USE OF NORMAL TISSUE TOLERANCE DOSES INTO LINEAR QUADRATIC EQUATION TO  ESTIMATE  NORMAL TISSUE COMPLICATION PROBABILITY.
 

T. S. KEHWAR, Ph. D., D. Sc. &  *S. C. SHARMA, M.D.
 

Department of Radiation Oncology, Sanchez Cancer Center, Mercy Health Center, Laredo, Texas, USA.

*Department of Radiotherapy, Postgraduate Institute of Medical Education and Research, Chandigarh – 160 012, India.
 

Corresponding Address :

Dr. T. S. Kehwar, Dip. R. P., Ph. D., D. Sc.

Department of Radiation Oncology

Sanchez Cancer Center,

Mercy Health Center,

1700  E. Saunders ST.
 

Laredo, Texas 78041 USA

E-mail: tskehwar@rediffmail.com

 

ABSTRACT

Prediction of normal tissue complication probability (NTCP) after external beam radiotherapy (EBRT) is an important issue in the optimization of a treatment plan and should be considered because during EBRT a considerable volume of normal tissues receive radiation dose along with the tumour. Hence normal tissue complications arises during and after irradiation. Normal tissue complication probability (NTCP), in a normal tissue / organ, is the function of delivered dose and irradiated volume of the normal tissue / organ. Hence to compute NTCP, we used  modified form of the Kallman et al’s (1992) Poisson cell kill model of NTCP based on linear-quadratic model. This model has three tissue specific parameters, aG, k & N0, and three variables (NTCP, dose and partial volume of the organ).  The model has been applied to compute above said three parameters of the NTCP model using clinical tolerance doses of various normal tissues / organs extracted from published reports of various authors. The normal tissue tolerance doses are calculated for partial volumes of the organs using the values of above-said  parameters for Emami et al’s (1991) data and a combined set of Emami et al (1991) and authors data. Only few organs have good correspondence between calculated tolerance doses for 2 sets of the data. To compute the values of coefficients a, b of the LQ model, the values of a/b for the listed organs are extracted from the literature and are used in the factor aG. In this article, a graphical representation of the computed NTCP  for bladder, brain, heart and rectum is presented. A fairly good correspondence is found between the  curves of 2 sets of data for brain, heart and rectum. Hence the model may, therefore, be used to interpolate clinical data to provide an estimate of NTCP for these organs  for any altered fractionated treatment schedule.
 

Key Words:- Normal tissue complication probability, Normal tissue tolerance dose, Linear-quadratic model, a/b ratio,  External beam radiotherapy, volume effect.

 

INTRODUCTION

In the external beam radiotherapy (EBRT), the normal tissues / critical organs within the radiation beam and at the vicinity of the tumour receive a higher amount of radiation dose, and sometimes may be equal to the tumour dose, which causes normal tissue injury. Hence, often a practicing radiation oncologists must have to estimate the likelihood of radiation induced normal tissue complication probability (NTCP), which is generally based on the published data on normal tissue complications and clinical experience of the radiation oncologist (Rubin and Cassarett, 1968a, b). Initial systematic work was done by Rubin and Cassarett (1972), to report normal tissue tolerance doses, and have introduced the concepts of TD5/5 and TD50/5 (the NTCP at 5% and 50%, respectively, within 5 years after radiotherapy) and published normal tissue tolerance data, in terms of TD5/5 and TD50/5, for a number of normal tissues and organs. Other than the work of Rubin and Cassarett (1972) little comprehensive and systematic work had been done by few researchers (Mah et al, 1984, 1986;  Wara et al, 1973, 1975) in this direction.

Emami et al (1991) have compiled and published the normal tissue tolerance doses for selected number of normal tissue / organs in terms of TD5/5 and TD50/5. These normal tissue tolerance data are defined for uniformly irradiated 1/3, 2/3 and 3/3 partial volumes of the normal tissues and organs only for conventional fractionation schedules of 1.8 to 2 Gy per fraction, 5 fractions a week. Many other researchers have also reported the tolerance doses for individual organs, but the data are scattered in the literature and also a number of values of the tolerance doses for same organ are reported by different investigators, which creates problem to decide a wide accepted value for routine clinical practice.

In this study, an empirical model based on linear-quadratic (LQ) model, proposed by Kallman et al (1992) and later by Zaider & Amols (1999), is used to fit these data with consideration of quadratic term, i.e. b term.  A method of least square fit was used to compute the values of the parameters of the model for the normal tissue tolerance doses of Emami et al (1991) and combined set of tolerance doses of Emami et al (1991) and others researchers. The values of the tissue specific LQ parameters, a and b, are determined using the value of a factor, aG, of the NTCP equation obtained from the above said least square fit and other researches using the published values of the a/b ratio for different normal tissue and organs extracted from the literature, where G =  [1+d/(a/b)]. In this paper, some representative curves have also been plotted between dose and computed NTCP to demonstrate the applicability of the NTCP model.
 

METHODS AND MATERIALS

NTCP model

To compute the value of the NTCP for an irradiated normal tissue Kallman et al (1992) have modified the LQ model to propose a NTCP concept which is based on Poisson cell kill model and further was modified by Zaider and Amols (1999). Zaider and Amols (1999) have considered only linear term of the LQ model in their work. While in this article, we have used both linear as well as quadratic term, i.e. a-component + b-component of the LQ model. Hence the proposed equation of the NTCP model is similar to that proposed by Zaider & Amols (1999). The expression of the equation of the NTCP model may be written as

NTCP(D, v) = exp[-N0 v –k exp{-aDG}]                                                                       (1)

Where G  =  [1+d/(a/b)],  a is the coefficient of lethal damage and b/a is the reciprocal of the a/b ratio with their respective units of Gy–1 and Gy. The N0 and k are the tissue / organ specific, non-negative adjustable parameters, v is the uniformly irradiated partial volume of the tissue / organ (i.e. v = V/Vref, where V is uniformly irradiated volume of the normal tissue / organ and Vref is the reference volume of the normal tissue / organ). D is the normal tissue dose in terms of TD5/5 or TD50/5, delivered with d dose per fraction. The expression in the exponent, exp (-aDG), is the reminiscent of the LQ model for cellular survival.

