose values for all voxels within the liver

(liver volume minus the gross tumor volume) and dividing

the sum by the number of voxels.

Lyman NTCP model

Data were fit to the empiric Lyman NTCP model, which

describes the probability of a complication after uniform

radiation of a fractional volume of normal tissue (v) to a

dose (D), assuming a sigmoid dose–response relationship,

with no threshold, as follows (9):

NTCP ? ?(t) ? 1??2??

??

t

e?x2/2dx

where

t ? ?D ? TD50?v?/?m ? TD50?v??

and TD50(v) represents the tolerances doses associated with

a 50% chance of complications for uniform partial liver

irradiation, where TD50(v) is related to the whole liver (v ?

1) tolerance through the power law relationship:

TD50??? ? TD50?1? ? ??n

and TD50(1) represents the tolerance of the whole organ to

irradiation, m characterizes the steepness of the dose–

response at TD50(1), and n represents the volume effect,

which relates the tolerance doses of uniform whole organ

irradiation to uniform partial organ irradiation. When n is

near 1, the volume effect is large and when it is near 0, the

volume effect is small.

The partial volume-dose–complication risk relationship

for the liver was graphically displayed in dose–NTCP plots

(as a function of Veff), Veff–NTCP plots (as a function of

dose), and dose–Veffplots (as a function of NTCP).

Maximal likelihood estimation

Normal liver DVHs and the occurrence or lack of occur-

rence of RILD from 203 patients comprised the input data

for the determination of the LKB model parameters using a

maximal likelihood analysis. The NTCP model parameters

TD50(1), m, and n were adjusted to maximize the probability

of predicting complications for those patients who experi-

enced complications and maximize the probability of pre-

dicting no complications for those patients who were com-

plication free, as detailed in Appendix 1.

Subset specific estimates of TD50(1) were obtained by

estimating the n and m parameters from the entire data set

and allowing TD50(1) to vary depending on the patient

subset (e.g., diagnosis).

Confidence intervals for the parameters were determined

by exploring the space around the maximal likely parameter

set using profile-likelihood methods (21, 22). Confidence

intervals were also obtained and displayed on dose–Veff

iso-NTCP curves using the methods outlined in Appendix 2.

Goodness of fit

The deviance of a given set of parameters is related to the

log-likelihood and can be used to assess the goodness of fit.

The deviance has an approximate ?2distribution, where

values closer to 0 indicate a significant lack of fit. Although

this approximation is poor when modeling binary data with

continuous variables (23), the statistic was used as a general

guide. The details are outlined in Appendix 3.

p values were used to compare across sample sizes. A

large goodness-of-fit p value implies a better fit than a

smaller p value.

812I. J. Radiation Oncology ● Biology ● PhysicsVolume 53, Number 4, 2002

Page 4

Exploration of factors associated with RILD

Logistic regression analysis was used to measure the

influence of potential clinical, demographic, and treatment

factors on the occurrence of RILD. In this logistic regres-

sion analysis model, age, gender, diagnosis, prescribed

dose, use of chemotherapy (FUdR vs. BUdR), use of whole

liver irradiation, treatment regimen, and liver volume

(whole liver minus gross tumor volume) were combined

with a single predictor related to NTCP (NTCP based on

parameters obtained for all 203 patients [logit-transformed]

or mean liver dose). If a factor was significantly associated

with RILD, then, when the distribution of events permitted,

the NTCP model parameters, or a subset of parameters,

were reestimated within the patient subgroups as previously

described.

RESULTS

A total of 203 patients were assessable for RILD analysis.

Two patients, who were lost to follow-up after 2 months,

were considered to be without RILD; all other patients were

followed for a minimum of 4 months after RT completion.

Of the 203 patients, 19 developed Grade 3 or higher RILD

(Table 2). Of the 19 patients, 6 were treated with whole liver

RT, 6 were treated with whole liver RT plus higher dose

partial liver RT, and 7 were treated with partial liver RT

alone.

Using the maximal likelihood method, an estimation of

the LKB model parameters based on the DVHs and the

presence or absence of RILD was completed. For the entire

group of 203 patients, the calculated values of TD50(1) and

m were 43.3 Gy (95% confidence interval [CI] 41.9–52.8)

and 0.18 (95% CI 0.14–0.24), respectively. The volume

effect parameter n was estimated to be 1.1 (95% CI 0.88–

1.6).

