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Practical Time–Dose Evaluations, or How to Stop Worrying and Learn to Love Linear Quadratics

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Technical Basis of Radiation Therapy

Part of the book series: Medical Radiology ((Med Radiol Radiat Oncol))

Abstract

This 9-section chapter begins with an elementary explanation of the Linear Quadratic model of Radiation Response, to make sure readers haven’t missed out on understanding this robust and reliable way of comparing different schedules in Radiation Oncology. A detailed account of its many applications has recently been published as “21 Years of BED (Biologically Effective Dose)” (Fowler Br J Radiol 83:554–568, 2010). The essential feature of this modeling is that a given dose has very different biological effects on neighbouring but different tissues because of their biological alpha/beta ratios and their “kick-off” or “onset” times of repopulation during continuing irradiation. In Sections 4 and 5 comparisons of actual clinical trials are presented that have shaped the current and emerging schedules of treatments of Head & Neck tumors, going on to SBRT (Stereotactic Body Radiation Therapy), IMRT (intensity Modulated Radiation Therapy) and IGRT (Image Guided Radiation Therapy). Some insights into how the biological strategies of fractionated radiotherapy actually deliver therapeutic advantages are introduced. Section 6 explains how Optimum Overall Times can now be predicted, using basially least two constraints, one for Late Complications and the other for Acute Tolerance Doses. This is a fairly new break-through (2008). Section 7 goes into detail on why Overall Times might be too short or too long, with examples from modern schedules still being clinically trialed. Section 8 goes further into non-standard schedules, with updated emphasis on the Recovery Times of various tissues and tumors, intervals between fractions and extended fraction times. The chapter ends with an explanatory table of best and next-to-best schedules for Head and Neck radiation oncology. The continuing need to obtain data on individual tumor T-\( {\raise0.5ex\hbox{$\scriptstyle {1}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {2}$}} \) and repopulation is emphasized.

This chapter is written mainly for those who say “I don’t understand this α/β business—I can’t be bothered with Linear Quadratic and that sort of stuff.” Well, it might seem boring—depending on your personality—but it is easy, and it makes so many things in radiation therapy wonderfully and delightfully clear. Experienced readers can turn straight to Sect. 4, about a quarter of the way through.

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Abbreviations

α, alpha:

Intrinsic radiosensitivity. Loge of the number of cells sterilized non-repairably per gray of dose of ionizing radiation

β, beta:

Repair capacity. Loge of the number of cells sterilized in a repairable way per gray squared

α/β, alpha/beta ratio:

The ratio of “intrinsic radiosensitivity” to “repair capability” of a specified tissue. This ratio is large (>8 Gy) for rapidly proliferating tissues and most tumors. It is small (<6 Gy) for slowly proliferating tissues, including late normal-tissue complications. This difference is vital for the success of radiotherapy. When beta (β) is large, both mis-repair and good-repair are high. It is the mis-repair that causes the cell survival curve to bend downward

Accelerated fractionation:

Fractionated schedules with shorter overall times than the conventional 7 (or 6) weeks

BED:

Biologically effective dose, proportional to log cell kill and therefore more useful as a measure of biological damage than physical dose, the effects of which vary with fraction size and dose rate. Formally, “the radiation dose equivalent to an infinite number of infinitely small fractions or a very low dose-rate”. Corresponds to the intrinsic radiosensitivity (α) of the target cells when all repairable radiation damage (β) has been given time to be repaired. In linear quadratic modeling, BED = total dose × relative effectiveness (RE), where RE = (1 + d/[α/β]), with d = dose per fraction, α = intrinsic radiosensitivity, and β = repair capacity of target cells

bNED:

Biochemically no evidence of disease. No progressive increase of prostate specific antigen (PSA) level in patients treated for prostate cancer

CI:

Confidence interval (usually ±95%)

CLDR:

Continuous low dose rate

Con-Len:

Constructive lengthening: when adding a day (or two) followed by a not-too-small fraction (or two) adds to the accumulated radiation damage in the tumor, rather than allowing it to fall by tumor repopulation, or minimizes any loss

CTV:

Clinical tumor volume. The volume into which malignant cells are estimated to have spread at the time of treatment, larger than the gross tumor volume (GTV) by at least several millimeters, depending on site, stage, and location. See also GTV and planning treatment volume (PTV)

Δt :

Time interval between fractions, recommended to be not less than 6 h

EBR:

External beam radiation

EGFR:

Epithelial growth factor receptor, one of the main intracellular biochemical pathways controlling rate of cell proliferation

EQD:

Biologically equivalent total dose, usually in 2 Gy dose fractions. The total dose of a schedule using, for example, 2 Gy per fraction that gives the same log cell kill as the schedule in question. If so, should be designated by the added digit “2” EQD2 Gy

EUD:

Equivalent uniform dose. A construct from the DVH of a non-uniformly irradiated volume of tissue or tumor that estimates the surviving proportion of cells for each volume element (voxel), sums them, and calculates that dose which, if given as a uniform dose to the same volume, would give the same total cell survival as the given non-uniform dose. Local fraction size is taken into account by assuming an α/β ratio for the tissue concerned

FLT:

18F Fluorothymidine, a radioactive label for freshly synthesized DNA to indicate actively dividing cells. The radioactive label 18F emits positrons

Gamma, γ-50, γ-37:

Slope of a graph of probability, usually tumor control probability (TCP), versus total fractionated dose (NTD or EQD), as percentage absolute increase of probability per 1% increase in dose. The steepest part of the curve is at 50% for logistic-type curves and at 37% for Poisson-type curves. Tumor TCP is usually between a gamma-50 (or -37) of 1.0 and 2.5. The difference between γ-50 and γ-37 is rarely clinically significant

G:

Dose rate factor. A number less than 1 that describes the decrease of biological effect if the duration of irradiation is longer than a few minutes

Gy, gray:

The international unit of radiation dose: one joule per kilogram of matter. Commonly used radiotherapy doses are approximately 2 Gy on each of 5 days a week

