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# Verification - PowerPoint PPT Presentation

Planning. Clinical Aspects. Radiobiological Aspects. Delivery. Arthur Boyer Stanford University School of Medicine Stanford, California. Verification. Conventional planning. Time. IMRT planning. Complexity. Establish the Correspondence Between Output and Input. Output. Input.

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Verification

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#### Presentation Transcript

• Planning

• Clinical Aspects

Delivery

Arthur Boyer

Stanford University School of Medicine

Stanford, California

• Verification

Conventional planning

Time

IMRT planning

Complexity

Establish the Correspondence Between Output and Input

Output

Input

Specify quantities that describe a patient’s

quality of life (e.g., Karnofsky status)

Desired

output

Specify TCP and NTCP--biological model

Specify a dose distribution--dose based model

Procedures of Inverse Planning Computation

Optimal Input

Output

Construct an objective function

F = F (input parameters) = F (w1,w2,w3,….,wJ)

Optimize F and find the optimal beam profiles

Convert beam profiles into MLC leaf sequences

Dosimetric:

F = [Dc(1)-D0(1)]2 +[Dc(2)-D0(2)]2 + ...

w1

Beam profile

Dc(1)

D0(1)

Dc(2)

D0(2)

• An objective function is a mathematical “measurement” of radiation treatment.

• ~2000 pencil beam weights, non-linear system.

• It should, ideally, include all of our knowledge of radiotherapy: dosimetry based and biological model based objective function.

• Optimization of a multi-dimensional

• objective function

• Matrix Inversion

• Iterative methods

• Computer simulated annealing

• Genetic optimization

• Filtered backprojection

• Direct Matrix Inversion

n=4

F = S [Dc(n)-D0(n)]2

Calculated dose

n=1

w3

w4

Prescribed dose

3

4

D3

D4

1.0

0.5

w2

1

2

D1

D2

w1

1.0

1.0

w4

w3

n=4

F = S [Dc(n)-D0(n)]2

n=1

D3

D4

w2

D1

D2

w1

D1= w1 d11+ w2 d21 + w3 d31 + w4 d41

D2= w1 d12+ w2 d22 + w3 d32 + w4 d42

D3= w1 d13+ w2 d23 + w3 d33 + w4 d43

D4= w1 d14+ w2 d24 + w3 d34 + w4 d44

• Direct Matrix Inversion

A Simple Iterative Algorithm

Dose to point n:

1

dn = w1d1n + w2d2n + w3d3n

target

organ

2

3

Algebraic Iterative Method:

Initial beam profiles

Calculate dose at a voxel n

Compare Dc(n) with D0(n)

n+1

Dc(n) > D0(n) ?

Yes

No

Decrease wi

Increase wi

Algebraic Iterative Method:

n=6

F = S [Dc(n)-D0(n)]2

Calculated dose

n=1

0.5

0.5

Prescribed dose

1.0

1.0

1.0

1.0

0.5

1.0

0.5

1.0

1.0

0.5

1.0

1.0

1.0

1.0

0.5

Algebraic Iterative Method:

Iteration step = 5

Iteration step = 1

0.51

0.45

0.50

0.49

1.01

0.95

0.50

0.99

1.00

0.50

0.95

0.99

0.90

0.44

0.97

0.49

1.02

1.01

0.99

1.00

0.50

0.50

Objective function

Iteration step = 10

i=6

F = S [Dc(i)-D0(i)]2

0.30

0.51

0.42

i=1

0.25

0.20

0.15

0.10

0.51

1.02

0.92

0.05

0.91

0.41

0.82

0

20

40

80

60

1.02

0.92

100

0

0.51

Iteration step

Algebraic Iterative Method:

### Planning Parameters

• Number of beams

• Beam/Coll orientation

• Isocenter placement

• Beamlet size

• Intensity levels

• Margins & Targets

• Tuning structure

### Beam Orientation

• Coplanar vs Non-coplanar

• Ease of setup

• Ease of planning

• Speed of treatment

• Equi-spaced vs Selected angles

• Entrance through table/immobilization device

### Beam Orientation

9 equi-spaced beams

9 selected beams

### Collimator Orientation

180o collimator angle

Collimator angle

### Isocenter Placement

• Issues

• Can a better plan be achieved by isocenter placement ?

