1 Radiation.pdf

8/14/2019 1 Radiation.pdf

1/17

9/26/20

1

ENGG 167

MEDICAL IMAGING

Lecture 1: Sept. 20

Radiation & -ray Interaction with Matter

References: The Essential Physics of Medical Imaging, Bushberg et al, 2nd ed.

Radiation Detection and Measurement, Knoll, 2nd Ed.

Intermediate physics for medicine and biology, Hobbie, 3rd ed.

2

Assigned Reading

Ref: Bushberg

Chapter 14 Intermediate Physics for Medicine and

Biology R. K. Hobbie

Chapters 2& 3 The Essential Physics of Medical

Imaging, Bushberg


2/17

9/26/20

3

Assigned Reading & LAB 1 report

The Essential Physics of Medical Imaging, Bushberg et al,Chapter 20 Radiation Detection & Measurement

LAB 1 Thursday,

Complete the online radiation traininghttp://www.dartmouth.edu/~ehs/training.shtml (click on the link to Radiation Safety

Training (Annual Retraining))

Read the handout before going to the lab Location Cesium Irradiator Level 2 in Borwell Research Building at DHMC.

(take main elevator down to level 2, turn left, look for radiation sign, across from the

snack machines)

Lab director Auggie Ong

TA Summer Gibbs

4

Part 1 Radiation Review

Ref: Bushberg

(i) Atomic structure

(ii) Nuclear particles

(iii) Radiation decay

(iv) Sources of Radiation


3/17

9/26/20

5

(i) Atomic electronic energy levels

Typical nuclear diameter = 10-14

mTypical atomic diameter = 10-10 m

Volume of the atom taken up by the

nucleus is 10-12

Ref: Bushberg

(i.e. very small nucleus

Most of the atom is

electron cloud)

6

(i) Energy calculations

Units:

Joule = kg m2/s2 (SI unit)

Electron Volt = kinetic energy gained by an electron accelerated through 1Volt

1 eV = 1.6 x 10-19 J

Energy calculations:

E = h h = Planks constant, = photon frequency

h = 6.626x10-34 J s = 4.135 x 10-15 eV s

Rest energy of a mass E = mc2

Energy conservation occurs in all decays and transitions

Momentum conservation occurs in all elastic interactions

Ref: Knoll

What is the rest mass energy of an electron ?


4/17

9/26/20

7

(i) Electronic energy levels and binding energies (Eb)

The energy required to remove

an electron from the atom is calledthe binding energy, and increases

with proximity to the nucleus. It

also increases with increasing

number of protons in the nucleus.

Ref: Bushberg

Why is the energy to the valence band so low (large negative number)

for tungsten compared to hydrogen ?

8

(ii) Sub-atomic nuclear particles

Ref: Bushberg

1 amu = 1.6726 1027 kg or 938.3 MeV/c2


5/17

9/26/20

9

(ii) Nuclear structure

Ref: http://serc.carleton.edu/images/usingdata/nasaimages/periodic-table.gif

10

(ii) Nuclear famil ies

Ref: Bushberg

Why are there more N than P in

higher atomic number nuclei ?


6/17

9/26/20

11

(iii) Nuclear decay product ion of radiation

The fundamental law of radioactive decay is that the rate is proportional to thenumber of nucleipresent:

dN/dt = - N

Leading to the solution:

N(t) = N0e-t

The nuclear decay half-life can be estimated when N(t)/N0 = 0.5, leading to t1/2 =

ln(2)/. This is the time for the radioactive source to decay by half.

Fundamental units of radioactivity, in terms of disintegration rate:

Definition abbreviation

Curie = 3.7 x 1010 disintegrations/sec Ci (common unit)

Becquerel = 2.703 x 10-11 Ci Bq (SI unit)

Specific activity of a source is activity divided by mass:

Specific activity = activity/massRef: Knoll

What is l ?

12

(iv) Sources of Radiation

Ref: Knoll

(a) Electrons - Beta decay

- Internal conversion

- Auger electrons

(b) Heavy Particles - Alpha decay

(charged) - spontaneous fission

(c) Electromagnetic - Gamma rays following Beta decay

(photons) - Annihilation radiation

- Bremsstrahlung

- Characteristic x-rays

(d) Neutrons - spontaneous fission

- radioisotopes

- photo-neutrons

- reactions with accelerated charged particles


7/17

9/26/20

13

(iv.a) Electron Sources - Beta decay

Ref: Knoll

X and Y are initial and final nuclear species, radiation given off is an electron (beta-

minus) and anti-neutrino. Nucleus Y recoils, but with very little energy. Beta

emitters are readily produced by neutron bombardment of stable materials. Pure Beta

emitters decay to a ground state of Y, whereas other atoms which decay to excited

state products also exist.