Gy10, Gy3, Gy1.5:

Biologically effective dose (BED), with the subscript representing the value of that tissue’s α/β ratio = 10 Gy for early radiation effects, 3 Gy for late radiation effects, and 1.5 Gy for prostate tumors. The subscript confirms that this is a BED, proportional to log cell kill, and not a real physical dose

GTV:

Gross tumor volume. The best estimate of tumor volume visualized by radiological, computed tomography (CT) scan, magnetic resonance, ultrasound imaging, or positron emission tomography

HDR:

High dose rate. When the dose fraction is delivered in less than five or ten minutes; that is, much shorter than any half-time of repair of radiation damage

Hyperfractionation:

More (and smaller) dose fractions than 1.8 or 2 Gy

Hypofractionation:

Fewer (and larger) dose fractions than 1.8 or 2 Gy

IGRT:

Image Guided Radiotherapy. Using superimposed images from CT-scans or Magnetic Resonance Imaging or PET-scans

IMRT:

Intensity Modulated Radiotherapy: instead of a constant dose rate from all angles, the dose rate is made to vary with the angle from which it is delivered, by computerized dose planning; leading to deliberately non-uniform dose-planning and ‘dose-painting’ in tumors or ‘dose-avoidance’ of critical organs

IR, Incomplete Recovery:

Residual radiation damage that may add to the effect of the next fraction if a too short interval occurred (Thames and Hendry 1987). Repair usually refers to intracellular repair. Recovery refers to other processes too and is a more general term

Isoeffect:

Equal effect

LC:

Local control (of tumors)

LDR:

Low dose rate. Officially (ICRU), less than 2 Gy/h; but this is deceptive because any dose rate greater than 0.5 Gy/h will give an increased biological effect compared with the traditional 0.42 Gy/h (1000 cGy per day). For example at 2 Gy/h, the biological effects will be similar to daily fractions of 3.3 and 2.8 Gy on late complications and on tumors respectively

Linear effect:

Directly proportional to dose

Ln, loge :

Natural logarithm, to base e. One log10 is equal to 2.303 loge

Log10 :

Common logarithm, to base 10. “Ten logs of cell kill” are 23.03 loge of cell kill

LQ:

Linear quadratic formula: loge cells killed = α × dose + β × dose-squared

LQ(L):

A linear cell survival curve suggested by some authors to replace the higher dose downward curvature of a standard LQ curve, which some authors fear, probably wrongly, but the issue is not yet resolved

Logistic curve:

A symmetrical sigmoid or S-shaped graph relating the statistically probable incidence of “events”, including complications or tumors controlled, at a specified time after treatment, to total dose (NTD). This curve is steepest at the probability of 50%

LRC:

Loco-regional tumor control. LC would be local control

MRI:

Magnetic Resonance Imaging. Scans of body tissues which can show the chemical state of molecules, instead of only their density as CT scanning does

NTCP:

Normal tissue complication probability

NTD:

Normalized total dose of any schedule. The total dose of a schedule using 2 Gy per fraction that gives the same log cell kill as the schedule in question. The NTD will be very different for late effects (with α/β = 3 Gy and no overall treatment time factor) than for tumor effect (with α/β = 10 Gy and an appropriate time factor)

NSCLC:

Non-small-cell lung cancer

Oligo-fractionation:

The use of a few large fractions, say 5–20 Gy or higher, and only a few of them, say ten or less (Ling et al. 2010)

PET:

Positron Emitting Tracer. A radioactive nuclide that emits positrons, that is, a pair of oppositely charged electrons in exactly opposite directions, so that they can be detected in PET Scanning within a few millimeters of accuracy to indicate parts of a tumor that might contain dangerously live cells

Poisson curve:

A near-sigmoid graph of probability of occurrence of “events”, such as tumor control at X years, versus total dose or NTD. Based on random chance of successes among a population of tumors or patients, the probability of curve P = exp (–n), where an average of n cells survive per tumor after the schedule, but 0 cells must survive to achieve 100% cure. If an average of 1 cell survives per tumor, P = 37%. If 2 cells survive, P = 14%. If 0.1 cells survive on average, P = 90%. This curve is steepest at the probability of 37%

PTV:

Planning treatment volume—larger than CTV to allow for setup and treatment-planning errors

PSA:

Prostate-specific antigen: can be measured in a blood specimen as a measure of activity of the prostate gland. Often taken as a measure of activity of prostate cancer

P rec :

Proportion of a dose fraction that is recoverable, the beta-only term, which is d/[α/β] or Gd/[α/β] as a proportion of the whole RE = (1 + d/[α/β]) or (1 + Gd/[α/β]). The “1” part of the RE is the non-recovering, fixed part, independent of time after irradiation

Quadratic:

Effect proportional to dose squared, for example from two particle tracks passing through a target

QED:

Quod Erat Demonstrandum – Latin for “That’s what we wanted to show!”

RE:

Relative effectiveness. We multiply total dose by RE to obtain BED. RE = (1 + d/[α/β]), where d is the dose per fraction

Red Shell:

An annuloidal shell surrounding a PTV, during treatment planning, to delineate tissues at risk from late reactions when prescription doses exceed normal tissue tolerance of nearby organs, at mm distances before sufficient dose falloff has occurred (Yang et al. 2010)

RTOG:

Radiation Therapy Oncology Group, USA

SF:

Surviving fraction after irradiation, usually of cells

SIB:

Simultaneous Internal Boost. The addition of a deliberate “hot spot” into a planned non-uniform tumor dose distribution to enhance the local effect; a form of ‘dose painting’ by IMRT

SBRT:

Stereotactic Body Radiatiotherapy. Very accurately guided beams, often of small diameter and usually delivered by only a few large dose fractions, to treat cancer in certain organs outside the brain

SRT:

Stereotactic Radiosurgery: it usually means in radiotherapy the use of a single treatment fraction, often in brain. Originated from the precise localizations in brain physiotherapy research. Has sometimes been wrongly used for SBRT

