Dose Calculations A 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)

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

Dose in Patient IMRT Proton

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

Field Dose Shaping

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

Range Compensator DRi

Spread-out Bragg peak

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

Equipment Modeling

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

History of Proton Radiotherapy

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

Measurements Dose Depth Field size

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.

Proton pencil-beam

Proton pencil-beam