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Int. J. Radiation Oncology Biol. Phys., Vol. 67, No. 3, pp. 660–669, 2007Copyright © 2007 Elsevier Inc.
Printed in the USA. All rights reserved0360-3016/07/$–see front matter
doi:10.1016/j.ijrobp.2006.09.021
LINICAL INVESTIGATION Head and Neck
THE IMPACT OF DOSE ON PAROTID SALIVARY RECOVERY IN HEADAND NECK CANCER PATIENTS TREATED WITH RADIATION THERAPY
YUN LI, M.S.,* JEREMY M. G. TAYLOR, PH.D.,*† RANDALL K. TEN HAKEN, PH.D.,†
AND AVRAHAM EISBRUCH, M.D.†
*Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI; †Department of RadiationOncology, School of Medicine, University of Michigan, Ann Arbor, MI
Purpose: A common side effect experienced by head and neck cancer patients after radiation therapy (RT) isimpairment of the parotid glands’ ability to produce saliva. Our purpose is to investigate the relationship betweenradiation dose and saliva changes in the 2 years after treatment.Methods and Materials: The study population includes 142 patients treated with conformal or intensity-modulated radiotherapy. Saliva flow rates from 266 parotid glands are measured before and 1, 3, 6, 12, 18, and24 months after treatment. Measurements are collected separately from each gland under both stimulated andunstimulated conditions. Bayesian nonlinear hierarchical models were developed and fit to the data.Results: Parotids receiving higher radiation produce less saliva. The largest reduction is at 1–3 months after RTfollowed by gradual recovery. When mean doses are lower (e.g., <25 Gy), the model-predicted averagestimulated saliva recovers to pretreatment levels at 12 months and exceeds it at 18 and 24 months. For higherdoses (e.g., >30 Gy), the stimulated saliva does not return to original levels after 2 years. Without stimulation,at 24 months, the predicted saliva is 86% of pretreatment levels for 25 Gy and <31% for >40 Gy. We do notfind evidence to support that the overproduction of stimulated saliva at 18 and 24 months after low dose in 1parotid gland is the result of low saliva production from the other parotid gland.Conclusions: Saliva production is affected significantly by radiation, but with doses <25–30 Gy, recovery issubstantial and returns to pretreatment levels 2 years after RT. © 2007 Elsevier Inc.
Head and neck cancer, Intensity-modulated radiation therapy, Parotid salivary glands, Radiation dose, Bayesian
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INTRODUCTION
ead and neck cancer patients are frequently treated withadiation therapy (RT) in combination with other treatmentsuch as surgery and chemotherapy. However, the exposureo radiation can cause damage to parotid glands and impairheir ability to produce saliva. The loss of salivary output is
major complication because it leads to dry mouth (xero-tomia) and oral discomfort for patients after radiotherapy1). It causes difficulty in chewing, swallowing, food-tast-ng, and does harm to dental health. In some patients, theeduction in saliva output is transient, and in others it canersist for a year or longer. Therefore, treatment strategieshat lead to long-term adequate saliva output are of vitallinical importance to the patient.
Conventional treatment planning, in general, requiresigh radiation dosage to both parotid glands and, hence,ften leads to severely reduced salivary flow. Thus, attemptso minimize the radiation dosage to these normal tissues to
Reprint requests to: Jeremy M. G. Taylor, Department of Bio-tatistics, School of Public Health, University of Michigan, 1420
ashington Heights, Ann Arbor, MI 48109–2029, USA. Tel:734) 936-3287; Fax: (734) 763-2215; E-mail: [email protected]
Supported by the National Institutes of Health, grant number
O1 CA095096.660
iminish this side effect have been necessary. Three-dimen-ional (3-D) conformal and multisegmental intensity-mod-lated radiotherapy treatment planning makes it possible toeduce the dose to the parotid. Yet, at the same time, theechnique gives adequate dosage to the tumors and lymphodes (2–8). A common treatment strategy is to allow highoses to the ipsilateral parotid gland while delivering asmall a dose as possible to the contralateral gland. Thistrategy should ensure that the patient at least has somealiva production. It is also plausible that the patient’s salivaroduction from the contralateral gland will overcompen-ate if the saliva production from the ipsilateral gland isery low, a hypothesis we will investigate in this report.The mechanisms by which radiation damages the cells in
he parotid, and by which this leads to reduced saliva output,s obviously complex and beyond the scope of this paper.imilarly, how damage in the parotid may be repaired over
ime and saliva production recovered is also complicated.
cknowledgments—We thank Tim Johnson, Ph.D., for computingssistance.
