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Regarding scoring of radiation pneumonitis
Int. J. Radiation Oncology Biol. Phys., Vol. 48, No. 2, pp. 609 – 617, 2000 Copyright © 2000 Elsevier Science Inc. Printed in the USA. All rights reserved 0360-3016/00/$–see front matter
LETTERS TO THE EDITOR distribution, in a tumor or an organ, by a single parameter. For a fractionated course of radiotherapy, given in n fractions, an inhomogeneous physical dose distribution can easily be transformed into a corresponding inhomogeneous biologically effective dose (BED) distribution (1), by using the standard linear quadratic model formula, BED ⫽ D[1 ⫹ D/(n( ␣ /  ))]. The problem of reducing that BED distribution to a single parameter would still remain. Hoban et al. (2, 3) have proposed the volume integral of the biologically effective dose (IBED) as such a parameter. The average biologically effective dose (ABD) is the IBED divided by the organ or tumor volume. However, Zaider (4) has shown, using a simple model, that the normal tissue complication probability (NTCP) can not be a function of the IBED, since identical values of the IBED can be associated with different values of the NTCP. A more useful parameter, that is directly related to the NTCP is the equivalent uniform biologically effective dose (EUD) defined by O’Donoghue (5) and Niemierko (6). For a tumor, the EUD is the biologically effective dose which, when given as a uniform dose to the entire tumor, would produce the same tumor control probability as the inhomogeneous BED distribution. O’Donoghue has derived a simple expression for the EUD for tumor control. A similar expression can be obtained, for normal tissue damage, in organs with “parallel architecture.” In analogy with electrical circuits, a “parallel organ” is defined to be one that contains a large number of functional subunits, all performing the same function “in parallel” (7, 8). An example of a “parallel” organ is the kidney, whose subunit is the nephron. Since the total output of such an organ, however measured, is the sum of the outputs of the subunits, the severity of the damage to the organ will be determined by the number of subunits that have been inactivated. Consider an organ of volume V containing N subunits, each of which contains m stem cells. If the subunits are uniformly distributed through the organ, then the number of subunits per unit volume will be the density where ⫽ N/V. The organ can be divided into subvolumes ⌬V i in which the biologically effective dose, BEDi , is constant. The number of subunits in ⌬V i will be n i ⫽ ⌬V i and V ⫽ ¥ ⌬V i , N ⫽ ¥ n i . If the radiosensitivity parameter for a stem cell is ␣, then the cell survival probability for a cell in ⌬V i is
REGARDING SCORING OF RADIATION PNEUMONITIS To the Editor: In their recent report, Graham et al. correlated the incidence and severity of clinical radiation pneumonitis with 3D treatmentplanning data (1). However, their claim to have scored pneumonitis using the Radiation Therapy Oncology Group (RTOG) Acute and Late Lung Morbidity Scoring Criteria, as reported by Byhart et al. (2), is misleading. All 14 of Graham’s patients who were assessed to have developed “moderate pneumonitis (Grade 2)” were treated with steroids. In the abovementioned RTOG criteria, the use of steroids results in a score of Grade 3 toxicity, which was defined as “severe cough unresponsive to narcotic antitussive agents or dyspnea at rest; clinical or radiologic evidence of acute pneumonitis; and the use of intermittent oxygen or steroids” (2). Recent publications in this field, including an analysis of data on pulmonary toxicity from 540 patients (3) and a radiation dose-escalation study in non– small- cell lung cancer (4), have instead used the Southwest Oncology Group (SWOG) toxicity criteria for scoring radiation pneumonitis. In the SWOG criteria, Grade 2 (moderate) toxicity is scored when steroids are required, and Grade 3 (severe) toxicity, when oxygen is necessary. The incidence of symptoms that are sufficiently severe as to merit the use of oxygen, as opposed to only steroids, are clinically relevant. The inability of the RTOG Morbidity Scoring Criteria to distinguish between such grades of toxicity has led some authors to modify this scheme to include steroid use in Grade 2 pneumonitis (5). A number of aggressive radiation and/or concurrent chemoradiotherapy schemes have been recently evaluated in lung cancer and some, e.g., the CHART trial (6), have used neither of the above schemes. The failure to adhere to uniform criteria for defining radiation pneumonitis will continue to add to the difficulty in determining precisely the incidence or severity of this important complication. PII S0360-3016(00)00596-4 1. Graham MV, Purdy JA, Emami B, et al. Clinical dose-volume histogram analysis for pneumonitis after 3D treatment for non-small cell lung cancer (NSCLC). Int J Radiat Oncol Biol Phys 1999;45:323–329. 2. Byhardt RW, Martin L, Pajak TF, et al. The influence of field size and other treatment factors on pulmonary toxicity following hyperfractionated irradiation for inoperable non-small cell lung cancer (NSCLC)— Analysis of a Radiation Therapy Oncology Group (RTOG) protocol. Int J Radiat Oncol Biol Phys 1993;27:537–544. 3. Kwa SL, Lebesque, JV, Theuws, JC, et al. Radiation pneumonitis as a function of mean lung dose: An analysis of pooled data of 540 patients. Int J Radiat Oncol Biol Phys 1998;42:1–9. 4. Robertson JM, Ten Haken RK, Hazuka MB, et al. Dose escalation for non-small cell lung cancer using conformal radiation therapy. Int J Radiat Oncol Biol Phys 1997;37:1079 –1085. 5. Oetzel D, Schraube P, Hensley F, et al. Estimation of pneumonitis risk in three-dimensional treatment planning using dose–volume histogram analysis. Int J Radiat Oncol Biol Phys 1995;33:455– 460. 6. Saunders MI, Dische S, Barrett A, et al. Continuous hyperfractionated acclerated radiotherapy (CHART) versus conventional radiotherapy in non-small cell lung cancer: Mature data from a randomised multicentre trial. Radiother Oncol 1999;50:161–165.