T pot :

Potential doubling time of cells in a population; before allowing for the cell loss factor. T pot is the reciprocal of cell birth rate. It can only be measured in a tissue before any treatment is given to disturb its turnover time

T p :

Cell doubling time in a tissue during radiotherapy; probably somewhat faster than T pot. Determined from gross tumor (or other tissue) results when overall time is altered

T k :

Kick-off or onset time: the apparent starting time of rapid compensatory repopulation in tumor or tissue after the start of treatment, when it is assumed that there are just two rates of cell proliferation during radiotherapy: zero from start to T k, then constant doubling each T p days until end of treatment at T days. Accelerating repopulation is discussed in Sect. 5.6

TCP:

Tumor control probability

References

  • Amer AM, Mott J, MacKay RI et al (2003) Prediction of the benefits from dose-escalated hypofractionated intensity-modulated radiotherapy for prostate cancer. Int J Radiat Oncol Biol Phys 56:199–207

    Article  PubMed  Google Scholar 

  • Arvidson NB, Khunyia D, Tomé WA (2009) Dose escalation model for limited-stage small-cell lung cancer. Radiother Oncol 91:379–385

    Article  PubMed  Google Scholar 

  • Barendsen GW (1982) Dose fractionation, dose rate, and isoeffect relationships for normal tissue responses. Int J Radiat Oncol Biol Phys 8:1981–1997

    Article  PubMed  CAS  Google Scholar 

  • Baumann M, Saunders MI, Joiner MC (2002) Modified fractionation. In: Steel GG (ed) Basic clinical radiobiology, 3rd edn. Arnold, London, pp 147–157 (Chap 14)

    Google Scholar 

  • Begg AC, Steel GG (2002) Cell proliferation and the growth rate of tumours. In: Steel GG (ed) Basic clinical radiobiology, 3rd edn. Arnold, London, pp 8–22 (Chap 2)

    Google Scholar 

  • Bentzen SM (2009) From cellular to high-throughput predictive assays in radiation oncology: challenges and opportunities. Sem Radiat Oncol 18:75–88

    Article  Google Scholar 

  • Bentzen SM, Yarnold JR (2010) Reports of unexpected late side effects of accelerated partial breast irradiation–radiobiological considerations. Int J Radiat Oncol Biol Phys 77:969–973

    Article  PubMed  Google Scholar 

  • Bentzen SM, Overgaard J, Thames HD et al (1989) Clinical radiobiology of malignant melanoma. Radiother Oncol 16:168–187

    Article  Google Scholar 

  • Bentzen SM, Saunders MI, Dische S (1999) Repair half-times estimated from observations of treatment-related morbidity after CHART or conventional radiotherapy in head and neck cancer. Radiother Oncol 53:219–226

    Article  PubMed  CAS  Google Scholar 

  • Bentzen SM, Saunders MI, Dische S (2002) From CHART to CHARTWEL in non-small-cell lung cancer: clinical radiobiological modelling of the expected changes in outcome. Clin Oncol (Roy Coll Radiol) 14:372–381

    Article  CAS  Google Scholar 

  • Bernier J (2009) Current state of the art for concurrent chemoradiation. Sem Radiat Oncol 19:3–10

    Article  Google Scholar 

  • Borst GR, Ishikawa M, Nijkamp J, Lebesque JV, Sonke J–J (2010) Radiation pneumonitis after hypofractionated radiotherapy: evaluation of the LQ(L) model and different dose parameters. Int J Radiat Oncol Biol Phys 77:1596–1603

    Article  PubMed  Google Scholar 

  • Bourhis J, de Crevoisier R, Abdulkarim B et al (2000) A randomized study of very accelerated radiotherapy with and without amifostine in head and neck squamous cell carcinoma. Int J Radiat Oncol Biol Phys 46:1105–1108

    Article  PubMed  CAS  Google Scholar 

  • Bourhis J, Etessami A, Pignon JP et al (2004) Altered fractionated radiotherapy in the management of head and neck carcinomas: advantages and limitations. Curr Opin Oncol 16:215–219

    Article  PubMed  Google Scholar 

  • Bourhis J, Overgaard J, Audry H, Ang KK et al (2006) Hyperfractionated or accelerated radiotherapy in head and neck cancer: a meta-analysis. Lancet 368:843–845

    Article  PubMed  Google Scholar 

  • Brenner DJ (1993) Accelerated repopulation during radiotherapy. Quantitative evidence for delayed onset. Radiat Oncol Invest 1:167–172

    Article  Google Scholar 

  • Brenner JD (2000) Towards optimal external-beam fractionation for prostate cancer (editorial). Int J Radiat Oncol Biol Phys 48:315–316

    Article  PubMed  CAS  Google Scholar 

  • Brenner JD (2003) Hypofractionation for prostate cancer therapy. What are the issues? (Editorial.) Int J Radiat Oncol Biol Phys 57:912–914

    Google Scholar 

  • Brenner DJ (2004) Fractionation and late rectal injury (editorial). Int J Radiat Oncol Biol Phys 60:1013–1015

    Article  PubMed  Google Scholar 

  • Brenner DJ, Hall EJ (1999) Fractionation and protraction for radiotherapy of prostate cancer. Int J Oncol Biol Phys 43:1095–1101

    Article  CAS  Google Scholar 

  • Brenner DJ, Hall EJ (2000) In response to Drs King and Mayo. Low α/β ratios for prostate appear to be independent of modeling details. Int J Radiat Oncol Biol Phys 47:538–539

    Article  Google Scholar 

  • Brenner DJ, Martinez AA, Edmundson GK et al (2002) Direct evidence that prostate tumors show high sensitivity to fractionation (low α/β ratio) comparable to late-responding normal tissue. Int J Radiat Oncol Biol Phys 52:6–13

