1. Dose Calculations A qualitative overview of Empirical Models and Algorithms
Hanne Kooy

2. Dose
Dose is the energy, in Joules (or calories), imparted to mass, in kg:
J / kg
Unit is Gy “gray,” after
Louis Harold Gray ( ) was a British physicist who worked mainly on the effects of radiation on biological systems, inventing the field of radiobiology as he went.
There is NO unit for biological dose
Practice CGE, recommendation Gy (RBE)

3. Dose
Energy is imparted by the passage of ionizing, charged, particles through matter
Particles collide with orbital electrons or nuclei
EM processes dominate
“Dose” is a measure of the damage to cells inflicted by direct hits to DNA or free radicals (water ions)

4. Radiation Types Controls All: Intensity e-: Distal depth
Typically over the field area
e-: Distal depth
HCP: Distal and Proximal Depth

5. Dose in Patient
IMRT
Proton

6. Dose Problem Equipment with many dials to set radiation field
Patient’s anatomy and presentation dictates dose distribution in situ
Dose calculation is “missing” link
For photon RT, problem is to 1st order GEOMETRIC
Reduces problem to intensity control
Permitted RT to evolve based on X-ray analysis of patient only

7. Field Dose Shaping

8. Range Compensation
Compute radiological, density-corrected, path lengths, Pi, for each ray from skin surface to the points along the distal edge of target volume
For each ray compute “overshoot” range as: Pi R0 { Pi
DRi

9. Range Compensator
DRi

10. Spread-out Bragg peak

11. Dose Modeling Equipment Physics Description in terms of parameters
Jaw size, energy, devices
Physics as a function of those parameters
Either in terms of measurements
– or – in terms of explicit MC modeling
Physics
Develop models to quantify dose in patient
Phenomenological to Exact

12. Equipment Modeling

13. Dose Modeling #0 The “old” days Measure ad nauseam
Cover all equipment parameters
Measurements in lieu of physics model
Make plots and tables
Overlay on patient anatomy based on external contour and extents of target

14. History of Proton Radiotherapy

15. Dose Modeling Physics, in general, was always known
Computational equipment, hardware & software, evolved to permit a transition, in clinical practice, from
Measurements to empirical models (70-80)
Empirical to exact to MC (80-Now)
Large scale calculations (Now)
Not just dose but also “optimized” dose

16. Dose Modeling #1
“Orthogonal” set of measurements to quantify dose deposition as a function of equipment

17. Measurements
Dose
Depth
Field size

18. Empirical Dose Model
Generalize from measurements in specific conditions to predictions in patient

19. The Big Problems
Radiation scatters which introduces secondary components
Scattered photon interacts again
Scatter depends on internal patient features
Patient more complex than a water tank
Tissue inhomogeneities (bone, tissue, lung)
Irregular geometries

20. Scattered Radiation
Consider “primary” contributions separately from “scattered” contributions
Primary dose contribution is easy
Simple lines from source to point of interest
Scatter dose:

21. Computer Implementation #1
First codes implemented the parameterized models based
Comprehensive, orthogonal, measurements of dose as function of parameters in water
Models of dose in water
Patient = Water (Fair assumption for X-rays)
Description of patient’s anatomy by a few external contours obtained at time of simulation

22. Process #1 Simulate patient on simulator
Has the same DOF’s as LINAC
Produces X-ray’s to give a Beam’s Eye View of anatomy in path of radiation
Allows MD to assess, based on empirical knowledge of anatomy, appropriateness of this beam approach
Planner uses X-ray’s to
Reconstruct internal anatomy
Define the LINAC beams (= Sim beams)
Paradigm completely driven by the original availability of X-ray

23. Dose Modeling #2 Use of MC in RT (Rogers ~1980)
Parameterization of interaction details

24. Dose Modeling #2 + = Tissue Fluence calculation
(“Primary” type calc, specified how many particles pass through the point of interest)
Lung

25. Dose Modeling #2
Increased availability of CT scans enabled dose calculations on a “natural” patient representation with
A measure of the local (electron) density
Appropriate scaling of energy spread function
A geometric representation of the patient

26. Equipment Modeling #2
Monte Carlo allows a replacement of the physical machine with a “virtual” machine
Obviates the need for measurements
Improves knowledge of such measurements

28. Pencil-beam algorithms
A PB is a convenient approximation of how the particle stream distributes through a medium
Both e and p have nice MCS Gaussian formalism, which has a convenient numerical implementation
Photon energy kernels are more complex to implement
A PB permits local “probing” of the medium to account for heterogeneities.

29. Pencil-beam algorithms
Transport “primary” radiation, fluence, through patient’s anatomy represented by a CT slices
Trace radiation rays, “pencils,” through anatomy
At each step of the trace, transform local intensity to energy, “dose,” released in the medium.

30. Proton pencil-beam

31. Proton pencil-beam