• Dosimetry and/or QA

• Patient setup

### Isocenter Placement

Isocenter in geometric center of targets

### Isocenter Placement

Isocenter in geometric center of GTV

Yi et al. 2000

### Intensity Levels

Lehmann et al. 2000

### Tuning Structure

• A structure added to control the dose distribution in IMRT plans

• Reduce normal tissue dose

• Reduce/Increase target dose

### Summary of Planning Parameters

• Number of beams

• Beam/Coll orientation

• Isocenter placement

• Beamlet size

• Intensity levels

• Margins & Targets

• Tuning structure

Verification

Planning System Commissioning

a

b

c

d

e

f

specially designed intensity patterns

Planning System Commissioning

90%

90%

50%

50%

40%

10%

20%

20%

40%

70%

70%

10%

80%

80%

90%

90%

30%

50%

30%

10%

10%

50%

90%

90%

Calculated Measured

specially designed intensity patterns

Patient Specific Field Verification

Quantitative Comparison of Two Fluence Maps

• Maximum difference in

• pixel values---local quantity.

• Correlation coefficient—

• global quantity.

Film

### QUANTITATIVE FILM ANALYSIS

Courtesy, Tim Solbert

Quantitative Film Analysis

White = measurement

Red = calculation

Courtesy, Tim Solberg

Calculated

Measured

### Quantitative Film Analysis - Profiles

Horizontal and vertical profiles of measured data, calculated data, and  index.

Courtesy, Tim Solberg

40 cm

1.5 cm

4.5 cm

30 cm

Measurement Tissue Equivalent Phantom

50%

70%

90%

-1.8%

1mm

-3.5%

2mm

Cylindrical Phantom Dose Verification

Measured in Plane of Isocenter

BANG gel Dosimetry

Courtesy, Tim Solberg

Periodic IMRT QA

Periodic IMRT QA

Test Pattern with Leaf Error

Test Pattern after leaf replacement and MLC calibration

IMRT MU Checks

QUALITY ASSURANCE OF IMRT TREATMENT PLAN

DEPARTMENT OF RADIATION ONCOLOGY ,STANFORD UNIVERSITY SCHOOL OF MEDICINE

PATIENT NAME: xxx, xxxxxxx

PATIENT ID: xxx-xx-xx

TPS PLAN #: 2512

Treatment Machine: LA7

Beam Energy: 15 MV

Calibration Setup: SSD

Delivery Mode: Step and Shoot

Beamlet Size: 1.0 x 1.0 (cm x cm)

Calibration Factor: 1.000

Isocenter Dose Verification Report

Field MU x1 x2 y1 y2 SSD beam-dose

F 180-000 170 7.80 6.80 4.20 16.20 88.79 50.2

F 180-080 118 4.80 6.80 4.20 17.20 82.03 40.6

F 180-145 108 8.00 1.00 5.00 18.00 90.87 24.0

F 180-145a 101 1.00 8.00 4.00 18.00 90.87 17.9

F 180-215 80 9.00 0.00 3.00 18.00 90.49 1.6

F 180-215a 107 2.00 7.00 5.00 18.00 90.49 48.7

F 180-280 115 6.80 5.80 4.20 17.20 81.68 41.2

IMRT MU Checks

Calculated Isocenter Dose: 224.2 cGy

TPS Isocenter Dose: 221.3 cGy

Percentage Difference: 1.3 (%).

Leaf Sequence Verification Report

Field ID Gantry Angle Correlation Coefficient Maximum Difference

1 0 1.0000 0.5112 (%)

2 80 1.0000 0.4017 (%)

3 145 1.0000 0.6799 (%)

4 215 1.0000 0.7275 (%)

5 280 1.0000 0.4034 (%)

Physicist: _________________________

DATE: 7/20/2001

Isocenter Setup Verification with DRRs

Anterior Isocenter Verification

Isocenter Setup Verification with DRRs

Lateral Isocenter Verification

Align DRR with EPID Image To Verify Patient Positioning

DRR Image

AmSi EPID Image

DELIVERY OF IMRT BY COMPUTER CONTROLLED MLC

1 cm

m

1 cm

Tl,m,k

Beam Modulation Patterns

• Velocity Modulation

• Step and Shoot

Velocity Modulation

Fluence Profile Required for IMCRT

Velocity Modulation

.

(x) =  (x) [tA(x) - tB(x)]

B

A

Velocity Modulation

.

(x) =  (x) [tA(x) - tB(x)]

 (x)

.

