dose calculation and verification for tomotherapy

Dose Calculation and Verificationfor Tomotherapy

John P. Gibbons, PhD

Chief of Clinical PhysicsMary Bird Perkins Cancer Center

Baton Rouge, LA

Associate ProfessorDepartment of Physics and Astronomy

Louisiana State University

2004 ACMP Meeting – Scottsdale, AZ Tennis Anyone?

Tennis Anyone?

Outline

• Introduction– TomoTherapy Experience at Mary Bird Perkins

Cancer Center

• Dose Calculation with TomoTherapy– Helical TomoTherapy delivery system

– Planning system algorithm and implementation– Independent Check Algorithm

• Conclusions

TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center

Facilities and Equipment

• Facilities: 2000 patients/year– Baton Rouge– Hammond– Covington– Gonzalez (2008)

• Equipment– 4 Varian 21EX– 1 BrainLab Novalis– 1 TomoTherapy unit


Staffing Levels

• 13 Medical Physicists– 7 PhD’s, 6 MS’s– 9 Clinical FTEs

• 9 Radiation Oncologists• 8 Dosimetrists


TomoTherapy Timeline

• October 2004:– System Installed

• November 2004:– Unit Accepted

• January 2005:– First patient treated

• March 2006:– Research cluster added

• February 2007:– 1 cm jaw commissioned


Patient Load - 2005

TomoTherapy Patient Load - 2005

0

2

4

6

8

10

12

14

16

18

20

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

New

Pat

ient

Sta

rts

Budgeted (130) totalActual (74) total


Patient Load - 2006


0

2

4

6

8

10

12

14

16

18

20


New

Pat

ient

Sta

rts

Budgeted (168) totalActual (122) total


Patient Load - 2007


0

2

4

6

8

10

12

14

16

18

20


New

Pat

ient

Sta

rts

Budgeted (168) total

Actual (173) total


Treatment Sites: First Year

TomoTherapy Treatments by Site ProstateHead&NeckPelvisMediastinumCNSAbdomenBladderBreastSkinMantlePancreasUrethraMet(s)


Treatment Sites: Through Jan 2008

Total: 399 Patients Treated

TomoTherapy Patients by Site

Thorax (Lung, Chest, Mantle) (72)

Prostate (58)

Head and Neck (64)

Superficial (Chest Wall, Scalp) (71)

Pelvis (Pelvis, Bladder, Rectum) (37)

CNS (Spine, Brain) (27)

Abdomen (Abdomen, Liver, Pancreas) (24)

Other (14)

Helical TomoTherapy Delivery Mechanical Design

Helical TomoTherapy DeliveryHelical Delivery

Helical TomoTherapy Delivery Beam Modulation

• Binary MLC system

• 64 Leaves, width 6.25mm at axis

• Thickness ~10 cm (<1% leakage)

• Transition ~20 ms

TomoTherapy Dose CalculationProjections and Beamlets

• Projection defined by beam from fixed gantry angle

• Beamlet defined by radiation through single leaf

• Beamlets computed only for rays which pass through a tumor ROI

• Calculation uses 51 projections per rotation (approximately every 7o)

TomoTherapy Dose CalculationSinograms

• Sinograms are 2D histograms which define the machine state versus time (e.g., projection, beam pulse)

• TomoTherapy sinograms are usually of two categories:

� Leaf Open Time Sinograms

� Exit Detector Signal Sinograms

TomoTherapy Dose CalculationExample Planning Sinograms

On-axis cylinder Off-axis cylinder Head & Neck Patient

Leaf open time versus projection number

TomoTherapy Dose Calculation General

• Tomotherapy uses a convolution/superposition (C/S) algorithm to compute dose

• TERMA is calculated first, followed by convolution with poly-energetic point kernels

• Heterogeneities handled by density scaling

( ) ( ) ( ) ( )V

D r r r K r r dVµρ

′ ′ ′= Ψ −∫r r r r r

( ) ( ) ( ' ) ( ' )V

D r r r K r r dVµ ρ ρ ρρ

′ ′ ′= Ψ ⋅ ⋅ − ⋅∫r r r r r

TomoTherapy Dose Calculation “Tomo is Pinnacle”, except…

• Differences in C/S implementation

�Resolution of fluence calculation

�Resolution of convolution integrations

�Kernels computed at 15o increments

�Less mass-energy absorption

�No electron contamination

• ROIs of the same type may not overlap

• Optimization procedure different

TomoTherapy Dose Calculation TERMA / Fluence Attenuation Table

Density

Dep

th (

cm)

