Cavity Theory, Ion Chambers, and Dose

Definition of Exposure?

Amount of charge - of one sign - liberated per mass of air (C/kg)

Definition of TERMA? Equation (coefficient relation)?

Total Energy Released in MAtter

T = Ψ(μ/ρ)… related to mass attenuation coefficient, μ

Definition of KERMA? Equation (coefficient relation)?

Kinetic Energy Released per unit MAss to charged particles

K = Ψ(μ_tr/ρ)… related to mass energy transfer coefficient, μ_tr

What are 2 contributions to KERMA?

K_coll and K_rad

What is K_coll? Equation (coefficient relation)?

Energy released in collision type interaction by charged particles

K_coll = Ψ(μ_en/ρ)…related to mass energy absorption coefficient, μ_en (presumably the same as μ_ab)

What is K_rad? Equation?

Energy released in radiation interactions.

→ the particles that get this kinetic energy can radiate Bremsstrahlung… K_rad accounts for Brem and positron annihilation photons

K_rad = K_coll(g/1-g) … g: fraction of energy lost to radiative processes

KERMA > TERMA. T/F?

False. TERMA > KERMA

Why is TERMA > KERMA?

TERMA includes ALL energy losses, KERMA only include KE transfer to electrons

not all energy is transferred to charged particles (e^-) from photons entering medium → some carried away in Compton scattering and photonuclear interactions

Definition of Dose (D)?

Energy absorbed per unit mass (J/kg)

What is Charged-Particle Equilibrium?

when the number of charged particles entering a volume = the number leaving (of the same energy and type)

If CPE exists, what can we say about dose as it relates to Kerma?

Dose in volume = collision Kerma

D = K_coll

Do we see true CPE in practice? why/why not?

No, because scattering & attenuation

What type of CPE do we see in practice?

Transient CPE

Transient CPE gives what relation to Dose and Kerma?

D = Kcoll * β

β is proportionality between Kerma and Dose

Bremsstrahlung deposits dose in a cavity. T/F, and what relation does this give?

False. Bremsstrahlung generally escape the volume.

Thus, K_rad = 0

What relationship do ion chambers provide between Kerma and exposure?

(K_coll)_air = X * W_air/e

What is W_air/e? What does it mean?

Work function for dry air, 33.97 J/C

Amount of energy required to form 1 ion pair in air

Is Brem included in dose calculations? Equation of Dose?

Generally no, because brem escapes the cavity volume…

D ≈ X (W_air/e)

Equations for Dose in medium for photons? Electrons?

photons → D_med=Ψ(μ_en/ρ)

electrons → D_med=φ(S/P)…

φ is partial fluence (# electrons).. S/P is mass collisional spring stopping power

Why we need cavity theory?

to relate dose to air in the chamber to dose in medium of interest

3 main types of cavities?

Bragg-Gray. Spencer-Attix. Burlin

Equation associated with BG cavity theory?

D_med/D_gas = (S/ρ)_med/(S/ρ)_gas

(S/ρ) is mass collisional stopping power

What causes ionization in BG cavity?

electrons from outside cavity… requires CPE/TCPE

How does BG cavity presence affect secondary electron spectrum? What does this mean for the size of a BG cavity?

it doesn’t → implies small cavity

T/F, delta rays contribute more dose to the opposite wall of a BG cavity.

False. BG cavity theory IGNORES delta rays

Equation for Spencer-Attix Cavity theory?

D_med/D_gas = (Lbar/ρ)_med/(Lbar/ρ)_gas

Restricted stopping power ratio

How are secondary electrons impacted in SA theory?

2 groups defined by cutoff energy, Δ.. E ∝ Δ required for electron to just cross cavity

1. 1. E < Δ (Slow electron) deposit energy where created

2. 2. E > Δ (fast. DELTA RAYS) deposit energy according to CSDA

Size of SA cavity?

Small. Because restricted Stopping powers ∝ Δ

Differences between BG and SA cavity theories?

BG → ignores delta rays. Uses normal mass collisional stopping powers

SA → Includes deltas. Uses Restricted mass collisional stopping powers

Size of Burlin Cavity?

Medium… bridges gap between small and large

CPE requirement for all 3 cavities?

BG → CPE or TCPE

SA → CPE or TCPE

Burlin → CPE in medium, but not cavity

Equation of Burlin cavity theory?

Dmed/Dgas = d(ratio of restricted stopping powers) + (1-d)(ratio of mass attenuation coefficients over rho)

d is parameter related to size of cavity → d=1 if small. d=0 if large

Full equation for D_air? (with those 6 scaling parameters)

D_air = D_air,chamber∗P_fl∗P_gr∗P_wall∗P_cel∗P_ion∗P_pol

D_air,chamber=X∗Work function

What is P_fl? two main issues?

Chamber fluence effects

1. In-scattering - more electrons scatter in than out of chamber, because electrons don’t scatter as readily by air as they do water

   1. Presence of chamber INCREASES fluence, therefore readings

2. Obliquity - gas doesn’t scatter secondary electrons as much as phantom

   1. electron travel straighter in chamber… reduces ionization and therefore DECREASES reading

Which chamber fluence effect is most pronounced in RT sized chambers?

In scattering

T/F, when using a plane parallel chamber, it is especially important to include chamber fluence corrections

False. Plane parallel chamebrs don’t need these corrections at all

What is P_gr? For what chambers?

Gradient effects, for cylindrical chambers…

cylindrical chamebrs behave like they read upstream of chamber’s center → if reading where fluence is changing, ERRORS (like descending portion of %DD curve)

P_ion?

Recombination effects - accounts for ion pairs recombining before collection

P_pol? More severe in which species of beam?

Polarity effects - changes in reading when voltage is reversed on chamber

More severe for electron beams

2 types of polarity effects?

1. Compton current - secondary e^- may be counted as ionized charge in cavity

2. Extracameral current - current collected outside of sensitive volume

P_wall?

Wall corrections - if chamber wall is different material than phantom → accounts for ionization events in wall

P_cel?

Central electrode corrections - materials of central electrode

What is full theoretical equation for Dose in medium?

D_air = Q∗N_x∗P_TP∗P_fl∗P_gr∗P_wall∗P_cel∗P_ion∗P_pol

Q∗N_x∗P_TP is the dose in air equation from earlier, just written with N_X correction for TG-21

What is the TG-51 Dose equation?

D_w,Q=M_raw∗(N_Co-60/N_D,w)∗K_Q∗P_TP∗P_elec∗P_ion∗P_pol

D_w,Q is dose to water for beam quality Q

M_raw is raw chamber reading

N ratio is cal factor in a Co-60 beam in water

P_elec is cal factor for different electrometers

K_Q relates chamebr response in C0-60 to your beam of quality Q (K_Q has all the corrections from the theoretical equation)

Equation for K_Q in TG-51 D_w,Q equation?

K_Q = (Ratio of L/ρ for water to air ∗P_fl∗P_gr∗P_wall∗P_cel∗P_ion)_Q divided by (Ratio of L/ρ for water to air ∗P_fl∗P_gr∗P_wall∗P_cel∗P_ion)_Co-60