Conflict of interest: none.Received July 11, 2006, and in revised form Sept 3, 2006.
ccepted for publication Sept 6, 2006.
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661Dose and parotid salivary recovery in head and neck cancer patients ● Y. LI et al.
his suggests the need to examine the whole time course ofaliva measurements to properly assess the impact of theadiation.
Previous publications from our own data and from othernstitutions have demonstrated a clear impact of dose onaliva production rates after treatment (9, 10). Besides Theniversity of Michigan, other centers have collected and
nalyzed similar data; these include datasets from The Neth-rlands (11), Washington University at St. Louis (12), Hel-inki University Central Hospital in Finland, and Universityospital Gasthuisberg in Belgium (13, 14). These studiesiffer from the current one in a number of aspects, includingethods for measuring saliva and the length of the fol-
ow-up period. Also, more patients are included in theurrent study. Our focus will be on using state-of-the-arttatistical methods to use the available data to the maximumfficiency and give accurate quantitative information abouthe effect of radiation on saliva flow rates. Previous analysesometimes dichotomize the saliva flow rate into a binaryariable, whereas we utilize the full range of the measure-ents to make efficient use of the data.The purpose of our study is to accurately examine the
unctional relationship between radiation dosage and the ratesf functional recovery in parotid glands over the course of 2ears after radiotherapy. We prospectively followed theatients and investigated the functional alternations in thearotid glands in the course of 2 years. We used a sophis-icated statistical model and a Bayesian estimation scheme.he model allows for a dose–response relationship that canary with follow-up time. The model also accounts for theorrelation among saliva flow rates of the same parotidlands over time and captures the excess of zero salivautput in our data. Besides the relationship between radia-ion dose and salivary flow rates, we also examine theypothesis that the contralateral side may compensate forhe loss of saliva secretion functionality on the ipsilateralide.
METHODS AND MATERIALS
atient populationThe study population included 142 head and neck cancer pa-
ients who received conformal or intensity-modulated therapy athe University of Michigan from 1994 to 2003. Informed consent
orms approved by the Institutional Review Board of The Univer-ity of Michigan were signed by all patients. These patients werereated with radiotherapy primarily or in combination with otherypes of treatment, such as surgery or chemotherapy, before irra-iation. These data are an updated version of data that have beenescribed previously (6). Previous analyses showed that neitherhemotherapy or pre-RT surgery nor type of medications receivedmpacted saliva flow rates, thus these were not considered (6). Allatients had data available on radiation dose to the parotid, and ateast one saliva flow rate measurement. It was a prospective study
nd patients were followed for up to 2 years after RT. dadiation treatment planningThree-dimensional conformal or intensity-modulated radiother-
py allows customized radiation beam arrangement and moreccurate delivery of specific radiation dosage to tumor cells ac-ording to each patient’s tumor location and the disease severity.he detailed University of Michigan planning system has beenescribed previously (2–6, 15). The goal of the treatment plannings, in general, to give the contralateral parotid gland a low dose ofadiation, to minimize the damage, while still allowing sufficientadiation to the tumor cells. The treatment scheme delivers radia-ion in small fractions: 1.8–2.0 Gy per fraction to the tumor, 1raction per day, 5 fractions per week. The total dose prescribed tohe tumor is about 60–75 Gy. The computed tomography-basedadiation therapy records give accurate 3-D dose distributions inach parotid gland and the dose distribution is summarized byose–volume histogram (DVH) (16). In our analysis, the meanadiation dose to each gland was calculated from the DVH.
aliva measurementsSalivary flow rates are measured before RT and 1, 3, 6, 12, 18,
nd 24 months after RT. Patients are measured separately on bothpsilateral and contralateral parotid glands using Carlson-Crit-enden cups. Patients are not allowed to drink or eat for at least 90inutes before the saliva collection, and all the samples are col-
ected in the morning to reduce diurnal variations in the salivautput. For the parotid gland of each patient, unstimulated andtimulated parotid saliva was collected. Stimulation of saliva flowas obtained by applying 2% citric acid on the dorsolateral sur-
aces of the tongue. Saliva samples were collected in small plasticontainers. The flow rates are calculated as described previously6) and the units of the flow rate are in milliliters per minute.
