*** Modelling TCP and NTCP Flashcards
What do TCP and NTCP stand for?
TCP - tumour control probability
NTCP - normal tissue complication probability
What are the purposes of modelling TCP and NTCP?
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
What are the advantages and disadvantages of theoretical TCP and NTCP models?
Adv: Gives insight into how tissues respond to RT
Disadv: Sensitive to radiobiological parameters which have large uncertainties
What are the advantages and disadvantages of emperical TCP and NTCP models?
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
Why should models be used with caution?
Individual patients can deviate from the mean
Some parameters have large uncertainties
Models are complex so require expertise
How do TCP models work?
Calculate the probability of no surviving clonogens in each dose bin and multiply them together to get the overall TCP
How do NTCP models work?
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
What is the equation for the survival fraction for n fractions?
SF = e^-D(alpha + beta.d)
What is the equation for the TCP?
TCP = e^-k0(alpha.BED)
where alpha.BED = D(alpha + beta.d)
What is the equation for BED?
BED = ln(SF)/alpha = D(1 + (d/(alpha/beta))
How does the TCP curve shift as k0 increases?
Moves to the right
How does the TCP curve shift as alpha increases?
Moves to the left and gets steeper
What is the equation for the total TCP of a treatment?
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
Why are cold spots worse than hot spots?
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
What happens to the TCP when the volume of a tumour decreases?
Increases
What terms are added to the total TCP equation to make it more accurate?
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
What is the most common NTCP DVH reduction method used?
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
What are the steps of the Lyman-Kutcher-Burman model?
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
What is the NTCP function?
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))
What are the meanings of the factors in the NTCP function?
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
What dose regime is the tolerance data for TD50 tolerances given in? What does this mean?
2Gy/# - need to convert to EQD2