What is 14C dating ?

14

(iv.a) Electron Sources - Internal conversion

Ref: Knoll

Internal conversion begins with an excited nuclear state, typically formed by a

preceding process, often Beta decay. The nuclear state energy, Eex, is transferred

directly to one of the orbital electrons, which has binding energy Eb. The electron

then attains kinetic energy, Ee-, which tends to be narrow band. Typically multiple

levels of electrons are given off, often superimposed on a Beta spectrum, leading to a

complex energy spectrum in practice.


8/17

9/26/20

15

Assigned Reading

Ref: Bushberg

(i) The Essential Physics of Medical Imaging,

Bushberg et al, Chapters 2&3 only.

(ii) Intermediate Physics for Medical Imaging, 3rd

Ed., Hobbie, Chapter 14 only. (handed out in class)

16

Part 2 - Radiation Interaction with Matter

Ref: Hobbie,

Knoll, Bushberg

(i) Gamma ray photons

(ii) Heavy charged particles

(iii) Fast electrons

(iv) Neutrons


9/17

9/26/20

17

(i) Gamma photons interaction wi th matter

Ref: Knoll,

Bushberg

(a) Rayleigh scattering (, )

(b) Compton scattering (, e- )

(c) Photoelectric absorption (, e- )

(d) Pair Production (, e+ e- )

18

(i.a) Rayleigh Scattering

Ref: Bushberg

(, ) notation for input and output products

Probability is low

and decreases

significantly with

increasing energy


10/17

9/26/20

19

(i.b) Compton Scattering

Ref: Bushberg

(, / e)

20

(i.b) Compton scattering cross section - I

Ref: Hobbie


11/17


12/17

9/26/20

23

(i.b) Compton scattering cross section IV

Ref: Hobbie

24

(i.b) Compton scattering cross section V

Ref: Hobbie


13/17

9/26/20

25

(i.c) Photoelectric Effect

Ref: Bushberg

Hobbie

A photon of energy

h is absorbed and

an electron of kinetic

energy EKE = h - Ebis ejected.

As the energy of the

electron decreases

below the binding

energy of a shell, then

the contribution to the

overall cross section

drops to zero from thatshell.

26

(i.d) Pair Production (, e+ e-)

Ref: Bushberg


14/17

9/26/20

27

(i) Physical interactions versus photon energy and Z number

Ref: Knoll

28

(i) Relative contributions of physical interactions in Carbon

Ref: Hobbie

Note: barns/atom units


15/17

9/26/20

29

(i) Relative contributions of physical interactions in tissue

Ref: BushbergNote: cm2/g units

30

(i) Gamma ray attenuation

Ref: Knoll

The linear attenuation coefficient can be defined as:

= (Rayleigh) + (Photoelectric) + (Compton) + (pair)

Which is the total probability of interaction per unit length.

The transmission of photons in a parallel beam through

a thin medium is then:

dI/dx = - I

With general solution, I(x) = I0 e- x

The mean free path is defined as lmfp = 1/

The mass attenuation coefficient is defined as /

where is the density of the medium.


16/17

9/26/20

31

(i) Gamma ray attenuation

Ref: Knoll

Since Compton scattering processes dominate in many cases,

there can be photons that scatter out of the beam beingdetected, and then later scatter back into the direction of the

beam. The fraction of photons that contribute to this

additional signal is called Build Up Factor, B(x,E).

Simplistically, this could be included by the following

equation:

I(x) = I0 B(x,E) e- x

What is the relationship between cross section and

attenuation coefficient?

= NA tot /A, where A = atomic mass in g/mol

32

(i) Gamma ray attenuation example problem

Ref: Hobbie

What is the transmission of 1 MeV photons through 10 cm of

carbon, assuming only Compton Scattering was dominant ?

from Figure 14.7 = 2 x 10-29 m2per electron,

Carbon has 6 electrons, so tot= 1.2 x 10-28 m2per atom

= 2000 kg/m3, NA = 6.022x1023 atom/mol, A=12 g/mol

= NA tot /A = 12.7 m-1

I/I0 = exp(- x) = 0.28


17/17

Documents

1 Radiation.pdf