Margins in SBRT
Mischa Hoogeman
MARGIN CONCEPTS
Why do we use margins?
Target / tumor
To a-priori compensate for (unknown) deviations between the intended target
position and the real target position during dose delivery
Deviations are estimated from population-based measurements of geometrical
errors (can be patient specific, e.g. respiratory motion)
Healthy tissue
To avoid unintended dose to a critical organs after aligning the beam to the
displaced target (in case of differential motion between target and OAR)
How large should the margin be?
What is the incentive?
99% of the target volume receives 95% of the prescribed dose or more
(coverage probability) - Stroom et al.
90% of patients in the population receives a minimum cumulative CTV
dose of at least 95% of the prescribed dose - van Herk et al.
Not all patients will be treated to 100% of the prescription dose in all fractions
M = 2.5S + 0.7s
Categorization of Errors: a 2D Example
Random error s
Systematic error S
Systematic error M
Probability Density Function: Normal Distribution
Random Errors Only: Mrand=0.7s
The CTV experiences daily shifts of the dose distribution due to daily random
variations in the position of the CTV
If we add the daily shifted dose distributions the dose distribution appeares
to be blurred (motion blurring)
The effect of the random error can be calculated by convolving the random
error distribution with the dose distribution => blurred dose distribution
=random error
s
Margin Recipe for Random Error
block positionpenumbrasp
random errors
95%
50%
Water sp= 3.2 mmLung sp = 6.4 mm
Margin Calculation: Random Component
The margin that would be needed to ensure a coverage of at least 95%
pp ss === ,0,95.0norminv
22,0,95.0norminv sss === ppM = 1.64s2sp2 - 1.64spM = 0.7s
Random Error and Minimum Dose Requirement
The margin for random decreases with decreasing prescription isodose line /
minimum dose requirement
95%
50%
73%M = bs2sp
2 - bsp
Prescription level b
95% 1.64
80% 0.84
70% 0.52
60% 0.25
Random Margin and Prescription Level
Prescription level b
95% 1.64
80% 0.84
70% 0.52
60% 0.25
Systematic Errors Only (Msys = 2.5 S)
The systematic set-up errors are described by a 3D Gaussian distribution
How to choose Msys to ensure a high probability that the prescribed dose is
delivered to the CTV?
Choice: for 90% of all possible systematic set-up errors (treatments), the full
CTV is within the PTV (=95% isodose)
95%
Systematic Errors Only (Msys = 2.5 S)
Spherical Tumor
0𝑀𝑠𝑦𝑠 𝑝 Σ 𝑑𝑟 = 0.9
0𝑀𝑠𝑦𝑠 𝑟2
𝜋
2Σ3𝑒−
𝑟2
2Σ2𝑑𝑟 = 0.9
Population (%) S
80 2.16
90 2.50
95 2.79
99 3.36
Margin Recipe: Systematic Error and Random Errors
Systematic errors are assumed to have an independent effect on the blurred
dose distribution
Cumulative minimum dose ≥ 95%
Mr = bs2+sp2 - bsp
≥ 90% of population receives acumulative CTV dose of ≥ 95%
M = 2.5S + Mr
How to Add Various Error Contributions?
For a simple criteria as a probability level of the minimum dose the
systematic error and random error are added linearly
For various systematic errors and various random errors the errors (SDs)
should be added in quadrature:
)10(9.103310 222
222
==S
SSS=S cba
Emphasis on large errors!
APPLICATION TO SRT AND SBRT
Number of Fractions and Residual Systematic Error
Limited number of fractions results in a residual shift of the dose distribution
Residual error
Error after 35 fractions = 0.1 mm
Error after 5 fractions = -1.6 mm
-8
-6
-4
-2
0
2
4
6
8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Erro
r (m
m)
Fraction Number
Effective Standard Deviation of the Errors
Effective Systematic Error
Effective Random Error
22 1s
Neffective S=S
Error in estimating the average
211 ss
-=
Neffective
de Boer H C and Heijmen B J 2001 A protocol for the reduction of systematic patient setup errors with minimal portalimaging workload Int. J. Radiat. Oncol. Biol. Phys. 50 1350–65
Margin and Number of Fractions
Seff
seff
Margin
S = 2 mm, s = 2 mm, P=80%
Including Error due to Respiratory Motion
Respiratory motion modeled as sin6t
The respiratory motion can be described as a standard deviation for a given
amplitude
s = 0.358A
0 5 10 15 20 250
1
2
3
4
5
6
7
8
9
Without Synchrony
Intr
a-f
ractio
n e
rro
r (1
SD
) [m
m]
Respiratory motion amplitude (mm)
Intra-fraction error vs. motion amplitude (CC)
)(cos6
0
-=
tAyy
A358.0=s
Slope = 0.36
Hoogeman M, Prévost JB,
Nuyttens J, Pöll J, Levendag
P, Heijmen B, Clinical
accuracy of the respiratory
tumor tracking system of the
cyberknife: assessment by
analysis of log files. Int J
Radiat Oncol Biol Phys.
