Radiation Dosimetry. Electron interactions with matter. Important processes in radiotherapy. Contents. Alun Beddoe

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1 Radiation Dosimetry Alun Beddoe Medical Physics University Hospital Birmingham NHS Trust Contents ABSOLUTE DOSIMETRY (CALIBRATION) Photon interactions (recap) Energy transfer and absorption Electron range Electron spectra created by photon interactions Deriving dose using Bragg-Gray cavity theory Free air chambers (quick mention) Deriving dose from exposure calibration factors (mention) Calibration using UK megavoltage photon protocol RELATIVE DOSIMETRY (cursory coverage) Thermoluminescence dosimetry, photographic film Diode, diamond detectors Detector arrays - DOSI NB Diagrams and tables from Johns and Cunningham The Physics of Radiology th edition (Charles C Thomas Illinois, USA) unless stated. 2 Photon Interaction Processes (assumed knowledge) Photon Interaction Processes in Water Important processes in radiotherapy Photoelectric τ/ρ Z 3 /hν 3 Compton σ/ρ ~ 1/ 1/hν Pair production п/ρ Z 2 ln hν 3 4 Electron interactions with matter Collisional and radiative stopping power (Bethe and Heitler respectively) Ionizational Losses Function of Bohr radius (r 0 ), number of electrons per gram (N e ), electron velocity, mean excitation energy of target atoms, electron energy and a density correction factor. Radiative Losses (Bremsstrahlung) Electrons passing close to nucleus decelerate and radiate energy so called breaking radiation 5 6 1

2 Ratio of radiative to collisional losses (Bethe/Heitler approximation) In any medium Electron LET in Water (from Spiers Radioisotopes in the human body 1968 (Academic Press London) (de/dx) rad / (de/dx) coll = E. Z / 800 where E is in MeV. Example: For Z= 8 and E=10 MeV then ratio of radiative to collisional losses = 0.1; at 100 KeV then ratio = Electron collisional and radiative stopping power for lead and carbon as a function of energy Stopping power and range for electrons

3 Electron fluence spectrum arising from setting in motion one 10 MeV electron per gram of water Calculation of stopping powers S1= [ (dφ/de)1 S(E) de ] / (dφ/de)1 de dφ(e)/de= N/Stot(E) N = number of electrons released per gram of water S2 = [ (dn/de)i S(E)i R(E)i de ] / (dn/de)i R(E)i de or S2= [ (dφ/de)2 S(E) de ] / (dφ/de)2 de S3= [ (dφ/dhν)3 S(E) dhν ] / (dφ/dhν)3 dhν 13 Number of electrons (dn(ei)/dei) released with initial energy Ei per unit mass per unit energy 15 Calculation of stopping powers S1= [ (dφ/de)1 S(E) de ] / (dφ/de)1 de S2 = [ (dn/de)i S(E)i R(E)idE ] / (dn/de)i R(E)idE or S2= [ (dφ/de)2 S(E) de ] / (dφ/de)2 de S3= [ (dφ/dhν)3 S(E) dhν ] / (dφ/dhν)3 dhν 14 Spectrum of electrons produced (seen) in medium per unit energy photon fluence (per unit 10MeV photon fluence) Stopping power calculation for spectrum of photons, dφ/dhν, at some point within medium In general a spectrum of photon energies will be incident on the patient and these will in turn give rise to scattered photons so that the photon energy spectrum is dependent on depth and beam area. Each photon energy gives rise to electron spectrum, (dφ/de)2. Assuming you know what the photon spectrum is at any point you can calculate the stopping power as shown on next slide. 18 3

4 Calculation of stopping powers Electronic Equilibrium S 1 = [ (dφ/de) 1 S(E) de ] / (dφ/de) 1 de S 2 = [ (dn/de) i S(E) i R(E) i de ] / (dn/de) i R(E) i de or S 2 = [ (dφ/de) 2 S(E) de ] / (dφ/de) 2 de D = Φ.(µ/ρ).E ab = Κ (1 - g) where g is radiative loss. (D = dose and K = kerma) S 3 = [ (dφ/dhν) 3 S(E) dhν ] / (dφ/dhν) 3 dhν Electron ranges Calculation of Dose from Bragg-Gray principles It is assumed that the presence of the cavity does not perturb the photon or electron fluence. D gas = (Q/m gas ).W where W = ev per ion pair or joule per kg So far we we have the dose in the gas but we want to know the dose in the medium (or wall) around the gas cavity. Since the gas cavity is assumed not to perturb the electron fluence then dφ/de is the same in wall and cavity so that Stopping power ratios for various media

