Replacing 2 Gy Per Fraction Equivalent Dose with Fractionation-Specific Biological Equivalent Dose for Normal Tissues

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.