d pr therapeutic ratio n.b. for a given fraction size
TRANSCRIPT
Radyobiyolojik Tedavi Planlama(Radiobiologically Guided Radiotherapy)
Alan E. Nahum PhD
Physics DepartmentClatterbridge Centre for OncologyBebington, Wirral CH63 4J Y UK([email protected])
XI. ULUSAL MEDIKAL FIZIK KONGRESI, 14-18 KASIM 2007, CONCORDE HOTEL, ANTALYA
Dose (Gy)
20 40 60 80 100
TC
P &
NT
CP
(%
)
0
20
40
60
80
100 TCP
NTCP
Dpr
Therapeutic Ratio
N.B. for a given fraction size
What uses might we have for TCP and NTCP models?
Analyze clinical+dose-volume data (retrospectively)
Evaluate treatment plans retrospectively
Modify treatment plans/Plan the treatment(!)
Put into an optimization/inverse -planning ‘loop’
Make direct use of clonogen radiosensitivity to improve the prediction of local control for an individual patient
Evaluate/estimate the benefit/harm of
- Changing the fraction size and total dose
- ‘Dose painting’ (e.g. to mitigate hypoxia ‘seen’ with PET)
- Patient movement
- Dosimetric errors, cold spots, partial tumour boosts etc.
The bottom lineA Mechanistic model for tumour (local) control probability
Poisson-based TCP model
NeNPTCP )0,(
The tumour is “controlled” when
NO SINGLE CLONOGENIC CELL SURVIVES (y = 0)
where N is the average value of the final number of clonogens
Single 2-Gy 0.6 0.3 2Dose fractions
1 10.876341 0.8763410.749762 0.7497620.626254 0.6262540.510686 0.5106860.40657 0.40657
0.316004 0.3160040.239788 0.2397880.177639 0.1776390.128478 0.1284780.090718 0.0907180.062537 0.07950.042088 0.0680170.027654 0.0568120.017739 0.0463280.011109 0.0368830.006792 0.0286670.004054 0.0217530.002363 0.0161150.001344 0.0116550.000747 0.008230.000405 0.0072120.000214 0.00617
CELL KILL IN 2-GY FRACTIONS
1E-16
1E-15
1E-14
1E-13
1E-12
1E-11
1E-10
1E-09
1E-08
1E-07
1E-06
1E-05
0.0001
0.001
0.01
0.1
1
0 2 4 6 8 10 12
DOSE(Gy)
SU
RV
IVIN
G F
RA
CT
ION
Single dose
2-Gy f ractions
Clonogenic cells after n fractions is given by
2220
dddddd eeeNN
N after 1st fraction
N after 2nd fraction...
n times
What do we know about cell killing by radiation?
NB the LQ expression assumes that the doserate is HIGH (cf. LDR brachy)and may be invalid below ≈ 0.8 Gy (low-dose hypersensitivity: HRS)
The Linear-Quadratic Model:
dDNN os
1exp
No. of cells surviving after n fractions (D = total dose = d * n):
Poisson-statistics-based TCP model
dDNTCP o
1expexp
Thus the expression for TCP is
for total dose D delivered in n equal fractionsof size d [final term 0 as 0
Fitting the Batterman et al ca. bladder data (Nahum and Tait 1992)
TLCP model:
Batterman data
Slope too steep
Building inter - patient heterogeneity into the TLCP model
It is assumed that radiosensitivity is normallydistributed over the patient population with SD =
dDNDTCP i
ii
1expexp),( 0
),()()( ii
i DTCPgDTCP
dDN io
1exp
TCP(D,
Fitting the Batterman et al ca. bladder data (Nahum and Tait 1992)
TLCP model:
Batterman data
ii DD
iio
ii eNNN
1
,
Inhomogeneous dose distributions
But … not all the cells receive the same doseDVHs summarise the dose distributions in a convenient way
Volume
Dose
Cells in each single dose bin i
receive an uniform dose Di
vi
Di
icio vN ,
Total no. surviving cells
Differential DVH
Clonogen density
Effect of dose non-uniformity on TCP - Tumour dose distribution (diff DVH) normally distributed with varying width but constant mean dose of 60 Gy.
- inter-patient radiosensitivity varied from 0 to 0.05 to 0.10 to 0.15
TLCP as f'n of fraction size for N-T isoeffect (=3)
40
50
60
70
80
90
100
0 1 2 3 4 5
Fraction size [Gy]
TLC
P [%
]
TLCP (a/b = 1.5); 3groups
TLCP (a/b = 10); 3groups
TLCP (Chapman-Nahum); 3 groups
N-T isoeffect
Modelling Normal-Tissue Complication Probability
Lyman NTCP model (1985)
Basic assumptions:• sigmoid- shape dose response curve (error
function)• power law relationship for tolerance doses. It can be applied independently to each volume
element of the organ
• a ‘single step’ DVH represents the case of uniform irradiation of a partial volume (of the organ/tissue)
• extension to non-uniform irradiation through an algorithm (“DVH reduction”)
• Formal Equations (Lyman-Kutcher-Burman)for uniform partial irradiation: (with dose D of the partial volume v)
• Parameters: D50 dose to the whole organ 50% NTCP
m steepness
n volume exponent (volume effect : n=1 large,
n=0 small)
dttNTCPt
2/exp2
1 2
nvvDD *)1( 5050 v
v
Dm
DDt
50
50
*
- Error function- Doesn’t exhibit a “threshold” effect
Large volume effect
NTCP = ??