A comparison of this fit of 203 patients to the original

LKB model parameters estimated from the literature (24)

and our initial fit of 79 patients (16) is shown in Fig. 1. The

deviance (D) for the newest parameter set was 100.6 (p

?0.99), implying a good fit. The fit would have been much

worse using the original estimates of the LKB model pa-

rameters [n ? 0.32, m ? 0.15, TD50(1) ? 45 Gy [25],

D ? 210, p ? 0.30), but only somewhat diminished using

our previously obtained parameter set based on the first 79

patients (n ? 0.67, m ? 0.15, TD50(1) ? 45 Gy [16], D ?

106.8, p ? 0.99).

Qualitatively, the observed complication rates for rank

order patient subgroups of the entire group corresponded to

the complication rates for those patients predicted by the

LKB model using the revised parameters (Fig. 2).

Because an n of 1 in the LKB model suggests a large

volume effect and a strong correlation of RILD with the

mean liver dose, the mean liver dose was studied in more

detail. As expected, the mean liver dose was associated with

the predicted NTCP, based on the LKB model, in a sigmoi-

dal relationship (Fig. 3). For all 203 patients studied, after a

threshold mean liver dose of 30 Gy (below which no patient

developed RILD), the LKB NTCP increased by approxi-

mately 4%/Gy increase in the mean dose. A mean liver dose

Table 2. Patient, tumor, and treatment characteristics for all patients, and for patients with and without radiation induced liver disease

CharacteristicAll patients (n ? 203)Patients without RILD (n ? 184, 91%)Patients with RILD (n ? 19, 9%)

Age (y)

Median

Range

Gender

Female

Male

Diagnosis

Hepatocellular carcinoma

Cholangiocarcinoma

Liver metastases

Prescribed dose (Gy)

Median

Range

Whole liver radiation

Yes

No

LKB NTCP*

Median

Range

Mean liver dose (Gy)

Median

Range

60

28–85

60

29–85

62.5

28–72

85 (29)

118 (58)

82 (45)

102 (55)

3 (16)

16 (84)

58 (29%)

47 (23%)

98 (48%)

46 (25%)

45 (24%)

93 (51%)

12 (63)

2 (11)

5 (26)

52.8

24–90

52.8

24–90

48.0

38.0–60.0

65 (32)

138 (68)

59 (32)

125 (68)

6 (32)

13 (68)

0.05 0.040.17

0.1–0.460.00–0.460.00–0.46

32.0

14.9–44.0

31.3

14.9–44.0

37.0

31.6–43.7

*NTCP for RILD, based on LKB model fit for all 203 patients (n ? 1.1, m ? 0.18 and TD50(1) ? 43.3 Gy).

Abbreviations: RILD ? radiation-induced liver disease; LKB ? Lyman-Kutcher-Burman; NTCP ? normal tissue complication

probability.

813Dose–volume tolerance for radiation-induced liver disease ● L. A. DAWSON et al.

Page 5

of 31 and 43 Gy corresponded with a 5% and 50% proba-

bility of RILD, respectively.

Analysis of prognostic factors for RILD

The characteristics of patients who developed RILD were

compared with those of the patients who did not develop

RILD (Table 1). The median prescribed radiation dose to

the tumor was not significantly different between those who

developed RILD and those who did not (53 and 48 Gy,

respectively). However, as expected, the median NTCP and

mean liver dose were higher in the patients who developed

RILD than in those who did not (NTCP: 0.17 vs. 0.04; mean

liver dose: 37 vs. 31 Gy).

In addition to dosimetric factors, we investigated the

influence of clinical and demographic factors on the devel-

opment of RILD using a logistic regression model to com-

plete a multivariate analysis. The mean liver dose (p

?0.0001), primary hepatobiliary carcinoma diagnosis (p ?

0.005), use of BUdR chemotherapy (p ?0.0001), and male

gender (p ? 0.002) were statistically significant factors

associated with the development of RILD, when the mean

dose was put into the model before NTCP. Because the

mean liver dose and NTCP correlated highly when NTCP

was put into the regression model before the mean dose,

NTCP replaced the mean liver dose as a significant factor

associated with RILD (p ?0.0001). Age, use of whole liver

irradiation, liver volume, treatment regimen, and prescribed

dose were not independently associated with the develop-

ment of RILD (Table 3).