    Article  PubMed  Google Scholar 

  • Carlson DJ, Stewart RD, Li X et al (2004) Comparison of in vitro and in vivo α/β ratios for prostate cancer. Phys Med Biol 49:4477–4491

    Article  PubMed  Google Scholar 

  • Chappell RJ, Fowler JF (2004) New data on the value of alpha/beta: evidence mounts that it is low. Int J Radiat Oncol Biol Phys 60:1002–1003

    PubMed  Google Scholar 

  • Chen F, Wallace M, Mitchell C et al (2010) Four-year efficacy, cosmesis, and toxicity using three-dimensional conformal external beam radiotherapy to deliver accelerated partial breast irradiation. Int J Radiat Oncol Biol Phys 76:991–997

    Article  PubMed  Google Scholar 

  • Curtis SB (1986) Lethal & potentially lethal lesions induced by radiation—a unified repair model. Radiat Res 106:252–270

    Article  PubMed  CAS  Google Scholar 

  • Dale RG, Fowler JF, Jones B (1999) A new incomplete repair model based on a “reciprocal-time “pattern of sublethal damage repair. Acta Oncol 38:919–929

    Article  PubMed  CAS  Google Scholar 

  • Dasu A (2007) Is the α/β value for prostate tumors low enough to be safely used in clinical trials? Clin Oncol (Roy Coll Radiol UK) 19: 289-301

    Google Scholar 

  • Dasu A, Fowler JF (2005) Comments on the “Comparisons of in vitro and in vivo α/β ratios for prostate cancer”. Phys Med Biol 50:11–14

    Article  Google Scholar 

  • Dasu A, Toma-Dasu I, Fowler JF (2003) Should single or distributed parameters be used to explain the steepness of tumor control probability curves? Phys Med Biol 48:387–397

    Article  PubMed  Google Scholar 

  • Denekamp J (1973) Changes in the rate of repopulation during multifraction irradiation of mouse skin. Br J Radiol 46:381–387

    Article  PubMed  CAS  Google Scholar 

  • Denham JW, Kron T (2001) Extinction of the weakest. Int J Radiat Oncol Biol Phys 51:807–819

    Article  PubMed  CAS  Google Scholar 

  • Dische S, Saunders M, Barrett A et al (1997) A randomised multicentre trial of CHART versus conventional radiotherapy. Radiother Oncol 44:123–136

    Article  PubMed  CAS  Google Scholar 

  • Dörr W, Hendry JH (2001) Consequential late effects in normal tissues. Radiother Oncol 61:223–231

    Article  PubMed  Google Scholar 

  • Dörr W, Hamilton CS, Boyd T et al (2002) Radiation-induced changes in cellularity and proliferation in human oral mucosa. Int J Radiat Oncol Biol Phys 52:911–917

    Article  PubMed  Google Scholar 

  • Douglas BG, Fowler JF (1976) The effect of multiple small doses of X-rays on skin reactions in the mouse and a basic interpretation. Radiat Res 66:401–426

    Article  PubMed  CAS  Google Scholar 

  • Fenwick JD, Lawrence GP, Malik Z et al (2008) Early mucosal reactions during and following head and neck radiotherapy: Dependence of treatment tolerance on radiation dose and schedule duration. Int J Radiat Oncol Biol Phys 71:625–634

    Article  PubMed  Google Scholar 

  • Fowler JF (1978) Int J Radiat Oncol Biol Phys. Final comments on Rome Symposium on the biological bases of tumor radioresistance. Int J Radiat Oncol Biol Phys 8:115–116

    Article  Google Scholar 

  • Fowler JF (1989) Review article: the Linear-Quadratic formula and progress in fractionated radiotherapy: a review. Br J Radiol 62:679–694

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF (1992a) Brief summary of radiobiological principles in fractionated radiotherapy. Semin Radiat Oncol 2:16–21

    Article  Google Scholar 

  • Fowler JF (1992b) Intercomparisons of new and old schedules in fractionated radiotherapy. Semin Radiat Oncol 2:67–72

    Article  Google Scholar 

  • Fowler JF (2001) Biological factors influencing optimum fractionation in radiation therapy. Acta Oncol 40:712–717

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF (2002) Repair between dose fractions: a simpler method of analyzing and reporting apparently biexponential repair. Radiat Res 158:141–151

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF (2008a) Optimum Overall Times II: Extended modelling for head and neck radiotherapy. Clinical Oncology 20:113–126

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF (2008b) [Letter] Linear Quadratric is alive and well: In regard to Park et al. (IJROBP 2008;70:847-852) Int J Radiat Oncol Biol Phys 72:957−959.

    Google Scholar 

  • Fowler JF (2008c) [Editorial] Correction to Kasibhatla et al. How much radiation is the chemotherapy worth in advanced head and neck cancer? IJROBP 68:1491–1495. Int J Radiat Oncol Biol Phys 71:326–329

    Article  PubMed  Google Scholar 

  • Fowler JF (2009) Sensitivity analysis of parameters in L-Q Radiobiologic modeling. Int J Radiat Oncol Biol Phys 73:1532–1537

    Article  PubMed  Google Scholar 

  • Fowler JF (2010) 21 years of “biologically effective dose”. Br J Radiol 83:554–568

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF, Chappell RJ (2000) Non-small-cell lung tumors repopulate rapidly during radiation therapy (letter). Int J Radiat Oncol Biol Phys 46:516–517

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF, King CR (2009) Don’t squeeze hypofractionated schedules into too-short overall times [Editorial] Fowler JF and King CR (2009) Int J Rad Oncol Biol Phys 75:323-325

    Google Scholar 

  • Fowler JF, Lindstrom MJ (1992) Loss of local control with prolongation in radiotherapy. Int J Radiat Oncol Biol Phys 23:457–467

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF, Chappell RJ, Ritter MA (2001) Is α/β for prostate tumors really low? Int J Radiat Oncol Biol Phys 50:1021–1031

