Ciencia

Monterrey, December 2009

Radiobiological comparison of
treatment plans
 Visual inspection of isodose distributions (2D, 3D)
• highly subjective

 Visual comparison of DVHs
• fairly subjective

 Quantitative measures of plan “quality” from DVH
• Dmin, Dmax, D90, D100, V90, V100, etc.
• Veff, Deff, EUD
• TCPs, NTCPs

Visual inspection of isodose plans:
very subjective
Fourplans for
comparison:
•photons + electrons
•5-field photons
•5-field IMRT
•9-field IMRT

Comparison of tumor DVHs
(from Andrzej Niemierko, ASTRO, 2001)

Median dose = 63.7 Gy
for both plans

Some quantitative
measures to go by
D100

V90

Range Std. dev.
V100
(Gy)
(Gy)

IMRT 59Gy 30Gy

94%

50%

30 - 65

2.5

83%

50%

55 - 73

3.5

Plan

APPA

D9057Gy 55Gy

IMRT: most uniform (lower standard deviation), higher V90, but lower D100
AP-PA: higher D100, but lower V90 and also higher Dmax

But which is the better plan?
 Need to consider both tumor and normal
tissue DVHs
 Want good coverage of the target, low
Dmax to normal tissues, and low volume
of normal tissues receiving doses close
to “tolerance”

Can the DVH be reduced to asingle
“biologically relevant” number?

Need a volume-effect
model of dose response
• most common is the powerlaw model

Power-law volume-effect models (they’ve
been around for a long time and we still
use them today)

Skin ttolerance dose  A
A
Skin olerance

--0.33
0.33

Cube - r oot r ule,Meyer, 1939
Meyer, 1939
Cube

Tissue tolerance dose  V
V
Tissue

--0.11
0.11Jolles,1946
Jolles,

General power-law model
Dv = D1.v-n
where Dv is the dose which, if delivered to
fractional volume, v, of an organ, will produce the
same biological effect as dose D1 given to the
whole organ
This is the basis of most dose-volume histogram
reduction methods

What does the volume
effect exponent “n” mean?
 n is negative for tumors
 n is positive for normaltissues
 n = 0 means that cold spots in tumors or hot spots
in normal tissues are not tolerated
 n = 1 means that isoeffect doses change linearly
with volume
 n large means that cold spots in tumors or hot
spots in normal tissues are well tolerated

Hot-spots not tolerated - spinal cord (n small)
Hot-spots well tolerated – liver (n large)
150

D50 (Gy)

100

Liver (U.Michigan)
Cord (B. Powers)

50

0

0

0.2

0.4
0.6
Partial volume

(from Andrzej Niemierko, ASTRO, 2001)

0.8

1

Dose-volume histogram
reduction methods
As a very simple
demonstration, a twostep DVH is reduced to
one step:
Kutcher & Berman:
effective volume at
maximum dose, Veff
Lyman & Wolbarst:
effective dose to whole
(or reference) volume,
Deff

Determination ofDeff
Need to sum the effects for
the subvolumes of tissue
represented by each step
of the DVH

Mohan et al (1992) expression for Deff (derived
from the Kutcher and Burman method)

Deff



1/ n
  Di  (Vi / Vtot )
i


n

where Vi is the subvolume irradiated to dose Di,
Vtot is the total volume of the organ or tissue, and
n is the tissue-specific volume-effect parameterin
the power-law model
Mohan et al called this the “effective uniform dose”

Equivalent Uniform Dose (EUD)
(Niermierko, 1999)
For any dose distribution, the EUD is the
dose which, if distributed uniformly across
the entire target volume or organ at risk,
causes the same biological effect as the
actual inhomogeneous dose distribution
(originally defined for tumors only in 1997 butextended to normal tissues in 1999)

The generalized EUD equation
(Niemierko, 1999)
1/ a


a
gEUD   vi Di 
i


where vi is the volume of the tissue in dose bin Di as a
fraction of the volume of the total organ or tumor i.e.
vi = Vi/Vtot
Note that gEUD is identical to Deff of Mohan et al with a
= 1/n

Generalized Equivalent Uniform Dose (gEUD)
D1 < D2

D1

D2

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