tatistical methodsWe develop a Bayesian nonlinear hierarchical regression model
or the saliva data. Because saliva output from the same parotidland tends to be similar over time relative to that from otherlands, we account for the possible correlations among salivautput of the same parotid with this model. Preliminary analysesuggested that there is little correlation between the flow rates onhe ipsilateral and contralateral sides for the same person, so thisotential correlation is not included in the model. Because salivautput under stimulated conditions is very different from thatnder unstimulated conditions, we modeled responses from stim-lated and unstimulated conditions separately. An initial postulates that saliva flow rates have a Poisson distribution, which wouldequire integer counts. Thus, we transformed the units of salivaow rates by multiplying it by a factor of 150 and then round themp to be integers, which becomes our outcome of interest. Whenhe radiation dosage is very high, e.g., �45 Gy, a majority of theatients did not produce saliva even after 1 or 2 years of recovery.he excess of zero saliva output can likely cause overdispersion;ence, we assumed an overdispersed Poisson distribution, alsoalled a negative binomial distribution, for the transformed countata.Let Yij be saliva output at time j for parotid i. When j � 0, it
epresents baseline before the treatment and j � 1,2,3,4,5, and 6epresent 1, 3, 6, 12, 18 and 24 months after the treatment respec-ively. Let d*i be the average dose for parotid i. Let dij representshe average radiation dose for parotid gland i at time j. Thus, di0 �
and dij � d*i for j �0. Yij follows the negative binomial
istribution with mean �ij, which can be parameterized as:
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662 I. J. Radiation Oncology ● Biology ● Physics Volume 67, Number 3, 2007
r (Yij � yij) � � yij � ��ij � 1
yij�� �
� � 1���ij� 1
� � 1�yij
,
yij � 0, 1, 2, . . .
e model the outcome through the mean parameter �ij with ainear spline model and log link,
log(�ij) � �0 � �1jdij � �2(dij � 25)� � �3(dij � 45)� � �i (i)
n this model, (dij –25)� represents the difference between radia-ion dose and 25 if the dose is �25, otherwise, the quantity equals, similarly for (dij –45)�; exp��0� is the transformed baselinealiva flow rate; �1j represents the dose effect on saliva at timeoint j when dose is �25 Gy; �2 and �3 denote the additionalinear dose effect beyond 25 Gy and 45 Gy, respectively. Thisinear spline model allows for a continuous and different effect ofose at each time point. The parameters �2 and �3 were initiallylso allowed to depend on time j, but this did not improve the fito the data.
The term �i is a random effect assumed to follow a normalistribution with mean 0 and variance ��
2, which allows eacharotid to have its own initial level. By using �i, we capture theorrelation among the saliva flow rates over time for the samearotid. The negative binomial distribution has a mean of �ij andariance of �ij�� � 1⁄��; the factor �� � 1⁄�� is the overdispersionactor relative to the Poisson distribution to capture the excess zeroaliva flow rates in our data. A Bayesian estimation method wassed to estimate the model parameters; the details are given in theppendix.We extend our model to evaluate the compensation hypothesis;
hat is, higher than expected saliva flow rate from one parotid, ifhe other parotid had very low flow rate. This was achieved by theollowing modification:
og(�ij) � �0 � �1jdij � �2(dij � 25)� � �3(dij � 45)�
� �4I(Yij C)I(j 0) � �i (ii)
here Yij is the saliva flow rate from the parotid in the oppositeheek from that labeled as i, and C denotes the cut-off value.�Yij C� equals to 1 if yij is less than or equal to C; otherwise, itquals 0. I�j 0� is an indicator variable with value of 0 for theaseline measurement and 1 for other time points. The coefficient
4 being positive would suggest overcompensation. A cut-off value of� 1 is used for stimulated data and about 1% of the baseline
ransformed saliva counts are 1. The cut-off for the unstimulatedondition is C � 0, which accounts for 3% of the baseline counts.
