Basic Clinical Radiobiology Ch. 5 Dose–response relationships in radiotherapy SØREN M. BENTZEN

 Clinical radiobiology is concerned with the relationship between a given physical absorbed dose and the resulting biological response and with the factors that influence this relationship.  there is no clear-cut limit of tolerance.  the risk of a specific radiation reaction increases from 0% -100% with increasing dose ◦ dose–response relationship 5.1 INTRODUCTION

 dose–response plot 5.1 INTRODUCTION 需要確認此資料， Electron and Photon beam 有相同的劑量來源 （ energetic electrons ），應該有 相同的 quality factor (RBE) telangiectasia 可能發生於表面， 需確認光子與電子的淺部劑量

 Radiation dose–response curves have a sigmoid (i.e. ‘S’) shape.  Three standard formulations are used: ◦ The Poisson Distribution ◦ The logistic Distribution ◦ The probit Distribution 5.2 SHAPE OF THE DOSE–RESPONSE CURVE TCP-NTCP relationship in clinical radiotherapy

 In reality, both clinical and experimental dose–response data are too noisy to allow statistical discrimination between these models and in most cases they will give very similar fits to a dataset.  The situation where major discrepancies may arise is when these models are used for extrapolation of experience over a wide range of dose. 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 The Binomial Distribution  This is the most general model and is widely applicable to all constant-p processes. computationally cumbersome  The Poisson Distribution  This model is a direct mathematical simplification of the binomial distribution under conditions that the success probability p is small and constant  The Gaussian or Normal Distribution  a further simplification if the average number of successes is relatively large (say greater than 20 or 30)

 The Poisson Distribution 5.2 SHAPE OF THE DOSE–RESPONSE CURVE the success probability is small and constant, and the binomial distribution reduces to the Poisson p << 1 Where P(x) is the probability for x observations

 The Poisson Distribution ◦ In the case of solid tumors irradiation, since damage of one cell by irradiation is random and independent from the damage of the rest cells, Poisson distribution is applied. ◦ The event studied in this case is cell survival and number of observations is represented by the variable x. 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 The Poisson Distribution 5.2 SHAPE OF THE DOSE–RESPONSE CURVE Monte Carlo (i.e. random number) simulation of the number of surviving clonogens per tumour tumour surviving clonogens cured tumour

 The Poisson Distribution ◦ The average number was 0.5 surviving clonogens per tumour, ◦ According to Poisson distribution. Percentages of tumors that contain 0,1,2,3… survived clonogens, arise by placing x= 0,1,2,3… in turn. So we get P(0) = e -0.5 ·0.5 0 /0! = 60.7%, ◦ Similarly P(1)=30.3%, P(2)= 7.6% etc. 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 The Poisson Distribution ◦ For TCP, end point = cure, zero surviving clonogens in a tumour. x = SHAPE OF THE DOSE–RESPONSE CURVE

 The Poisson Distribution ◦ For L-Q model, SF =, ◦ N = N 0  SF,  N 0 =the number of clonogens per tumour before irradiation  N=average number of clonogens per tumour after irradiation ◦ TCP = exp[ - ] ◦ the Poisson model is that the model parameters appear to have a biological or mechanistic interpretation. 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 The logistic Distribution ◦ Used with more pragmatism than the Poisson model. ◦ no simple mechanistic background and consequently the estimated parameters have no simple biological interpretation. 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 The logistic Distribution ◦ when analysing data from fractionated radiotherapy  D is total dose and d is dose per fraction, 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 The logistic Distribution 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 The probit Distribution ◦ Probit Analysis is a specialized regression model of binomial response variables ◦ Probit analysis is used to analyze many kinds of dose-response or binomial response experiments in a variety of fields. 5.2 SHAPE OF THE DOSE–RESPONSE CURVE The Gaussian or Normal Distribution

5.2 SHAPE OF THE DOSE–RESPONSE CURVE  The Gaussian or Normal Distribution

 The probit Distribution 5.2 SHAPE OF THE DOSE–RESPONSE CURVE

 For tumours, the most frequently used position parameter is the TCD 50  For normal-tissue reactions, the analogous parameter is the radiation dose for 50 percent response (RD 50 ) or  in the case of rare (severe) complications RD 5, that is, the dose producing a 5 percent incidence of complications. 5.3 POSITION OF THE DOSE–RESPONSE CURVE

 quantify the steepness of the dose–response curve ◦ γ-value 5.4 QUANTIFYING THE STEEPNESS OF DOSE–RESPONSE CURVES

 γ 50 : at a 50 percent response level.  A compact and convenient way to report the steepness of a dose–response curve is by stating the γ-value at the level of response where the curve attains its maximum steepness: ◦ at the 37% response level for the Poisson curve and at the 50% response level for the logistic model. 5.4 QUANTIFYING THE STEEPNESS OF DOSE–RESPONSE CURVES

 Clinical dose–response curves generally originate from studies where the dose has been changed while keeping either the dose per fraction or the number of fractions fixed  γ-value at the steepest point of the dose–response curve is that it is independent of the dose- fractionation details in the case of a dose–response curve generated using a fixed dose per fraction 5.5 CLINICAL ESTIMATES OF THE STEEPNESS OF DOSE–RESPONSE CURVES

 Figure 5.4 Estimated γ 37 values from a number of studies on dose-response relationships for squamous cell carcinoma in various sites of the head and neck.  fixed dose per fraction 5.5 CLINICAL ESTIMATES OF THE STEEPNESS OF DOSE–RESPONSE CURVES γ 37 Typical values range from 1.5–2.5

