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Dose Calculations A qualitative overview of Empirical Models and Algorithms

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### Dose CalculationsA qualitative overview of Empirical Models and Algorithms

Hanne Kooy

Dose

- Dose is the energy, in Joules (or calories), imparted to mass, in kg:
- J / kg
- Unit is Gy “gray,” after
- Louis Harold Gray (1905 - 65) 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)

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)

Controls

All: Intensity

Typically over the field area

e-: Distal depth

HCP: Distal and Proximal Depth

Radiation TypesEquipment 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

Dose ProblemRange 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

Dose Modeling

- Equipment
- 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

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

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

Dose Modeling #1

“Orthogonal” set of measurements to quantify dose deposition as a function of equipment

Empirical Dose Model

- Generalize from measurements in specific conditions to predictions in patient

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

Scattered Radiation

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

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

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

Dose Modeling #2

- Use of MC in RT (Rogers ~1980)
- Parameterization of interaction details

Dose Modeling #2

+

=

Tissue

Fluence calculation

(“Primary” type calc, specified how many particles pass through the point of interest)

Lung

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

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

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.

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.

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