5 Calculation of dose to medium when the cavity has a wall (ie ionisation chamber) which is different to the medium Mass energy absorption coefficient ratios At equilibrium D med /D wall = K med /K wall The final calculation Calculation of k c D med = (Q/m).S wall:air.(µ/ρ) med:wall.k c where k c = [k(a wall ). k (c med )] / k(c wall ) is the perturbation correction for the presence of the chamber. Note: In practice you have to correct all measurements for pressure, temperature, humidity and ion recombination Measurement of Exposure Exposure was the original unit of radiation measurement defined ~75 years ago. X = dq/dm C/kg Unit was originally the roentgen ( 1 esu of charge liberated by X-rays per 1cc of air at STP, equivalent to 2.58 x 10-4 C/kg). Only defined for X-rays and air under equilibrium conditions. Free Air Chambers (for measuring exposure, the charge collected per unit volume of air) Equilibrium can only be established by ensuring that the distances between the focus and the charge collection volume and the collection plates and the collection volume are at least equal to the electron range in air (eg about 15m at 3MeV), which puts a practical limit on measurement of exposure. Not very useful as a radiotherapy unit!!

6 Calculation of dose from exposure calibration factors Some standardising labs still provide calibrations based on exposure. D med = M.N x (µ/ρ) med:air.k(c med ).b (b = ratio of dose to kerma, usually ~1.01) For energies above the calibrating energy (usually 2MV or 60 Co) it is necessary to use a fudge (known as cavity-gas calibration factor which is considered energy-independent). UK (IPEM) Calibration Code of Practice (for megavoltage photons Phys Med Biol 35: , 1990) D = R N D where R is the instrument reading corrected for temperature, pressure, humidity and ion recombination and N D is the NPL calibration factor to convert the corrected meter reading to absorbed dose to water at the chamber centre. This is specified in terms of the quality index (which is the ratio of instrument readings at 20cm and 10cm depth for 10x10 cm 2 field at a constant source to chamber distance) Code of Practice (cont) Relative Dosimetry Measured in water phantom with secondary standard chamber (NE 2561) in a water-proof close-fitting perspex sheath. Centre of chamber at 5cm depth (or 7cm if nominal beam energy above 12 MV). Measured in 10cm x 10cm field (or 11.3 cm diameter) with radiation field size determined by 50% isodose contour. The estimated overall uncertainty for secondary standard calibration factors at the 95% confidence level is ± 1.5% Other details in appendices. Limitations of ionization chambers include sensitivity, spatial resolution and energy response (for electron fields) and their dependence on temperature, pressure, humidity and recombination effects. Nevertheless for absolute dosimetry in standard radiotherapy they are both highly reproducible and accurate and can be used for relative dosimetry in most situations where data for steep dose gradients are not required. We briefly consider TLD and film (as integrating devices) and then small-field relative dosimetry for any situations involving high dose gradients using diodes and diamond detectors Thermoluminescence Detectors and Photographic Film (integrating devices) TLD is useful for spot verification (eg eye doses) but must be calibrated for each energy and batch. It suffers from fading and at best reproducibilty is only ± 5% (95% confidence). Photographic film measures 2D but must be very carefully calibrated (OD v dose - characteristic curves) for each experimental situation. Suffers energy dependence (scatter), variations in processing conditions, emulsion non-uniformity on film, within same film batch and between batches. Reproducibility at best only about ± 5%. Diode and Diamond Detectors Diodes Pros Good spatial resolution Good sensitivity Cons Response is dependent on dose history Dose-rate dependent Energy dependent Direction dependent Temperature dependent Diamonds Pros Good spatial resolution Good sensitivity Energy independent Dose history independent Temperature independent Cons Dose-rate dependent Pre-measurement priming dose required Direction dependent (less)

7 Detector Comparisons - some results Heydarian et al Phys Med Biol 41:93-110,1996 and Physica Medica 13:55-60,1997 (University of Adelaide and Royal Adelaide Hospital, South Australia) Depth dose curves for 10cm x 10cm versus 0.5cm x 0.5cm (6MV photon beams) 6MV response v dose rate 6MV v field size at 5cm depth 10cmx 10cm 0.5cm x 0.5cm Brief Summary A Novel Diode Array the DOSI 128-Channel Dosimeter (Manolopoulos et al Phys Med Biol 54: , 2009) a glimpse into the future!!! Small field dosimetry (eg Stereotactic Radiosurgery) Both diamond and diode detectors are fine (the latter because scattered radiation is minimal) Can be used for output (field size factors), depth dose and profiles Large field dosimetry Diamond (with appropriate correction) is OK for all measurements (except absolute calibration) Diodes must be used with caution because of the effects of scattered radiation on response Specifications: Single Silicon crystal detectors 128 channels 0.25 mm pitch t INT > 10 µsec Q max = 15 pc ASIC Sub-millimetre spatial resolution Real time information & data display PC DAQ medical consultants physicist 41 7