(x) =

(x)

(x) = tA(x) - tB(x) > 0

“Velocity” leaf sequencing

250

200

Leaf A

(x)

150

100

50

0

Leaf B

0

5

10

15

20

25

30

35

40

Position, X (cm)

Interpretation as Trajectories

“Velocity” leaf sequencing

250

200

150

(x)

100

50

0

0

5

10

15

20

25

30

35

40

Position, X (cm)

Reflection Operation to Remove Time Reversals

(x) = (x) - 

“Velocity” leaf sequencing

250

200

150

(x)

100

50

0

0

5

10

15

20

25

30

35

40

Position, X (cm)

Translation Operation to Remove Discontinuities

(x) = (x) + (x)

“Velocity” leaf sequencing

Reflection Operation to Remove Time Reversal

250

200

150

(x)

100

50

0

0

5

10

15

20

25

30

35

40

Position, X (cm)

“Velocity” leaf sequencing

250

Leaf A

200

150

(x)

100

Leaf B

50

0

0

5

10

15

20

25

30

35

40

Position, X (cm)

Shear Operation to Remove Infinite Velocity

(x) = (x) + x/vmax

“Velocity” leaf sequencing

 (x)

.

(x) =

(x)

d(x) =

dx

d (x)/dx

.

(x)

Differentiation of Opening Time

“Velocity” leaf sequencing

Differentiation of Shear Operation

(x) = (x) + x/vmax

d(x) = d(x) + 1

dx dx  vmax

d(x) = 1

dx v(x)

“Velocity” leaf sequencing

d (x)/dx

1

1

.

+

=

vmax

v(x)

(x)

vmax

=

v(x)

d (x)/dx

.

vmax

1 

(x)

Substitutions to Obtain Velocity Relation

“Velocity” leaf sequencing

80

70

Leaf A

60

50

Time (sec)

40

30

20

Leaf B

10

0

0

5

10

15

20

25

30

35

Position (cm)

“Velocity” leaf sequencing

Step and Shoot

“Step-and-Shoot” leaf sequencing

5.0

4.0

3.0

Intensity Level

2.0

1.0

12

13

0.0

14

-3

Leaf Pair

15

-2

-1

0

+1

+2

+3

x-Position

-3 -2 -1 0 +1 +2 +3

-3 -2 -1 0 +1 +2 +3

Leaf Pair 12

Leaf Pair 13

-3 -2 -1 0 +1 +2 +3

-3 -2 -1 0 +1 +2 +3

Leaf Pair 14

Leaf Pair 15

A

B

5

5

1

4

8

4

4

2

5

7

3

Levels

3

3

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

Position

Instance 1

A

B

5

5

1

4

8

4

4

2

5

7

3

Levels

3

3

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

Position

Instance 2

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

6

7

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 3

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

6

7

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 4

B

A

8

5

7

6

6

7

5

5

1

4

4

2

4

7

3

3

Levels

3

2

2

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 5

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 6

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 7

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 8

B

A

8

5

7

6

6

7

5

1

4

4

5

2

4

7

3

3

Levels

3

2

2

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 9

B

A

5

1

4

8

4

5

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 10

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 11

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 12

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

Position

Instance 13

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

Position

Instance 14

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 15

B

A

5

5

1

4

8

4

2

4

7

5

3

3

Levels

3

7

6

6

2

2

7

1

1

8

0

-3 -2 -1 0 +1 +2 +3

-

-

-

1

2

3

3

2

1

Position

Instance 16

Leaf Pair 12

Leaf Pair 13

Leaf Pair 14

Leaf Pair 15

15

1&2

14

13

12

15

3&4

14

13

12

15

5&6

14

13

12

15

14

13

7&8

12

15

14

13

9&10

12

15

14

13

11&12

12

15

14

13

12

13&14

15

14

13

12

15&16

15

14

13

12

17&18

15

14

12

13

19&20

File Structure

Static File Structure

File Rev = G

Treatment = Static

Last Name = Collimator

First Name = M.L.

Patient ID = 555-1212

Number of Fields = 13

Number of Leaves = 52

Tolerance = 0.3

Field = Left Lung

Index = 0.0

Carriage Group = 1

Operator = DNR

Collimator = 0.0

Leaf 1A = 0.00

Leaf 2A = 1.00

Leaf 3A = 2.00

Leaf 4A = 3.00

Leaf 5A = 4.00

Leaf 6A = 5.00

Leaf ...

