Modelling Algorithms Flashcards
Measurement vs modelling approach
Measurement: measure absorbed dose in water and correct for inhomogeneities (still used in RadCalc etc)
Modelling: model physics of what is going on, can use pencil beam and collapsed cone to aggregate large no’s of particles, don’t need water dose distribution as pre-requisite
What is a history?
The transport of a single primary particle and all the subsequent secondary particle
What is a track?
The path of an individual particle until it is absorbed. Collection of tracks of primary and secondaries makes history.
Comprised of many steps
What is a simulation?
All of the histories in a given geometry
What 4 elements characterise the history?
Free path between events
Interaction
Energy loss and angular deflection
New particles
What random number is generated?
Between 0 and 1
How do we get a random number to correspond to a quantity?
Sampling using Cumulative probability distribution method
Steps to get random number
Integrate probability distribution to find cumulative probability function
Invert cumulative probability function
What is the geometry and what defines it?
The description of the surfaces and bodies through which the particles are transported
Defined by linac and patient
Patient derived from CT scan
What is scoring
Accumulation of dose in each voxel for each interaction for a single particle
How is dose dist. built up?
Summing contributions in each voxel from large number of particle histories
What is statistics and how does increasing the number of histories affect it?
The dose in each voxel has an uncertainty which is referred to as the statistics, increasing no. of histories reduces the uncertainty but increases computation time
What models are used to model particles starting from linac target?
Phase space model
Patient specific model
(Phase space often divided into:
Beam phase space
Patient modifiers phase space)
What is phase space?
A record consisting of each particles position, energy, direction as it exits treatment head
What is input for patient specific model?
Phase space data, used as basis of dose calculation in specific patient
What is a condensed electron history?
Condense many small interactions into one large virtual reaction, as nearly all electron interactions involve small energy losses and scattering angles.
Each step transfers the same amount of energy as the large number of small losses, and scatters the electron by an angle equal to a large number of scattering angles.
10^5-10^6 electron interactions per electron history - impossible to model all of them.
How can calculation time be cut down?
Variance reduction techniques:
Transport cutoffs
Zonal discard
Decrease calculation time to achieve a given statistical variance which is still clinically acceptable
What are transport cutoffs?
Stop tracking an energy below a threshold and deposit all energy at last position. Photon cut off lower than electron due to range
What is zonal discard?
If electron does not have enough energy to escape the voxel, deposit all energy in that voxel.
What parameters can you have in raystation?
Number of histories per cm^2
Calculation resolution
When is plan approved?
When mean relative statistical uncertainty is less than 2%
How does number of histories affect uncertainty?
More histories, lower the uncertainty, more accurate and less noisy doses.
How does resolution affect uncertainty?
Increasing dose grid voxel size means number of histories per voxel increases, uncertainty decreases but resolution worse.
What does uncertainty ultimately depend on?
Number of histories per voxel
When is MC modelling crucial?
In MR-linacs.
The B field makes the movement of secondary electrons non-isotropic. Electron return effect.
What is simulation approach
Simulates man individual particles and their history with probabilities and interaction processes, most accurate but computationally intensive.
Can use MC to help with model based approaches
Idea behind Digital Signal Processing
Take (usually) analogue data and convert it into digital form.
Uses signals that can originate as sensory data and convert to digital form.
Signal and system in DSP
Signal: real world data or parameter that relates to input signal
System: process that produces and output signal in response to an input signal
What is superposition and what does it require?
Can break down signal into number of smaller simpler components that are processed individually
Requires homogeneity and additivity
Is dose distribution a linear system?
Yes: homogeneity, greater number of photons means greater dose
Additivity: dose from two beams can be added to give the total dose, or dose from individual sites can be added
Synthesis and decomposition
Synthesis is adding things up
Decomposition is breaking things down into constituent parts, can be done an infinite number of ways
How can we decompose dose distribution problem?
Split into primary fluence and head scatter fluence so these can be adjusted for a variety of factors
Input signal and impulse response in dose distribution
Input signal is fluence map, modelling primary beam photons and photons scattered in head
Impulse response is scatter kernels
What is fluence map?
Map of photons passing through medium from head of linac
Shows how beam exits linac and diverges and is attenuated
In inhomogeneous medium this is modified to account for differing densities and effect of attenuation
What is scatter kernel and how is it created?
Describes how does is deposited around an interaction site by electrons released at the site and photons scattered
Known as PSF/impulse response/ filter or convolution kernel
Built up from modelling many interactions at same site with MC
What is the total dose to a point and how are the fluence map and scatter kernal related to it?
Total dose is sum of contributions to that point from interactions in all other points
Fluence map dictates how many photons interact at given point and scatter kernel describes how dose will be deposited
Convolution for dose
Fluence * K = D
Convolution theorum
Taking the inverse FT of the product of the FTs of fluence and dose kernel gives the convolution
Using fast fourier transform does this quickly
Problems with correction based approach?
Radiation scatters (photon interacts again, scatter depends on patient internal)
Patient more complex than water tank (inhomogeneities and irregularities)
Fields are the same as measured (can’t measure all irregular fields, treatment fields not likely to be measured)
Advantage of model based approach
need less measured data (but maybe more non-standard conditions data), good models can predict dose far better in complex situations
What are two steps of model based dose calculation algorithm?
Model head of linac and what comes out
Model patient and how beam is deposited as energy
What is the difference between type A and type B algorithms?
