Basic principles of dosimetry

Eirik Malinen

• Radiation field striking a small sphere:

• Fluence:

• Energy Fluence:

Ionizing radiation field

dN

daΦ = (da is the great circle area)

dA

dE=Ψ

• A photon field with total energy Rin,u enters a volume, while

Rout,u-rl is the energy leaving the volume:

• Energy transferred:

• KERMA (kinetic energy release per mass):

KERMA

Rin,u Rout,u-rl

V

QRR rlu,outu,intr Σ+−=ε −

ρ

µΨ=

ε= trtr

dm

dK

• Kerma includes all kinetic energy given to secondary

electrons, and this energy may be lost by:

– Collisions

– Radiative losses

• Kerma may be divided into two components:

• K=Kc+Kr

• Kc: collision Kerma; provides a measure of the energy loss per

unit mass from photons resulting in collisional losses for

secondary electrons!

Components of KERMA

• Is defined by:

• Net energy transfer : total kinetic energy of secondary

electrons which is not lost as brehmsstrahlung

• May take radiative losses into account by defining the qantity

g; the fraction of kinetic energi lost as brehmsstrahlung

• Definition:

• µen/ρ: mass energy absorption coefficient

Collision Kerma

n

trc

dK

dm

ε=

trcK K(1 g) (1 g)

µ= − = Ψ −

ρ

en tr (1 g)µ µ

≡ −ρ ρ

n

trε

• Look at all energy transport (both charged and uncharged

particles) through the volume of interest:

• Absorbed dose:

Absorbed dose

Rin,u+Rin,c

in ,u in ,c out ,u out ,cR R R R Qε = + − − + Σ

Rout,u+Rout,c

dD

dm

ε= unit: [Gy] = [J/kg]

• If charged particle equilibrium (CPE) is present, Rin,c = Rout,c

• Energy imparted:

• In this case, absorbed dose equals collision Kerma:

Dose from photons, CPE

v

CPE:

n

in,u in ,c out ,u out,c in ,u out,u trR R R R R Rε = + − − = − = ε

nCPEtr en

cD Km m

ε µε= = = = Ψ

ρ

• Transient Charged Particle Equilibrium: electrons originating

from upstream contributes to the dose, while the photon

contribution (Rin,u-Rout,u) is given by the collision Kerma

• Assumption: absorbed dose propotional to Kc

TCPE

TCPE

c TCPE

TCPE

D K (1 f )

f 0

= +

≥

• If no photon interactions, equilibrium of secondary electrons,

constant stopping power over point of interest:

Dose from charged particles

ρΦ= colS

D

• Exposure, X : number of charges Q (either positive or

negative) prodused in a gass of mass m:

• Number of charges per mass proprtional to dose:

X ∝ Dair

• The quantity relating X to Dair is the mean energy per ion

pair:

Exposure

dQX

dm=

Energy lost by ionizing particle

Number of ion pairs producedN

E e/W =

• For air, is 33.97 J/C

• The dose to air:

• Thus, by measuring the number of charges produced per mass

unit of air, Dair may be determined – indepedent of the

radiation quality ( is close to being constant for all

electron- and photon energies)

Dose to air, Dair

W / e

W / e

airair

aire

WX

e

W

m

Q D

=

=

Bragg-Gray cavity theory

B-G conditions:

1. Charged particle fluence is not perturbed by cavity

2. Absorbed dose entirely due to charged particles

wall

cav

e-,p, ....

wall

wall

cav

cav

S D

S D

=

=

ρΦ

ρΦ

cav

wallwall

cav S

D

D

=⇒

ρ

• Estimate dose to medium from measurements of

ionizations in air:

Applied BG theory

med

air

air

med

airairmed Se

WXSD D

==

Stopping power ratios

• Ionometry: the art of measuring ionizations

• Number of ionizations proportional to dose

• Air filled ionization chamber (”thimble”):

Ionization chamber

~ 300 V

Parallel-plate ionization chamber

• Problems with ion chambers is e.g. inacuracies in determining

air volume

• In practice, the ion chamber is calibrated at a point where the

dose is known – performed at a primary standards laboratory

(PSDL)

Dosimeter calibration (ion chambers)

H2O

γ, e- …A given dose gives reading M

electrometer

Ion chamber

• For a given dose to water, Dw, an ion chamber reading M is

obtained. Thus:

• The calibration factor is:

• Thus, the dose may be determined without using W/e, µen/ρetc

Dosimeter calibration

w w D,wD M D MN∝ ⇔ =

wD,w

DN

M=

• Calibration factor is dependent on radiation type and energy

• Usually, the chamber is calibrated in a well defined field, e.g. 60Co γ-rays (average energy 1.25 MeV)

• Corrections of the calibration factor, kQ, is thus introduced for

other energies (radiation ”qualities”, e.g. 15 MV X-rays)

Dosimeter calibration Film dosimeters

• Radiographic film: Ionization of AgBr in the grains forms the

latent image in the film

• Light transmission is a function of the film opacity and can be

measured in terms of optical density (OD) with densitometers

Film dosimeters

• Radiochromic film: special dye gets polymerized upon

exposure to radiation. The polymer absorbs light and the

transmission of light through the film can be measured with a

suitable densitometer

Thermoluminescence dosimetry

• Thermoluminescence (TL): thermally activated luminescence

• Measures the amount of visible light emitted from a crystal

when heated

Thermoluminescence dosimetry

• Glow curve

Thermoluminescence dosimetry

• Supralinear dose response

Thermoluminescence dosimetry

• Energy dependence

Diode dosimetry

• Radiation produces electron-hole (e-h) pairs. The charges

(minority carriers) produced in the dosimeter are swept across

the depletion region under the action of the electric field. In

this way a current is generated in the reverse direction in the

diode.

spherical

droplet

Diode dosimetry

Detector temperature

after placing on patientSensitivity dependence

Diode dosimetry

• Dependence on accumulated dose

Diode dosimetry

• Field size dependence• In vivo: In the living

• Verification of delivered dose

to individual patients

• Radiotherapy requires

accurate dose deliveryerror

Prescribed dose

Pro

bal

ilit

y

In vivo dosimetry

• Patient contour / planning basis (CT images)

• Patient motion

• Organ motion

• Dose calculations (inhomogeneities, scatter)

• Patient positioning

• Transfer of treatment data from simulator to linac

• Linac settings (energy, monitor units, field size) and

calibration

• Beam modifiers (blocks, wedges)

In vivo dosimetry – sources of error Dose characteristics

Patient curvature

beam

wedge

Output, SSD

Wedge, curvature

Thickness, density

Entrance dose:

Exit dose:

Point detector

2D detector array

Measurement issues

• Accurate and precise

• Multiple readouts

• Reusability

• No cables

• Non-destructive readout

High accuracy

Low precision

Low accuracy

High precision

Desired dosimeter properties

• Absorbed dose, D:

R: dosimeter reading

ND: calibration factor

Ci: correction factor

ii

D CRND ∏=

Dosimeter reading →→→→ absorbed dose

Rcal

Dcal

beam

dmax

water phantom

ion chamber

dosimeter

cal

calD

R

DN =

• Under reference conditions:

Calibration

Clinical example

Action level: 2.5%

measured dose

dose after correction

%2.1

008.1r

=

=

σ

Measured dose / prescribed dose

Distribution of measurements