Fluence Attenuation Table

0 0.5 1 1.5 2 2.5 3 3.5

0

10

20

30

40

50

600.042

0.044

0.046

0.048

0.05

0.052( ) ( )TERMA r r

µρ

′ ′= ⋅Ψr r

( )

0( )l

r eµ ρρµ

ρ

− ′= ⋅Ψ ⋅r

TomoTherapy uses Fluence Attenuation Table to calculate TERMA:

0( ) ( , )r FAT lµ ρ ρρ

′= ⋅Ψ ⋅r

TomoTherapy Dose Calculation Mass Attenuation Coefficients

,

,

,

water

water

w b w b

water bone

bone

bone

w w

µ ρ ρρ

µ µ µ ρ ρ ρρ ρ ρ

µ ρ ρρ

≤ = + < <

≥

Mass attenuation coefficients interpolated using values for water and bone:

Mass Attenuation Coeff.(from NIST website)

0.01

0.10

0.00 2.00 4.00 6.00

Energy (MeV)

Mas

s A

tten

uatio

n (c

m^2

/g)

Water

Lung

Tissue (Soft)

Bone (Cortical)

hννννi

Ki

TomoTherapy Dose Calculation Poly-energetic Kernel

Energy (MeV)

Wi

hννννi

Monoenergetic kernel database

ΣΣΣΣ Wi(hννννi) Ki(hννννi)

K(MV)

TomoTherapy Dose CalculationDose calculation parameters

TomoTherapy Dose CalculationOptimization Modes

During optimization, “dose” may be calculated using three modes:

� TERMA: No convolutions performed

� Full Scatter: At each iteration, 24 convolutions performed using TERMA calculated in 15o arc segments

� Beamlet: Convolution calculations performed for each beamlet.

Full Scatter calculation performed after optimization complete

TomoTherapy Dose CalculationBeamlet optimization

• Number of beamlets can be large.

Example:

• Dose from each beamlet calculated, but dose matrix is compressed if dose < threshold (0.025% for used ROIs; 1% for normal tissue). Compression is ~5x in version 2.2.

• Much larger beamlet compression (~600x) is performed in version 3.

[ ]

64 51 30

97920

beamlets projections rotations

projection rotation fraction

beamlets

× ×

=

TomoTherapy Dose CalculationDose Calculation Grid

• Calculation dose grid is fixed in size and covers entire planning CT volume

• Dose grid resolution may be set to three values:

� Fine: Resolution matches CT voxel resolution

� Normal: Resolution is ½ the CT resolution in the axial plane and matches in the longitudinal direction

� Coarse: Resolution is ¼ the CT resolution in the axial plane and matches in the longitudinal direction

TomoTherapy Dose CalculationDose Grid Effects

10487663923

917652174

674412-3-76

316-32-154-261

-11-89-191-303-433

-54-267-302-476-522

HU’s from CT

(Grid: Fine)

6921

8-107

-212-433

HU’s from CT

(Grid: Normal)

CalculatedDoses in Gy

(Grid: Normal)


64 Gy60 Gy

61 Gy53 Gy

54 Gy46 Gy

CalculatedDoses in Gy

(Grid: Normal)


64646060

64646060

61615353

61615353

54544646

54544646Upsampling of dose matrix creates artificial “boxy”isodoses.


Dose Calc Grid: Fine


Dose Calc Grid: Normal


Dose Calc Grid: Coarse

TomoTherapy Dose CalculationCT Resolution Effects

512 x 512 256 x 256 128 x 128

TomoTherapy Dose Calculation Convolution Origin (v2.2)

r/2

r = voxel sizedeff = r/2

Convolution originates from voxel center

TomoTherapy implementation:Convolution originates from

voxel proximal end

TomoTherapy Dose Calculation Surface Dose Calculation

Depth Determined using Voxel Center

Koren Smith, LSU MS Thesis, 2007

TomoTherapy Dose Calculation Surface Dose Calculation

Depth Determined using Voxel Distal End

Koren Smith, LSU MS Thesis, 2007

TomoTherapy Dose Calculation CT to Density Table (IVDT)

1. Use physical density, not electron density

The fluence attenuation table used in the dose calculator contains mass-attenuation coefficients. The mass-density is thus needed to calculate attenuation. The IVDT should therefore map to mass-density.