    Article  PubMed  CAS  Google Scholar 

  • Fowler JF, Ritter MA, Fenwick JD, Chappell RJ (2003a) How low is the α/β ratio for prostate cancer? In regard to Wang et al. 2003. IJROBP 55:194–203

    Google Scholar 

  • Fowler JF, Ritter MA, Chappell RJ, Brenner JD (2003b) What hypofractionated protocols should be tested for prostate cancer? Int J Radiat Oncol Biol Phys 56:1093–1104

    Article  PubMed  Google Scholar 

  • Fowler JF, Harari PM, Leborgne F, Leborgne JH (2003c) Acute radiation reactions in oral and pharyngeal mucosa: tolerable levels in altered fractionation schedules. Radiother Oncol 69:161–168

    Article  PubMed  Google Scholar 

  • Fowler JF, Tome WA, Fenwick JD, Mehta MP (2004a) A challenge to traditional radiation oncology. Int J Radiat Oncol Biol Phys 60:1241–1256

    Article  PubMed  Google Scholar 

  • Fowler JF, Welsh JS, Howard SP (2004b) Loss of biological effect in prolonged fraction delivery. Int J Rad Oncol Biol Phys 59(1):242–249

    Article  Google Scholar 

  • Fu KK, Pajak TF, Trotti A et al (2000) A Radiation Therapy Oncology Group (RTOG) phase III randomized study to compare hyperfractionation and two variants of accelerated fractionation to standard fractionation radiotherapy for head and neck squamous cell carcinomas; first report of RTOG 90–03. Int J Radiat Oncol Biol Phys 48:7–16

    Article  PubMed  CAS  Google Scholar 

  • Fuks Z, Persaud RS, Alfieri A et al (1994) Basic fibroblast growth factor protects endothelial cells against radiation-induced programmed cell death in vitro and in vivo. Cancer Res 54:2582–2590

    PubMed  CAS  Google Scholar 

  • Gilbert CW, Hendry JH, Major D (1980) The approximation in the formulation for survival S = exp–(〈d + ®d2). Int J Radiat Biol 37:469–471

    Article  CAS  Google Scholar 

  • Giraud P, Antoine M, Larrouy A et al (2000) Evaluation of microscopic tumor extension in non-small-cell lung cancer for three-dimensional conformal radiotherapy planning. Int J Rad Oncol Biol Phys 48:1015–1024

    Article  CAS  Google Scholar 

  • Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L (1999) Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res 59:4770–4775

    PubMed  CAS  Google Scholar 

  • Hanks GE, Hanlon AL, Pinover WH et al (2000) Dose selection for prostate cancer patients based on dose comparison and dose response studies. Int J Radiat Oncol Biol Phys 46:823–832

    Article  PubMed  CAS  Google Scholar 

  • Harari PM (2004) Epidermal growth factor receptor inhibition strategies in oncology. Endocr Relat Cancer 11:689–708

    Article  PubMed  CAS  Google Scholar 

  • Harari PM, Wheeler DL, Grandis JR (2009) Molecular target approaches in head and neck cancer; epidermalgrowth factor receptors and beyond. Sem Radiat Oncol 19:3–68

    Article  Google Scholar 

  • Hartley A, Sanghera P, Glaholm J, Mehanna H, McConkey C, Fowler J (2010) Radiobiological modelling of the therapeutic ratio for the addition of synchronous chemotherapy to radiotherapy in locally advanced squamous cell carcinoma of the head and neck. Clinical Oncology (UK RCR) 22:125–130

    Article  CAS  Google Scholar 

  • Haustermans K, Fowler JF (2000) A comment on proliferation rates in human prostate cancer (letter). Int J Radiat Oncol Biol Phys 48:303

    Article  Google Scholar 

  • Hendry JH, Bentzen SM, Dale RG et al (1996) A modelled comparison of the effects of using different ways to compensate for missed treatment days in radiotherapy. Clin Oncol (Roy Coll Radiol) 8:297–307

    Article  CAS  Google Scholar 

  • Hepel JT, Tokita M, Macausland SG et al (2009) Toxicity of three-dimensional conformal radiotherapy for accelerated partial breast irradiation. Int J Radiat Oncol Biol Phys 75:1290–1296

    Article  PubMed  Google Scholar 

  • Hobson B, Denekamp J (1984) Endothelial proliferation in tumours and normal tissues: continuous labelling studies. Br J Cancer 49:405–413

    Article  PubMed  CAS  Google Scholar 

  • Horiot JC, Le Fur R, N’Guyen T et al (1992) Hyperfractionation versus conventional fractionation in oropharyngeal carcinoma: final analysis of a randomized trial of the EORTC cooperative group of radiotherapy. Radiother Oncol 25:231–241

    Article  PubMed  CAS  Google Scholar 

  • Huang EH, Pollack A, Levy L et al (2002) Late rectal toxicitry: dose-volume effects of conformal radiotherapy fot prostate cancer. Int J Radiat Oncol Biol Phys 54:1314–1321

    Article  PubMed  Google Scholar 

  • Iwata H, Shibamoto Y, Murata R et al (2009) Estimation of errors associated with use of L-Q formalism for evaluation of biologic equivalence between single and hypofractionated radiation doses: an in vitro study. Int J Radiat Oncol Biol Phys 75(2): 482-48

    Google Scholar 

  • Jagsi R, Bne-David MA, Moran JM et al (2010) Unacceptable cosmesis in a protocol investigating intensity-modlated radiotherapy with active breathing control for accelerated partial breast irradiation. Int J Radiat Oncol Biol Phys 76:71–78

    Article  PubMed  Google Scholar 

  • Joiner MC, Bentzen SM, Baumann M (2002) Time–dose relationships: the linear-quadratic approach and the model in clinical practice. In: Steel GG (ed) Basic clinical radiobiology, 3rd edn. Arnold, London, pp 120–146 chap 12 and 13

    Google Scholar 

  • Kaanders JH, van der Kogel AJ, Ang KK (1999) Altered fractionation: limited by mucosal reactions? Radiother Oncol 22:81–91