The expression of the relative effectiveness (RE) per unit dose can be written as

            RE   = G                                                                                                           (A)

Now using equation (A) into equation (1) the expression of NTCP will have the form

 NTCP(D, v) = exp[-N0 v –k exp{-D aRE}]                         

Or         NTCP(D, v) = exp[-N0 v –k exp{-a BED}]                                                     (2)

Where BED = DG. In equation (1), if N0 is considered to be the clonogenic stem cell density of the tumour cells, and the exponent of the partial volume v is taken as k =  -1, then the product of N0v represents the total number of the clonogenic stem cells in the tumour volume and the expression will be of the tumour control probability (TCP) model based on the LQ equation. But in equation (1) the N0 is assumed to be a tissue specific adjustable parameter rather than the clonogenic stem cell density and k is allowed to vary depending on the type of the tissue / organ. To get best fit of normal tissue tolerance data, it is required that parameter k should be greater than zero, i.e. k>0, as the volume of the irradiated tissue / organ increases, the NTCP of the tissue must also increase.

Normal Tissue Tolerance doses

1. Normal Tissue tolerance doses of Emami et al, (1991).

Emami et al (1991) have reviewed available clinical data and presented normal tissue tolerance doses, in terms of TD5/5 (the normal tissue tolerance dose at 5% NTCP within 5 years after radiotherapy) and TD50/5 (the normal tissue tolerance dose at 50% NTCP within 5 years after radiotherapy), for 1/3, 2/3 and 3/3 partial volumes of the normal tissue / organ or a reference volume (length or area) of the normal tissue/organ. The partial volume of a tissue or/and organ is presented in terms of fraction with reference to the reference volume Vref. In some cases the reference volume of the organ is considered to be the whole volume of the organ or in some it is assumed to be a part of the tissue / organ, such as spinal cord, the tolerance doses are compiled for 5, 10 and 20 cm lengths instead of the volume and 20 cm length of the cord is taken to be the reference length, where volume represents the length. For skin, the tolerance doses are provided for the areas of 10, 30 and 100 cm2, where the area of 100cm2 is selected as the reference volume. 

Emami et al (1991) have designed their study to compiled 6 points normal tissue tolerance doses for 1/3, 2/3 and 3/3 partial volumes of the different organs at NTCP 5% and 50% (3 points data at NTCP = 5% and 3 point data at NTCP = 50%, thus total data points are 6) (listed in Table-1 of   Emami et al, 1991). The authors were able to compile 6 points tolerance doses only for 11 organs and could provide 5, 4, 3 and 2 points data for 2, 6, 1 and 9 organs respectively. It is mentioned in the report that due unavailability of the data in the literature, all 6 points data could not be reported for a number of organs. In some cases the data are limited to only whole volume (or reference volume) due to small size of the organs, such as optic nerve, chiasma, cauda equina, eye lens and retina. In case of rectum the reference volume is taken as 100 cm3 and tolerance doses are given only for the reference volume. There is no data provided to show the volume effect.

2. Normal Tissue tolerance doses of other researchers’

Many other workers have also reported normal tissue tolerance doses for different organs / tissue, but these are widely scattered in the literature and is very difficult to extract from all reports. In this study we tried to collect normal tissue tolerance doses for the organs, which were compiled by Emami et al (1991) from the published reports. We have chosen the report where the tolerance doses are given at different NTCP levels for fractional (partial) volumes of the organs or at different NTCP levels for whole organ or at same NTCP level for fractional volumes The data extracted from the repots, other than Emami et al (8), are listed in Table –2. There has not been any control on the tolerance data and these may be of less severe endpoints.
 

RESULTS

Normal tissue tolerance data of Emami et al (1991) used to fit into the equation (1) to obtain the values of aG, k and N0 and the results are listed in Table -1 along with the end points for the normal tissues / organs. In case of 2 points data where these parameters cannot be computed, because no attempt could be made to set correlation between NTCP and volume. Hence the value of k is set equal to zero and values of other parameters are computed. Using the values of aG, k and N0 parameters, determined for included tissues/organs, the values of the tolerance doses for partial volumes of the organs are computed and are listed in Table-3 along with the tolerance doses compiled by Emami et al (1991). Since the parameter aG is a factor of the coefficients a and b (or a/b), so to determine the values of these coefficients, an accurate value of a/b for a tissue / organ must be known. Hence for the same, the published values of a/b, for different organs, are extracted from the literature, and are used to calculated values of a and b. The extracted values of a/b of different tissues / organs, along with their reference of the publication, and calculated values of a and b are listed in Table –5. In the calculation of the values of a and b from the factor aG for listed number of organs, it is assumed that the dose per fraction is 2Gy for the conventional treatment schedule.

Survey of the literature reveals that there is a wide scattering in the normal tissue tolerance data and there is no consensus on the issue among the practiceners. In this study suitable tolerance dose data for the organs have been extracted from the literature and combined together with Emami et al’s (1991) data to compute the values of above said parameters. Table –2 enlists the values of these parameters, i.e. aG, k and N0, for the listed organs, for the combined tolerance data along with the source of reference. With use of the values of aG, k and N0 parameters, from Table-2, the values of the tolerance doses for 1/3, 2/3 & 3/3 partial volumes of all listed organs are computed and are listed in Table-4 along with 95 % confidence interval with that of the computed tolerance doses. The parameter aG is used to compute the values of a and b , for combined data set of the tolerance doses for each organ, the published values of a/b for different organs, as used for Emami et al’s (1991) data, have taken into account. The extracted values of a/b of different tissues / organs, along with their reference of the publication, and calculated values of a and b are listed in Table –5.

Using the values of aG, k and N0, from Tables- 1 & 2, 2 set of curves have been plotted between dose and computed NTCP for bladder, brain, heart and rectum for reported partial and whole volume and are shown in Figures 1-4. The solid lines of the curves are for the Emami et al’s (1991) data and broken lines are for combined data. In the curve fitting, a method of least square fit was used and the data with more than 2 points tolerance doses give all three parameters of the model. Emami et al’s (1991) data with 2 points tolerance doses does not provide the best fit of 3-parameter model and hence the values of these parameters cannot be computed. So to solve the problem for the data with 2 points tolerance doses, the volume dependent parameter k is set to zero, because there is no conclusion could be made on volume dependency of the organ, and rest of the parameters are calculated from these data.
 

