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.