medphys 2 midterm

INTERACTIONS OF IONIZING RADIATION WITH MATTER

absorbed dose - energy deposited per unit mass of medium

em radiations: x rays and gamma rays

particulate radiations: electrons, protons, alpha particles, heavy charged particles

charged particles - directly ionizing radiation

em radiations, neutrons - indirectly ionizing radiation

E<13.6eV are non-ionizing

average energy to produce an ion pair in air is 33.85eV (W)

specific ionization is the number of ion pairs produced per unit track length (SI)

linear energy transfer is the average loss in energy per unit length of path of the incident radiation (units of kV/m) (LET)

LET = SI * W

narrow beam attenuation: N = N_0*exp(-mu*x) — multiply by B(x, hv, A, L) for broad beam

mu is linear attenuation coefficient - fraction of photons that interact per unit thickness of attenuator (units 1/cm)

thickness that attenuates beam to 50% is HVL

HVL = ln2 / mu

N = N_0 * 2^(-x / x_h)

TVL = ln10 / mu — use in radiation protection shielding calculations

N = N_0×10^(-x / x_t)

only mono-energetic beams can be characterized by a single value of HVL, but linac is mono

fraction “g” of energy is lost, especially in MeV range — E_ab = E_tr * (1 - g)

photons are absorbed by photoelectric effect, compton scattering, pair production, photonuclear itneractions, coherent scattering

charged particles interact through coulomb force of atom or nuclear (soft and hard collisions, nuclear interactions of heavy charged particles)

neutrons interact with nuclei of atoms

photoelectric effect - collision between photon and atom results in ejection of a bound electron

• photon disappears and is replaced by an electron efected from the atom with kinetic energy KE = hv - E_b

• highest probability if the photon energy is just above the binding energy of the electron

• additional energy may be deposited locally by auger electrons and/or fluorescence photons

• electron tends to be ejected at 90 degrees for low energy, goes to 0 as energy increases

• interaction probability = Z³/(hv)³

coherent scattering

• no energy is converted to KE, all is scattered

• bnroadens the angular width of beam slightly

• negligibly small for energies greater than 100keV in low atomic number materials

• photon is scattered by combined action of whole atom

• photons do not lose energy, just get redirected through small angle

compton scattering

• interaction between photon and electron, independent of Z, increases with E

• some energy scattered, some transferred to electron, depending on angle of emission of scattered photon and energy

• in soft tissue it is most important for photons in 100keV to 10MeV range

• inelastic scattering - energy and momentum are conserved

pair production

• photon is absorbed giving rise to electron and positron

• threshold energy is 1.022 MeV

• can get triplet production at 2.044 MeV

• energy transferred is KH = hv - 1.022

• attenuation coefficient per unit mass depends on Z

photonuclear reaction

• energy of a photon incident on a target atom is greater than the nucleon binding energy, typically 8-10MeV, depends on atomic number and incident beam energy

PLEASE MEMORIZE THE ENERGY VS Z GRAPH FOR WHICH PROCESS IS MOST LIKELY - goes in order of photoelectric, compton, pair production

photoelectric provides high contrast at low imaging energies

interactions of neutrons

• elastic collisions with hydrogen nuclei account for most of energy deposited in tissue by neutrons with KE<10MeV

• for neutrons with KE>10MeV, inelastic scattering with nuclei other than hydrogen also contributes to energy lost in tissue

• energetic charged particles (protons/alpha particles) are often ejected from nuclei excited by inelastic interactions with neutrons

• neutron fields can be fast (E>10keV), intermediate (0.5eV<E<10keV), or thermal (E<0.5eV)

thermal neutron interactions in tissue

• neutron capture by nitrogen and neutron capture by hydrogen are most important

• thermal neutrons have a larger probability of capture by hydrogen atoms in muscle because there are 41 times more H atoms than N atoms in tissue

• BPE used to capture neutron in treatment bunker door

• MEMORIZE TYPICAL NEUTRON ABSORPTION CROSS SECTION GRAPH

interactions by intermediate and fast neutrons

• dominated below 100eV by (n,p) reactions, mostly in nitrogen

• resonance peaks occur when the binding energy of a neutron plus the KE of the neutron are equal to the amount required to raise a compound nucleus from its ground state to one of quantum levels

• above 100eV elastic scattering of hydrogen nuclei contributes nearly all of the kerma

charged particle interactions

• all charged particles lose kinetic energy through Coulomb field interactions with charged particles (electrons or nuclei) of the medium

• in each interaction typically only a small amount of particle’s KE is lost

• typically undergo very large number of interactions, therefore can be roughly characterized by a common path length in a specific medium

