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THE GEC ESTROHANDBOOKOF BRACHYTHERAPY | Part I: The Basics of Brachytherapy
Version 1 - 22/10/2015
Radiobiology of LDR, HDR, PDR and VLDR Brachytherapy
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tive schedule assuming that irradiation was given at 2 Gy per
fraction would become:
[8]
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:
[9]
For comparing different LDR dose rates we must first translate
continuous LDR into an equi-effective fractionated HDR dose
using the Liversage formula:
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:
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:
[10]
Starting from formula [7] EQD2 values for PDR schedules can
be calculated as follows:
[11]
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
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.
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.
EQD2
HDR
= D (α/β + d) / (α/β + 2)
EQD2
LDR
= D (α/β + gDR) / (α/β + 2)
EQD2
LDR
= D (α/β + 2.9 T
1/2
. DR) / (α/β + 2)
EQD2
PDR
= D { α/β + (1+Hm )d} / (α/β + 2)
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.