Within the group of 169 patients treated with FUdR, the

difference in risk of RILD between those with primary

hepatobiliary cancer and those with metastatic liver cancer

appeared to be largest in men. In that group of patients, men

with primary hepatobiliary cancer had a significantly higher

risk of RILD than did all other patients (p ? 0.007).

NTCP in patient subgroups

LKB model parameters were then fit for patient sub-

groups predicted to have different risks of RILD based on

the multivariate analysis of clinical factors. The LKB model

parameters for the 169 patients treated with FUdR chemo-

therapy were as follows: n ? 0.86 (95% CI 0.63–1.68), m

? 0.11 (95% CI 0.07–0.23), and TD50(1) ? 42.7 Gy (95%

CI 40.4–49.8; D ? 74.6, p ?0.99). The LKB model pa-

rameters for the 34 patients treated with BUdR chemother-

apy were n ? 0.62 (95% CI 0.55–0.71), m ?0.001 (95%

CI ?0.001–0.001), and TD50(1) ? 33.8 Gy (95% CI 32.2–

37.3), indicating a substantially lower tolerance of the liver

to radiation.

To better describe the different risk of RILD in patients

with primary hepatobiliary malignancies and those with

liver metastases, another fit was completed in which the

LKB model parameters n and m were fit to the entire group

of patients treated with FUdR (169 patients), but the

TD50(1) was separately fit for patients with primary hepa-

tobiliary cancer [TD50(1)HB; 84 patients] and liver metasta-

ses [TD50(1)LM; 85 patients]. The parameters were as fol-

lows: n ? 0.97 (95% CI 0.69–2.3), m ? 0.12 (95% CI

0.07–0.25), TD50(1)HB? 39.8 Gy (95% CI 38.8–41.1), and

TD50(1)LM? 45.8 Gy (95% CI 43.4–50.4; D ? 66.0, p

?0.99). The two TD50(1) values were significantly different

(p ?0.02). This indicates a higher tolerance of the liver to

radiation for patients with liver metastases compared with

those with primary hepatobiliary malignancies. On the basis

of this analysis, an opportunity exists for higher doses to be

Fig. 1. Comparison of original estimates (25), previous fit (16), and

newest fit [n ? 1.1, m ? 0.18, and TD50(1) ? 43.3 Gy] for the

LKB NTCP model. Ten percent iso-NTCPs are displayed in an

effective volume (organ volume that if irradiated to the prescribed

dose uniformly would be associated with the same NTCP as the

nonuniform dose distribution) vs. dose (prescribed dose normal-

ized to 1.5 Gy b.i.d.) graph.

Fig. 2. Observed complication rates for all 203 patients studied, in

rank order groups of 30 patients vs. predicted rates of complica-

tions according to the LKB NTCP model and revised parameters:

n ? 1.1, m ? 0.18, and TD50(1) ? 43.3 Gy.

814I. J. Radiation Oncology ● Biology ● PhysicsVolume 53, Number 4, 2002

Page 6

delivered than previously estimated, especially for patients

with liver metastases.

Figures 4 and 5 demonstrate the difference in the partial

volume–dose-complication risk relationship in patients with

primary liver cancer and liver metastases treated with

FUdR. A threshold volume effect appears to be present,

because the probability of complications is near 0 if the

treated effective liver volume is less then one-third. The

complication risk is also predicted to be low (?5%) if the

whole effective liver volume treated is ?32 Gy for primary

liver cancer and ?36 Gy for liver metastases (in 1.5-Gy

fractions b.i.d.). The RILD risk is predicted to be 5% for an

effective liver volume of two-thirds treated to 46 Gy for

primary liver cancer and 54 Gy for liver metastases (in

1.5-Gy fractions b.i.d.). Other partial volume–dose-compli-

cation risks can be extrapolated from the curves in Figs. 4

and 5.

When LKB model parameter fits were separately com-

pleted for patients with primary hepatobiliary malignancies

and liver metastases treated with FUdR (allowing all three

parameters to vary in these two groups), similar results were

obtained, although the confidence intervals were larger. The

LKB parameters, 95% CIs, and deviance values for 84

patients with primary hepatobiliary cancer treated with

FUdR were n ? 0.90 (95% CI 0.66–2.0), m ? 0.09 (95%

CI 0.05–0.23), and TD50(1)HB? 39.6 Gy (95% CI 37.1–

43.7; D ? 42.6, p ?0.99). The LKB parameters, 95% CIs,

and deviance values for the 85 patients with liver metastases

treated with FUdR were n ? 1.27 (95% CI 0.70 to ?3), m

? 0.18 (95% CI 0.10–0.4), and TD50(1)LM? 50.8 Gy

(95% CI 45.4–99.0; D ? 22.4, p ?0.99).