DISCUSSION

A number of models have been proposed to predict the NTCP by many authors (Kallman et al, 1992, Lyman, 1985, Zaider & Amols, 1999). All the models predict an increase in NTCP with increasing absorbed dose and irradiated volume. The model, presented in this study, is the Kallman’s (1992) Poisson cell kill model, modified by Zaider and Amols (1999), which had a radiobiological base. Normal tissue tolerance doses of Emami et al (1991) and combined set of the tolerance doses of Emami et al (1991) and other authors, for a number of organs, are used to fit into equation (1) to determine the values of its parameters aG, k and N0. In the computation of the parameters, the method of least square fit is used and equation (1) is transformed into the linear form to get linear regression line. Theoretically calculated values of the tolerance doses using the computed parameters, aG, k and N0, of Emami et al’s (1991) data are very close to the clinical tolerance doses of listed organs (Emami et al, 1991) (Table-3). The theoretical tolerance doses are also calculated for 1/3, 2/3 & 3/3 partial volumes of the organs using the values of aG, k and N0 from Table –2 for the combined set of data.  Values of the parameter, k, in Table-1, reveals that the tolerance doses, compiled by Emami et al (1991), either show volume dependency, i.e. the tolerance dose decreases with increasing the irradiated volume of the organ, or no volume dependency, i.e. there is no change in the tolerance dose with an increase of the irradiated volume for the organs. No volume dependency could be estimated for the organs where only 2 points data set are given, such organs are femoral head and neck, rib cage, skin (telangiectasia), optic nerve, optic chiasma, cauda equina, eye lens, retina, ear (middle/external), parotid, larynx (edema), rectum and thyroid. The value of parameter, k, for these organs is adjusted to zero. The values of the parameters, (a+bd), k and N0 (Table-2), for the combined set of data, the correlation between tolerance dose and volume is similar to that for Emami et al’s (1991) data, except for 2 organs such as spinal cord and larynx (edema), where the value of k is negative which show that the tolerance dose increases with increasing the irradiated volume of these organs which is contrary to the available data and our own experience.

The accuracy of the computed values of the parameters of the model depends on the accuracy of the clinical tolerance data, which are used to compute the parameters. The cases for which the tolerance data, for all defined partial volumes, are provided at both NTCP levels leads to some confidence. The values of the parameters became less accurate for the tolerance data, where the tolerance doses are not provided for one or more partial volumes at either 5% or at 50% or at both NTCP levels. For these data, the dependency of the parameters is more skewed towards data provided for the partial volumes and NTCP.  For example, in case of Emami et al’s (1991) data of skin (necrosis) and brain stem, the tolerance data at NTCP of 5% are provided for all 3 partial volumes, while at NTCP of 50% the data are provided only for whole organ. Hence the parameters, aG, k and N0, of the model have more dependency on the tolerance data provided for NTCP at 5%. Similarly the dependency of the parameters can be seen for other data set. In the cases for which the clinical tolerance data are provided only for one partial volume for NTCPs at 5% and 50%, the volume dependent parameter, k, could not be computed, and hence there will be much less confidence in the results. For the cases for which only 2 points data are provided, the computation of the parameters, (a+bd) and N0, is done by adjusting k = 0, because the reported data show volume independency. The values of the parameters, aG and N0, for 2 points data have less confidence. When other author’s data are combined with the Emami et al’s (1991) data, to compute the values of the parameters, aG, k and N0, the values of these parameters become highly inaccurate. Because most of the other authors data are for single volume of the organ and have a wide variation in there values.  These tolerance data, even sometimes, do not have same endpoint of the complications. Some of the data, included in this study, may have less severe endpoints.

To get more accurate values of the parameters, aG, k and N0, and accurate, additional tolerance dose data are needed. The best use of these parameters can be obtained if radiation oncologist compares the NTCP with his own experience. If the values the parameters match with his own values, then this suggests that the computed values of the parameters are reasonable and can be used to estimate the NTCP of critical organs. But if the computed values of the parameters consistently differ from the values of the radiation oncologist, the new values of the parameters could be used to reflect the local experience.

 The model used, in this study, to generate the NTCP curves is connected with three variables viz. NTCP, delivered dose (D) and partial volume (v) of the irradiated organ. In 2 D graphical representation, a curve can be plotted between any two quantities while keeping the third one constant. While in this study a set of curves have been plotted between dose and NTCP for 1/3, 2/3 and 3/3 partial volumes for bladder, brain, heart and rectum to demonstrate the applicability of the model. These curves are shown in Figures (1-4). It is clear from these curves that these organs demonstrate threshold type behaviour, i.e. for a given partial volume of a organ, the NTCP does not vary with dose until a certain amount of dose is delivered, and then NTCP increases rapidly depending on the partial volume and behaviour of the organ. The NTCP Vs dose curve for these organs have sigmoid shape. There is only difference in the threshold doses and increment in the NTCP with dose (after crossing the threshold dose) and can be seen between the curves of the organs. The 2 points tolerance data for rectum are reported only for one partial volume, hence the curve between NTCP and dose is a single line and does not show volume dependency (Figure-4).

Figure – 1 show that the calculated NTCP, for Emami et al’s (1991) data, increases sharply than that of the combined data. The threshold doses for 1/3, 2/3 and 3/3 partial volumes of combined data are in the range of 35-40 Gy, which are quite lower than that predicted for Emami et al’s (1991) data. For Emami et al’s (1991) data, the threshold doses are 85 Gy, for 1/3 volume; 70 Gy, for 2/3 volume and 60 Gy for 3/3 volume and the window of variation of tolerance doses between the partial volumes, at all NTCP levels, is wider than that of the combined data set, which says that NTCP in bladder is highly volume dependent. On the other hand, a narrow window for combined tolerance data set indicates that NTCP in bladder is less volume dependent. At all dose levels there is a wide variation in the predicted NTCP for both the data sets, which is highly confusing to decide that which data set should be used in the practice. This is also a problem to consider whether NTCP in bladder is a highly volume dependent or less volume dependent. Hence it is recommended that to predict NTCP in bladder, the radiation oncologist should use his own experience.

It is seen in Figure –2 that the predicted NTCP in brain for 2 sets of data in the therapeutic range is reasonably accurate. The threshold dose for these sets of data are almost at the same level and window of variation of tolerance dose is similar between partial volumes. Hence any set of prediction can be used in the practice in the therapeutic range of the doses. At higher doses the predicted NTCP, for tolerance doses of Emami et al (1991), is higher than that of the combined set of the data.

