Nuymber of atoms per gram atomic weight

Avogadro's number = 6 x 10²³

Atomic mass unit = 1/12 mass of a carbon nucleus

1 amu = 1.66x10^-27 kg

1 amu = 931 MeV

^A_ZX

Z = atomic number = number of protons

^A_ZX

Atomic mass number = A = number of protons + neutrons

Proton = 938 MeV

Neutron = 939 MeV

Electron = 0.511 MeV

Electron shells

(order and max number of electrons per shell)

Order of electron shells: k, l, m, n, o

Max number of electrons per shell = 2n²,

where n is the order number.

An electron leaves an inner shell, and an outer electron moves to an inner shell. Energy is released as a characteristic photon.

For example: Ephoton = E_K - E_L (difference in binding energies)

Electron transitions to inner shell.

Energy from transformation is transferred to outer-shell electron which is then ejected.

High Z --> emission of characteristic x-ray more probable.

Low Z --> emission of Auger electron more probable.

Isotope = atom having same number of protons, but different number of neutrons

Isomer = same number of protons and neutrons, but different nuclear energy state

example ¹³¹_m54Xe (where m stands for a metastable state)

Neutron --> proton + electron + anti-neutrino.

Occurs in nuclei with a high n/p ratio. Example of an isobaric decay (same number of nucelons)

Proton --> neutron + positron + neutrino.

Occurs in low n/p nuclei. Example of isobaric transformation.

proton + inner shell electron --> neutron + neutrino.

This creates a hole in an inner shell, so the atom creates either a characteristic x-ray, or an Auger electron. Competes with Beta-plus decay.

1 Bacquerel (Bq) = 1 discintegration per second.

1 Curie (Ci) = 3.7 x 10¹⁰ Bq.

Specific activity = λ * (N_A / A_w).

Where N_A = Avogadro's number (6x10²³), and A_w = atomic weight.

A(t) = A⁰ e^-λt.

1/2 = e^-λt.

t_1/2 = ln2 / λ = 0.693 / λ.

Daughter half life is only slightly shorter than parent half life (or daughter decay constant is barely shorter than parent), then there is a gradual buildup until daughter exceeds the activity of parent (but both slope downward).

A_d = A_p * (t_1/2,p / (t_{1/2, p} - t_{1/2, d})).

(n,γ): neutron absorbed into nucleus, and gamma ray emitted.

(n, α): neutron absorbed and alph emitted.

(n, p): neutron absorbed and proton emitted.

The LET represents the rate of energy loss per unit path length (keV/μm) in collisions in which energy is "locally" absorbed, rather than being carried away by energetic secondary particles. LET is higher with lower energy particles.

⁶⁰Co 0.3 keV/μm

250 keV x-ray: 3 keV/μm

3 MeV x-ray: 0.3 keV/μm

1 keV electron: 12 keV/μm

1 MeV electron: 0.25 keV/μm

2.5 MeV neutron: 20 keV/μm

5 MeV alpha: 100

Often made by accelerating deuterons in a cyclotron, and then colliding the deuteron into Berylium target to strip neutrons.

Problem is that they have a wide penumbra because of difficulty collimating the beam.

Make electrons: heat cathode, which releases electrons via thermionic emission.

Accelerate electrons: potential difference between cathode and anode accelerates electrons.

Decelerate electrons: electrons collide with target (tungsten), and part of their energy is released as x-rays.

Universal problem is heat dissipation.

Solutions: rotating anode, dual focal spots (one larger for blurry images, and one smaller for fine images).

Can turn low voltage to high voltage (or vice versa).

Law of transformers: V₁/N₁ = V₂/N₂,

where V = voltage, and N = number of turns of coil.

Voltage rectification removes the negative current with AC power.

Negative current would cause electrons to form in wrong place, and damage x-ray machine.

For photons, flatness measured over 80% of field size at 10 cm depth.

This creates horns (higher doses at edge of beam) at shallower depths.

Goal is to prevent radiation from leaking from machine head.

Projects a 40cm circular field towards the isocenter.

Can be 30%.

Probably lower with tongue-and-groove MLC design.

c = νλ,

where ν = frequency (1/s), λ = wavelength (λ), and c = speed of light (3x10⁸ m/s).

E = hν = hc/λ

where h = plank's constant.

Photon interacts with matter while transferring some or all of the photon energy to the electron in the form of kinetic energy.

Kerma is the energy transfer from uncharged particles (photons) to charged particles (electrons).

Kerma = kinetic energy released in matter.

After collision of a photon with an atom, a primary electron is released.

Absorbed dose is the energy absorbed in a material per unit mass.

1 Gy = 1 J/kg = 100 rad.

N_e = N_A*Z / A_W.

where N_A = avogadro's number, A_w is atomic weight, Z is atomic number.

Low energy (up to 50 KeV).

Photon is scattered by atom (actually absorbed and emitted), without any loss of photon energy.

Probability is proportional to Z/E

The photon is absorbed by an orbital electron, which is then ejected from the atom.

E_{photoelectron} = E_photon - E_binding.

Probability is proportional to Z³/E³.

Electron vacancy filled (characteristic x-ray, or Auger electron).

Grazing hit: max energy still in photon, and min energy in electron.

90 degree photon scatter: scattered photon ≤0.511 MeV.

180 degree photon scatter: scattered photon ≤0.255 MeV.

Photon interacts with nucleus, and discintegrates into an electron and positron.