 In the absence of other sources of variation, the maximum steepness of a tumour-control curve is determined only by the Poisson statistics of survival of clonogenic cells. ◦ values as high as γ 37 =7 are not achieved even in transplantable mouse tumour models under highly controlled experimental conditions  The principal reason why dose–response curves in the laboratory and in the clinic are shallower than this theoretical limit is dosimetric and biological heterogeneity.  patient and treatment characteristics will influence both the position (TCD 50 ) and the steepness (  -value) of the dose–response curve 5.5 CLINICAL ESTIMATES OF THE STEEPNESS OF DOSE–RESPONSE CURVES

 many tumour and treatment variables, for example tumour volume and overall treatment time, are thought to affect the (effective) number of clonogens to be sterilized.  Therefore, in a multivariate analysis, γ 37 will depend on all the significant patient and treatment characteristics 5.5 CLINICAL ESTIMATES OF THE STEEPNESS OF DOSE–RESPONSE CURVES

 Figure 5.5 Estimated γ 50 values for various late normal-tissue endpoints. Estimates are shown for treatment with a fixed dose per fraction and a fixed number of fractions. The shaded horizontal band corresponds to the typical γ-values at the point of maximum steepness for dose- response curves in head and neck tumours. fixed number of fractions with a higher γ 50 values,

5.5 CLINICAL ESTIMATES OF THE STEEPNESS OF DOSE–RESPONSE CURVES  when treating with a fixed number of fractions, increasing the dose leads to a simultaneous increase in dose per fraction, and this is associated with an increased biological effect per gray. fixed number of fractions with a higher γ 50 values,

5.5 CLINICAL ESTIMATES OF THE STEEPNESS OF DOSE–RESPONSE CURVES  γ N denote the steepness of the dose–response curve for a fixed fraction number, and γ d the steepness for a fixed dose per fraction, ◦ d r : dose per fraction ◦ γ N is always larger than γ d

5.6 THE THERAPEUTIC WINDOW  radiotherapy must represent a balance between risks and benefits. Several parameters are found in the literature for quantifying the effect of treatment modifications on the therapeutic window. specify the tumour control probability at isotoxicity with respect to a specific end-point

5.7 METHODOLOGICAL PROBLEMS IN ESTIMATING DOSE–RESPONSE RELATIONSHIPS FROM CLINICAL DATA  Clinical aspects ◦ Evaluation of well-defined endpoints for tumour and normal- tissue effects. Endpoints requiring prolonged observation of the patients, such as local tumour control or late complications, should be analysed using actuarial statistical methods.

5.7 METHODOLOGICAL PROBLEMS IN ESTIMATING DOSE–RESPONSE RELATIONSHIPS FROM CLINICAL DATA  Dosimetric aspects ◦ involve a detailed account of treatment technique and quality assurance procedures employed. ◦ the identification of biologically relevant dosimetric reference points and a proper evaluation of the doses to these points  highly non-uniform dose distribution in the relevant normal tissues-IMRT tech,

5.7 METHODOLOGICAL PROBLEMS IN ESTIMATING DOSE–RESPONSE RELATIONSHIPS FROM CLINICAL DATA  Statistical aspects ◦ include the choice of valid statistical methods that are appropriate for the data type in question and which use the available information in an optimal way. ◦ Statistical tests for significance or, preferably, confidence limits on estimated parameters should be specified.

5.8 CLINICAL IMPLICATIONS: MODIFYING THE STEEPNESS OF DOSE–RESPONSE CURVES  If the standard deviation of the absorbed-dose distribution in a population of patients is 5%, a γ-value of 3 would yield an estimated 15% standard deviation on the response-probability distribution. ◦ This provides an indication of the precision required in treatment planning and delivery in radiotherapy.

5.8 CLINICAL IMPLICATIONS: MODIFYING THE STEEPNESS OF DOSE–RESPONSE CURVES  patient-to-patient variability in tumour biological parameters could strongly affect the steepness of the dose–response curve  dose–incidence curve got steeper when stratifying patients according to clinico- pathological risk group.

5.9 NORMAL TISSUE COMPLICATION PROBABILITY (NTCP) MODELS  The most widely used of these is the Lyman model (Lyman, 1985).  These models aim to predict the probability of a complication as a function of the dose or biologically equivalent dose and volume

 Dose-volume histogram  the location of high-dose or other regions cannot be determined from the DVHs  the geometric distribution of dose was irrelevant to its biological impact

 Biological indices ◦ Normal tissue complication probability (NTCP) ◦ Tumor control probability (TCP)

 The probability of uncomplicated tumor control (P UTC ): P UTC =TCP(1-NTCP)

TD 50 (1) : the tolerance dose for reference volume irradiation m : the steepness slope of the dose response curve V ref : the reference volume n : tissue-specific parameter

Key points  There is no well-defined ‘tolerance dose’ for radiation complications or ‘tumouricidal dose’ for local tumour control: rather, the probability of a biological effect rises from 0% to 100% over a range of doses.  The steepness of a dose–response curve, quantified by γ n, that is the increase in response in percentage points for a 1% increase in dose.

Key points  Dose–response curves for late normal-tissue endpoints tend to be steeper (typical γ 50 =2 - 6) than the dose–response curves for local control of squamous cell carcinoma of the head and neck (typical γ 50 = ).  The steepness of a dose–response curve is higher if the data are generated by varying the dose while keeping the number of fractions constant (‘double trouble’) than if the dose per fraction is fixed.

Key points  Dosimetric and biological heterogeneity cause the population dose–response curve to be more shallow.  NTCP models, incorporating dose fractionation as well as irradiated volume, have not been validated in any clinical setting and should not be routinely used outside a research protocol.

Thank you for your attention ！