2009 May 1;74(1):297-303.
PRACTICAL EXAMPLES
A Practical Example: SRT Case
Intracranial lesion: 3 x 8 Gy @ 80%
SD of the penumbra is 3.2 mm
E2E test device error (1 SD) = 0.4 mm (measured over a long period)
Localization (delineation) error = 1.0 mm (1 SD)
Systematic error = 0.5 mm (1 SD) [measured from 30-fraction treatments]
Random error = 0.5 mm (1 SD) [measured from 30-fraction treatments]
Intra-fraction error = 0.5 mm ( 1 SD) [measured from 30-fraction treatments
at end of treatment]
A Practical Example: SRT Case
Intracranial lesion: 3 x 8 Gy @ 80% N=3, b=0.84
SD of the penumbra is 3.2 mm spen=3.2 mm
E2E test device error (S) = 0.4 mm S1=0.4 mm
Localization (delineation) error = 1.0 mm (1 SD) S2=1.0 mm
Systematic error = 0.5 mm (1 SD) Seff=0.58 mm
Random error = 0.5 mm (1 SD) seff=0.41 mm
Intra-fraction error = 0.5 mm ( 1 SD) seff=0.20 mm
Results SRT Example
No delineation error
Evaluation of Treatment Accuracy
Seravalli E, van Haaren PM, van der Toorn PP, Hurkmans CW. A comprehensive evaluation of treatment accuracy, including end-to-end tests and clinical data, applied to intracranial stereotactic radiotherapy. Radiother Oncol. 2015 Jul;116(1):131-8.
A Practical Example: SBRT Lung Case
T1 primary lung lesion: 3 x 18 Gy @ 80%
Alignment on time-averaged tumor position by CBCT
Tumor in lung tissue
E2E test device error (1 SD) = 0.4 mm (measured over a long period)
Localization (delineation) error = 2.0 mm (1 SD)
Systematic error = 1.0 mm (1 SD) [measured from 3-fraction treatments]
Random error = 1.0 mm (1 SD) [measured from 3-fraction treatments]
Intra-fraction amplitude = 1 – 25 mm
A Practical Example: SBRT Lung Case
T1 primary lung lesion: 3 x 18 Gy @ 80% N = 3, b = 0.84
Alignment on time-averaged tumor position by CBCT
SD of the penumbra is 6.4 mm spen = 6.4 mm
E2E test device error (S) = 0.4 mm S1 = 0.4 mm
Localization (delineation) error = 2.0 mm (1 SD) S2 = 2.0 mm
Systematic error = 1.0 mm (1 SD) Seff = 1.0 mm
Random error = 1.0 mm (1 SD) seff = 1.0 mm
Intra-fraction amplitude = 1 – 25 mm sr = 0.4 – 9.0 mm
Margins SBRT Lung Case
No breathing
INTERNAL TARGET VOLUME
ITV Concept in ICRU-62 Report
PTV margin should be derived from
Internal Margin (IM) or Internal Target Volume (ITV)
Setup Margin
IM or ITV should compensate for physiological movements and variations in
size, shape, and position of the CTV in relation to an internal reference point
ITV often applied in lung SBRT where it encloses the full CTV in all respiratory
phases
PTV
ITV
CTV
Margin vs ITV for Perfect Inter-fraction Alignment
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20
Mar
gin
(m
m)
Amplitude (mm)
Margin ITV
Margin Water
Margin lung
Margin Recipe for Random Error
80%
50%
+
--
Some Concluding Remarks
In radiosurgery often 0-mm margins are being advocated
There will always be residual geometrical uncertainties
Target definition
Errors in image-guidance systems
Indirect measures of tumor position
Always verify the margin algorithm used in the Treatment Planning System
3D margin algorithm (and not 2D)
What is the resolution of the margin algorithm (e.g. CT resolution?)
Verify that margin are not truncated to voxel positions, especially in
the superior-inferior direction
References for Further Reading
Stroom JC, de Boer HC, Huizenga H, Visser AG. Inclusion of geometrical uncertainties in radiotherapy treatment planning by
means of coverage probability. Int J Radiat Oncol Biol Phys. 1999 Mar 1;43(4):905-19.
Van Herk M, Remeijer P, Rasch C, Lebesque JV. The probability of correct target dosage: Dose population histograms for deriving
margins in radiotherapy. Int J Radiat Oncol Biol Phys. 2000;47:1121-1135.
van Herk M, Remeijer P, Lebesque JV. Inclusion of geometric uncertainties in treatment plan evaluation. Int J Radiat Oncol Biol
Phys. 2002 Apr 1;52(5):1407-22.
Witte MG, van der Geer J, Schneider C, Lebesque JV, van Herk M. The effects of target size and tissue density on the minimum
margin required for random errors. Med Phys. 2004 Nov;31(11):3068-79
International Commission on Radiation Units and Measurements. Prescribing, recording and reporting photon beam therapy.
ICRU Report 50. Bethesda; 1993.
International Commission on Radiation Units and Measurements. Prescribing, recording and reporting photon beam therapy
(Supplement to ICRU Report 50). ICRU Report 62 Bethesda; 1999.
International Commission on Radiation Units and Measurements. Prescribing, recording and reporting Photon Beam Intensity-
Modulated Radiation Therapy (IMRT). ICRU Report 83; 2010.
Wolthaus JW, Sonke J-J, van Herk M, et al. Comparison of different strategies to use four-dimensional computed tomography in
treatment planning for lung cancer patients. Int J Radiat Oncol Biol Phys 2008;70:1229–1238.
van Herk M, Witte M, van der Geer J, Schneider C, Lebesque JV Int. J. Radiation Oncology Biol. Phys., Vol. 57, No. 5, pp. 1460–
1471, 2003.
Wunderink W PhD Thesis Erasmus University, Rotterdam, The Netherlands http://hdl.handle.net/1765/23257.
Gordon JJ, Siebers JV. Convolution method and CTV-to-PTV margins for finite fractions and small systematic errors. Phys Med Biol.
2007 Apr 7;52(7):1967-90.
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