total of 20 people have occurrences of saliva measurements forne parotid but are missing measurements for the opposite parotidt that time point. Besides excluding these observed but unpairedaliva measurements from the model, we performed two sensitivitynalyses in which we assumed either that all the missing measure-ents were less than the cut-off or all were greater than the cut-off.he results from these sensitivity analyses were similar to those
rom the analyses that excluded these patients, so we present only
esults from these later analyses. uRESULTS
atient characteristics.Characteristics of the 142 patients are shown in Table 1.
here are 30 patients treated unilaterally and 112 treatedilaterally. Patients treated unilaterally received high radi-tion dose on their ipsilateral sides and very scattered radi-tion dose on their contralateral sides. One hundred twenty-our patients had dose and at least one saliva floweasurement for both parotids, and the other 18 had both
ata only for one parotid.
adiation dosage.The median of the mean radiation dose received by the
69 parotids is 28.6 Gy, with an interquartile range of8.7–55.4 Gy.
alivary flow rates.The number of parotid glands with saliva flow rateseasured at baseline, 1, 3, 6, 12, 18, and 24 months are 252,
83, 182, 169, 143, 96, and 84 respectively. Most of thettrition is the result of patients’ reluctance to continue thetudy procedure and a small fraction is because of diseaserogression. We assessed the potential bias because of drop-ut and found that there was no significant difference inadiation dosage received or baseline saliva flow rates be-ween patients who do not have saliva data and those whoo, at 1 year and at 2 years.
rradiation effect on saliva outcome.Figure 1 shows the stimulated saliva flow rates at eacheasured time plotted against the mean radiation dose re-
eived. The figure shows a dose–response relationship be-ween saliva production and average dose. Most parotidshat receive a dose of �40 Gy produce zero or very littlealiva in the first year after radiation. There is a clearncrease in saliva flow as the follow-up time increases. Thiss particularly evident for parotids that received doses of
30 Gy. Also, some of the parotids that received higheroses did increase their saliva flow rate with increasingollow-up time. For some parotids that received �25 Gy, itppears that the 18- and 24-month values can be higher thanhe pretreatment values. Figure 2 shows the relationshipetween radiation dose and the amount of saliva produced
Table 1. Patient and tumor characteristics
Total patients (n) 142Males 75.4%Age, median (minimum, maximum) 56 (25,83)Surgery pre-RT (%) 67Chemotherapy (%) 28Tumor Sites
Oral cavity 20%Oropharynx 57%Larynx 19%Other 4%
nder unstimulated conditions. The saliva flow rates under
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663Dose and parotid salivary recovery in head and neck cancer patients ● Y. LI et al.
nstimulated conditions are much less than under stimulatedonditions. There is a similar pattern to that in Fig. 1. Theres a dose–response relationship and some evidence of re-overy with time except at the highest doses; however, theecovery does not return the saliva flow rates to their pre-reatment values.
tatistical model fit to stimulated data.Table 2 lists the parameter estimates and their 95% cred-
ble intervals from fitting the negative binomial model to theata. The effect of radiation is the largest at one month afteradiation, indicated by the largest negative coefficient at oneonth after RT. The coefficients becoming less negative
rom one month to 24 months shows a gradual recovery inhe parotid gland’s ability to produce saliva. For glandseceiving dose dij �25 Gy, the model predicted mean salivaate equals exp(3.97–0.025* dij) at 1 month, exp(3.97 �
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Fig. 1. Stimulated saliva flow rates versus mean radiatiocompletion of radiation therapy. The flow rates are plottThe solid line is the LOESS smoothing line describing
0008* dij) at 12 months, and exp(3.97 � 0.014* dij) at 24 p
onths after RT, respectively. Thus, the predicted averagealiva production is reduced by �50% at one month afterT if dose is �25 Gy. By 12 months after RT, the average
aliva production achieves complete recovery, and by 24onths the parotid glands are able to produce more saliva
han that at baseline. The coefficient of (dij –25)� is nega-ive and its 95% credible interval does not include zero,hich implies significant additional radiation damage, be-ond the linear projection, with doses �25 Gy. In otherords, the rate of reduction in saliva flow becomes much
arger when the radiation dose is �25 Gy. For glandseceiving doses between 25 Gy–45 Gy, the predicted meanaliva flow rates are exp(6.97–0.145* dij) at one month andxp(6.97–0.106* dij) at 24 months after RT. When radiationosage is �45 Gy, the significant positive coefficient indi-ates the rate of reduction decreases as the dose receivedpproaches a very high level. Our data shows that, for
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at baseline and 1, 3, 6, 12, 18, and 24 months after thea log(flow rates � 1) transformed scale for each gland.ationship between flow rates and mean doses.
