{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T00:08:54Z","timestamp":1784333334442,"version":"3.55.0"},"reference-count":42,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,11,30]],"date-time":"2024-11-30T00:00:00Z","timestamp":1732924800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>The 2 Gy per fraction equivalent dose (EQD2) is an important quantity used in determining equivalent prescription doses for different fractionation regimens and evaluating different fractionation regimens, but it does not match its definition when it is used for normal tissues. We propose to use the fractionation-specific biological equivalent dose to determine normal tissue dose constraints for different fractionation regimens. The concept of the biological equivalent dose is defined based on the linear-quadratic equation. The EQD2 is derived based on the biological effective dose (BED), mimicking the prescription dose of a standard fractionation regimen with a fractional dose of 2 Gy and a fixed number of fractions. The FEQD(n) is also defined based on the BED as a function of the number of fractions, n, which is determined by the dose prescription. The FEQD(n) mimics any fractionation regimens with any fractional doses and numbers of fractionations. A given dose constraint can have different BED values and EQD2 values for different fractionation regimens. The number of fractions for a given 2 Gy per fraction regimen derived from the EQD2 for the target dose is different from that for the normal tissues. The value of the EQD2 derived for the target represents the total dose for the target for the 2 Gy fractional dose regimen, but the EQD2 value derived for the normal tissues does not represent the total dose for the normal tissue for the same fractionation regimen. The fractionation-specific biological equivalent dose (FEQD(n)) for both target and normal tissues has the same number of fractions for any fractionation regimen, and represents the total dose for either the target or the normal tissue. Based on the clinical outcomes, the FEQD(n) curves for the brainstem, spinal cord, rectum, and lung were derived and can be directly used as dose constraints for various fractionation regimens in clinical practice. The EQD2 does not match its definition and is not realistic when describing the biological equivalent dose for normal tissues. It is also not practical when used in determining tolerance doses or dose constraints. Instead, the FEQD(n) can be used to determine or convert the normal tissue dose constraints for any fractionation regimens in a realistic and practical manner. Using the FEQD(n), the dose constraints as a function of the number of fractions for the brainstem, spinal cord, rectum, and lung, which correspond to the given toxicity rates, were derived and can be directly used in clinical practice.<\/jats:p>","DOI":"10.3390\/ijms252312891","type":"journal-article","created":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T05:43:43Z","timestamp":1733118223000},"page":"12891","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Replacing 2 Gy Per Fraction Equivalent Dose with Fractionation-Specific Biological Equivalent Dose for Normal Tissues"],"prefix":"10.3390","volume":"25","author":[{"given":"Wei","family":"Luo","sequence":"first","affiliation":[{"name":"Department of Radiation Medicine, University of Kentucky, Lexington, KY 40536, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"St Clair","sequence":"additional","affiliation":[{"name":"Department of Radiation Medicine, University of Kentucky, Lexington, KY 40536, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0360-3016(91)90171-Y","article-title":"Tolerance of normal tissue to therapeutic irradiation","volume":"21","author":"Emami","year":"1991","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"S10","DOI":"10.1016\/j.ijrobp.2009.07.1754","article-title":"Use of normal tissue complication probability models in the clinic","volume":"76","author":"Marks","year":"2010","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_3","first-page":"35","article-title":"Tolerance of Normal Tissue to Therapeutic Radiation","volume":"1","author":"Emami","year":"2013","journal-title":"Rep. Radiother. Oncol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0009-9260(69)80043-7","article-title":"Dose, time and fractionation: A clinical hypothesis","volume":"20","author":"Ellis","year":"1969","journal-title":"Clin. Radiol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0009-9260(71)80044-2","article-title":"Cumulative radiation effect part I: Fractionated treatment regimes","volume":"22","author":"Kirk","year":"1971","journal-title":"Clin. Radiol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1259\/0007-1285-46-547-529","article-title":"A simplification the NSD concept in practical radiotherapy","volume":"46","author":"Orton","year":"1973","journal-title":"Br. J. Radiol."},{"key":"ref_7","first-page":"103","article-title":"Review: Total doses in fractionated radiotherapy implications of new radiobiological data","volume":"46","author":"Fowler","year":"1984","journal-title":"Int. J. Radiat. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1259\/0007-1285-62-740-679","article-title":"The linear-quadratic formula and progress in fractionated radiotherapy","volume":"62","author":"Fowler","year":"1989","journal-title":"Br. J. Radiol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1259\/0007-1285-33-390-389","article-title":"Dose-rate effects: Some theoretical and practical considerations","volume":"33","author":"Fowler","year":"1960","journal-title":"Br. J. Radiol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1088\/0031-9155\/18\/1\/007","article-title":"A Molecular Theory of Cell Survival","volume":"18","author":"Chadwick","year":"1973","journal-title":"Phys. Med. Biol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.semradonc.2008.04.005","article-title":"The Linear-Quadratic Model Is Inappropriate to Model High Dose per Fraction Effects in Radiosurgery","volume":"18","author":"Kirkpatrick","year":"2008","journal-title":"Semin. Radiat. Oncol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4825","DOI":"10.1088\/0031-9155\/49\/20\/012","article-title":"Exteending the linear-quadratic model for large fractional doses pertinent to stereotactic radiotherapy","volume":"49","author":"Gurrero","year":"2004","journal-title":"Phys. Med. Biol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1016\/j.ijrobp.2007.10.059","article-title":"Universal survival curve and single fraction equivalent dose: Useful tools in understanding potency of ablative radiotherapy","volume":"70","author":"Park","year":"2008","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4161","DOI":"10.1118\/1.2969065","article-title":"Some implications of linear-quadratic-linear radiation dose-response with regard to hypofractionation","volume":"35","author":"Astrahan","year":"2008","journal-title":"Med. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1981","DOI":"10.1016\/0360-3016(82)90459-X","article-title":"Dose fractionation, dose rate and iso-effect relationships for normal tissue responses","volume":"8","author":"Barendsen","year":"1982","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1259\/0007-1285-58-690-515","article-title":"The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy","volume":"55","author":"Dale","year":"1985","journal-title":"Br. J. Radiol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/S0360-3016(98)00364-2","article-title":"The assessment of RBE effects using the concept of biologically effective dose","volume":"43","author":"Dale","year":"1999","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_18","first-page":"71","article-title":"The Role of Biologically Effective Dose (BED) in Clinical Oncology","volume":"13","author":"Jones","year":"2001","journal-title":"Clin. Oncol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1259\/bjr\/31372149","article-title":"21 years of Biologically Effective Dose","volume":"83","author":"Fowler","year":"2010","journal-title":"Br. J. Radiol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S0167-8140(83)80021-8","article-title":"A new isoeffect curve for change in dose per fraction","volume":"1","author":"Withers","year":"1983","journal-title":"Radiother. Oncol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1016\/S0360-3016(97)00364-7","article-title":"Brainstem tolerance to conformal radiotherapy of skull base tumors","volume":"39","author":"Debus","year":"1997","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1016\/S0360-3016(02)02823-7","article-title":"Intensity-modulated radiation therapy (IMRT) for meningioma","volume":"53","author":"Uy","year":"2002","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/j.adro.2020.09.009","article-title":"Moderately Hypofractionated Radiation for Benign Meningiomas and Schwannomas: A Report of 70 Patients Treated Between 2008 and 2018","volume":"5","author":"Dhere","year":"2020","journal-title":"Adv. Radiat. Oncol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.ijrobp.2007.10.010","article-title":"Patterns of Failure and Toxicity after Intensity-Modulated Radiotherapy for Head and Neck Cancer","volume":"71","author":"Schoenfeld","year":"2008","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0360-3016(90)90126-5","article-title":"The incidence of myelitis after irradiation of the cervical spinal cord","volume":"19","author":"Marcus","year":"1990","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1002\/1097-0142(197506)35:6<1558::AID-CNCR2820350613>3.0.CO;2-7","article-title":"Radiation tolerance of the spinal cord","volume":"35","author":"Wara","year":"1975","journal-title":"Cancer"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s13566-015-0212-9","article-title":"Radiation dose-fractionation effects in spinal cord: Comparison of animal and human data","volume":"4","author":"Jin","year":"2015","journal-title":"J. Radiat. Oncol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.radonc.2007.06.013","article-title":"Late radiotherapy-induced lower intestinal toxicity (RILIT) of intensity-modulated radiotherapy for prostate cancer: The