For conventional MLC treatments, the STATIC mode is used.

Dynamic Treatment Files

File Rev = G

Treatment = Dynamic dose

Last Name = Patient

First Name = QA

Patient ID = 555-1212

Number of Fields = 12

Number of Leaves = 120

Tolerance = 0.3

Field = Shape1

Index = 0.000

Carriage Group = 1

Operator = DNR

Collimator = 0.0

Leaf 1A = 0.00

Leaf 2A = 1.00

Leaf 3A = 2.00

Leaf 4A = 3.00

Leaf 5A = 4.00

Leaf 6A = 5.00

Leaf ...

• Identical file format and syntax as for static treatment

• Each specified leaf pattern is correlated to value of some Clinac parameter

• “Treatment = ” and “Index = ” file entries determine behavior

Field = Shape2

Index = 0.050

Carriage Group = 1

Operator = DNR

Collimator = 0.0

Leaf 1A = 0.00

Leaf 2A = 1.00

Leaf 3A = 2.00

Leaf 4A = 3.00

Leaf 5A = 4.00

Leaf 6A = 5.00

Leaf ...

Field = Shape3

Index = 0.072

Carriage Group = 1

Operator = DNR

Collimator = 0.0

Leaf 1A = 0.00

Leaf 2A = 1.00

Leaf 3A = 2.00

Leaf 4A = 3.00

Leaf 5A = 4.00

Leaf 6A = 5.00

Leaf ...

Treatment Field Index

File Rev = G

Treatment = Dynamic Dose

Last Name = John

First Name = Smith

Patient ID = 1234

Number of Fields = 20

Number of Leaves = 80

Tolerance = 0.1

Field = 1 of 20

Index = 0.0000

Carriage Group = 1

Operator = Physicist

Collimator = 180.0

Leaf 1A = 0.00

Leaf 2A = 0.00

Leaf 3A = 3.00

The file must specify the total number of instances that will be used.

Treatment Field Index

File Rev = G

Treatment = Dynamic Dose

Last Name = John

First Name = Smith

Patient ID = 1234

Number of Fields = 20

Number of Leaves = 80

Tolerance = 0.1

Field = 1 of 20

Index = 0.0000

Carriage Group = 1

Operator = Physicist

Collimator = 180.0

Leaf 1A = 0.00

Leaf 2A = 0.00

Leaf 3A = 3.00

Varian has 52-leaf, 80-leaf, and 120-leaf MLCs. The file must identify the MLC.

Treatment Field Index

File Rev = G

Treatment = Dynamic Dose

Last Name = John

First Name = Smith

Patient ID = 1234

Number of Fields = 20

Number of Leaves = 80

Tolerance = 0.1

Field = 1 of 20

Index = 0.0000

Carriage Group = 1

Operator = Physicist

Collimator = 180.0

Leaf 1A = 0.00

Leaf 2A = 0.00

Leaf 3A = 3.00

Tolerance parameter is in units of centimeters.

Treatment Field Index

File Rev = G

Treatment = Dynamic Dose

Last Name = John

First Name = Smith

Patient ID = 1234

Number of Fields = 20

Number of Leaves = 80

Tolerance = 0.1

Field = 1 of 20

Index = 0.0000

Carriage Group = 1

Operator = Physicist

Collimator = 180.0

Leaf 1A = 0.00

Leaf 2A = 0.00

Leaf 3A = 3.00

Dose (MU) fraction ranging from 0.0 (beginning of treatment) to 1.0 (end of treatment).

Treatment Field Index

File Rev = G

Treatment = Dynamic Dose

Last Name = John

First Name = Smith

Patient ID = 1234

Number of Fields = 20

Number of Leaves = 80

Tolerance = 0.1

Field = 1 of 20

Index = 0.0000

Carriage Group = 1

Operator = Physicist

Collimator = 180.0

Leaf 1A = 0.00

Leaf 2A = 0.00

Leaf 3A = 3.00

Dose (MU) fraction ranging from 0.0 (beginning of treatment) to 1.0 (end of treatment).Leaf positions (cm) are specified as a function of dose fraction.