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664 I. J. Radiation Oncology ● Biology ● Physics Volume 67, Number 3, 2007
eduction approaches a maximum and many parotids pro-uce zero saliva output. The easier way to understand theesults from this model is through a graph to visualize theelationship between radiation dose and salivary recovery.he model-predicted saliva mean trajectory is described inig. 3. It shows a complete recovery of saliva flow by thend of two years after radiotherapy if the radiation dosage is30 Gy. When the dose received is larger, e.g., 40 Gy,
ecovery continues during the course of two years; however,he extent of recovery is small relative to the saliva produc-ion at baseline. Because most of the ipsilateral sides re-eived �45 Gy, complete recovery happened mostly on theontralateral sides.
tatistical model fit to unstimulated data.Similarly, we model the mean saliva output under no
timulated conditions, assuming a negative binomial distri-
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Fig. 2. Unstimulated saliva flow rates versus mean radiathe completion of radiation therapy. The flow rates are plThe solid line is the LOESS smoothing line describing
ution. The parameter estimates are given in Table 3. The s
odel-predicted saliva output is plotted in Fig. 4. It showshat the recovery appears to be much slower compared withtimulated conditions. The recovery begins only about 12onths after radiotherapy. After two years, the salivary
unction has recovered to �86% of that at baseline when theadiation dosage is �25 Gy and �31% when dosage is �40y. In general, when radiation dosage is �30 Gy, theamage is substantially larger and the recovery rate appearso be much slower.
As well as the predicted mean values presented in Figs. 3nd 4, the models can also give whole distributions of likelyaliva measurements. These are illustrated in Fig. 5. Thisraph illustrates the heterogeneity in saliva flow rates be-ween patients. The plots show the predicted saliva flowistributions at 18 months for a patient who receives a meanose of 0 Gy (pretreatment), 20 Gy, 30 Gy, and 40 Gy. Withr without stimulation, there is a considerable spread of pos-
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ose at baseline and 1, 3, 6, 12, 18, and 24 months aftern a log(flow rates � 1) transformed scale for each gland.ationship between flow rates and mean doses.
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tion dotted o
ible saliva values, particularly at 20 Gy, but much less spread
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665Dose and parotid salivary recovery in head and neck cancer patients ● Y. LI et al.
t 40 Gy. Under stimulation, the spread at 20 Gy is slightlyarger and slightly shifted to the right relative to that at 0 Gy,ndicating parotid glands likely generating more saliva at 18onths after RT than that before RT. However, no such
henomenon is observed under the unstimulated condition.The extended negative binomial model in (ii) allows for
s to evaluate the possible overcompensation effect in onearotid gland because of very low saliva flow rates from theatient’s other parotid gland. It is fit to both stimulated andnstimulated data. The extra coefficients are insignificant inoth cases, indicating a lack of compensation from thepposite parotid, i.e., for stimulated saliva flow rates: �4 �0.051, 95% CI: (–0.16, 0.056); and for unstimulated salivaow rates: �4 � –0.11, 95% CI: (–0.28, 0.058). Theseesults provide no evidence that the parotid with more
Table 2. Posterior means of parameter estimates of modelspecified in Equation (i) for stimulated saliva flow rates and
their 95% equal-tailed Bayesian credible intervals (CIs)
Time ParameterPosterior
mean (95% CI)
aseline �0 3.97 (3.87, 4.07)ose (1 mo) �11 �0.025 (�0.034, �0.018)ose (3 mo) �12 �0.019 (�0.026, �0.012)ose (6 mo) �13 �0.0094 (�0.016, �0.0021)ose (12 mo) �14 0.00008 (�0.0072, 0.0074)ose (18 mo) �15 0.0096 (0.0022, 0.017)ose (24 mo) �16 0.014 (0.0063, 0.022)( Dose – 25)� �2 �0.12 (�0.15, �0.099)(Dose – 45)� �3 0.070 (0.018, 0.12)
* (Dose – 25)� represents the difference between radiation dosend 25 if the dose is �25Gy; otherwise, the quantity equals 0.Dose – 45)� is similarly defined.
