1. UNIVERSAL SURVIVAL CURVE AND SINGLE FRACTION EQUIVALENT DOSE: USEFUL TOOLS IN UNDERSTANDING POTENCY OF ABLATIVE RADIOTHERAPY
CLINT PARK, M.D. M.S., LECH PAPIEZ, PH.D., SHICHUAN ZHANG, M.D., PH.D.,
MICHAEL STORY, PH.D., AND ROBERT D. TIMMERMAN, M.D.
Department of Radiation Oncology, University of Texas Southwestern Medical Center, Dallas, TX
Int. J. Radiation Oncology Biol. Phys., Vol. 70, No. 3, pp. 847–852, 2008

2. Purpose
To offer an alternative method of analyzing the effect of SBRT by constructing a universal survival curve (USC) that provides superior approximation of the experimentally measured survival curves in the ablative, high-dose range without losing the strengths of the LQ model around the shoulder.

3. Introduction
Conventionally fractionated RT (CFRT), 1.8–4 Gy). The most prevalent method of radiotherapy (RT) in the past 100 years.
normal tissue repairs sublethal injury between fractions better than does tumor tissue.
stereotactic radiosurgery (e.g., 12–30 Gy in a single fraction) to treat intracranial tumors
Stereotactic body RT (SBRT) (8–30 Gy/fraction) to extracranial sites.

4. Introduction
The available clinical outcomes for primary and metastatic lung and liver malignancies have shown that SBRT is efficacious and extremely well tolerated
Wider acceptance of SBRT, however, has been hampered by a limited understanding of the radiobiology of such extreme hypofractionations

5. linear quadratic (LQ) model
where d is the dose and a and b are expansion parameters

6. The biologically effective dose (BED)

7. The biologically effective dose (BED)
lnS= -and[1+d/(a/b)]
lnS/a = -nd[1+d/(a/b)]=BED ,
lnS = a BED

8. Introduction
The data sets used for the second order polynomial fit of the LQ model are for dose ranges below the biologically ablative doses commonly used in SBRT.

9. Introduction Semin Radiat Oncol 18:240-243 © 2008
the therapeutic effect of radiosurgery on tumor response was far greater than that predicted from the LQ model derived from low- dose/fraction estimates.
12 Gy
Semin Radiat Oncol 18: © 2008

10. Introduction
the LQ model overestimates the effect of radiation on clonogenicity in the high doses commonly used in SBRT
The multitarget model
it fits the empirical data well, especially in the high-dose range
where d1 and D0 are the parameters that determine the initial (first log kill) and final ‘‘slopes’’ of the survival curve.

11. Introduction
The multitarget model

12. Introduction
Aim
reconcile the strengths of these two models into a single, unifying model.
The validity of the model was tested by fitting a survival curve obtained for H460 non–small-cell lung cancer (NSCLC) cell line and by applying it to the published results of in vitro experiments and clinical trials

13. METHODS AND MATERIALS Universal survival curve model
hybridizes the LQ model survival curve for the low-dose range and the multitarget model asymptote for high- dose range was constructed

14. METHODS AND MATERIALS Universal survival curve model
The lnS in fractionated CFRT and SBRT

15. METHODS AND MATERIALS Universal survival curve model
Isoeffect relations for arbitrarily fractionated RT

16. METHODS AND MATERIALS Universal survival curve model
Isoeffect relations for arbitrarily fractionated RT

17. METHODS AND MATERIALS Universal survival curve model
Isoeffect relations for arbitrarily fractionated RT
where CFRT and SBRT denote whether d is less than DT or d is greater than DT, respectively.

18. Results
From the reports of 12 NSCLC lines from National Cancer Institute, we obtained the value for a, D0, or Dq
The mean value for a, D0, and Dq was 0.33 Gy-1, Gy, and 1.8 Gy
DT, was calculated to be 6.2 Gy

19. Results
the goodness of fit of the LQ model with that of the USC model using high-dose range survival curve data from a clonogenic assay of the H460 NSCLC cell line for a wide dose range (0–16 Gy)

20. Results
The use of equivalent functions (BED, SFED, and SED) allowed us to compare the treatment potency from different clinical SBRT trials for NSCLC SBRT regimens
By letting dCFRT = 2 Gy, the equation for DCFRT can be used to calculate the standard effective dose (SED), total dose in 2-Gy fractions with equivalent effect.

21. Discussion
one of the developers of the LQ model stated that ‘‘LQ is not intended for doses higher than 8–10 Gy.
In this study, they constructed a USC by combining the LQ and multitarget models.
The USC describes the measured data better than the LQ model,
the USC model does not account for an altered fractionation schedule such as acceleration or twice-daily fractionation.

22. Discussion
determining the effective treatment dose without unnecessarily exceeding the normal tissue dose tolerance
the prospective Phase I dose escalation trials from Indiana
Peripheral Stage T1-T2 tumors could be treated with a dose as great as 20 Gy times three fractions (60 Gy total) without exceeding acceptable limits of severe toxicity

23. Discussion
using the USC model is helpful for the assessment of toxicity and predicting dose tolerance.
in the Indiana Phase II trial, the actual treatment dose of 18 Gy x 3 fractions (SED of 96 Gy) was associated with unacceptable Grade 3 toxicity for the central chest structures.
RTOG 0813, used a starting dose of 45 Gy in five fractions (SED of 71 Gy), to be escalated to 57.5 Gy in five fractions(11.5x5) (SED of 96 Gy), if tolerated.

24. Discussion
The true survival of in vivo tumors depends on multiple factors that cannot possibly be contained in simplified mathematical formulas
The only way to truly know the tumor control rates or the tolerance of different fractionation schemes is through performing prospectively designed trials.

25. CONCLUSION
The USC is a new model that may offer a superior description of the mammalian cell survival curve in the ablative dose range well beyond the shoulder
The equivalent functions derived from the USC model (BED,SFED, and SED) are useful tools to compare and analyze all fractionation schemes, particularly those used in SBRT.

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