The mean liver dose was also evaluated further in the

patient subgroups. The mean liver dose was not statistically

different in patients with liver metastases and those with

primary hepatobiliary cancer (average mean liver dose 31.6

and 30.6 Gy, respectively). Five percent of patients with

liver metastases developed RILD, and 13% of patients with

primary hepatobiliary cancer developed RILD. In patients

treated with hepatic arterial FUdR, the mean liver dose

associated with a 5% risk of RILD was 32 Gy for primary

hepatobiliary cancer and 37 Gy for liver metastases (in 1.5

Gy per fraction). The mean liver dose associated with a 50%

risk was 40 Gy for primary hepatobiliary cancer and 47 Gy

for liver metastases.

Fig. 3. Observed and predicted NTCP, according to the LKB NTCP model vs. mean liver dose (in 1.5 Gy b.i.d.).

Observed NTCP calculated from patients grouped in 4-Gy bins, with 80% confidence intervals displayed. Predicted

NTCP based on the LKB NTCP model, with n ? 1.1, m ? 0.18, and TD50(1) ? 43.3 Gy.

Table 3. Factors associated with RILD based on multivariate

analysis

Prognostic factor

p

Odds ratio95% CI

Mean liver dose*

BUdR chemotherapy

Primary

hepatobiliary

cancer diagnosis

Male gender

Age

Normal liver volume

Treatment regimen

Use of whole liver

radiation

?0.0001

?0.0001

1.6

71

1.4–2.1

8.9–890

0.005

0.002

NS

NS

NS

6.4

9.9

1.7–30

2.2–63

—

—

—

NS—

Mean liver dose was put into regression model before NTCP.

*Because mean liver dose and NTCP are highly correlated,

when NTCP was put into the regression model before mean liver

dose, NTCP was substituted for mean liver dose as a significant

factor, with similar results (NTCP p ?0.0001, OR for logit

(NTCP) ? 6.7 (95% CI [3.0–19]).

Abbreviations: RILD ? radiation-induced liver disease; CI ?

confidence interval; BUdR ? bromodeoxyuridine; NS ? not sig-

nificant; NTCP ? normal tissue complication probability; OR ?

odds ratio.

815 Dose–volume tolerance for radiation-induced liver disease ● L. A. DAWSON et al.

Page 7

DISCUSSION

Inherent biologic uncertainties are present in all NTCP

models, and some authors have challenged their utility (25).

Thus, clinical correlation with the NTCP predictions is

needed. This report describes the largest series of patients

with intrahepatic cancer treated with prospective dose–vol-

ume analyses and evaluation for RILD. We used the LKB

NTCP model to study the dose–volume tolerance for RILD.

Using this model with revised parameters, we were better

able to describe the risk of RILD, compare rival radiation

plans, and assign radiation doses for an individual patient on

the basis of the predicted NTCP. The revised models sug-

gest that patients with primary hepatobiliary malignancies

have a lower tolerance to liver radiation than do patients

with liver metastases. In addition, patients with a smaller

volume of liver irradiated may be able to receive higher

doses than previously estimated.

In this study, a diagnosis of primary hepatocellular car-

cinoma was associated with a significantly increased risk of

RILD compared with a diagnosis of liver metastases. Al-

though no patient had liver disease that substantially altered

synthetic liver function (as assessed by prothrombin time),

most patients with primary hepatobiliary carcinoma have

preexisting cirrhosis or hepatitis, which may decrease the

liver tolerance to radiation. It is not possible to comment on

the development of RILD in patients with more advanced

preexisting liver disease, because these patients were ex-

cluded from our studies. Not only may a different dose–

volume relationship exist for RILD in patients with abnor-

mal liver function, different types of radiation-associated

liver injury may also occur, including exacerbation of pre-

existing hepatitis. Male gender was also associated with an

increased risk of RILD, and this effect was most substantial

among patients with a diagnosis of primary hepatobiliary

cancer. BUdR hepatic arterial chemotherapy was associated

Fig. 4. Five and fifty percent iso-NTCP curves and 80% confidence limits for patients with primary hepatobiliary

carcinoma and liver metastases treated with hepatic arterial FUdR using the LKB NTCP model [n ? 0.97, m ? 0.12,

TD50(1)HB? 39.8 Gy, and TD50(1)LM? 45.8 Gy]. Effective volume (normal liver volume that, if irradiated uniformly,

would be associated with the same NTCP as the nonuniform dose distribution actually delivered) vs. reference dose

(prescribed dose normalized to 1.5 Gy b.i.d.).