Average Dose
Sal
iva
Flow
Rat
es (m
L/m
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0 15 30 45 60 75
0.0
0.2
0.4
0.6
BaselineMonth 1Month 3Month 6Month 12Month 18Month 24
ig. 3. Mean stimulated saliva counts predicted by the estimatedodel specified in equation (i) for baseline and 1, 3, 6, 12, 18, and
4 months after radiation therapy. 2
unctionality is producing more saliva to compensate forery low productivity from the other more impaired side.
DISCUSSION
In this article we examined the radiation damage to thearotid glands and their functional recovery over the coursef two years after radiation therapy. The amount of radiationxposure plays a central role in this process. A dose–esponse is observed, with the higher the radiation doseeceived the higher the extent of damage from radiation toarotid glands. The relationship between radiation dose andhe reduction in saliva output is not linear. It appears thathere is a significant increase in the extent of damage whenadiation dose is greater than �25 Gy. When the radiationose is �45 Gy, approximately, the damage seems to reach
Table 3. Posterior means of parameter estimates of modelspecified in Equation (i) for unstimulated saliva flow rates and
their 95% equal-tailed Bayesian credible intervals (CI)
Time ParameterPosterior
mean (95% CI )
aseline �0 2.44 (2.261, 2.40)ose (1 mo) �11 �0.0447 (�0.0625, �0.0491)ose (3 mo) �12 �0.0499 (�0.0688, �0.0544)ose (6 mo) �13 �0.0499 (�0.0701, �0.0544)ose (12 mo) �14 �0.0262 (�0.0415, �0.0302)ose (18 mo) �15 �0.0229 (�0.0396, �0.0272)ose (24 mo) �16 �0.00633 (�0.0226, �0.0107)(Dose – 25)� �2 �0.0609 (�0.108, �0.0741)(Dose – 45)� �3 �0.0734 (�0.205, �0.110)
* (Dose – 25)� represents the difference between radiation dosend 25 if the dose is �25Gy; otherwise, the quantity equals 0.Dose – 45)� is similarly defined.
Average Dose
Sal
iva
Flow
Rat
es (m
L/m
in)
0 15 30 45 60 75
0.00
0.02
0.04
0.06
0.08
BaselineMonth 1Month 3Month 6Month 12Month 18Month 24
ig. 4. Mean unstimulated saliva counts predicted by the estimatedodel specified in equation (i) for baseline and 1, 3, 6, 12, 18, and
4 months after radiation therapy.
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666 I. J. Radiation Oncology ● Biology ● Physics Volume 67, Number 3, 2007
maximum, with most parotid glands producing negligiblealiva. The saliva reduction is the largest in the first monthfter radiotherapy followed by a gradual recovery. By thend of two years, most of the parotid glands receiving �30y have completely recovered their functionality in produc-
ng secretions under stimulated conditions. Although webserve a very slow but gradual recovery for some parotidlands that received �45 Gy, most of them can only pro-uce very small or negligible amounts of saliva two yearsfter RT.
Most of the parotid glands that received �30 Gy canenerate more stimulated saliva output two years after RThan before RT. The reason for this is not clear, but it doesot appear to be associated with the saliva flow from thepposite parotid being very low. A similar phenomenon ofvershoot in recovery after low doses is observed in radia-ion to the jejunum in animal experiments (17). In thosexperiments the number of cells per crypts after low dosesf radiation is, on average, higher than in unirradiatednimals. The theory is that a low dose of irradiation is not
Fig. 5. Distribution of saliva flow rates with and withoutradiation dose is 0, 20, 30, and 40 Gy, respectively.
nough to kill all the cells in the stem cell compartment, but p
s sufficient to damage the compartment; the compartmenthen reacts by regenerating itself. However, the mechanismor regeneration overshoots. Whether such a similar phe-omenon is plausible for the parotid cannot be assessedrom our data.