Curves, in Figure –3, show that the predicted NTCP in heart for 2 sets of data is fairly accurate at all doses. The threshold dose for these sets of data are almost at the same level and window of variation of tolerance dose is similar between partial volumes. Hence any set of prediction can be used in the practice.

In case of rectum, Emami et al (1991) have provided 2 points tolerance data from which no correlation could be made between NTCP and volume, hence the value of the parameter k is adjusted equal to zero, which shows volume independency of the NTCP in rectum. While some other reports (Boersma et al, 1998; Dale et al, 2000; Kutcher et al, 1996; Schultheiss et al, 1997; Storey et al, 2000) show that the NTCP increases with increasing the volume of the rectum. Using combined set of tolerance data of Emami et al (1991) and others author’s data, the value of k was found equals to 0.200074, which shows that NTCP is a function of irradiated volume of rectum. The values of all 3 parameters, aG, k and N0, of 2 sets of data, are used to generate the curves between dose and NTCP (Figure-4). In Figure-4, the solid line is for Emami et al’s (1991) data, while broken lines are for combined set of data of Emami et al (1991) and others authors. It is clear from these curves that tolerance doses of Emami et al (1991) do not show volume dependency for rectum. While combined data set have shown volume dependency, but the window of tolerance dose between partial volumes is narrow, hence NTCP in rectum could be considered to be volume independent. The Emami et al’s (1991) data predicts a sharp increase in NTCP and at higher doses it is more than that of the Emami et al (1991) & others authors data. While in therapeutic range both the data set predict NTCP in reasonably accurate.

It can be seen from above said Tables-3 and 4 that some of the organs show wider window of variation in the tolerance doses between partial volumes, and some have very narrow window, while others do not have any variation in the tolerance doses with the change in partial volume. The organs which have very narrow window of tolerance dose variation with the change in partial volume or no window of tolerance dose variation, show that even if a small volume of a organ is irradiated to a sufficiently high dose, a whole organ NTCP will occur, which is independent of the irradiation to the rest of the organ. While in the organs where window of tolerance dose variation with change in partial volume is wider, show that NTCP, in that organ, is a function of dose and volume. In other words, the intensity of NTCP depends on the amount of radiation dose and irradiated volume of the organ i.e. a smaller volume of the organ could tolerate a higher amount of radiation dose than does a large volume in order to cause same NTCP.

Burman et al (1991) used Emami et al’s (1991) data to generate the NTCP curves for these organs. In their study, the Lyman’s (1985) NTCP model has been used to compute its parameters and to generate the NTCP curves. Since the Lyman’s (1985) model is based on the normal distribution of the tolerance data and do not have any correlation with radiobiological processes and findings, hence can not be accounted for varying tissue specific radiobiological parameters. In the present model, the factor aG has two tissue specific radiobiological coefficients, such as a and b, which account for a-cell kill (lethal damage) and b-cell kill (sublethal damage) of the LQ model. For a conventional treatment schedule where 2 Gy per fraction radiation dose is delivered to the organ, the value of the factor aG can directly be used from Tables-1 & 2 to interpret the NTCP of the organ, for any amount of the radiation dose and partial volume of the organ, if the delivered dose is uniform throughout the irradiated volume of the organ. When an altered dose fractionation schedule is used to irradiate the organ, then radiobiological coefficients, a & b (a/b), play an important role in the prediction of the NTCP for a particular dose and volume of the organ. Burman et at (1991) did not say any thing about altered fractionation schedules that by using Lyman’s (1985) model how one could predict NTCP.

To compute the values of a & b from the factor aG, the published values of a/b extracted from the literature, are used and listed in Table –5 along with their source of reference. The main difficulty with the choice of a/b is that in the literature there is no definite value of a/b is reported. Always one can find a range of a/b values reported by different researchers, which made our work somewhat difficult during the search of the literature. We have taken the values of a/b from the published reports, but in the prediction of NTCP for altered fractionation schedules the radiation oncologist must use the value of a/b of his own choice with careful selection to match his own experience.  
 

CONCLUSION

A radiobiological model of NTCP, presented in this study, was used to fit the normal tissue tolerance data compiled by Emami et al (1991) and combined data of Emami et al (1991) and some other investigators. These data sets have provided reasonable estimate of the values of the parameters, aG, k and N0, of the model for all the listed organs. In this model volume correction factor is represented by a power-law and the curves between dose and NTCP are presented.  However, volume wise response of the tissue is a complicated process and is not well understood. There have been attempts other than the power-law to understand the volume dependent complication process (Schultheiss et al, 1983). It has been discussed that in some cases there are insufficient data to determine the values of the parameters, aG, k and N0, more accurately. Hence the calculated values of the parameters represent a substantial extrapolation of the normal tissue tolerance data, like in case of rectum the tolerance data are given only for one volume which show no volume effect which is not true, because in some studies (Boersma et al, 1998; Dale et al, 2000; Kutcher et al, 1996; Schultheiss et al, 1997; Storey et al, 2000) it is seen that rectum has volume dependency.  In case of spinal cord and larynx (edema) the value of k, for combined data set, is negative which shows that the tolerance dose, for these organs, increases with increasing the volume of the organ, which contrary to our experience. This is because of wider variation in tolerance doses of these organs. Hence to find out appropriate reasonable values of the tolerance doses for the organs, more data are required, and widely accepted values of the tolerance doses will be estimated. The model used in this study can be used to estimate the outcome of altered multifractionation schedules because it has a radiobiological basis. The generated curve can be used to estimate the NTCP for a fractional (partial) volume of the organ if it is being irradiated uniformly and match with local experience. The values of a and b along with two other parameters of the model could be used to compute the value of the NTCP for an altered fractionation schedules.
 

Table-1: Parameters  aG, k and N0, for different organs (Emami et al (1991) data).

