Modelling TCP and NTCP

Question 1

What do TCP and NTCP stand for?

Answer 1

TCP - tumour control probability

NTCP - normal tissue complication probability

Question 2

What are the purposes of modelling TCP and NTCP?

Answer 2

Dose distributions are complex and their effects need to be assessed
Understand and quantify the effects of uncertainties in dose or dose distribution
Use TCP and NTCP to drive treatment planning

Question 3

What are the advantages and disadvantages of theoretical TCP and NTCP models?

Answer 3

Adv: Gives insight into how tissues respond to RT
Disadv: Sensitive to radiobiological parameters which have large uncertainties

Question 4

What are the advantages and disadvantages of emperical TCP and NTCP models?

Answer 4

Adv: Have reasonable agreement with the patient data - can make plausible mathematical constructions
Disadv: Need lots of data, not adaptable to situations without a lot of data

Question 5

Why should models be used with caution?

Answer 5

Individual patients can deviate from the mean
Some parameters have large uncertainties
Models are complex so require expertise

Question 6

How do TCP models work?

Answer 6

Calculate the probability of no surviving clonogens in each dose bin and multiply them together to get the overall TCP

Question 7

How do NTCP models work?

Answer 7

Transform the complex distribution through an organ at risk into an EUD. Calculate the NTCP based on clinical data for partial organ uniform dose irradiation

Question 8

What is the equation for the survival fraction for n fractions?

Answer 8

SF = e^-D(alpha + beta.d)

Question 9

What is the equation for the TCP?

Answer 9

TCP = e^-k0(alpha.BED)

where alpha.BED = D(alpha + beta.d)

Question 10

What is the equation for BED?

Answer 10

BED = ln(SF)/alpha = D(1 + (d/(alpha/beta))

Question 11

How does the TCP curve shift as k0 increases?

Answer 11

Moves to the right

Question 12

How does the TCP curve shift as alpha increases?

Answer 12

Moves to the left and gets steeper

Question 13

What is the equation for the total TCP of a treatment?

Answer 13

TCP = product(e^(-pc.vi.e^(-Di(alpha+beta.(Di/n)))))
where pc = clonogenic cell density
Di = dose received to dose bin i
vi = volume receiving dose Di
n = number of fractions

Question 14

Why are cold spots worse than hot spots?

Answer 14

The overdose portion of the TCP curve does not compensate for a similarly sized underdose portion of the curve as TCP quickly falls to 0 for cold spots

Question 15

What happens to the TCP when the volume of a tumour decreases?

Answer 15

Increases

Question 16

What terms are added to the total TCP equation to make it more accurate?

Answer 16

Variations in radiobiological parameters - get different alpha values due to tumour cell heterogeneity - makes TCP slope shallower
Variations in tumour cell density - decreases from centre of tumour to edge
Tumour proliferation

Question 17

What is the most common NTCP DVH reduction method used?

Answer 17

The true DVH shape is converted into a radiobiological equivalent DVH where only part of the tumour is irradiated but at the max dose of the real DVH

Question 18

What are the steps of the Lyman-Kutcher-Burman model?

Answer 18

1 - each element is considered to be subject to a power law dose relationship: deltaVeff = deltaVi(Di/Dmax)^1/n
Calculate the sum of these elements to give a uniform partial organ irradiation at max dose that is radiobiologically equivalent
2 - Calculate NTCP based on the emperical function

Question 19

What is the NTCP function?

Answer 19

NTCP = 1/(2.pi)^0.5 . sum(exp(-t^2/2) . dt = 1/2 (1+erf(x/2^0.5))
where x = (Dmax-TD50(v))/m.TD50(v)
TD50(v) = TD50(1).v^-n
v = Veff/Vref
erf = 2/pi^0.5 . sum((-1)^n.z^(2n+1)/n!(2n+1))

Question 20

What are the meanings of the factors in the NTCP function?

Answer 20

Dmax = max dose from DVH
Veff = effective volume
Vref = total OAR volume
TD50 = tolerance dose for 50% complications in the partial volume
m = variable that controls the slope of NTCP vs dose curve

Question 21

What dose regime is the tolerance data for TD50 tolerances given in? What does this mean?

Answer 21

2Gy/# - need to convert to EQD2