The unstimulated saliva flow rates are significantly lowerhan the stimulated flow rates. They also show a dose–esponse relationship. However the process of recoveryoes not start until at least 12 months after radiation, and theow rates do not return to the original pretreatment levelsven after 24 months.
Our results show that the recovery process for the parotidlands to generate saliva is different between stimulatedonditions and unstimulated conditions. Perhaps this resultsrom the different biologic mechanisms under the two con-itions. For example, during resting conditions withouttimulation, the submandibular glands secrete more salivahan the parotid glands; however, under stimulating condi-ions, the main contributors for producing saliva are thearotid glands (7). Although this indicates the biologic
tion at 18 months after radiation therapy when the mean
stimularocess can be different under the two conditions, it does
nesassed
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667Dose and parotid salivary recovery in head and neck cancer patients ● Y. LI et al.
ot explain the difference in the recovery. Another hypoth-sis is that mechanisms that cause the parotid to respond totimulation and produce more saliva are only minimallyffected by radiation doses �25 Gy. These and other pos-ible factors may contribute to the difference between thetimulated and unstimulated recovery. However, the fullxplanation of the differences cannot be deduced from theata in this paper.The fact that there is recovery of the saliva flow rate over
ime has been noted by us and other authors (11, 18–22).hether there are different mechanisms at play for the early
1–3 months) and the late (12–24 months) damage has beentudied in in vivo experiments (23, 24). Zeilstra (24) sug-ests that the early loss in function is the result of compromisedunctioning of the acini, whereas the late effects are the resultf death of the normally proliferating cells. Vissink (21) con-ludes that early changes are the result of irradiation damage toembrane structures, whereas late changes are dependent on
epopulation of surviving stem cells. Stephens suggests thaterous acini are the target cells and that interphase death islso important in early-phase death, whereas late atrophy isconsequence of early injury rather than being the result ofamage to the vasculature. Thus the differences we seeetween early and late effects do have a rationale from thesen vivo studies, and the suggestion that the late damage is aonsequence of early damage would be consistent with theharp drop-off in saliva production and minimal recoveryor doses �40 Gy.
In this paper we have summarized the dose DVH to thearotid by its mean. There is much literature studying normalissue complication models (NTCP), which includes differentays to summarize DVHs (25–27). Others have investigatedhether there are summaries of the DVH more strongly asso-
iated with saliva flow rates. For example, power law NTCPodels have been used (6) and the optimal percentile of theVH has been considered (28). By summarizing the dose by
he mean, we are implicitly ignoring the spatial aspects of theose distribution, thus effectively assuming that the parotid isomogeneous. Other factors that may play a role in impactinghe saliva production are fractionation effects; in particular weight expect a different effect of fraction size for the early and
ate responses. The statistical model we have presented can bextended to allow for these additional features, although largerample sizes may be needed to get reliable information abouthese effects.
Our study uses an updated version of the data presented byisbruch et al. (6). The number of patients increased from 88
o 142, the number of parotids increased from 152 to 266, andhe maximum follow-up time is two years instead of one.isbruch et al. (6) examined the possible threshold valueshere saliva flow reduced to zero after radiotherapy and useddifferent statistical approach. They found that the best value
or a threshold was 26 Gy for stimulated saliva and 24 Gy fornstimulated saliva. At doses higher than these thresholds,
here was very little saliva production and no significant re- rovery over time. At doses below the threshold, they found aodel that described the data that showed recovery over time
nd no relationship with dose. In a later paper by Eisbruch etl. (22), they showed further recovery of the saliva flow ratefter one year. In the current paper, we focus on modeling theelationship between saliva production and its recovery andadiation dosage received. There are some differences in thessumed model between our work and that shown in Eisbrucht al. (6), for example, we assume that the dose–responseelationship is continuous, rather than assuming that an abso-ute threshold exists. We chose a 2-knot spline to give aexible yet continuous curve for the dose–response relation-hip. We placed the knots at 25 Gy and 45 Gy because theyere well spaced interior doses and preliminary analysis sug-ested there may be noticeable changes in the effect of radia-ion at around these doses. In the model we also allow thealivary recovery as a smooth function of radiation dose re-eived. We assume that the saliva production is roughly theame as the baseline at different time points when the radiationose is zero and should only differ slightly from the baselinealues when the radiation dose is very small. Because of thearger sample size, the longer follow-up, and different statisti-al approach, we are able to examine some other features of theata. For example, rather than an absolute threshold in theose–response, we found a steep decline in the saliva produc-ion in the range of 25–35 Gy. We were also able to detect aodest but incomplete recovery of saliva flow rates at doses in
he range 25–40 Gy. For example, when patients receive8-Gy doses based on the fitted model, the stimulated salivaow rates increase from 7% one month after RT to 35% of theaseline two years later.