816I. J. Radiation Oncology ● Biology ● PhysicsVolume 53, Number 4, 2002

Page 8

with an increased risk of RILD compared with FUdR he-

patic artery chemotherapy. Many of the patients who re-

ceived hepatic artery BUdR also received a component of

whole liver irradiation (24–31 Gy). Because the whole liver

tolerance to radiation with hepatic arterial FUdR in this

study was no different than the whole liver tolerance with-

out chemotherapy previously reported (26), we hypothesize

that hepatic arterial FUdR does not substantially alter the

partial liver tolerance to radiation and the NTCP model

parameter estimates. However, the use of other concurrent

chemotherapeutic agents has been associated with a lower

whole liver tolerance to radiation.

On the basis of our analysis using the LKB NTCP model,

a larger volume effect for RILD than originally described

(24) has been substantiated. Although the newest parameter

estimates described our data well, our previous parameters

estimates also predicted a large volume effect, and a clear

distinction between these two parameter sets for all 203

patients was not observed. This was probably due to the lack

of complications at low effective volumes/high doses (no

complications observed with tumor dose ?60 Gy), which

would have a large influence on the exact value of the

volume–effect parameter “n.” However, the strong influ-

ence of the nondosimetric prognostic factors, including liver

cancer type (primary vs. metastatic liver cancer), likely

obscured the ability to make more refined estimates for the

group as a whole.

Thus, in accordance with the large volume effect, the

mean liver dose was found to be strongly associated with

the development of RILD. The mean liver dose was related

to NTCP (based on the LKB model) in a sigmoidal rela-

tionship, with a threshold for RILD at a mean liver dose of

30 Gy, and a 5% and 50% probability of RILD associated

with a mean liver dose of 31 and 43 Gy, respectively (for the

group of 203 patients studied). Of note, these liver toler-

ances are similar to the whole liver tolerances described by

Emami et al. (27) in 1991 (5% and 50% risk of RILD with

whole liver irradiation of 30 and 40 Gy, respectively). The

mean liver dose is a relatively simple parameter that may be

used to help rank plans and estimate the risk of RILD. The

importance of the mean dose in predicting NTCP has been

previously observed in the liver (16) and has also been

Fig. 5. NTCP vs. reference dose as a function of the volume irradiated uniformly (Veff) (top row) and NTCP vs. Veff,

as a function of reference dose (prescribed dose normalized to 1.5 Gy b.i.d.) (bottom row), based on LKB NTCP model

[n ? 0.97, m ? 0.12, TD50(1)HB? 39.8 Gy, and TD50(1)LM? 45.8 Gy], for patients with primary hepatobiliary cancer

(left) and colorectal liver metastases (right).

817Dose–volume tolerance for radiation-induced liver disease ● L. A. DAWSON et al.

Page 9

described for conformal therapy related to other organs,

including the parotid salivary glands and lungs (28, 29).

Although the NTCP and mean liver dose may be useful in

estimating the risk of RILD, there are limitations to using

these factors as predictors. The LKB NTCP model and

mean liver dose do not take into consideration volume

thresholds for RILD, and they continually penalize (in-

crease the NTCP prediction) for even very small volumes

irradiated to high doses. As previously described by Jackson

et al. (17), when the partial liver volume irradiated is kept

below a threshold volume, the risk of RILD is estimated to

be near 0, regardless of the radiation dose delivered. Our

data are consistent with a threshold effect. For small vol-

umes of normal liver treated (approximately one-third of the

whole liver), doses as high as 100 Gy are predicted to be

associated with little or no risk of toxicity for each of the

patient subgroups studied. Finally, different radiation tech-

niques or fractionation schemes used in other patient popula-

tions may be associated with different RILD partial organ

tolerances, and our results may not be widely applicable.