File Footer - CRC

Leaf 51B = 2.25

Leaf 52B = 2.25

Leaf 53B = 1.75

Leaf 54B = -6.20

Leaf 55B = -6.20

Leaf 56B = -6.20

Leaf 57B = -6.20

Leaf 58B = -6.20

Leaf 59B = -6.20

Leaf 60B = -6.20

Note = 0

Shape = 0

Magnification = 0.00

CRC = CF95

â

File Structure

CRC

• Ensures file data integrity

• Against file corruption

• Against unintentional editing outside of authorized data editing tools

• Uses industry-standard algorithm

Step-and-shoot

Dynamic delivery

fMU=0.0

1st MLC

position

fMU=0.0

1st MLC

position

step

fMU=0.14

1st MLC

position

fMU=0.14

2nd MLC

position

shoot

fMU=0.14

2nd MLC

position

fMU=0.25

3rd MLC

position

step

fMU=0.25

2nd MLC

position

fMU=0.33

4th MLC

position

shoot

Clinical Applications of IMRT

Planning

180o

140o

Immobilization

Aquaplast

Position Verification

Ximatron

Network File Management

Varis

Plan Verification

Wellhöfer

Structure Segmentation

AcQsim

Inverse Planning

Corvus

CT/MRI Acquisition

PQ 5000

240o

100o

260o

60o

300o

Delivery

20o

340o

Treatment Delivery

C-Series Clinac Dynamic MLC

IMRT Process

180o

140o

220o

100o

260o

60o

300o

20o

340o

Example

80%

90%

55%

85%

90%

55%

55%

80%

90%

80%

90%

55%

90%

55%

85%

80%

80%

90%

55%

### IMRT: Clinical Aims in Prostate Cancer

• Improve conformality; dose escalation

• Reduce high dose volumes in rectalwall & bladder

• Reduced small bowel dose in nodal therapy

80o

280o

320o

40o

0o

Prostate

Nodes

Irradiate Prostate and Nodal Region in Pelvis

### IMRT: Prostate Cancer

SV

CTV

Rectum

GU or GI Toxicity

80

70

60

IMRT-Prostate and

50

Nodes

40

3D-Prostate and Nodes

30

20

10

0

0

1

2

3

P = 0.002

Maximum RTOG Score

Steven Hancock, 2002

IMRT: Prostate and Nodes

Intensity Modulated Plan

Field Intensity Maps

70%

50%

60%

80%

30%

20%

40%

10%

90%

40%

80%

50%

70%

30%

60%

20%

90%

10%

40%

80%

50%

70%

60%

90%

40%

30%

20%

10%

### 3D-CRT v. IMRT: Dose DeliveryProstate and Seminal Vesicles

Organ3D CRTIMRT

Mean±SDMeanMax Min

Small field:

Prostate: 74.0 ± 1.5 75.7 82.8 65.3

Seminal Vesicles:50.0 ± 1.0 63.5 79.1 50.1

Large field:

Prostate:50.0 ± 1.0 55.1 61.8

+ Boost:70.0 ± 1.4 77.3 87.7

Nodes:50.0 ± 1.0 54.2 63.5

Steven Hancock, 2002

P = 0.05

Steven Hancock, 2002

### Prostate IMRT: Prescription Doses

MSKCC: Dose to 98 ± 2% of CTV: 81. Gy

Dose to 95% of PTV:78. Gy

5% of Bladder > 83. Gy

25-30% Rectum> 75.6 Gy

Dose per fraction 1.8 Gy

2 yr risk of GI bleeding: 2% IMRT v. 10% 3D-CRT

Zelefsky et al. Radiother & Oncol 55:241

IMRT for Gynecological Cancers

• CTV in a cervical cancer

• pt s/p hysterectomy

• Note the posteriorly and

• laterally placed lymph

• nodes regions

• The central region is

• where the small bowel

• is now located

Mundt, 2002

Intensity Modulated-WPRT

100%

90%

70%

50%

Mundt, 2002

100

90

80

70

60

50

40

30

20

10

0

Acute GI toxicity IM-WPRT vs. WPRT

IM-WPRT

WPRT

P = 0.002

Mundt et al. Int J Radiat Oncol Biol Phys 52:1330-1337, 2002

Chronic GI Toxicity IM-WPRT vs. WPRT

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

0

1

2

3

IM-WPRT

WPRT

Multivariate analysis controlling for age, chemo, stage and site,

IMRT remained statistically significant ( p = 0.002)

Mundt et al. ASTRO 2002 (New Orleans)

SPECT-CT Image Fusion

Based on image fusion, highest intensity BM was contoured and used in planning process

Mundt, 2002

Isodose Comparison – Mid Pelvis

BM-Sparing Plan

100%

90%

70%

50%

100%

90%

70%

50%

IM-WPRT Plan

Mundt, 2002

Localization of the prostate can also be achieved with cone-beam CT.