S i ⫽ e ⫺␣BEDi.
(1)
If a subunit can be regenerated by a single surviving stem cell, then a subunit is “killed” if all of its m stem cells are killed, and so the probability, p i , of subunit death in ⌬V i would be
p i ⫽ e ⫺mSi.
(2)
The mean number of subunits killed in ⌬V i would be n i p i ⫽ p i ⌬V i so that the mean number of subunits killed in the entire tumor, n, would be
n⫽ SURESH SENAN, MRCP, FRCR, Ph.D. University Hospital Rotterdam Groene Hilledijk 301 3075 EA Rotterdam The Netherlands
冘 共N/V兲 p ⌬V i
i
(3)
It is the mean number of subunits that have been killed that determines the severity of the complication. Consider the same organ receiving a uniform biologically effective dose equal to EUD. The corresponding cell survival probability and probability of subunit death, for the entire organ, would be
S ⫽ e ⫺␣EUD, P ⫽ e ⫺mS.
DEFINING A UNIFORM BIOLOGICALLY EFFECTIVE DOSE FOR ORGANS WITH PARALLEL ARCHITECTURE
(4)
The mean number of surviving subunits would be n⬘ ⫽ NP. Setting n ⫽ n⬘, and replacing the sum by a volume integral,
To the Editor: To compare the biological effects of different treatment plans, it is useful to be able to characterize an inhomogeneous dose 609
LETTERS TO THE EDITOR distribution, in a tumor or an organ, by a single parameter. For a fractionated course of radiotherapy, given in n fractions, an inhomogeneous physical dose distribution can easily be transformed into a corresponding inhomogeneous biologically effective dose (BED) distribution (1), by using the standard linear quadratic model formula, BED ⫽ D[1 ⫹ D/(n( ␣ /  ))]. The problem of reducing that BED distribution to a single parameter would still remain. Hoban et al. (2, 3) have proposed the volume integral of the biologically effective dose (IBED) as such a parameter. The average biologically effective dose (ABD) is the IBED divided by the organ or tumor volume. However, Zaider (4) has shown, using a simple model, that the normal tissue complication probability (NTCP) can not be a function of the IBED, since identical values of the IBED can be associated with different values of the NTCP. A more useful parameter, that is directly related to the NTCP is the equivalent uniform biologically effective dose (EUD) defined by O’Donoghue (5) and Niemierko (6). For a tumor, the EUD is the biologically effective dose which, when given as a uniform dose to the entire tumor, would produce the same tumor control probability as the inhomogeneous BED distribution. O’Donoghue has derived a simple expression for the EUD for tumor control. A similar expression can be obtained, for normal tissue damage, in organs with “parallel architecture.” In analogy with electrical circuits, a “parallel organ” is defined to be one that contains a large number of functional subunits, all performing the same function “in parallel” (7, 8). An example of a “parallel” organ is the kidney, whose subunit is the nephron. Since the total output of such an organ, however measured, is the sum of the outputs of the subunits, the severity of the damage to the organ will be determined by the number of subunits that have been inactivated. Consider an organ of volume V containing N subunits, each of which contains m stem cells. If the subunits are uniformly distributed through the organ, then the number of subunits per unit volume will be the density where ⫽ N/V. The organ can be divided into subvolumes ⌬V i in which the biologically effective dose, BEDi , is constant. The number of subunits in ⌬V i will be n i ⫽ ⌬V i and V ⫽ ¥ ⌬V i , N ⫽ ¥ n i . If the radiosensitivity parameter for a stem cell is ␣, then the cell survival probability for a cell in ⌬V i is