A limitation of using one CT scan to obtain the DVHs on

which the NTCP parameters are based is that the NTCP

estimates can differ when ventilatory liver motion and setup

uncertainty are accounted for (30). Although patients in the

present study treated since 1996 were scanned in a breath-

hold position, previous patients were scanned during free

breathing. We are currently studying the magnitude of the

effect of organ positional uncertainties on NTCP parameter

determination for RILD. As we develop techniques for

control of respiratory organ motion during radiation (31),

the DVHs will better reflect the treatment delivered.

We now treat patients with unresectable intrahepatic ma-

lignancies with hepatic arterial FUdR and escalated focal

liver irradiation, using the revised LKB NTCP model (169

patients/FUdR/4-parameter fit) to facilitate dose escalation,

up to a maximal dose of 90 Gy (13). The use of separate

models [different TD50(1) values] for patients with primary

hepatobiliary malignancies and patients with liver metasta-

ses reflects the lower tolerance of the liver to radiation in

primary hepatobiliary malignancies. In this approach, the

iso-NTCP curve displaying the dose–volume pairs that sub-

ject a patient to an acceptable risk is chosen (15). After

treatment planning has been performed to minimize the

volume of liver treated, the dose prescribed is that which

subjects each patient to a predetermined risk of RILD. As

new technology that decreases the volume of normal liver

irradiated is introduced, higher doses of radiation may be

delivered by moving up the NTCP curve with the same risk

of RILD. An alternative option is to use the mean liver dose

to describe the risk of RILD. Using the revised LKB pa-

rameters, patients with small volumes of their liver irradi-

ated may be able to receive much higher radiation doses to

intrahepatic tumors than previously possible. Thus, it is

possible that extrahepatic organs such as the small bowel

may become dose limiting in the RT for some intrahepatic

malignancies.

In an effort to allow even more patients with unresectable

intrahepatic malignancies to receive higher doses safely, we

use active breathing control (32) to suspend breathing dur-

ing RT. By treating patients with their respiration suspended

using active breathing control, we are able to decrease the

amount of normal liver that has to be treated to account for

organ motion due to breathing, producing a lower risk of

RILD (33). Other potential methods of increasing the radi-

ation dose safely include the use of radioprotective agents

directed to the normal liver. Preclinical studies have dem-

onstrated that amifostine can protect the normal liver with-

out compromising tumor cell kill (34). Finally, it may be

possible to select patients at low risk of RILD for higher

dose escalation on the basis of serum transforming growth

factor-? levels or other as yet unknown serum markers that

may predict RILD risk before its clinical development. These

interventions, along with a better understanding of the dose–

volume tolerance of the liver to radiation, may allow additional

dose escalation to tumors and avoidance of radiation injury to

normal organs, leading to improved outcomes for patients with

unresectable intrahepatic malignancies.

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APPENDIX 1

Maximal likelihood estimation

Normal liver DVHs and the occurrence or lack of occur-

rence of RILD from 203 patients comprised the input data

for the determination of the NTCP model parameters using

a maximal likelihood analysis. The parameters TD50(1), m,

and n were adjusted to maximize the probability of predict-

ing complications for those patients who experienced com-

plications and to maximize the probability of predicting no

complications for those patients who were complication

free.

For each patient i, let the vectors diand vibe the normal-

ized dose (di)–volume (vi) histogram, when the components

of visum to 1 and the components of diare divided by the

reference dose (the prescribed target dose), Di, so that the

largest component of diequals, or is very close to, 1. Let the

components of diand vibe dijand vij, respectively, where “j”

represents the number of dose–volume bins for each pa-

tient’s DVH (range of j approximately 50–150). Let Ri? 1

if the patient i experienced RILD and Ri? 0 otherwise.

Using the LKB NTCP model, the effective volume (Veff)

of the liver is

Veffi??

j

vijdij

1/n

where n represents the volume effect parameter relating the

tolerance dose of uniform whole organ irradiation to uni-

form partial organ irradiation.

The dose associated with a 50% risk of complication

(D50i), related to Vefffor patient i is then as follows:

D50i? TD50?1? ? Veffi

?n

where TD50(1) is the dose associated with a 50% risk of

complication for whole organ irradiation.

819 Dose–volume tolerance for radiation-induced liver disease ● L. A. DAWSON et al.

Page 11

A probit model was assumed for the probability of RILD

of patient i:

pi? pi?m, n, TD50?1?; Di, di, vi? ? ??

Di? D50

m ? D50i?