One feature of this article is the sophisticated statisticalodeling. The hierarchical nonlinear regression model we
eveloped for these data enabled us to capture the relation-hip between saliva and radiation dosage and the recoveryf saliva over time. This model cannot be fit using standardoftware; it was fit using a Bayesian estimation method withode written specifically to fit this model to these data. Itill also be possible to generalize and extend this analysis
o accommodate a more complex framework. Using such aodel, we can more efficiently use the data by making
easonable distributional assumptions. In our analysis, wessume a negative binomial distribution for the roundedaliva flow rates and introduce a random effect, whichllows each parotid to have a generally higher- or lower-han-expected saliva flow rate and can accommodate thexcess of zero saliva flow rates after high doses of radiation.e can use these models to predict the extent of radiation
amage on parotid glands in terms of their ability to producealiva. The results of the model can be graphically repre-ented, as in Figs. 3, 4, and 5. These figures are designed toelp the physician and the patient in planning the dose toach parotid and in understanding the extent to which it may
ecover over time.
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668 I. J. Radiation Oncology ● Biology ● Physics Volume 67, Number 3, 2007
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2nd edition. London: Chapman and Hall; 2004.IX
he prior distributions of all regression parameters, �0,
2, �3, �4, were assumed to be normal distributions N(0,000). We specify an informative prior Gamma (4, 4)or � so that � is around 1. The prior distribution forhe variance parameter ��
2 is inverse Gamma (2.001, 2)o that it has a very large variance. Then the joint pos-erior density of all parameters f ���data� is propor-
�i��
i� yij � ��ij � 1
yij�� �
� � 1���ij� 1
� � 1�yij� (�i)
� (�0)�j�1
6
(�1j) (�2) (�3) (��2) (�)
here, ��0�, ��1j�, ��2�, ��3�, ���2� and ��� are prior
istributions for those parameters.
MifetTg
S
S
S
S
S
adpodim
mfi
669Dose and parotid salivary recovery in head and neck cancer patients ● Y. LI et al.
The estimates for the above model are obtained using aarkov Chain Monte Carlo (MCMC) procedure. This is an
terative procedure in which each parameter is drawn in turnrom its conditional distribution given the remaining param-ters and the data. Upon convergence we have draws fromhe posterior distribution, which are then used for inference.he conditional distributions for each of the parameters areiven below.
Sample ��2 from inverse gamma�n
2� �,
�i2 � 2�
2 �ample �i’s from f(�i� ·) � �
j� yij � ��ij � 1
yij�
� � �
� � 1���ije��i
2 ⁄� 2���2�
��
ample �0 from f(�0� ·) � �i��
j� yij � ��ij � 1
yij�
� � �
� � 1���ij�e��0
2 ⁄ (2�10000)
yij � ��ij � 1
ample �ij from f(�1j� ·) � �j� yij
� a
� � �
� � 1���ij
e��1j2 ⁄ (2�10000)
ample �2 from f(�2� ·) � �i��
j� yij � ��ij � 1
yij�
� � �
� � 1���ij�e��2
2 ⁄ (2�10000)
ample �3 from f(�3� ·) � �i��
j� yij � ��ij � 1
yij�
� � �
� � 1���ij�e��3
2 ⁄ (2�10000)
A C program was developed to fit the MCMC. Wessessed the convergence using trace plots starting fromifferent initial values. After 250,000 iterations of burn-ineriod, we saved every 100th iteration and collected a totalf 2,500 simulation draws. We can obtain the mean, me-ian, credible intervals, and other summary statistics ofnterest from these draws of the posterior distributions of theodel parameters.Posterior predictive checks are used to assess the fit of theodel (29). In this method, data are simulated from thetted model and summary statistics from the original data
re compared with those from the fitted data.