Organ

aG

         k

          N0

  End Point

Kidney

0.0177

4.6091

123.37

Clinical nephritis

Brain

0.0975

1.3390

235.36

Necrosis / infraction

Brain stem

0.0956

0.8815

345.81

Necrosis / infraction

Ear(Mid/Ext)

0.1464

0

241.84

Acute serious otitis

Ear(Mid/Ext)

0.1464

0

9391.38

Chronic serious otitis

Esophagus

0.1180

0.4681

2132.37

Clinical stricture/ perforation

Heart

0.1395

2.5911

669.16

Pericarditis

Bladder

0.1171

2.9239

7007.99

Symptomatic bladder contracture and volume loss

Larynx

0.1291

1.1778

19147.40

Cartilage necrosis

Larynx

0.0418

0

19.67

Laryngeal edema

Liver

0.1587

2.5643

349.84

Liver failure

Lung

0.0977

3.0007

11.90

Pneumonitis

 

Skin

0.0886

0.0976

0.5867

0

351.42

393.94

Necrosis / ulceration

Telangiectasia

Small intestine

0.1126

0.7617

302.92

Obstruction / perforation

Colon

0.1464

1.3323

2172.96

Obstruction / perforation / ulceration / fistula

Spinal cord

0.0714

0.1211

90.68

Myelitis / necrosis

 

Stomach

0.1151

0.7637

1118.77

Ulceration / perforation

 

Temporomandibular joint & mandible

0.1195

0.5782

3508.31

Marked limitation of the joint function

Cauda equine

0.0976

0

1045.23

Clinically apparent nerve damage

Brachial plexus

0.0976

0.1736

1054.43

Clinically apparent nerve damage

Femoral head & neck

0.1126

0

1045.23

Necrosis

Eye lens

0.1824

0

18.67

Cataract requiring intervention

Optic nerve

0.0976

0

393.94

Blindness

Optic chiasma

0.0976

0

393.94

Blindness

Retina

0.0732

0

80.68

Blindness

Rectum

0.0732

0

241.84

Severe proctitis / necrosis / stenosis / fistula

Rib cage

0.0975

0

393.94

Pathologic fracture

Parotid

0.1046

0

85.01

Xerostomia

Thyroid

0.0419

0

19.76

Clinical thyroiditis



Table-2: Parameters 
aG, k and N0, for different organs (Emami et al (8) + others tolerance data).

Organ

 aG

         K

          N0

References

Kidney

0.0962

2.3462

15.55

Emami et al,1991; Rubin et al, 1975; Rubin, 1989; Rubin & Cassarett, 1973; Willett et al, 1986

Brain

0.0683

0.7031

75.43

Emami et al,1991; Rubin et al, 1975; Rubin, 1989; Marks et al 1972; Schultheiss et al 1995

Brain stem

0.1062

0.6210

814.40

Emami et al,1991; Rubin et al, 1975;  Lee et al, 1992

Ear(Mid/Ext)

0.1464

0

241.84

Emami et al,1991

Ear(Mid/Ext)

0.1289

0.1647

4033.12

Emami et al,1991; Devineni, 1997, Lee et al, 1992

Esophagus

0.0976

0.1811

748.82

Emami et al,1991; Rubin et al, 1975; Coia et al 1995

Heart

0.1158

2.5685

183.67

Emami et al,1991; Rubin et al, 1975; Rubin, 1989;

Bladder

0.0476

0.1582

42.61

Emami et al,1991; Rubin et al, 1975; Rubin, 1989; Storey et al, 2000; Marks et al, 1995

Larynx (Cartilage necrosis)

0.1291

1.1778

19147.40

Emami et al,1991

Larynx (Edema)

0.0613

-1.2949

153.94

Emami et al,1991; Mendenhall et al, 1997.

Liver

0.1050

1.6023

56.491

Emami et al,1991; Rubin et al, 1975; Rubin, 1989; Jirtle et al 1990

Lung

0.0468

1.0299

3.93

Emami et al,1991; Rubin et al, 1975; Emami & Graham, 1997; McDonald et al 1995

Skin->    Necrosis:

     

      Telangiectasia:

0.0857

 

0.0885

0.6015

 

0

283.51

 

219.39

Necrosis:- Emami et al,1991; Rubin et al, 1975; Archambeau et al 1995

Telangiectasia:- Emami et al,1991; Archambeau et al 1995

Small intestine

 0.1071

0.3737

345.60

Emami et al,1991; Rubin et al, 1975; Rubin, 1989

Colon

0.1464

1.3323

2172.96

Emami et al,1991

Spinal cord

0.0614

-0.0489

56.12

Emami et al,1991; Rubin et al, 1975;  Rubin, 1989; Marcus & Million, 1990; Schultheiss et al, 1990; Fowler et al, 2000; Schultheiss et al 1995; Schultheiss & Stephens, 1992; Schultheiss  1990

Stomach

0.0968

1.0179

277.26

Emami et al,1991; Rubin et al, 1975 

Temporomandibular joint & mandible

0.0796

0.0227

361.39

Emami et al,1991; Rubin et al, 1975; Rubin, 1989; Lee et al 1992; Withers et al, 1995a & b; Beumer 1976; Bedwinek 1976; Murray 1980a & b; Morrish 1981; Cooper 1995

Cauda equina

0.0885

0

538.20

Emami et al,1991; Rubin et al, 1975

Brachial plexus

0.0832

0.2908

351.65

Emami et al,1991; Powell et al 1990

Femoral head & neck

0.0842

0

280.26

Emami et al,1991; Rubin et al, 1975

Eye lens

0.1450

0

7.99

Emami et al,1991; Rubin, 1989; Marriam & Focht, 1957

Optic nerve

0.0828

0

177.81

Emami et al,1991; Rubin et al, 1975; Parsons et al, 1994a & b; Harris & Levens, 1976

Optic chiasma

0.0418

0

23.73

Emami et al,1991; Jiang et al, 1994

Retina

0.0866

0

143.02

Emami et al,1991; MacFaul & Bedford, 1970 ; Gordan et al 1995

Rectum

0.0490

0.2001

42.44

Emami et al,1991; Rubin et al, 1975; Rubin, 1989; Chen et al, 2000; Wachter et al, 2002;Storey et al, 2000; Schultheiss et al, 1997; Boersma et al, 1998; Kutcher et al, 1996

Rib cage

0.0944

0

415.08

Emami et al,1991; Overgaard, 1988

Parotid

0.0569

0.0192

13.16

Emami et al,1991; Rubin et al, 1975

Thyroid

0.0139

0

4.39

Emami et al,1991; Rubin et al, 1975



Table-3. Tolerance doses of Emami et al (1991) predicted tolerance doses by proposed model.