The log-likelihood for the entire data set,

L?m, n, TD50?1? ??

i

log?pi?Ri? log?1 ? pi?1?Ri

(1)

was then maximized over all feasible values of TD50(1), m,

and n using the Newton-Raphson method implemented in

Statistical Analysis System PROC Mixed software (SAS

Institute, Cary, NC).

Given the limited number of complications (19), esti-

mates of all three parameters in arbitrary subsets of the 203

patients were not generally possible. Subset specific esti-

mates of TD50(1) could be obtained while estimating the n

and m parameters from the entire data set. For instance, the

whole liver tolerance was estimated for patients with pri-

mary hepatobiliary cancer (HB) vs. metastatic liver (LM)

cancer by maximizing the log-likelihood:

L?m, n, TD50?1?HB, TD50?1?LM?

? ?

HB patients

log?pi?m, n, TD50?1?HB, Di, di, vi??Ri

? log?1 ? pi?m, n, TD50?1?HB, Di, di, vi??1?Ri

? ?

LM patients

log?pi?m, n, TD50?1?LM; Di, di, vi??Ri

? log?1 ? pi?m, n, TD50?1?LM; Di, di, vi??1?Ri

APPENDIX 2

Confidence intervals for the dose–Veffiso-NTCP curves

The confidence intervals for the dose–Veffcurves were

obtained using a method to determine the confidence inter-

vals for nonlinear functions of parameters estimates from a

nonlinear model, as follows.

The confidence intervals for a given risk level are con-

structed by determining a confidence band for Vefffor each

dose. The NTCP model is given by

p ? ??

D ? TD50?1? ? Veff

m ? TD50?1? ? Veff

?n

?R?

For a given risk, p, solve this for Veffin terms of D:

Veff(D; n, m, TD50?1?) ??

D

nm??1?p? ? 1/m?

?1/n

substituting TD50(1)HBor TD50(1)LMin the above formula

depending on whether the patient has primary (HB) or

metastatic cancer (LM).

For a given D, this is a nonlinear function of the param-

eter estimates. The estimates themselves have an approxi-

mate variance–covariance matrix that is a function of the

Hessian [3 ? 3 second-derivative matrix for parameters n,

m, and TD50(1)] at the end of the iterative solution process.

Given the function Veff[D, n, m, TD50(1)], parameter

estimates ? ? [n m TD50(1)] and estimated covariance

matrixˆ?, the delta method (35) may be applied, which, in

brief, states that the distribution of the function of parame-

ters about the function applied to their expected value is

asymptotically normal, with variance:

Var(??) ??Veff?

???

?Veff

??

Estimates for ? and ? are substituted into the above formula

to produce the estimated variance, and Wald confidence

intervals are thereby calculated. This is available directly in

Statistical Analysis System PROX NLMIXED software

(SAS Institute).

APPENDIX 3

Goodness of fit

The deviance of a given set of parameters is related to the

log-likelihood (Eq. 1) as follows:

D?m, n, TD50?1? ? ?2?

i

log?pi?Ri? log?1 ? pi?1?Ri

The deviance has, asymptotically, an approximate ?2distri-

bution with N ? 3 degrees of freedom, where N is the

number of observations (3 is the number of estimated pa-

rameters). Thus, the goodness of fit of a given set of pa-

rameters can be assessed by 1 ? ?2{D[m, n, TD50(1)], N ?

3}, where ?2(?,?) is the cumulative central ?2distribution

function, and values closer to 0 indicate a significant lack of

fit. Although this approximation is poor when modeling

binary data with continuous variables (23), the statistic was

used as a general guide.

If two models are fit according to the maximal likelihood

method in which one is a nested within the other (i.e., the

models are of the same form but certain parameters in one

model are constrained to equal 0), the difference of the

820I. J. Radiation Oncology ● Biology ● PhysicsVolume 53, Number 4, 2002

Page 12

deviances has an approximate ?2distribution with degrees

of freedom equal to the number of constrained parameters,

and values close to 0 indicate that constraining the param-

eters significantly degrades the fit. This statistic converges

to the ?2significantly faster than the deviances of the

individual models. This statistic cannot be used to compare

two non-nested models.

p values were used to compare across sample sizes. A

large goodness of fit p value implies a better fit than a

smaller p value.

821Dose–volume tolerance for radiation-induced liver disease ● L. A. DAWSON et al.

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