need for adapting toxicity scales and the appearance of the sigmoid colon as co-responsible organ for lower intestinal toxicity","volume":"84","author":"Fonteynea","year":"2007","journal-title":"Radiother. Oncol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/j.ijrobp.2008.04.063","article-title":"Role of intensity-modulated radiotherapy in reducing toxicity in dose escalation for localized prostate cancer","volume":"73","author":"Heemsbergen","year":"2009","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1016\/j.ijrobp.2006.07.1337","article-title":"Analysis of clinical and dosimetric factors associated with treatment-related pneumonitis (TRP) in patients with non\u2013small-cell lung cancer (NSCLC) treated with concurrent chemotherapy and three-dimensional conformal radiotherapy (3D-CRT)","volume":"66","author":"Wang","year":"2006","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.ijrobp.2012.03.041","article-title":"Clinical and Dosimetric Predictors of Radiation Pneumonitis in a Large Series of Patients Treated With Stereotactic Body Radiation Therapy to the Lung","volume":"85","author":"Baker","year":"2013","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1093\/jrr\/rru080","article-title":"Results and DVH analysis of late rectal bleeding in patients treated with 3D-CRT or IMRT for localized prostate cancer","volume":"56","author":"Someya","year":"2015","journal-title":"J. Radiat. Res."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109628","DOI":"10.1016\/j.radonc.2023.109628","article-title":"Validation of prediction models for radiation-induced late rectal bleeding: Evidence from a large pooled population of prostate cancer patients","volume":"183","author":"Cicchetti","year":"2023","journal-title":"Radiother. Oncol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.semradonc.2008.04.004","article-title":"The Linear-Quadratic Model Is an Appropriate Methodology for Determining Isoeffective Doses at Large Doses Per Fraction","volume":"18","author":"Brenner","year":"2008","journal-title":"Semin. Radiat. Oncol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.rpor.2017.02.010","article-title":"Radiobiology of stereotactic body radiation therapy (SBRT)","volume":"22","author":"Garau","year":"2017","journal-title":"Rep. Pract. Oncol. Radiother."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2038","DOI":"10.1002\/mp.14690","article-title":"A unified multi-activation (UMA) model of cell survival curves over the entire dose range for calculating equivalent doses in stereotactic body radiation therapy (SBRT), high dose rate brachytherapy (HDRB), and stereotactic radiosurgery (SRS)","volume":"48","author":"Li","year":"2021","journal-title":"Med. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/0167-8140(89)90084-4","article-title":"Time-dependent tumour repopulation factors in linear\u2013quadratic equation\u2014Implications for treatment strategies","volume":"15","author":"Dale","year":"1989","journal-title":"Radiother. Oncol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3105","DOI":"10.1118\/1.2229427","article-title":"Effects of oxygen on intrinsic radiation sensitivity: A test of the relationship between aerobic and hypoxic linear-quadratic (LQ) model parameters","volume":"33","author":"Carlson","year":"2006","journal-title":"Med. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1667\/RR2773.1","article-title":"Radiation-Induced Vascular Damage in Tumors: Implications of Vascular Damage in Ablative Hypofractionated Radiotherapy (SBRT and SRS)","volume":"177","author":"Park","year":"2012","journal-title":"Radiat. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1089\/ars.2017.7267","article-title":"Targeted and Off-Target (Bystander and Abscopal) Effects of Radiation Therapy: Redox Mechanisms and Risk\/Benefit Analysis","volume":"29","author":"Pouget","year":"2018","journal-title":"Antioxid. Redox Signal."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1667\/RADE-24-00040.1","article-title":"Abscopal Effects, Clastogenic Effects and Bystander Effects: 70 Years of Non-Targeted Effects of Radiation","volume":"202","author":"Lyng","year":"2024","journal-title":"Radiat. Res."},{"key":"ref_42","first-page":"2","article-title":"A systematic review of normal tissue neurovascular unit damage following brain irradiation\u2014Factors affecting damage severity and timing of effects","volume":"6","author":"Nakkazi","year":"2024","journal-title":"Neuro-Oncol. Adv."}],"container-title":["International Journal of Molecular Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1422-0067\/25\/23\/12891\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:43:14Z","timestamp":1760114594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1422-0067\/25\/23\/12891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,30]]},"references-count":42,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["ijms252312891"],"URL":"https:\/\/doi.org\/10.3390\/ijms252312891","relation":{},"ISSN":["1422-0067"],"issn-type":[{"value":"1422-0067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,30]]}}}