Dose Calculation and Verification for Tomotherapy John P. Gibbons, PhD

Dose Calculation and Verification for Tomotherapy

John P. Gibbons, PhD

Chief of Clinical Physics

Mary Bird Perkins Cancer Center

Baton Rouge, LA

Associate Professor

Department of Physics and Astronomy

Louisiana State University

2004 ACMP Meeting – Scottsdale, AZ

Tennis Anyone?

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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


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

6

4

2

0

12

10

8

20

18

16

14

TomoTherapy Patient Load - 2005

Budgeted (130) total

Actual (74) total

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



Patient Load - 2006

10

8

6

4

2

0

20

18

16

14

12



Actual (122) total




Patient Load - 2007

20

18

16

14

12

10

8

6

4

2

0



Actual (173) total




Treatment Sites: First Year

TomoTherapy Treatments by Site Prostate

Head&Neck

Pelvis

Mediastinum

CNS

Abdomen

Bladder

Breast

Skin

Mantle

Pancreas

Urethra

Met(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 Delivery


Beam Modulation

• Binary MLC system

• 64 Leaves, width 6.25mm at axis

• Thickness ~10 cm (<1% leakage)

• Transition ~20 ms

TomoTherapy Dose Calculation

Projections 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 7 o )


Sinograms

• 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


Example Planning Sinograms

Leaf open time versus projection number

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


General

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

=

V

µ

ρ

( ) ( ) (

− r dV

• TERMA is calculated first, followed by convolution with polyenergetic point kernels

• Heterogeneities handled by density scaling r

=

V

µ

ρ r

′ ρ r

) (

ρ r

ρ

' r

′

)


“Tomo is Pinnacle”, except…

• Differences in C/S implementation

Resolution of fluence calculation

Resolution of convolution integrations

Kernels computed at 15 o increments

Less mass-energy absorption

No electron contamination

• ROIs of the same type may not overlap

• Optimization procedure different


TERMA / Fluence Attenuation Table

TomoTherapy uses Fluence Attenuation Table to calculate

TERMA:

TERMA

=

µ

ρ

=

µ

ρ

=

µ

ρ r

′ ⋅Ψ r r

′ r

′ e

−

µ ρ l )

FAT

ρ ρ l )

0

10

20

30

40

50

Fluence Attenuation Table

60

0 0.5

1 1.5

2

Density

2.5

3 3.5

0.052

0.05

0.048

0.046

0.044

0.042


Mass Attenuation Coefficients

µ

ρ

Mass attenuation coefficients interpolated using values for water and bone:

Mass Attenuation Coeff.

(from NIST website)

=

µ

ρ w w

, water

µ

ρ water

+ w b water

µ

ρ bone

,

ρ w

ρ ρ b

0.10

Water

Lung

Tissue (Soft)

Bone (Cortical)

µ

ρ bone

,

ρ ρ bone

0.01

0.00

2.00

4.00

Energy (MeV)

6.00


Poly-energetic Kernel

W i h νννν i

Energy (MeV) h νννν i

K i

Monoenergetic kernel database

ΣΣΣΣ

W i

(h νννν i

) K i

(h νννν i

)

K(MV)


Dose calculation parameters


Optimization 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 15 o arc segments

Beamlet: Convolution calculations performed for each beamlet.

Full Scatter calculation performed after optimization complete


Beamlet optimization

• Number of beamlets can be large.

Example:

64 beamlets projection

×

51 projections rotation

×

30 rotations fraction

=

97920

[ beamlets

]

• 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.


Dose 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


Dose Grid Effects

-522 -476

-433

-433 -303

-302 -267

-212

-191 -89

-54

-11

-261 -154

-76

-107

-3

-32

8

12

6

44

31

67

4

23

21

17

39

52

69

76

66 87

91

104


Dose Grid Effects

46 Gy 54 Gy

Calculated

Doses in Gy

(Grid: Normal)

53 Gy

60 Gy

61 Gy

64 Gy


Dose Grid Effects

46

46

46

46

54

54

54

54

Upsampling of dose matrix creates artificial

“boxy” isodoses.

Calculated

Doses in Gy

53

(Grid: Normal)

53

60

53

53

60

61

61

64

61

61

64

60 60 64 64


Dose Grid Effects

Dose Calc Grid: Fine


Dose Grid Effects

Dose Calc Grid: Normal


Dose Grid Effects

Dose Calc Grid: Coarse


CT Resolution Effects

512 x 512 256 x 256 128 x 128


Convolution Origin (v2.2) r = voxel size d eff

= r

/2 r

/2

Convolution originates from voxel center

TomoTherapy implementation:

Convolution originates from voxel proximal end


Surface Dose Calculation

Depth Determined using Voxel Center

Koren Smith, LSU MS Thesis, 2007


Surface Dose Calculation

Depth Determined using Voxel Distal End

Koren Smith, LSU MS Thesis, 2007


CT to Density Table (IVDT)

Issues involved in IVDT Construction

1. Use physical density, not electron density

The fluence attenuation table used in the dose calculator contains mass-attenuation coefficients. The massdensity is thus needed to calculate attenuation. The

IVDT should therefore map to mass-density.




2. Avoid non-physical heterogeneity plugs near water

Typical IVDT

(close-up of water-like materials)

1.2

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/cm 3 .