    Google Scholar 

  • Kal HB, van Gellekom MP (2003) How low is the α/β ratio for prostate cancer? Int J Radiat Oncol Biol Phys 57:1116–1121

    Article  PubMed  Google Scholar 

  • Kasibhatla M, Kirkpatrick JP, Brizel DM (2008) How much radiation is the chemotherapy worth in advanced head and neck cancer? Int J Radiat Oncol Biol Phys 71:326–329

    Article  Google Scholar 

  • King CR, Fowler JF (2002) Yes the alpha/beta ratio for prostate cancer is low or “methinks the lady doth protest too much…”. about a low α/β ratio, that is. Int J Radiat Oncol Biol Phys 54:626–627

    Article  PubMed  Google Scholar 

  • King CR, Mayo CS (2000) Is the prostate alpha/beta ratio of 1.5 from Brenner and Hall a modeling artifact? Int J Radiat Oncol Biol Phys 47:536–538

    Article  PubMed  CAS  Google Scholar 

  • King CR, Brooks JD, Gill H et al (2009) Stereotactic body radiotherapy for localized prostate cancer : interim results of a prospective phase II clinical trial. Int J Radiat Oncol Biol Phys 73:1043–1048

    Article  PubMed  Google Scholar 

  • Knee R, Fields RS, Peters LJ (1985) Concomitant boost radiotherapy for advanced squamous cell carcinoma of the head and neck. Radiother Oncol 4:1–7

    Article  PubMed  CAS  Google Scholar 

  • Le Q-T, Raben D (2009) Integrating biologically targeted therapy in head and neck squamous cell carcinomas. Sem Radiat Oncol 19:53–62

    Article  Google Scholar 

  • Leborgne F, Fowler JF (2008) Acute toxicity after hypofractionated conformal radiotherapy for localized prostate cancer: nonrandomized contemporary comparison with standard fractionation. Int J Radiat Oncol Biol Phys 72(3):770–776

    Article  PubMed  Google Scholar 

  • Leborgne F, Zubizaretta E, Fowler JF et al (2000) Improved results with accelerated hyperfractionated radiotherapy of advanced head and neck cancer. Int J Cancer (Radiat Oncol Invest) 90:80–91

    Article  CAS  Google Scholar 

  • Lee I, Eisbruch A (2009) Mucositis versus tumor control: the therapeutic idex of adding chemotherapy to irradiaion of head, neck cancer. Int J Radiat Oncol Biol Phys 75:1060–1063

    Article  PubMed  Google Scholar 

  • Ling CC, Gerweck LE, Zaider M, Yorke E (2010) Dose-rate effects in external beam radiotherapy redux. Radiother Oncol 95:261–268

    Article  PubMed  Google Scholar 

  • Livsey JE, Cowan RA, Wylie JP et al (2003) Hypofractionated conformal radiotherapy in carcinoma of the prostate: five-year outcome analysis. Int J Radiat Oncol Biol Phys 57:1254–1259

    Article  PubMed  Google Scholar 

  • Lukka H, Hayter C, Warde P et al (2003) A randomized trial comparing two fractionation schedules for patients with localized prostate cancer (abstract 26). Radiother Oncol 59 [Suppl]:S7

    Google Scholar 

  • Maciejewski B, Taylor JMG, Withers HR (1986) Alpha/beta value and the importance of size of dose per fraction for late complications of the supraglottic larynx. Radiother Oncol 7:323–326

    Article  PubMed  CAS  Google Scholar 

  • Maciejewski B, Withers HR, Taylor JMG (1989) Dose fractionation and regeneration in radiotherapy of the oral cavity and oropharynx: tumor dose-response and repopulation. Int J Radiat Oncol Biol Phys 16:831–843

    Article  PubMed  CAS  Google Scholar 

  • Maciejewski B, Skladowski K, Pilecki B et al (1996) Randomized clinical trial on accelerated seven days per week fractionation in radiotherapy for head and neck cancer. Preliminary report on acute toxicity. Radiother Oncol 40:137–145

    Article  PubMed  CAS  Google Scholar 

  • McGinn CJ, Harari PM, Fowler JF et al (1993) Intensification in curative head and neck cancer radiation therapy: linear quadratic analysis and preliminary assessment of clinical results. Int J Radiat Oncol Biol Phys 27:363–369

    Article  PubMed  CAS  Google Scholar 

  • Miralbell R, Roberts SA, Zubizarreta E, Hendry JH (2010) Dose-fractionation sensitivity of prostate cancer deduced from radiotherapy outcome of 5969 patients in seven international institutional datasets: α/β = 1.4 (0.9-2.2) Gy. Int J Radiat Oncol Biol Phys 2009;75:S81. [Recently updated to α/β = 1.4 (0.9—2.2) Gy, Ms accepted December 2010 by IJROBP. Now “α/β = 1.4 (0.9-2.2) Gy” is added to the title].

    Google Scholar 

  • Moiseenko V (2004) Effect of heterogeneity in radiosensitivity on LQ based isoeffect formalism for low alpha/beta cancers. Acta Oncol 43:499–502

    Article  PubMed  Google Scholar 

  • Niemierko A (1997) Reporting and analyzing dose distributions: a concept of equivalent uniform dose. Med Phys 24:103–110

    Article  PubMed  CAS  Google Scholar 

  • Nimmadda S, Ford EC, Wong JW, Pomper MG (2009) Targeted molecular imaging in oncology: focus on radiation therapy. Sem Radiat Oncol 18:136–148

    Article  Google Scholar 

  • Overgaard J, Hansen HS, Lena S et al (2003) Five compared with six fractions per week of conventional radiotherapy of squamous-cell carcinoma of head and neck: DAHANCA 6&7 randomized controlled trial. Lancet 362:933–940

    Article  PubMed  Google Scholar 

  • Park CS, Papiez L, Zhang S, Story M, Timmerman RD (2008) Universal survival curve and single fraction equivalent dose: useful tools in understanding potency of ablative radiotherapy. Int J Radiat Oncol Biol Phys 70:847–852

