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Basics of treatment planning II

Sastry Vedam PhD DABR

Introduction to Medical Physics III: Therapy Spring 2015

Dose calculation algorithms

!  Correction based

!  Model based

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Dose calculation algorithms

!  Representation of patient and dose distribution !  Block of tissue of uniform density !  Contour external surface with solder

wire !  Contours obtained from CT

Dose calculation algorithms

!  Modern algorithms !   3D point by point/voxel by voxel description of

patient (CT) !   Spatial reliability of CT (<2%) !  Dose uncertainty (photon beams) <1% !  Typical CT scan !   50 – 100 images !   2.5 – 5 mm slice thickness !   512x512 pixels per imaging plane !   2-16 bytes to store HU value data

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Dose calculation algorithms

!  Speed !  Processor power !  Grid spacing !  Non uniform sample spacing within

grid !  Calculation algorithm

Correction based algorithms

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Dose calculation algorithms

!   Correction based !   Semi empirical !   Based on measured data (PDD, Profiles etc.,)

!   Reference calibration condition !   Dose/MU @ a defined location in water phantom for a defined field

size

!   Corrections for: !   Attenuation

!   Contour irregularity !   Beam modifiers !   Tissue inhomogeneities

!   Scatter (Scattering volume, field size, shape and radial distance) !   Geometry (Non reference SSD/depth)

MU – Isocentric setup

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MU – Non Isocentric setup

Correction based algorithms

!   Limited accuracy !   3D heterogeneity corrections at tissue interfaces

!   Lack of complete electronic equilibrium

!   Secondary check for MUs calculated from more complex model based algorithms

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Model based algorithms

Model based algorithms

!   Compute dose distribution with a physical model that actually simulates radiation transport through a patient

!   Radiation transport !   Production of megavoltage X-rays in treatment head

!   Interaction and scattering of photons by Compton Effect

!   Effects of transport of charged particles near boundaries and tissue heterogeneities

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Radiation Transport

Electron disequilibrium due to greater lateral range of electrons compared to field size

Radiation Transport

Pencil beam charge particle tracks in phantom

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Convolution

Convolution

Energy fluence

Energy deposition kernel (Patient density map)

Dose

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Convolution/Superposition !   Several variations

!   Common/essential components !   Energy imparted to medium by

interactions of primary photons (TERMA)

!   Energy deposited about a primary interaction site (Kernel)

!   Kernel !   Primary (Primary dose) !   First and multiple scatter dose (Can

be calculated together or separately)

!   Kernel also referred to as: !   Dose spread array !   Differential pencil beam !   Point spread function !   Energy deposition kernel

TERMA

!   Total energy released per unit mass !   Energy imparted to secondary charged particles

!   Energy retained by scattered photon

!   Sum of the above should equal energy of the primary photon for each interaction

Energy fluence

Mass attenuation coefficient TERMA

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TERMA

!   Poly energetic nature

!   Attenuation map for each energy and each depth ‘r’ from surface

!   Divergent beam (Inverse square fall off)

!   Inhomogeneity correction (Geometric vs Radiological depth)

TERMA

!   3D voxel array with TERMA values is obtained before convolution

!   Involves: !   Array of electron densities from CT slices

!   Calculating radiological depth for each of the voxels

!   Calculating TERMA for each voxel

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Convolution Process

!   Dose at each point in medium !   Primary photon interactions throughout the irradiated volume

!   Summing dose contributions from each voxel

TERMA Primary energy deposition kernel

Scatter energy deposition kernel

Convolution Process !   Convolution can be done by either:

!   Integrating dose deposited at successive points due to TERMA throughout the medium (Deposition point of view)

!   Calculating dose contribution throughout the medium due to TERMA at successive interaction points (Interaction point of view)

TERMA Primary energy deposition kernel

Scatter energy deposition kernel

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Convolution process

Deposition point of view Interaction point of view

Convolution process

!   Deposition point of view !   Best if dose is calculated only in a subset of the irradiated

volume

!   TERMA in each voxel must be stored in an array

!   Interaction point of view !   Only a single TERMA value needs to be stored at any time

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Fourier transform

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Convolution process: The Fourier Transform

!   Assuming the kernels are spatially invariant, if the convolution of TERMA with a kernel to obtain dose can be written as,

!   Fourier transform of the dose is given by,

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Convolution in Inhomogeneous medium

!   Kernels are functions of displacement only

!   In Inhomogeneous media, the fractional energy contribution will depend on both distance between interaction site and deposition site as well as densities at interaction and deposition sites

Convolution in Inhomogeneous medium

!   First approximation !   Energy loss by secondary electrons dependent on effective path

length (average density through ray tracing)

!   Incorrect for primary kernel !   Electron scattering !   No and energy of electrons depends not only on avg density but also on density

distribution

!   Good for scatter kernel ! Fluence of onee-scattered photons is proportional to average density

!   Range of electrons ejected by these photons is very small

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Convolution in Inhomogeneous medium

!   Since rate of energy deposition in each voxel is proportional to the density within voxel, kernel value can be obtained by

!   Substituting into the equation for dose,

Variations of convolution

!   Original Real-Space Convolution (Mackie et al, 1985)

!   Kernels separated into primary, truncated first scatter (TFS) and residual first and multiple scatter (RFMS) arrays

!   TFS – First scatter dose, relatively close to the interaction site

!   RFMS – Multiple scatter and first scatter not included in TFS

!   Scatter separation allowed for smaller higher resolution kernel arrays

!   Average density scaling for a range of densities between interaction and deposition sites for primary and TFS

! Avg density of phantom in kernel scaling for RFMS

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Variations of convolution

!   Differential pencil beam method (Mohan et al, 1986, Ahnesjo et al., 1987)

!   Infinitesimal segment of a pencil beam

!   Equivalent to a convolution kernel except, !   Dose deposited in water per unit primary photon collision

density, instead of per unit energy imparted by primary photons

Variations of convolution

!   Collapsed cone convolution (Ahnesjo et al., 1989)

! Polyenergetic TERMA and kernel

!   Kernel represented analytically and combines primary and scatter contributions

!   Functions used to characterize kernel are,

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Variations of convolution !   Collapsed cone convolution (Ahnesjo et al., 1989)

!   Finite number of polar angles w.r.t. primary beam along which the function is defined

!   Interaction site – apex of a set of radially directed lines spreading out in 3D

!   Each line is further considered the axis of a cone

!   Kernel function along each line – energy deposited within the entire cone at radius ‘r’ collapsed onto the line

!   TERMA is calculated and represented in a cartesian array

! Inhomogeneities are accounted for in TERMA array

!   Reduced computation time when compared to conventional convolution