NTCP = ??
• Histogram reduction methodsCRT / IMRT dose distributions are unlike partial irradiation : therefore one has to convert the DVH to an equivalent partial irradiation– Effective volume method [Kutcher 1991]
• a certain partial volume veff receives the max Dose ( Dmax )
– Equivalent Uniform Dose [Niemierko 1999]• the entire volume ( Vtot ) receives a certain equivalent uniform dose
(EUD)
n/1
max
i
iieff D
D*vv
n
i
n/1ii D*vEUD
EUD*VD*v totmaxeff
Parotid glands – xerostomiaClinical criteria: mean dose ≤ 25Gy
Available data: mean dose threshold 24 – 26 Gy
(suppression of salivary flow)
mean dose (no thereshold) 35 – 45 Gy
(decreased salivary flow)
1 (fixed)
0.45(0.33 - 0.65)
39 Gy(34 - 44)
Reisink (2001)
180 pts – prosp.95% CI
1 (fixed)
0.18(0.10 – 0.33)
28.4 Gy(25 – 34.7)
Eisbruch (1999)
88 pts – prosp.
0.70.1846 GyEmami (1991)
No 3D - retrosp.
nmTD50LKB model
L-K-B model TD50 m n
Emami (1991)
No 3D - retrosp.24.5 Gy 0.18 0.87
Seppenwolde (2003) 382 pts–retrosp.- both lungs as paired organ(95%CI)
30.8(23 – 46)
0.37(0.28 – 0.56)
0.99(0.8 – 1.6)
Relative Seriality (RS) model
D50 s
Gagliardi (1998)
68 pts–retrosp-1 lung68%CI
30.1(27-32.53)
0.97(0.77 – 1.21)
0.01(at limit; 0.16)
Seppenwolde (2003)
382 pts–retrosp- 2 lungs95%CI
34 0.97 0.06
Lung – Grade-2 pneumonitis
TREATMENT PLAN OPTIMISATION
through
CONFORMAL RADIOBIOLOGY
Original Schedule: 55 Gy in 20 fractions
0
1
2
3
4
5
6
2.5 3
3.5 4
4.5 5
5.5 6
6.5 7
7.5 8
8.5 9
9.5 10
10.5 11
11.5 12
12.5 13
13.5 14
14.5 15
NTCP (%)
Pat
ient
freq
uenc
yMalik Z, Eswar Vee C, Dobson J, Fenwick J and Nahum A E
Biomathematical-model-based analysis of a standard UK dose and fractionation lung-tumour radiotherapy protocol; 4th UK Radiation Oncology Conference 19-21 March 2007, Edinburgh
CCO protocol: 55 Gy in 20 fractions
NTCP calculated (using L-K-B model)
Biomathematical-model-based analysis of a standard UK dose and fractionation lung-tumour radiotherapy protocol; 4th UK Radiation Oncology Conference 19-21 March 2007, Edinburgh
Malik Z, Eswar Vee C, Dobson J, Fenwick J and Nahum A E
Local Control almost doubled
Int. J. Radiation Oncology Biol. Phys., Vol. 51, No. 5, pp. 1290–1298, 2001
Prescribed dose, EUD of the CTV, and minimum dose in the CTV as a function of field size for an AP-PA irradiation of a phantom simulating a tumor located centrally in a lung. The mean lung dose is 20 Gy for each field size. The ellipse indicates the field size for which the minimum dose in the CTV is 95% of the prescribed dose (ICRU Report 50 recommendation).
The message – Biological models must be “inside” the optimisation process/inverse planning
LEVEL-II OPTIMISATION
‘Biologically motivated’ optimization:
Use expressions for NTCP and TCP directly in the ‘objective function’ of the inverse-planning process, thus allowing the mathematical and radiobiological properties of the models to drive the search for the optimum plan (e.g. Hoffmann, Larsson et al 2004; Peñagarícano et al 2005).
What should the objective be?
Maximise TCP for fixed NTCP (e.g. 4%)OR
For fixed TCP (e.g. 80%), minimise NTCP
Maximise TCP
for
NTCP (Lungs–GTV) <= 3%
Max. Dose anywhere 90 Gy
ORBIT (RaySearch Laboratories)
Biologically optimised lung-tumour IMRT plan
Courtesy of Marnix Witte, Netherlands Cancer Institute, Amsterdam.
A GLIMPSE INTO THE FUTURE
Fraction size?
• What is the scope for increasing the therapeutic ratio by changing the fraction size? (depends on the ratio)
• Is there a connection between the degree of conformality of the treatment and the ‘fractionation sensitivity’?
Freeware, runs on PCs (Beatriz Sanchez-Nieto)
Calculates:
i. TLCP (Marsden model)
ii. NTCP (L-K-B and Relative-Seriality Models)
with user-choosable parameters, given the differential DVHs
EMAIL ME: [email protected]
BIOPLAN
April 22-25 2008
CHESTER, UK
www.ccotrust.nhs.uk