REGARDING SCORING OF RADIATION PNEUMONITIS To the Editor: In their recent report, Graham et al. correlated the incidence and severity of clinical radiation pneumonitis with 3D treatmentplanning data (1). However, their claim to have scored pneumonitis using the Radiation Therapy Oncology Group (RTOG) Acute and Late Lung Morbidity Scoring Criteria, as reported by Byhart et al. (2), is misleading. All 14 of Graham’s patients who were assessed to have developed “moderate pneumonitis (Grade 2)” were treated with steroids. In the abovementioned RTOG criteria, the use of steroids results in a score of Grade 3 toxicity, which was defined as “severe cough unresponsive to narcotic antitussive agents or dyspnea at rest; clinical or radiologic evidence of acute pneumonitis; and the use of intermittent oxygen or steroids” (2). Recent publications in this field, including an analysis of data on pulmonary toxicity from 540 patients (3) and a radiation dose-escalation study in non– small- cell lung cancer (4), have instead used the Southwest Oncology Group (SWOG) toxicity criteria for scoring radiation pneumonitis. In the SWOG criteria, Grade 2 (moderate) toxicity is scored when steroids are required, and Grade 3 (severe) toxicity, when oxygen is necessary. The incidence of symptoms that are sufficiently severe as to merit the use of oxygen, as opposed to only steroids, are clinically relevant. The inability of the RTOG Morbidity Scoring Criteria to distinguish between such grades of toxicity has led some authors to modify this scheme to include steroid use in Grade 2 pneumonitis (5). A number of aggressive radiation and/or concurrent chemoradiotherapy schemes have been recently evaluated in lung cancer and some, e.g., the CHART trial (6), have used neither of the above schemes. The failure to adhere to uniform criteria for defining radiation pneumonitis will continue to add to the difficulty in determining precisely the incidence or severity of this important complication. PII S0360-3016(00)00596-4 1. Graham MV, Purdy JA, Emami B, et al. Clinical dose-volume histogram analysis for pneumonitis after 3D treatment for non-small cell lung cancer (NSCLC). Int J Radiat Oncol Biol Phys 1999;45:323–329. 2. Byhardt RW, Martin L, Pajak TF, et al. The influence of field size and other treatment factors on pulmonary toxicity following hyperfractionated irradiation for inoperable non-small cell lung cancer (NSCLC)— Analysis of a Radiation Therapy Oncology Group (RTOG) protocol. Int J Radiat Oncol Biol Phys 1993;27:537–544. 3. Kwa SL, Lebesque, JV, Theuws, JC, et al. Radiation pneumonitis as a function of mean lung dose: An analysis of pooled data of 540 patients. Int J Radiat Oncol Biol Phys 1998;42:1–9. 4. Robertson JM, Ten Haken RK, Hazuka MB, et al. Dose escalation for non-small cell lung cancer using conformal radiation therapy. Int J Radiat Oncol Biol Phys 1997;37:1079 –1085. 5. Oetzel D, Schraube P, Hensley F, et al. Estimation of pneumonitis risk in three-dimensional treatment planning using dose–volume histogram analysis. Int J Radiat Oncol Biol Phys 1995;33:455– 460. 6. Saunders MI, Dische S, Barrett A, et al. Continuous hyperfractionated acclerated radiotherapy (CHART) versus conventional radiotherapy in non-small cell lung cancer: Mature data from a randomised multicentre trial. Radiother Oncol 1999;50:161–165.
S i ⫽ e ⫺␣BEDi.
(1)
If a subunit can be regenerated by a single surviving stem cell, then a subunit is “killed” if all of its m stem cells are killed, and so the probability, p i , of subunit death in ⌬V i would be
p i ⫽ e ⫺mSi.
(2)
The mean number of subunits killed in ⌬V i would be n i p i ⫽ p i ⌬V i so that the mean number of subunits killed in the entire tumor, n, would be
n⫽ SURESH SENAN, MRCP, FRCR, Ph.D. University Hospital Rotterdam Groene Hilledijk 301 3075 EA Rotterdam The Netherlands
冘 共N/V兲 p ⌬V i
i
(3)
It is the mean number of subunits that have been killed that determines the severity of the complication. Consider the same organ receiving a uniform biologically effective dose equal to EUD. The corresponding cell survival probability and probability of subunit death, for the entire organ, would be
S ⫽ e ⫺␣EUD, P ⫽ e ⫺mS.
DEFINING A UNIFORM BIOLOGICALLY EFFECTIVE DOSE FOR ORGANS WITH PARALLEL ARCHITECTURE
(4)
The mean number of surviving subunits would be n⬘ ⫽ NP. Setting n ⫽ n⬘, and replacing the sum by a volume integral,
To the Editor: To compare the biological effects of different treatment plans, it is useful to be able to characterize an inhomogeneous dose 609