Maths of Treatment Planning Flashcards
What is digital signal processing?
A process that converts signals from sensory data in the real world to digital form
What is the definition of a signal?
A description of how one parameter relates to another, whether it is discrete or analogue, 1D, 2D or multi-D
What is the definition of a system?
Any process that produces an output signal in response to an input signal
What is the process of superposition?
A complex signal is broken down into simple components, decompostion, which are processed and the results reunited, synthesis
What are the prerequisites of superposition being used on a signal?
Needs to be linear:
Homogeneous: a change in the input signal’s amplitude results in a corresponding change in the output signal’s amplitude
Additive: signals added at input results in added signals at output
What are the methods for decomposing signal in the TPS?
Impulse decomposition
Fourier decomposition
How are dose calculations decomposed?
Split by fluence map (input) which models the primary beam photons and scattered photons from the head, and scatter kernels (output) which models scatter and dose deposition in the patient
What is the process of performing a dose calculation for a patient?
Decompose beam into primary and scatter components
Adjust each component based on beam shape, intensity, surface topography, internal tissue density
Sum the contribution from all other scattering elements throughout the patient
How does treating a scatter kernel as a response function allow for the correction of lateral disequilibrium of electrons in narrow photon beams?
Apply an impulse-response analysis to the primary electrons launched by photons
What does the fluence map show?
How the beam exits the linac, how it diverges and how it is attenuatd as it travels
Can be modified in a heterogeneous medium to account for the change in density
What is a scatter kernel?
It describes how dose is deposited around an interaction site by electrons released at the site and by photons scattered at the site that cause electrons distant from the original site
What are the alternative names for a scatter kernel?
PSF, impulse response, convolution kernel
How are scatter kernels made?
Monte Carlo simulations
How is superposition achieved and what is the output?
Convolution - produces a third signal- the impulse response
What is the impulse response?
Impulse - the input fluence of primary beam and scattered photons
Response - how the system responds to the impulse - spread of dose
What is the equation and process of convolution?
Phi x K = D
Reverse impulse response, translate across input, multiply and summate the 2 to give the output signal
What is an example equation of numerical convolution?
y(i) = sum(h(j)-x(i-j))
What kind of filter is used in 2D convolution?
Window filter
How is 3D convolution sped up?
Use fourier transforms: Phi x K = FT(phi).FT(k)
What is a Fourier series?
Any function that periodically repeats itself can be expressed as a sum of sines and cosines with different coefficients
What is the process of discrete fourier tansforms?
Stimulus written as superposition of infinitely many sinusoids which are each analysed separately and their response computed due to superposition
The response is a sinusoid of the same frequency as the stimulus but different amplitude and phase - sinusoidal fidelity
Response to original stimulus is sum of all individual sinusoidal responses
How is Fourier decomposition achieved?
Correlation method- find a known waveform in a signal, multiply the 2 and summate, resulting in a single numerical result which is a measure of similarity
What are the equations for discrete Fourier transforms?
R(X(k)) = sum(x(i).cos(2.pi.k.i/N))
Im(X(k)) = -sum(x(i).sin(2.pi.k.i/N))
Frequency domain signals ar N/2 + 1 points long, and run from 0 to N/2