Type A does not model the variation of penumbra with density
Type B does
What is input for dose calculations?
Energy fluence
Defined as 2D array describing how energy of beam is distributed across plane
Fluence vs energy fluence
Fluence is particles passing per unit ae = number/area
Energy fluence = particles x energy / beam cross section
What are 2 energy fluence maps used?
Primary energy fluence - direct photons
Head scatter energy fluence - photons that have been scattered at least once in head
Sum arrays for total if needed
Direct energy fluence
Usually determined at isocentre distance
Source is origin focus
Divergence considered by ISL
Head scatter energy fluence
Modelled as if created at FF (more complex than this but this is source of most)
Scaled with ISL
Model of source / target
Oval shape
Fixed in space, does not rotate
Gaussian distribution
Discretised and represented as 2D array of numbers in TPS
Focal spot of electron beam on W target
How is direct fluence obtained?
Modulating open beam fluence with attenuation from elements of treatment head
Ray trace performed
What are large and small field penumbra most effected by?
Large field penumbra more affected by FF size
Small field penumbra affected by primary source
Projecting small point like primary, resulting fluence has sharp edges
How are HU values converted to mass density?
Linear interpolation in a CT to density table
Density scaling vs electron density scaling
Density scaling: all material assumed to be water, path length differs in water and other materials, use scaling based on mass density, but large discrepancies found for some materials
Electron density scaling more relevant because CS dominates, error much lower
Effective density scaling
Takes into account pair production, which becomes an issue at higher energies
Modification of electron density
Lower error over larger energy range
What is TERMA
Total energy released per unit mass
(by photons to secondary particles)
(energy taken away from beam at a point)
Total energy of electrons from PE effect, electrons from CS, photons participating in CS, electrons and positrons from pair production
What is needed to calculate TERMA?
Attenuation coefficients
Energy spectrum
Gaussians describing penumbra
KERMA and SCERMA
KERMA: energy transferred to collisions at point
SCERMA: energy transferred to photon scatter at point
Arguments for dose to water?
Consistent with absorbed dose to water CoP
Caution option for OARs: Dw usually greater than Dm
Clinical experience with Dw
Argument for dose to medium
More accurate representation of what patient receives
Calculating Dm then converting to Dw involves additional assumptions increasing uncertainty
How is dose deposition estimated?
Using predetermined energy deposition kernels to describe the energy spread around a primary interaction
Types of kernels
Pencil kernels: point kernel pre-convoluted over depth dimension
Planar kernels: point kernel pre-convoluted over 2D (slab dose)
Broad beam kernels: point kernel pre-convoluted over 3D (3D dose distribution)
Why use different kernel?
Speed advantages to using planar kernel if incident radiation only changing in 1D
If beam intensity intentionally varied in 2D, pencil beam more appropriate
If beam fluence changing in more complex way then point kernel should be used and full 3D integration necessary
What are the 2 main types of photon dose algorithms
Superposition / convolution: collapsed cone based on point kernels
Simple convolution (utilises FFT): pencil beam, pre convolved point dose kernels
Type A algorithm
Pencil beam
Pre convolve in depth direction
Only need to convolve in 1D, saves computational time
Sacrifice ability to perform density scaling for lateral heterogeneities
Problem with divergence too
Absorbed dose from TERMA type A
D = T * K
(TERMA convoluted with dose deposition kernel)
Type B Algorithm
Collapsed cone: convolution / superposition
Composition of patient affects spread of dose around point, can’t be accurately represented by one invariant pre-calculated point kernel
How do collapsed cone point kernels work?
PSF discretised into cones travelling out from interaction site
Energy emitted in solid angle cone assumed to be transported along cone axis
Therefore adapts to environment
Directions more closely distributed in forward direction where most of energy flows
Balance between accuracy and speed, TPS use hundreds of directions
Can no longer use FFTs to speed up calculation, not true convolution
Kernel depth dependence
Needed to account for depth hardening and off-axis softening
Mono-energetic PS kernels simulated and build poly-energetic kernels for each depth
Type A vs Type B
Type A: invariant kernels use fast FFT convolution techniques
Type B: adapt kernels to local environment and are therefore no longer true convolution and cannot use FFT techniques
What 5 components are needed for MC method?
Random numbers
Sampling
Photon and electron interaction models and probabilities
Geometry
Scoring and statistics
Uses random number generators and the probability distributions of all the interaction processes.
How are the following modelled in fluence:
no. particles
position
direction
energy
No. Particles: matrix element
Position: matrix element position
Direction: as if they’re coming from respective source to matrix element
Energy: given by beam spectrum common to all elements
What two things combine to give us the energy fluence?
Beam model
Treatment plan
What question determines type A vs type B algorithms?
Does the algorithm model the variation of penumbra with density?
What are overall steps to get dose?
Work out fluence
Use fluence along with attenuation information to get TERMA
Use TERMA and PSF to get dose
How is a pencil kernel created?
Pre-convolution over the depth direction
How do we get TERMA from CT information?
HU converted to mass density through linear interpolation of CT to density
Work out effective density from densities and then electron densities
Discretise effective densities into voxels
Use effective density to get average radiological depth
Calculate TERMA using average radiological depth in each voxel and energy fluence
How is effective density used to get radiological depth?
Effective density scaling
What path length in water results in same attenuation as corresponding path length in material i
l_w = l_i . rho_i/rho_w
What are the two obvious problems with pencil beam?
Lack of divergence
Heterogeneities: can’t be scaled laterally