Issues involved in IVDT Construction


2. Avoid non-physical heterogeneity plugs near water


Typical IVDT(close-up of water-like materials)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

-200 -100 0 100 200

Image Value (HU)

Den

sity

(g/c

m^3

)

TomoTherapy Procedure:• Do not use any plugs between +100

HU.• Water should be measured to obtain

an IVDT point near 0 HU and 1 g/cm3.• Air should be measured to obtain an

IVDT point near -1000 HU and 0.001 g/cm3


3. IVDT should produce a density of ~1.014 for the Virtual Water TomoPhantom


McEwen, M; Niven, D; “Characterization of the phantom material Virtual Water in high-energy photon and electron beams”, Med. Phys. 33 (2006).

TomoTherapy Dose CalculationCT to Density Table (IVDT)

4. Avoid using IVDT to correct for heterogeneities

In an open field, a bull mistakenly eats an explosive device. What word best describes this situation?

27%

15%

38%

8%

12%

Abominable (A-bomb-in-a-bull)

1. Ridiculous

2. Frightening3. Horrific

4. Abominable5. Hungry

Tomotherapy dose calculation time for tens of thousands of beamlets is reduced by

52%

0%

0%

6%

42% 1. Down-sampling the planning kVCT dataset

2. Reducing the modulation factor.3. Reducing the penalties for all regions at risk

4. Reducing min dose objective for all tumors5. All of the above

Helical TomoTherapy Dose Check Algorithm

Objective:

Verify patient treatment times within 5% produced by a TomoTherapy Planning System.


,P P i iD D t= ⋅∑ &

DP = Total dose to point PDP,i = Dose rate to point P from projection i

ti = Time for projection i

•

• Algorithm designed to compute dose to a point in a high dose, low gradient region

• Total dose = sum of doses from each projection


P

O

θ

SAD

SPD

d

X

P

DP = Total dose to point PD0 = Dose rate under normalization conditions

SAD = Source-axis distance (85 cm)SPD = Source-calculation point P distanceScp = Output factorTPR = Tissue phantom ratio

OARX = Transverse off-axis ratioOARY = Longitudinal off-axis ratio

( ){ }2

, 0 ( ) ( , )P i X i cp i Y i ii

SADD D OAR X S TPR d OAR Y d

SPD

= ⋅ ⋅ ⋅ ⋅ ⋅

&


Beam Modulation

0

1

2

3

4

5

m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4

Leaf

Ope

n T

ime

[sec

s]

0

1

2

3

4

5

m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4

Lea

f Ope

n T

ime

[sec

s]-1

0

1

2

3

4

5

m-4 m-3 m-2 m-1 m m+1 m+2 m+3 m+4

Leaf Number

Lea

f Ope

n T

ime

[se

cs]

a) Sinogram projection

b) Symmetrized sinogram projection

c) Decomposition into segments

a) Example projectionb) Symmetric (about leaf m)

approximation to (a)c) Decomposition of (b) into 4

unmodulated segments.

Sinogram approximated by a sum of symmetric, unmodulated segments:


Dosimetric Input Data:

• Data were obtained by simulating static fields on TomoTherapy planning system and extracting dose

• Measurements were made of a subset of these data to confirm agreement.

Dosimetric Input DataTPR

5.0-cm jaw

Depth [cm]

0 5 10 15 20 25 30

TP

R

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.6 x 5.0 cm2

3.1 x 5.0 cm2

9.4 x 5.0 cm2

40 x 5 cm2

40 x 5 cm2 (Measured)

Dosimetric Input DataScp

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

0 2 4 6 8 10Side of Equivalent Square [cm]

S cp

2.5-cm jaw - Measured

2.5-cm jaw - Simulated

5.0-cm jaw - Measured

5.0-cm jaw - Simulated

c) d=30 cm

Off-Axis Distance [cm]

0 1 2 3 4 5

OA

Ry

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1 open leaf5 open leaves15 open leavesAll open

Off-Axis Distance [cm]