    Article  PubMed  Google Scholar 

  • Peeters STH, Lebesque JV, Heemsbergen WD et al (2006) Localized volume effects for late rectal and anal toxicity after radiotherapy for prostate cancer. Int J Radiat Oncol Biol Phys 64:1151–1161

    Article  PubMed  Google Scholar 

  • Pignon JP, Bourhis J, Domenge C et al (2000) Chemotherapy added to locoregional treatment for head and neck squamous-cell carcinoma; three meta-analysis of updated individual data. Lancet 355:949–955

    PubMed  CAS  Google Scholar 

  • Poulsen M, Denham J, Spry N et al (1999) Acute toxicity and cost analysis of a phase III randomized trial of accelerated and conventional radiotherapy for squamous carcinoma of the head and neck: a Trans-Tasmanian radiation Oncology group study. Australas Radiol 43:487–494

    Article  PubMed  CAS  Google Scholar 

  • Poulsen M, Denham J, Peters L et al (2001) A randomized trial of accelerated and conventional radiotherapy for stage iii and IV squamous carcinoma of the head and neck: a Trans-tasman radiation Oncology group Study (TROG 91.01). Radiother Oncol 60:113–122

    Article  PubMed  CAS  Google Scholar 

  • Proust-Lima C, Taylor JMG, Sécher S, Willams S, et al (2010) Confirmation of a low α/β ratio for prostate cancer treated by external beam radiation therapy alone using a post-treatment repeated-measures model for PSA dynamics. Int J Radiat Oncol Biol Phys 79:195–201 (They found α/β = 1.55 Gy)

    Article  PubMed  Google Scholar 

  • Regnan R, Rosenzweig HE, Yorke E et al (2004) Improved local control with higher doses of radiation in large-volume stage III non-small-cell lung cancer. Int J Radiat Oncol Biol Phys 60:741–747

    Article  Google Scholar 

  • Roberts SA, Hendry JH (1999) Time factors in larunx tumor radiotherapy: lag times and intertumor heterogeneity in clinical datasets from four centers. Int J Radiat Oncol Biol Phys 45:1247–1257

    Article  PubMed  CAS  Google Scholar 

  • Sambrook DK (1974) Limited surgical treatment of carcinoma of the breast: radiotherapy experiences. Proc R Soc Med 67:476

    PubMed  CAS  Google Scholar 

  • Sanguinetti G, Sosa M, Endres E et al (2004) Hyperfractionated IMRT (HF-IMRT) alone for locally advanced oropharyngeal carcinoma: a phase 1 study. Radiother Oncol 73(Suppl 1):S300

    Google Scholar 

  • Saunders MI, Rojas AM, Parmar MKB, Dische S (2010) Mature results of a randomized trial of accelerated hyperfractionated versus conventional radiotherapy in head-and-neck cancer. Int J Radiat Oncol Biol Phys 77:3–8

    Article  PubMed  Google Scholar 

  • Skladowski K, Maciejewski B, Golen M et al (2000) Randomized clinical trial on 7-day-continuous accelerated irradiation (CAIR) of head and neck cancer—report on 3-year tumour control and normal tissue toxicity. Radiother Oncol 55:101–110

    Article  PubMed  CAS  Google Scholar 

  • Slevin NJ, Hendry JH, Roberts SA et al (1992) The effect of increasing the treatment time beyond three weeks on the control of T2 and T3 laryngeal cancer using radiotherapy. Radiother Oncol 42:215–220

    Article  Google Scholar 

  • Starmans MHW, Lieuwer NG, Bontros PC, Lambin P, et al (2010) Translating a prognostic tumor proliferation signature into a clinically relevant test. ESTRO annua meeting, Sept 2010. Abstract # 475

    Google Scholar 

  • Steel GG (ed) (2002) Basic clinical radiobiology, 3rd edn. Arnold, London

    Google Scholar 

  • Stewart FA (1986) Mechanisms of bladder damage and repair after treatment with radiation and cytostatic drugs. Br J Cancer 53(Suppl VII):280–291

    Google Scholar 

  • Stewart FA, van der Kogel A (2002) Proliferative and cellular organization of normal tissues. In: Steel GG (ed) Basic clinical radiobiology, 3rd edn. Arnold, London, pp 23–29 (Chap 3)

    Google Scholar 

  • Strigari L, Arcangeli G, Arcangeli S et al (2009) Mathematical model for evaluating incidence of acute rectal toxicity during conventional or hypofractionated radiotherapy courses for prostate cancer. Int J Radiat Oncol Biol Phys 73:1454–1460

    Article  PubMed  Google Scholar 

  • Stuschke M, Thames HD (1997) Hyperfractionated radiotherapy of human tumors: overview of the randomized clinical trials. Int J Radiat Oncol Biol Phys 37:259–267

    Article  PubMed  CAS  Google Scholar 

  • Thames HD, Hendry JH (1987) Fractionation in radiotherapy. Taylor and Francis, London

    Google Scholar 

  • Thames HD, Peters LJ, Withers HR, Fletcher GH (1983) Accelerated fractionation vs hyperfractionation: rationales for several treatments per day. Int J Radiat Oncol Biol Phys 9:127–138

    Article  PubMed  Google Scholar 

  • Thomlinson HR (1987) Cancer: the failure of treatment. Br J Radiol 60:735–751

    Article  PubMed  CAS  Google Scholar 

  • Timmerman RD, Paulus R, Galvin J, Michalski J, Choy H et al (2010) Stereotactic body radiation therapy for medically inoperable early-stage lung cancer patients: analysis of RTOG 0236. Int J Radiat Oncol Biol Phys 75:S3

    Article  Google Scholar 

  • Travis EL, Tucker SL (1987) Isoeffect models and fractionated radiation therapy. Int J Radiat Oncol Biol Phys 13:283–287