 

TD5/5 (Gy)

Volume

           TD50/5 (Gy)

             Volume

 

Organ

    1/3

    2/3

     3/3

    1/3

    2/3

     3/3

 End point

 

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

 

Kidney

50

49.64

30

31.38

23

21.06

--

57.88

40

39.63

28

29.30

Clinical nephritis

Brain

60

59.90

50

50.27

45

44.82

75

74.91

65

65.28

60

59.83

Necrosis/ infraction

 

Brain stem

60

59.86

53

53.39

50

49.73

--

75.14

--

68.67

65

65.02

Necrosis/ infraction

 

Ear(Mid/Ext)

30

30

30

30

30

30

40

40

40

40

40

40

Acute serious otitis

Ear(Mid/Ext)

55

55

55

55

55

55

65

65

65

65

65

65

Chronic serious otitis

Esophagus

60

60

58

57.23

55

55.66

72

72.41

70

69.63

68

68.07

Clinical stricture/ perforation

Heart

60

59.26

45

46.23

40

38.86

70

69.69

55

56.66

50

49.29

Pericarditis

 

Bladder

--

93.93

80

76.25

65

66.25

--

106.43

85

88.75

80

78.75

Symptomatic bladder contracture and volume loss

Larynx

79

78.02

70

71.56

70

67.90

90

89.36

80

82.90

80

79.25

Cartilage necrosis

 

Larynx

--

45

45

45

45

45

--

80

--

80

80

80

Laryngeal edema

 

Liver

50

47.60

35

36.27

30

29.86

55

56.78

45

45.45

40

39.04

Liver failure

 

Lung

45

47.88

30

26.36

17.5

14.19

65

62.93

40

41.41

24.5

29.24

Pneumonitis

 

Skin

10cm2

70

10cm2

69.07

30cm2

60

30cm2

61.79

100cm2

55

100cm2

53.81

10cm2

--

10cm2

85.60

30cm2

--

30cm2

78.32

100cm2

70

100cm2

70.34

Necrosis/ ulceration

 

Small intestine

50

48.50

--

43.71

40

41.00

60

61.50

--

56.71

55

54.00

Obstruction/ perforation

Colon

55

55

--

48.61

45

45

65

65

--

58.61

55

55

Obstruction/ perforation/ ulceration/fistula

Spinal cord

5cm

50*

5cm

50.14*

10cm

50

10cm

48.96

20cm

47

20cm

47.78

5cm

70*

5cm

70.64*

10cm

70

10cm

69.47

20cm

--

20cm

68.29

Myelitis/necrosis

 

 

                                                Table-3 (Cont.)

 

                                                TD5/5 (Gy)

                                                    Volume

                                                         TD50/5 (Gy)

                                                           Volume

 

Organ

              1/3

    2/3

     3/3

    1/3

    2/3

     3/3

 End point

 

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

Clinical

Calc.

 

Stomach

60

58.83

55.0

54.13

50

51.47

70

71.55

67

66.85

65

64.19

Ulceration/ perforation

 

Temporomandibular joint & mandible

65

64.46

60

61.06

60

59.13

77

76.70

72

73.29

72

71.37

Marked limitation of the joint function

Cauda equina

--

60

--

60

60

60

--

75.01

--

75.01

75

75.01

Clinically apparent nerve damage

Brachial plexus

62

62.06

61

60.82

60

60.11

77

77.07

76

75.82

75

75.12

Clinically apparent nerve damage

Femoral head & neck

--

52

--

52

52

52

--

65

--

65

65

65

Necrosis

Eye lens

--

10

--

10

10

10

--

18

--

18

18

18

Cataract requiring intervention

Optic nerve

--

50

--

50

50

50

--

65

--

65

65

65

Blindness

 

Optic chiasma

--

50

--

50

50

50

--

65

--

65

65

65

Blindness

Retina

--

45

--

45

45

45

--

65

--

65

65

65

Blindness

 

Rectum

--

61.38

--

60.50

60

60

--

81.38

--

80.50

80

80

Severe proctitis/ necrosis/ stenosis/ fistula

Rib cage

50

50

--

50

--

50

65

65

--

65

--

65

Pathologic fracture

 

Parotid

--

32

32

32

32

32

--

46

46

46

46

46

Xerostomia

 

Thyroid

--

45

--

45

45

45

--

79.91

--

79.91

80

79.91

Clinical thyroiditis

 


 

Table-4: Normal Tissue Tolerance doses with 95% confidence interval (Gy)( combined data of Emami et al (1991) and other researchers).

 

Organ

TD5/5(1/3)+/-95% CI

TD5/5(2/3)+/-95% CI

TD5/5(3/3)+/-95% CI

TD50/5(1/3)+/-95% CI

TD50/5(2/3)+/-95% CI

TD50/5(3/3)+/-95% CI

Kidney

43.92 (41.31–46.54)

27.02 ( 24.40-29.63)

17.12 ( 14.51-19.74)

59.14 (56.53-61.76 )

42.23 (39.62-44.85 )

32.34 (29.73-34.95 )

Brain

58.56 (55.34–61.78)

51.42 ( 48.21-54.64)

47.25 ( 44.03-50.46)

80 (76.78-83.21 )

72.86 (69.64-76.07 )

68.68 (65.47-71.90 )

Brain stem

59.20 (56.10–62.31)

55.15 ( 52.05-58.26)

52.78 ( 49.67-55.89)

72.99 (69.88-76.09 )

68.93 (65.83-72.04 )

66.56 (63.46-69.67 )

Ear(Mid/Ext)

29.99 (29.99-30 )

29.99 ( 29.99-30)

29.99 ( 29.99-30)

39.99 (39.99-40 )

39.99 (39.99-40 )

39.99 (39.99-40 )

Ear(Mid/Ext)

57.30 ( 54.74-59.86)

56.41 ( 53.85-58.98)

55.9 ( 53.33-58.46)

68.66 (66.06-71.22 )

67.77 (65.21-70.33 )

67.25 (64.69-69.81 )

Esophagus

59.10 ( 57.34-60.87)

57.82 ( 56.05-59.58)

57.07 ( 55.3-58.83)

74.1 (72.34-75.87 )

72.82 (71.05-74.58 )

72.07 (70.30-73.83 )

Heart

59.91 ( 58.25-61.56)

44.53 ( 42.88-46.19)

35.54 ( 33.88-37.20)

72.54 (70.89-74.20 )

57.17 (55.51-58.83 )