• Air should be measured to obtain an

IVDT point near -1000 HU and 0.001

g/cm 3

-200 -100

1.15

1.1

1.05

1

0.95

0.9

0.85

0.8

0

Image Value (HU)

100 200




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).



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?

12%

8%

38%

15%

27%

1. Ridiculous

2. Frightening

3. Horrific

4. Abominable

5. Hungry

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

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

42%

6%

0%

0%

52%

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 tumors

5. All of the above

Helical TomoTherapy

Dose Check Algorithm

Objective:

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

System.

Helical TomoTherapy


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

• Total dose = sum of doses from each projection

D

P

= & ⋅

t

, i

D

P

•

D

P,i

= Total dose to point P

= Dose rate to point P from projection i t i

= Time for projection i

Helical TomoTherapy


SAD

O

X d

P

P

SPD

Helical TomoTherapy


D

=

D

0

⋅

SAD

SPD i

2

⋅

OAR

X

( X i

)

⋅

{

S cp

⋅ ( ) ⋅

( ,

Y i i

)

}

D

P

D

0

= Total dose to point P

= Dose rate under normalization conditions

SAD = Source-axis distance (85 cm)

SPD = Source-calculation point P distance

S cp

= Output factor

TPR = Tissue phantom ratio

OAR

X

OAR

Y

= Transverse off-axis ratio

= Longitudinal off-axis ratio

Beam Modulation

Sinogram approximated by a sum of symmetric, unmodulated segments: a) Example projection b) Symmetric (about leaf m) approximation to (a) c) Decomposition of (b) into 4 unmodulated segments.

5

4 a) Sinogram projection

3

2

1

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

5 b) Symmetrized sinogram projection

4

3

2

1

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

5 c) Decomposition into segments

4

3

2

1

0

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

Leaf Number

Helical TomoTherapy


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 Data

TPR

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

5.0-cm jaw

0.6 x 5.0 cm

2

3.1 x 5.0 cm

2

9.4 x 5.0 cm

2

40 x 5 cm

2

40 x 5 cm

2

(Measured)

5 10 15

Depth [cm]

20 25 30


S cp

1.00

0.98

0.96

0.94

0.92

S cp

0.90

0.88

0.86

0.84

0.82

0.80

0

2.5-cm jaw - Measured

2.5-cm jaw - Simulated

5.0-cm jaw - Measured

5.0-cm jaw - Simulated

2 4 6 8

Side of Equivalent Square [cm]

10


Off-Axis Ratios

OAR x

OAR y

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

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

Off-Axis Distance [cm] b) 5 cm Jaw d=1.5

d=10 d=20 d=30

15 20 25

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1.0

0.9

0.8

0.0

0 1 2 3

Off-Axis Distance [cm] c) d=30 cm

1 open leaf

5 open leaves

15 open leaves

All open

4 5

Clinical Evaluation of Algorithm

I. Phantom Plan Studies

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

• Treatment Field Length

• Depth

• Off-Axis

Phantom Studies

Accuracy 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 Studies

Accuracy 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

Phantom/PTV Center

TomoTherapy Axis

Phantom Study Results

Phantom

20cm cyl

50cm cyl

Treatment Plan

10 cm width; 1 rotation

10 cm width; 3 rotations



Pitch MF

0.4

1

TomoPlan

Dose

[Gy]

60.0

Calculated

Dose

[Gy]

Difference

59.9

-0.2%

0.4

0.4

0.287

1

1

1

60.7

60.5

10.1

60.3

60.0

10.0

-0.6%

-0.8%

-0.6%

10 cm width; 29 rotations 0.287

20cm

On-axis

20cm

Off-axis

50 Gy to cylindrical PTV

(7 cm diameter, 5 cm length)

0.3

0.3

1

1.3

1.7

10.0

51.2

51.2

9.8

51.2

51.2

-1.5%

<0.1%

<0.1%


II. 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.


Choice 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


Choice of Calculation Point

Patient Plan Results

15

10

5

0

30

25

20

50

45

40

35

(Algorithm Dose – TomoTherapy Dose)/TomoTherapy Dose

Other

CNS

Superficial

Abdomen

Pelvis

Head and Neck

Prostate

Thorax

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

Difference [%]

4% 8% 12% 16%


All treatment plans excluding lung and superficial sites

50

45

40

35

30

25

20

15

10

Other

5

0

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

Difference [% ]


Lung and Superficial Sites Only

40

35

30

25

20

50

45

15

10

5

Thorax

0

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

Difference [% ]

40

35

30

50

45

15

10

5

25

20

Superficial

0

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

Difference [% ]

Patient Plan Results: Lung Sites

Heterogeneity Correction Errors d eff

a

Patient Plan Results: Lung Sites

Heterogeneity Correction Errors

CORK POLY

POLY

CORK

POLY

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

Patient Plan Results: Superficial Sites

Missing 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?

4%

4%

8%

4%

81%

1. Sad

2. Disgusting

3. Horrific

4. Silly

5. Noble

For beams traversing lung, radiological path length correction algorithms

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

0%

3.

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

100%

4.

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

0%

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 John P. Gibbons, PhD

Tennis Anyone?

Outline

= & ⋅

Dosimetric Input Data

Off-Axis Ratios

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Dose Calculation and Verification for Tomotherapy John P. Gibbons, PhD

Tennis Anyone?

Outline

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Off-Axis Ratios

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