5 Radiobiology of LDR, HDR, PDR and VLDR Brachytherapy

Radiobiology of LDR, HDR, PDR and VLDR Brachytherapy

12

THE GEC ESTROHANDBOOKOF BRACHYTHERAPY | Part I: The Basics of Brachytherapy Version 1 - 22/10/2015

tive schedule assuming that irradiation was given at 2 Gy per fraction would become:

EQD2

= D (α/β + d) / (α/β + 2)

[8]

HDR

This is assumed to give a good estimation of the equivalent dose of fractionated external beam and HDR. Starting from formula 3, the EQD2 value for a LDR schedule can then be calculated as:

EQD2

= D (α/β + gDR) / (α/β + 2)

[9]

LDR

For comparing different LDR dose rates we must first translate continuous LDR into an equi-effective fractionated HDR dose using the Liversage formula:

Fig 5.13: Dose and dose gradient distribution within an interstitial implant. The dose is pre- scribed at a peripheral reference isodose (D100 or D90). In the irradiated area higher doses and dose rates lead to a much higher biological effect than expected from physical dose distribution alone.

N = μt/{2 [1-1/μt (1 - e -μt )]}

Where N is number of fractions into which the HDR treatment must be divided in order to be equi-effective to the LDR treat- ment lasting t hours if both total time and total dose remain con- stant. When t exceeds 10 hours, the exponential term becomes negligi- ble and the formula is simplified to:

early reactions, and 186 Gy for late reactions. At the 30 Gy iso- dose, the dose rate is 0.21 Gy/h. The equivalent doses are 28Gy and 24 Gy, respectively. We can then calculate that the biological equivalent doses vary for a physical dose gradient of 4 by a factor 4.7 for early reactions and 6.8 for late reactions. The biological gradient is thus much steeper than the “physical” gradient. Let us now consider a 42 Gy HDR irradiation delivered in 6 frac- tions. At the 84 Gy isodose, the dose per fraction is 14 Gy, and the equivalent doses are 119 Gy and 143 Gy for early and late effects, respectively. At the 21 Gy isodose, the dose per fraction is 3.5 Gy, and the equivalent dose 17 Gy and 14 Gy. We can then calculate that the equivalent doses vary by a factor of 7 for early reactions, and 10 for late reactions. In the concept of the equivalent uniform dose (EUD), the inho- mogeneous dose distribution within one volume is converted to an homogeneous dose which would result in the same survival. Hence the concept is based on a homogeneous distribution of morbidity factors – or tissue tolerance. This might be applicable to early reactions and tumour responses. However for late effects this might be less clear, since these effects are based on a variety of target cells and their interactions.

N =μt/[2 (1-1/μt)]

When t approaches 100 hours, the last term becomes negligible and the formula can be simplified again; it becomes

N = μt/2 and d = 2.9 T 1/2

. DR where DR is the dose rate in Gy/h.

Combining this with formula [10] will simplify the formula to:

EQD2

= D (α/β + 2.9 T

. DR) / (α/β + 2)

[10]

LDR

1/2

Starting from formula [7] EQD2 values for PDR schedules can be calculated as follows:

[11]

EQD2

PDR = D { α/β + (1+Hm )d} / (α/β + 2)

7. BIOLOGICAL EFFECTS OF DOSE INHOMOGENEITY

In a BT implant, the dose gradient distribution is also a dose rate gradient distribution (Fig 5.13). The dose is prescribed at a peripheral reference isodose, the Minimum Target Dose (MTD) = D100, which should encompass the target, or at 90 % of the MTD = D90. Within the irradiated area higher doses delivered at higher dose rates (LDR) fraction sizes HDR) or pulse sizes (PDR) will lead to much greater biological effects than expected from physical dose distribution alone. Let us consider a classical low dose rate continuous irradiation of 60 Gy in 6 days and study the variation in biological effectiveness between 30 Gy and 120 Gy; a dose and dose rate gradient of a factor 4: At the isodose receiving 120 Gy, the dose rate is 0.83 Gy/h. Using formula [9] we can estimate the equivalent dose to be 133 Gy for

8. VOLUME, ANATOMICAL SITE, AND PATIENT-RELATED EFFECTS

It has been shown in animal studies as well as in clinical data that the total dose required to sterilise tumours increases with increasing tumour volume, but that at the same time the sensi- tivity of late responding normal tissues increases with increasing GTV/PTV. The volume of healthy tissues included in the plan- ning target volume is one of the major parameters of treatment morbidity. Mathematical models of the normal tissue compli- cation probability (NTCP), like the Lyman-Kutcher–Burmann model (1989) have been introduced to link the irradiated volume – in addition to the treatment protocol - to the complication rate.