Dose Cal c ulati o ns

Absorbed Dose from a charged particle beam

[Image removed due to copyright considerations]



  A (  dE / dx )  x

  dE 



D = dose rate

D  

A  x

   



 dx 

 = flue nc e ra te (cm -2 s -1 )

 = d e nsity A = ar ea

[Image removed due to copyright considerations]

Alpha and Low energy Beta em itters distributed in tissue.

A radionuclide, ingested or in haled, and distributed in various parts of the body is called an internal emitter .

Many radionuclides follow specific metabo lic pathways, acting as a chem ical element, and localize in specific tissues.

E.g. , iodine concentrates i n the thyroid

radium and strontium are bone seekers

tritium will distribute throughout the whole body in body water

cesium tends to dist ribute throughout the whole body.

If an internally deposited ra dionuclide em its particles that have a short range, then their energies will be absorbed in the tissue that contains them .

Let:

A = the activity concentration in Bq g -1 , of the radionuclide in the tissue

E = the average alpha or beta par tic le energy, in MeV per disinte g ration The rate of energy absorpt i on per gram tissue is A E (MeV g -1 s -1 ).

The absorbed dose rate is:

D ˙  A

E MeV

g s

x 1 . 60 x 10  13

J

MeV

x 10 3 g

kg

= 1.60 x 10 -10 A E Gy s -1

Point Source of Gamm a Rays

  µ en

CE µ en

D  Ψ

ρ

 4  r 2 ρ



D = Dose rat e



 = energy fluence rat e (MeV/cm 2 sec)

C = activity (Bq)

E = energy per decay (MeV)

 en /  = mass energy-absorption coefficien t of air (cm 2 g -1 ) (~ same for photons betw een ~60keV and 2MeV)

Beam of Photons

Dose = en ergy absorbed/mass

  en 

    N   E  (  x )  A 

  

Dose

  

  e n   N   E 

( A )(  x )

  

(µ en / ρ ) = mass energy absorption coefficient (cm 2 /g) N = photon fluence (phot ons/c m 2 )

E = energy per phot on

ρ = density

x = thickness A = ar ea

Absorbed dose from neutrons

 Elastic s c atter (higher energies)

 Capture (thermal neutrons)

Thermal neutrons

 N  E

D  

 = thermal neutron fluence (n/cm 2 ) N = a t o m d e n s i t y ( c m -3 )

 = capture cross secti on (for each element) E = en ergy from cap t ure reacti on

 = tissue density

The major thermal neutron ca pture reactions in tissue

14 N(n,p) 14 C  = 1.7 barns Q = 0.626 MeV

E p = 0.58 MeV, range in water ~ 8 µm E C = 0.04 MeV

Energy is deposited l o cally

1 H(n,  ) 2 H  = 0.33 barns 2.22 MeV gamma (µ/ ρ ) = 0.05 cm 2 /g

(µ en / ρ ) = 0.025 cm 2 /g

contribution to dose depends on the siz e of the “target”

Principl e elem ents in s o ft tissue of unit density

Element	Atom s cm -3	Captur e cr os s section , 
H	5.98 x 10 22	0.33 barns
O	2.45 x 10 22	0.00019 barns
C	9.03 x 10 21	0.0035 barns
N	1.29 x 10 21	1.70 barns

Absorbed dose from fast neutrons

Scattering: assu me average energy lost is ½ E ma x

First collision dose

 Represent ative of the absorbed dose when the mea n free path is large co mpared to the target.

 Expressed as dose delivered per indivi dual neutron

 Units are those of dose per neutron/cm 2 (Gy cm 2 )

D  N  S Q ave



N = atom density (cm -3 )

 S = s cattering cross section (for each el ement)

Q ave = av erage en ergy transferred in collision (½ E ma x )

 = tissue density

Must cal culate dose for each el em ent .

E.g. , Calculate the first collision dose fo r a 5 MeV neutron with tissue hydrogen. 5 MeV neutron  S = 1.61 barns

N = 5.98 x 10 22 cm -3

Mean ener gy per scat tering collision, Q ave = 2.5 MeV D = 3.88 x 10 -11 Gy cm 2