Tumor Motion During Respiraton

Courtesy, David Faffray

Rt Lung

heart

cord

Lt Lung

### Conclusions

• IMRT with MLCs can be implemented in the clinic.

• “Step-and-Shoot” or sliding window leaf sequence with dynamic MLCs can be used for IMRT.

• Dose distributions can be computed and delivered that provide treatment options for particularly difficult presentations.

• Imaging is required for variations in daily set-up.

• Special procedures are required to compensation for respiration motion

Phenomenological Lyman Model for NTCP

(Note: The Lyman model does not explicitly take fraction size into consideration.)

Lyman Model for NTCP

For a biological target uniformly irradiated to dose D, the upper limit of integration is expressed as

where is the dose at which the complication probability is 50%, and m is a slope parameter.

Lyman Model for NTCP

For a uniformly irradiated partial volume,

define

then the upper limit of integration is

Lyman Model for NTCP

for n > 0

The ntcp curve moves to the right vs. D for partial volume irradiation.

• Multiple sub-volumes, at different doses di are each translated to effective sub-volumes at some reference dose, such as the maximum dose in a dvh or TD50(1).

• The relationship must be reducible, i.e., the NTCP of two equal sub-volumes at a given dose must be the same as that of a single volume of twice the size at the same dose.

[Kutcher–Burman]

Equivalent Uniform Dose

Equivalent Uniform Dose (EUD) is the uniform dose that gives the same cell kill as a non-uniformly irradiated target.

(Niemierko, Med Phys. 24:103-110; 1997.)

For the simplest model of exponential cell kill, and uniformly distributed cells,

where really means the surviving fraction at dose Dref , which is often taken as 2 Gy

climbing the TCP curve

where we should be

Tumor Control Probability

where we are

complication curve

Dose

the unique biology of CaP

Striking similarities with slowly proliferating normal tissues

 Extremely low proportion of cycling cells (< 2.5%)

 Regression following RT is very slow

• PSA nadir times > 1 year

• regression of post-RT biopsies up to 3 years

 Potential doubling times

• median 40 days (range 15 – 170 days)

 PSA doubling times of untreated CaP

• median 4 years

s

cell survival curve

dose

Fractionated radiotherapy: n x d = D

S  s…s = s n

S = exp(-aBED)

BED = D(1+ d/(a/b))

Biologic

Equivalent

Dose

BED = D(1+ d/(a/b))units of Gy

brepair of sub-lethal damage

a/bsensitivity to dose-per-fraction

BED = D(1+ d/(a/b))

a/btumors > a/bNTLE

tumors a/b ~ 10

normal tissue late effects a/b ~ 3

tumors vs. NTLE

Tumors & early-

responding tissues

a/b ~ 10

Normal

Tissue late

effects

a/b ~ 3

surviving fraction

dose

tumor vs. NTLE

BED (Gy) = D(1+ d/(a/b))

D / d / n (Gy)BED a/b=10BED a/b=3

tumorNTLE

74 / 2 / 3788.8123.3

70 / 2.5 / 2887.5128.3

69 / 3 / 2389.7138

64 / 4 / 1689.6149.3

NTLE: Normal Tissue Late Effects

the a/b ratio for CaP

seriesmethoda/b95% CI

Brenner & Hall (1999)LDR / EBRT data1.5[0.8 – 2.2]

King & Fowler (2001)LDR / EBRT model1.8/2

Fowler et al. (2001)LDR / EBRT data1.49[1.25 – 1.76]

Brenner et al. (2002)HDR data1.2[0.03 – 4.1]

36.25 / 7.25 / 5211.5123.862.5

90 / 2 / 45210150108

what if a/b is that low?

D (Gy) / d / nBEDa/b=1.5BEDa/b=3BEDa/b=10

tumorNTLEacute effects

74 / 2 / 37172.6123.388.8

NTLE: Normal Tissue Late Effects

why hypo-fractionate?

Hypo-fractionation for CaP will:

 escalate dose biologically

 reduce acute sequelae

 keep same normal tissue late-effects

 reduce overall treatment course

potential tumor control

100

90%

62%

SRS

hypo-fractionation

50

Tumor Control Probability

43%

0

50

60

70

80

90

100

Dose (Gy)