-25 -20 -15 -10 -5 0 5 10 15 20 25

Lat

eral

Pro

file

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

d=1.5d=10d=20d=30

b) 5 cm Jaw

OARx OARy

Dosimetric Input DataOff-Axis Ratios

Clinical Evaluation of AlgorithmI. Phantom Plan Studies

Designed to test the accuracy of the dose calculation under different conditions

• Treatment Field Length• Depth

• Off-Axis

Phantom StudiesAccuracy vs. Field Length

• Treatment plans of varying field lengths performed on cylindrical phantom

• Dose in center of cylinder compared to algorithm

1 Rotation 20 Rotations

Phantom StudiesAccuracy vs. Off Axis Distance

• Treatment plans performed on phantom positioned on CAX and 10 cm off-axis

• Dose in center of cylinder compared to algorithm

TomoTherapy Axis

Phantom/PTV Center

Phantom Study Results

<0.1%51.251.21.70.320cmOff-axis

<0.1%51.251.21.30.350 Gy to cylindrical PTV (7 cm diameter, 5 cm length)

20cmOn-axis

-1.5%9.810.010.28710 cm width; 29 rotations

-0.6%10.010.110.28710 cm width; 4 rotations50cm cyl



-0.2%59.960.010.410 cm width; 1 rotation20cm cyl

DifferenceCalculated Dose

[Gy]

TomoPlanDose

[Gy]

MFPitchTreatment PlanPhantom

Clinical Evaluation of AlgorithmII. Patient Plan Studies

• 97 Patient Treatment plans were evaluated. Plans represented all treatment plans for which sinograms were available.

• Comparisons were made between doses calculated by treatment planning system and point dose algorithm.

Clinical Evaluation of AlgorithmChoice of Calculation Point

• Calculation point automatically placed in center of PTV.

• If auto placement failed, point manually moved to high dose, low gradient region

• Calculation point kept at least 1 cm from lung

Clinical Evaluation of AlgorithmChoice of Calculation Point

Patient Plan Results

0

5

10

15

20

25

30

35

40

45

50

-16% -12% -8% -4% 0% 4% 8% 12% 16%

Difference [%]

Num

ber

OtherCNSSuperficialAbdomenPelvisHead and NeckProstateThorax

(Algorithm Dose – TomoTherapy Dose)/TomoTherapy Dose


All treatment plans excluding lung and superficial sites

0

5

10

15

20

25

30

35

40

45

50

-8% -6% -4% -2% 0% 2% 4% 6% 8%

Difference [%]

Num

ber

Other


Lung and Superficial Sites Only

0

5

10

15

20

25

30

35

40

45

50

-8% -6% -4% -2% 0% 2% 4% 6% 8%

Difference [%]

Num

ber

Thorax

0

5

10

15

20

25

30

35

40

45

50

-8% -6% -4% -2% 0% 2% 4% 6% 8%

Difference [%]

Nu

mbe

r

Superficial

Patient Plan Results: Lung SitesHeterogeneity Correction Errors

deff

POLY

CORK

Mackie et al., Med Phys 12: 327 (1985)

POLY

a

CORK POLY

Patient Plan Results: Lung SitesHeterogeneity Correction Errors

Patient Plan Results: Superficial SitesMissing Phantom Scatter


• 97 Patient Plans Evaluated• 68 Treatment Plans excluding

Lung/Thorax:– 94% (64/68) Agreed within 2%– Average difference 0.4%

• 38 Treatment Plans in Lung/Thorax– Algorithm systematically overestimates dose– Average difference =3.1%

Conclusions

• Independent dose algorithm accurately predicts dose to simple phantom geometries

• Calculations to patient sites excluding lung and superficial targets agree well with TomoTherapy calculated doses.

• Calculations to lung and superficial sites demonstrate systematic differences of ~3%.

The bomb exploded. What word best describes this situation?

81%

4%

8%

4%

4% 1. Sad

2. Disgusting3. Horrific

4. Silly5. Noble

For beams traversing lung, radiological path length correction algorithms

0%

100%

0%

0%

0% 1. Underestimate the dose within lung, but overestimate the soft tissue dose on the distal end of the lung

2. Underestimate the dose within lung and on the distal end of the lung

3. Overestimate the dose on the proximal and distal end of the lung

4. Overestimate the dose within lung and on the distal end of the lung

5. Correctly predicts the dose within the lung, but underestimates the soft tissue dose on the distal end of the lung

Acknowledgements

• TomoTherapy– Eric Schnarr– Gustavo Olivera– Ken Ruchala

• Mary Bird Perkins/LSU– Koren Smith– Dennis Cheek– Ricky Hesston

Acknowledgements

• Nikos Papanikolau

dose calculation and verification for tomotherapy

Documents