48.18 (46.52-49.84 )

Bladder

59.40 ( 54.71-64.09)

57.1 ( 52.41-61.79)

55.75 ( 51.06-60.44)

90.14 (85.45-94.83 )

87.84 (83.15-92.53 )

86.49 (81.80-91.18 )

Larynx (Cartilage necrosis)

77.90 ( 76.52-79.26)

71.57 ( 70.19-72.96)

67.88 ( 66.49-69.26)

89.24 (87.85-90.62 )

82.91 (81.53-84.29 )

79.21 (77.83-80.60 )

Larynx (Edema)

41.05 ( 37.14-44.96)

55.69 ( 51.78-59.60)

64.25 ( 60.34-68.17)

64.92 (61.01-68.84 )

79.56 (75.65-83.48 )

88.13 (84.21-92.04 )

Liver

44.73 ( 42.51-46.94)

34.15 ( 31.94-36.37)

27.96 ( 25.75-30.18)

58.66 (56.45-60.88 )

48.09 (45.87-50.30 )

41.9 (39.69-44.12 )

Lung

29.93 ( 21.51-38.34)

14.69 ( 6.269-23.10)

5.771 ( -2.65-14.19)

61.18 (52.76-69.60 )

45.94 (37.52-54.35 )

37.02 (28.6-45.44 )

Skin->  

 

 

 

 

 

 

               Necrosis:

60.84 ( 58.48-63.20)

55.97 ( 53.61-58.33)

53.12 ( 50.76-55.48)

77.92 (75.57-80.28 )

73.06 (70.70-75.42 )

70.21 (67.85-72.57 )

      Telangiectasia:

48.54 ( 47.51-49.58)

48.54 ( 47.51-49.58)

48.54 ( 47.51-49.58)

65.09 (64.06-66.13 )

65.09 (64.06-66.13 )

65.09 (64.06-66.13 )

Small intestine

48.17 ( 45.77-50.56)

45.75 ( 43.36-48.14)

44.33 ( 41.94-46.73)

61.83 (59.44-64.23 )

59.41 (57.02-61.81 )

58 (55.61-60.39 )

Colon

55.00 ( 0.0-0.0)

48.69 (0.0-0.0)

45 ( 0.0-0.0)

65 (0.0-0.0 )

58.69 (0.0-0.0 )

55 (0.0-0.0 )

Spinal cord

46.89 ( 43.58-50.19)

47.44 ( 44.13-50.75)

47.76 ( 44.45-51.07)

70.74 (67.44-74.05 )

71.30 (67.99-74.61 )

71.62 (68.31-74.93 )

Stomach

58.33 ( 56.10-60.55)

51.04 ( 48.81-53.26)

46.77 ( 44.55-49.00)

73.45 (71.22-75.67 )

66.16 (63.93-68.39 )

61.9 (59.67-64.12 )

Temporomandibular joint & mandible

60.51 ( 57.75-63.27)

60.32 ( 57.56-63.08)

60.2 ( 57.44-62.96)

78.90 (76.14-81.66 )

78.7 (75.94-81.46 )

78.58 (75.82-81.35 )

Cauda equina

58.65 ( 47.06-70.25)

58.65 ( 47.06-70.25)

58.65 ( 47.06-70.25)

75.19 (63.60-86.79 )

75.19 (63.60-86.79 )

75.19 (63.60-86.79 )

Brachial plexus

61.09 ( 59.70-62.48)

58.67 ( 57.27-60.06)

57.25 ( 55.86-58.64)

78.67 (77.28-80.06 )

76.25 (74.86-77.64 )

74.83 (73.44-76.23 )

Femoral head & neck

51.61 ( 41.56-61.66)

51.61 ( 41.56-61.66)

51.61 ( 41.56-61.66)

63.70 (53.65-73.74 )

63.7 (53.65-73.74 )

63.7 (53.65-73.74 )

Eye lens

6.762 ( 4.29-9.23)

6.762 ( 4.294-9.229)

6.762 ( 4.294-9.229)

16.86 (14.39-19.32 )

16.86 (14.39-19.32 )

16.86 (14.39-19.32 )

Optic nerve

49.34 ( 46.06-52.62)

49.34 ( 46.06-52.62)

49.34 ( 46.06-52.62)

67.02 (63.74-70.31 )

67.02 (63.74-70.31 )

67.02 (63.74-70.31 )

Optic chiasma

49.54 ( 37.54-61.54)

49.54 ( 37.54-61.54)

49.54 ( 37.54-61.54)

84.57 (72.57-96.57 )

84.57 (72.57-96.57 )

84.57 (72.57-96.57 )

Retina

44.67 ( 43.04-46.29)

44.67 ( 43.04-46.29)

44.67 ( 43.04-46.29)

61.58 (59.95-63.20 )

61.58 (59.95-63.20 )

61.58 (59.95-63.20 )

Rectum

58.56 ( 55.15-61.97)

55.73 ( 52.32-59.14)

54.08 ( 50.66-57.49)

88.42 (85.00-91.83 )

85.59 (82.17-89.00 )

83.93 (80.52-87.35 )

Rib cage

52.23 ( 49.78-54.69)

52.23 ( 49.78-54.69)

52.23 ( 49.78-54.69)

67.74 (65.29-70.19 )

67.74 (65.29-70.19 )

67.74 (65.29-70.19 )

Parotid

26.38 ( 9.74-43.02)

26.14 ( 9.501-42.78)

26 ( 9.364-42.65)

52.09 (35.45-68.73 )

51.86 (35.22-68.50 )

51.72 (35.08-68.36 )

Thyroid

27.50 ( -2.21-57.20)

27.5 ( -2.2-57.2)

27.5 ( -2.2-57.20)

132.5 (102.8-162.2) )

132.5 (102.8-162.2 )

132.5 (102.8-162.2 )

 

Table – 5. Values of the a/b and calculated values of a & b for listed organs (Emami et al (8) and Emami et al (8) + others).

 

Emami et al (8)

Emami et al (8) + others

 

Organ

a/b (Gy)

a (Gy-1)

b (Gy-2)

a (Gy-1)

b (Gy-2)

End point

Reference

Kidney

3.0-3.5  

 

2.5

0.0106-0.0113

 

0.0099

0.0036-0.0032

 

0.0039

0.0577-0.0612

 

0.0534

0.0192-0.0175

 

0.0214

Clinical nephritis

Turesson & Notter, 1985; Stewart et al 1984a & b;

Van der Kogel & Ruifrok , 1991.