• charged particles are characterized by a range - a finite distance which can be calculated from stopping power in continuous slowing down approximation

slower moving particle (lower KE) transfers more energy in heavy charged particle interactions

mass collision stopping power - energy loss per unit track length in producing ionization in the absorbing medium

radiative stopping power - energy loss due to bremsstrahlung

no bremsstrahlung for heavy charged particles, only electrons

MEMORIZE PERCENT DEPTH DOSE GRAPH

MEMORIZE STOPPING POWER GRAPH

energy loss by radiation increases with atomic number and energy

ratio of radiation energy loss to energy lost by excitation and ionization is approximately E_k * Z / 820

in slowing down an electron may transfer all its energy in radiative recombination, resulting in a continuous spectrum with max energy equal to the electron kinetic energy

MEMORIZE BRAGG PEAK

slower moving charged particle (lower KE) transfers more energy, resulting in bragg peak at the end of its track

bragg peak is never observed for electrons due to their low lass, electrons constantly change direction as they slow down

MRI

earth’s magnetic field is 0.5 gauss

scanners are 1.5T or 3T

1T=10,000 gauss

MRI is based on imaging H2O molecule

source of signal in MRI is the nuclei of H atoms

a spinning hydrogen nucleus (proton) has magnetic field

billions of single-proton magnets in body in random directions cancel out

net magnetization in body normally is 0

under strong magnetic field, spins split about 50/50 parallel and antiparallel, with a few more parallel, making a small net magnetization M0

three features of M0:

• M0 is spinning around the direction of main magnet B0

• has T1 relaxation time

• has T2 relaxation time

resonance is maximum transfer of energy from RF pulse to the net M0 when frequency of RF pulse equals the frequency of the M0

the z direction is the direction of the main uniform magnetic field B0

relaxation times are unique to each tissue

T1 is the time taken for spinning protons to realign with the external magnetic field

• net magnetization is returning to equilibrium value through exponential process called T1 relaxation

T2 is the time taken for spinning protons to lose coherence among nuclei spinning perpendicular to the main field

• net magnetization is dephasing (micromagnets repelling each other) through T2 relaxation process

each MRI voxel contains unique net magnetization

the intensity in each MR image voxel is proportional to proton density within that voxel

the intensity in each CT image voxel is proportional to electron density within that voxel

all net magnetizations for all tissues have the same spinning frequency

TE is echo time

TR is repetition time

MRI signal depends on T1, T2, proton density, TE, TR

CT

each tissue has unique attenuation coefficient

relationship between emitted x ray intensity and the attenuated intensity is exponential based on the attenuation coefficient

CT is based on the synchronization of xray tube and detector movement

scanning time now is 3s with image matrix 512

detector width less than 0.5mm

mu (probability of interaction of x ray photons with material) is linearly proportional to electron density

HU represent the different electron density levels of tissues relative to water electron density

water has 0HU, air is -1000HU

HU = 1000 * (mu - mu_water)/(mu_water) where mu is the attenuation coefficient

CT image is a gray scale presentation of HU of numerically solved mu of all materials within selected slice

x ray image is a projected image

CT image is a reconstructed image

window width determines image contrast

contrast detectability is the ability of the imaging system to resolve different objects from the noisy background when the difference in x ray attenuation between the objects and the background is small compared to noise

NUCMED

radioactivity is the process through which an unstable nucleus loses energy by emitting nuclear particles or ionizing radiation (gamma ray)

equation of radioactive decay: N = N_0 * exp(ln2 * t / T_1/2)

nuclear medicine imaging is a functional and quantitative

Tc99m → Tc99 + 140.5keVgamma

usually use parallel-hole collimator, pin-hole for thyroid and heart, converging for brain and heart

the collimator is mounted in the front of the camera crystal

collimators are made from lead

primary function of the collimator in gamma cameras is for accurate spatial localization

the signal in nuclear medicine imaging is the electrical current (output of the PMT)

use windowing to exclude lower energy photons

XRAY

xrays use 20keV-160keV for diagnostic imaging

• kV: 25-140kV

• tube current: 50-400mA

• exposure time: 10-1000ms

• xray tube focal spot: 0.1-1.2mm

x ray imaging is based on differential attenuation of xray photons

• image spatial: display details of an object

• S/N: not noisy image

• image contrast: differentiate between objects

• image artifacts: no image distortions

smaller focal spot improves image spatial

image radiographic contrast is the density different between neighboring regions on a plain xray radiographic image

lower kVp improves image contrast

increasing mA improves S/N

for optimal image, select options that allow for highest differential attenuation