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
TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center
Staffing Levels
• 13 Medical Physicists– 7 PhD’s, 6 MS’s– 9 Clinical FTEs
• 9 Radiation Oncologists• 8 Dosimetrists
TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center
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
TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center
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
TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center
Patient Load - 2006
TomoTherapy Patient Load - 2006
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 (168) totalActual (122) total
TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center
Patient Load - 2007
TomoTherapy Patient Load - 2007
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 (168) total
Actual (173) total
TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center
Treatment Sites: First Year
TomoTherapy Treatments by Site ProstateHead&NeckPelvisMediastinumCNSAbdomenBladderBreastSkinMantlePancreasUrethraMet(s)
TomoTherapy Clinical Experience Mary Bird Perkins Cancer Center
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)
TomoTherapy Dose CalculationDose Grid Effects
64 Gy60 Gy
61 Gy53 Gy
54 Gy46 Gy
CalculatedDoses in Gy
(Grid: Normal)
TomoTherapy Dose CalculationDose Grid Effects
64646060
64646060
61615353
61615353
54544646
54544646Upsampling of dose matrix creates artificial “boxy”isodoses.
TomoTherapy Dose CalculationDose Grid Effects
Dose Calc Grid: Fine
TomoTherapy Dose CalculationDose Grid Effects
Dose Calc Grid: Normal
TomoTherapy Dose CalculationDose Grid Effects
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
TomoTherapy Dose Calculation CT to Density Table (IVDT)
2. Avoid non-physical heterogeneity plugs near water
Issues involved in IVDT Construction
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
TomoTherapy Dose Calculation CT to Density Table (IVDT)
3. IVDT should produce a density of ~1.014 for the Virtual Water TomoPhantom
Issues involved in IVDT Construction
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.
Helical TomoTherapy Dose Check Algorithm
,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
Helical TomoTherapy Dose Check Algorithm
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
= ⋅ ⋅ ⋅ ⋅ ⋅
&
Helical TomoTherapy Dose Check Algorithm
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:
Helical TomoTherapy Dose Check Algorithm
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
-0.8%60.060.510.410 cm width; 20 rotations
-0.6%60.360.710.410 cm width; 3 rotations
-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
Patient Plan Results
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
Patient Plan Results
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
Patient Plan Results
• 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