Brain

2.1

0.0499

0.0238

0.0350

0.0167

Necrosis/ infraction

Meeks et al, 2000; Hornsey et al ,1981

Brain stem

2.1

0.0491

0.0234

0.0544

0.0259

Necrosis/ infraction

Meeks et al, 2000; Hornsey et al, 1981

Ear(Mid/Ext)

3.0*

0.0878

0.0293

0.0878

0.0293

Acute serious otitis

Silva et al, 2000

Ear(Mid/Ext)

3.0*

0.0878

0.0293

0.0773

0.0258

Cronicserious otitis

Silva et al, 2000

Esophagus

3.0*

0.0708

0.0236

0.0585

0.0195

Clinical stricture/ perforation

Akagi et al, 1999

Heart

2.0

0.0702

0.0351

0.0579

0.0290

Pericarditis

Martel et al, 1998; McChesney et al, 1992; Stewart et al, 1995

Bladder

6.0

3.4 - 4.5 

0.0878

0.0737-0.0811

0.0146

0.0217-0.0780

0.0357

0.030-0.033

0.0060

0.0088-0.0073

Symptomatic bladder contracture and volume loss

Stewart et al, 1984a & b

Parez  et al, 1997a & b

Larynx

»3.4

<4.4

<4.2

»0.0813

0.0888

0.0875

»0.0239

0.0202

0.0208

»0.0813

0.0888

0.0875

»0.0239

0.0202

0.0208

Cartilage necrosis

Henk & James, 1978

Horiot et al, 1972

Flatcher et al, 1974; Stell et al 1973

Larynx

3.8

0.0274

0.0072

0.0402

0.0106

Laryngeal edema

Maciejewski et al ,1986

Liver

1.5

0.0683

0.0455

0.045

0.030

Liver failure

Lawrance et al ,1992

Lung

<3.8

4.4 – 6.9

£0.0637

0.0669-0.0754

³0.0168

0.0152-0.0109

£0.0307

0.0322-0.0363

³0.0081

0.0073-0.0093

Pneumonitis

Cox, 1987

Overgaard, 1985, 88

Skin

1.9 – 2.3

0.0432-0.0474

0.0227-0.0206

0.0417-0.0458

0.022-0.0199

Necrosis/ ulceration

Overgaard, 1985, 88

Small intestine

6.0-8.3

0.0845-0.0907

0.0141-0.0109

0.0803-0.0863

0.0134-0.0104

Obstruction/ perforation

Withers et al, 1975

Colon

3.1 - 5.0

0.0890-0.1046

 

0.0287-0.0209

 

0.0890-0.1046

 

0.0287-0.0209

 

Obstruction/ perforation/ ulceration/fistula

Terry & Denekamp, 1984

Spinal cord

 <3.3

2.0

0.0445

0.0357

0.0135

0.0179

£0.0382

0.0307

³0.0116

0.0153

Myelitis/necrosis

Disches et al ,1981

Van der Kogel & Ruifrok, 1991

Stomach

7-10

0.0895-0.0959

0.0128-0.0096

0.0753-0.0807

0.0108-0.00807

Ulceration/ perforation

Van der Kogel & Ruifrok, 1991

Temporomandibular joint & mandible

3.5

0.0761

0.0217

0.0507

0.0145

Marked limitation of the joint function

Bentzen et al ,1989

Cauda equina

2.0-3.0

0.0488-0.0586

0.0244-0.0195

0.0443-0.0531

0.0221-0.0177

Clinically apparent nerve damage

Roos et al, 2000

Brachial plexus

<5.3

0.0709

0.0134

£0.0604

 

³0.0114

 

Clinically apparent nerve damage

Powell et al, 1990

Femoral head & neck

0.8

0.0349

0.0388

0.0346

0.0432

Necrosis

Withers et al, 1995a & b

Eye lens

1.2

0.0686

0.0572

0.0544

0.0453

Cataract requiring intervention

Schenken & Hagemann, 1975

Optic nerve

3.0*

0.0586

0.0195

0.0497

0.0166

Blindness

--

Optic chiasma

3.0*

0.0586

0.0195

0.0251

0.0084

Blindness

----

Retina

3.0*

0.0439

0.0146

0.0519

0.0173

Blindness

----

Rectum

3.9

0.0484

0.0124

0.0324

0.0083

Severe proctitis/ necrosis/ stenosis/ fistula

Deore et al, 1993

Rib cage

1.8-2.8

0.0462-0.0569

0.0257-0.0203

0.0447-0.0551

0.0248-0.0197

Pathologic fracture

Overgaard, 1985, 88

Parotid

3.0*

0.0628

0.0209

0.0341

0.0114

Xerostomia

---

Thyroid

3.0*

0.0251

0.0084

0.0084

0.0028

Clinical thyroiditis

---

                 

*Assumed values of alpha/beta for late reacting tissues.
 

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Figure –1: Curves between bladder NTCP and dose for 2 data sets are plotted. The solid lines are for Emami et al (1991) tolerance doses and broken lines for combined set of data of Emami et al (1991) and other investigators. In both the sets, the thin, thick and thicker are for 1/3, 2/3 and 3/3 partial volumes respectively.

 

 

 

 

 

 

 

 

Figure –2: Curves between brain NTCP and dose for 2 data sets are plotted. The solid lines are for Emami et al (1991) tolerance doses and broken lines for combined set of data of Emami et al (1991) and other investigators. In both the sets, the thin, thick and thicker are for 1/3, 2/3 and 3/3 partial volumes respectively.
 

 

 

 

 

 

 

 



Figure –3: Curves between heart NTCP and dose for 2 data sets are plotted. The solid lines are for Emami et al (1991) tolerance doses and broken lines for combined set of data of Emami et al (1991) and other investigators. In both the sets, the thin, thick and thicker are for 1/3, 2/3 and 3/3 partial volumes respectively.

 

 

 

 

 

 

 


 

Figure –4: Curves between rectum NTCP and dose for 2 data sets are plotted. The single solid line is for Emami et al (1991) tolerance doses and broken lines for combined set of data of Emami et al (1991) and other investigators. In 2nd  sets, the thin, thick and thicker are for 1/3, 2/3 and 3/3 partial volumes respectively.