Basics of treatment planning II

Transcription

1 Basics of treatment planning II Sastry Vedam PhD DABR Introduction to Medical Physics III: Therapy Spring 2015 Dose calculation algorithms! Correction based! Model based 1

2 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! images! mm slice thickness! 512x512 pixels per imaging plane! 2-16 bytes to store HU value data 2

3 Dose calculation algorithms! Speed! Processor power! Grid spacing! Non uniform sample spacing within grid! Calculation algorithm Correction based algorithms 3

4 Dose calculation algorithms! Correction based! Semi empirical! Based on measured data (PDD, Profiles etc.,)! Reference calibration condition! 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 4

5 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 5

6 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 6

7 Radiation Transport Electron disequilibrium due to greater lateral range of electrons compared to field size Radiation Transport Pencil beam charge particle tracks in phantom 7

8 Convolution Convolution Energy fluence Energy deposition kernel (Patient density map) Dose 8

9 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 TERMA Mass attenuation coefficient Energy fluence 9

10 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 10

11 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 11

12 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 12

13 Fourier transform 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, 13

14 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 14

15 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 15

16 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, 16

17 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 17