    Article  PubMed  CAS  Google Scholar 

  • Trotti A, Fu KK, Pajak TF, Jones CU, Ang KK et al (2005) Long term outcomes of RTOG 90-03: a comparison of hyperfractionation and two variants of accelerated fractionation to standard fractionation radiotherapy for head and neck squamous cell carcinoma. Int J Radiat Oncol Biol Phys 63(Suppl 1):S70–S71

    Google Scholar 

  • Turesson I, Notter G (1984a) The influence of fraction size in radiotherapy on the late normal tissue reaction I. Comparison of effects of daily and once-a-week fractionation on human skin. Int J Radiat Oncol Biol Phys 10:593–598

    Article  PubMed  CAS  Google Scholar 

  • Turesson I, Notter G (1984b) The influence of the overall treatment time in radiotherapy on the acute reaction: comparison of the effects of daily and twice-a-week fractionation on human skin. Int J Radiat Oncol Biol Phys 10:607–619

    Article  PubMed  CAS  Google Scholar 

  • Van de Geijn J (1989) Incorporating the time factor into the linear-quadratic model (letter). Br J Radiol 62:296–2988

    Article  PubMed  Google Scholar 

  • Van Dyk J, Mah K, Keane T (1989) Radiation-induced lung damage; dose-time fractionation considerations. Radiother Oncol 14:55–69

    Article  PubMed  Google Scholar 

  • Vargas C, Kestin LL, Martinez AA et al (2003) Dose-volume analysis of predictors fpr chronic rectal toxicity following treatment of prostate cancer with high-dose conformal radiotherapy (ASTRO abstract # 2093). Int J Radiat Oncol Biol Phys 57(2S):S398–S399

    Article  Google Scholar 

  • Vargas C, Martinez A, Kestin LL et al (2005) Dose-volume ananlysis of predictors for chronic rectal toxicity after treatment of prostate cancer with adaptive image-guided radiotherapy. Int J Radiat Oncol Biol Phys 62:1297–1308

    Article  PubMed  Google Scholar 

  • Wadsley JC, Bentzen SM (2004) Investigation of relationship between change in locoregional control and change in overall survival in randomized controlled trials of modified radiotherapy in head-and-neck cancer. Int J Radiat Oncol Biol Phys 60:1405–1409

    Article  PubMed  Google Scholar 

  • Wang CC (1988) Local control of oropharyngeal carcinoma after two accelerated hyperfractionation radiation therapy schemes. Int J Radiat Oncol Biol Phys 14:1143–1146

    Article  PubMed  CAS  Google Scholar 

  • Wang JZ, Guerrero M, Li AX (2003) How low is the alpha/beta ratio for prostate cancer? Int J Radiat Oncol Biol Phys 55:194–203

    Article  PubMed  Google Scholar 

  • Withers HR (1967) Recovery and repopulation in vivo by mouse skin epithelial cells during fractionated irradiation. Radiat Res 32:227–239

    Article  PubMed  CAS  Google Scholar 

  • Withers HR (1971) Regeneration of intestinal mucosa after irradiation. Cancer 28:75–81

    Article  PubMed  CAS  Google Scholar 

  • Withers RH, Thames HD, Peters LJ (1983) A new isoeffect curve for change in dose per fraction. Radiother Oncol 1:187–191

    Article  PubMed  CAS  Google Scholar 

  • Withers HR, Taylor JMG, Maciejewski B (1988) The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Oncol 27:131–146

    Article  PubMed  CAS  Google Scholar 

  • Wurstbauer K, Deutschmann H, Kopp P et al (2010) Non-resected non-small-cell lung cancer in stages I through IIIB: accelerated, twice-daily, high-dose radiotherapy—a prospective phase I/II trial with long-term follow-up. Int J Radiat Oncol Biol Phys 77:1345–1351

    Article  PubMed  Google Scholar 

  • Yan D, Kestin LL, Krauss D, Lockman DL, Brabbins DS, Martinez AA (2005) Phase II dose escalation study of image-guided adaptive radiotherapy for prostate cancer: use of dose-volume constraints to achieve rectal isotoxicity. Int J Radiat Oncol Biol Phys 63:141–149

    Article  PubMed  Google Scholar 

  • Yang J, Fowler JF, Lamond J, Lanciano R, Feng J, Brady L (2010) Red shell: defining a high risk zone of normal tissue damage in stereotactic body radiation therapy. Int J Radiat Oncol Biol Phys 77:903–909

    Article  PubMed  Google Scholar 

  • Zackrisson B, Franzen L, Henriksson R, Littbrand B (1994) Tolerance to accelerated fractionation in the head and neck region. Acta Oncol 33:391–396

    Article  PubMed  CAS  Google Scholar 

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  1. Jack F. Fowler

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Authors and Affiliations

  1. Human Oncology and Medical Physics, Medical School of University of Wisconsin, Madison, WI, USA

    Jack F. Fowler

  2. Gray Laboratory, Northwood, London, UK

    Jack F. Fowler

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  1. Institutet Stockholm Sweden, MMC 436, Dept.of Oncol-Pathol Karolinska, Delaware St. SE 420, Minneapolis, 55455, Minnesota, USA

    Seymour H. Levitt

  2. UC Davis Cancer Center, Dept. Radiation Oncology, University of California, Davis, X Street 4501, Sacramento, 95817, California, USA

    James A. Purdy

  3. School of Medicine, Dept. Radiation Oncology, Washington University, Forest Park Ave. 4511, St. Louis, 63108-2138, Michigan, USA

    Carlos A. Perez

  4. Instituut Verbeeten, Tilburg, 5042 SB, Netherlands

    Philip Poortmans

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Fowler, J.F. (2011). Practical Time–Dose Evaluations, or How to Stop Worrying and Learn to Love Linear Quadratics. In: Levitt, S., Purdy, J., Perez, C., Poortmans, P. (eds) Technical Basis of Radiation Therapy. Medical Radiology(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/174_2011_305

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