Requires at least 1.02 MeV.

Positron is then annhilated with an electron (creating two 0.511 MeV photons traveling in opposite direction). Probability of interaction = Z².

Photon interacts with nucleus, and causes ejection of a neutron, proton, or etc.

Occurs in 8-16 MeV range.

This is why you get neutron contamination in high energy photon beams.

Photoelectric effect --> Compton = 25 keV.

Compton --> Pair production = 25 MeV.

Charge of the ions of one sign produced in air by photons when all the electrons are completely stopped in air.

Unit = Roentgen = R.

1 R = 2.58 x 10-4 C/kg air.

ONLY defined in air.

ONLY measured with photons.

ONLY defined up to energy of 3 MV.

Confinded to standards laboratories (primary standard). Measures exposure in free-air.

Only used for energies up to 3 MeV.

X-ray and electron output constancy (within 2%)

Laser (within 2mm)

Optical distance indicator (within 2mm)

Door interlock

AV monitor

Thickness of material required to reduce number of photons to 50% of it's initial value.

HVL = ln2 / μ.

CO-60: 56%

4 MeV: 61%

6 MeV: 67%

10 MeV: 73%

20 MeV: 80%

25 MeV: 83%

34 MeV: 88%

RBE dose describes the relative biologic effectiveness of a defined dose of radiation.

Defined as the absorbed dose times the RBE.

Equivalent dose = dose * quality factor.

Where quality factor represents the relative amout of linear energy transfer by various types of ionizing radiation.

X-ray, electrons, protons --> quality factor = 1.

Thermal neutrons (<10 keV) --> quality factor = 5.

Fast neutrons (10 keV-2MeV) --> quality factor = 20.

The f-factor is the roentgen-to-rad conversion factor (converts exposure to absorbed dose).

D_med = f_med * X

where D_med is the dose in the medium, fmed is the f-factor of the medium, and X is exposure.

f-factor in water is close to 1 for most photon energies.

OD is the degree of balckening of radiographic film.

OD = log₁₀(I₀/I_t)

where I_O is the incident radiation, and I_t is the transmitted radiation.

Different (and newer than) radiographic film. It also determines absorbed dose.

Doesn't require developing.

More expensive.

TLD is a crystalline structure in which photons excite electrons into higher energy levels, and traps them there.

Thermoluminescence - the trapped electron goes back to its ground state when heated and releases a photon.

I₂ / I₁ = (r₁ / r₂)²

D_max = f_med * X * BSF

where f_med is the f-factor in the medium, and

X is the exposure.

⁶⁰Co (1.25 MV) 0.5cm

4 MV 1.0

6 MV 1.5

10 MV 2.0

18 MV 3.3

24 MV 4.0

D_max is the depth at max dose.

D_max decreases with increasing field size.

Why? more internal scatter.

As field size increases, the PDD increases.

This is because of increased scatter.

As SSD increases, the PDD increases,

due to the inverse square law.

Mayneord F-factor

what is it, and what is the equation?

The Mayneord F-factor is used to determine the PDD when changing SSD.

F = ((SSD_new + d_max)/(SSD_old + d_max))² *

((SSD_old + d)/(SSD_new + d))².

Then it follows:

PDD_new = PDD_old * F.

Tissue air ratio (TAR)

Definition and dependencies

TAR is the dose at depth d in phantom /

dose in free space at the same point.

TAR varies with respect to:

Beam energy

Depth

Field size

TAR is independent of:

SSD

Tissue air ratio (TAR)

formula

PDD = (TAR/BSF)* ((SSD + d_max)/(SSD + d))².

TPR = dose at depth d in phantom /

dose at a specified reference depth in phantom.

This uses SAD, and assumes the same SAD when converting from old doses to new doses.

Tissue maximum ratio (TMR)

definition

TMR = dose at depth d in phantom /

dose at depth d_max in phantom.

[image]

Tissue maximum ratio (TMR)

equation with PDD

PDD = TMR * ((SSD + d_max)/(SSD + d))²(PSF_d/PSF_dmax).

Because (PSF_d/PSF_dmax) is close to 1, it is often eliminated.

Percent depth dose (PDD).

PDD_d = D_d/D_dmax.

D_d2 = D_d-iso*(TMR_d2/TMR_d-iso)*(SAD/(SSD+d₂))².

[image]

The optimal wedge angle (θ), and hinge angle (φ), come from the following equations:

θ = 90 - φ/2.

[image]

Higher isodose constrict, and lower isodose bow out.

[image]

Long SSD (300-400 cm).

Large plastic spoiler is placed in front of the patient to bring the skin dose up to 90% of the prescribed dose

Large SSD.

9 MeV

Beam spoiler used to bring dose higher in skin.

Two fields, one angled up, and one angled down, to reduce photon contamination.

X = ΓA/d²

where X = exposure rate

Γ = gamma constant for radionuclide (R-cm²/mg-hr, or R-cm²/mCi-hr)

A = activity of radionuclide (mg or mCi)

d is the distance from the source (cm)

⁶⁰Co

Half life 5.26 yrs.

Rate constant = 13 R-cm²/mCi-hr.

Gammay ray energy = 1.17, 1.33 (1.25 avg).

Specific activity = 200 Ci/g

Created by: neutron bombardment

²²⁶Ra

Half life = 1600 yrs.

Rate = 8.25 R-cm²/mCi-hr.

Decay's by alpha and beta decay.

Mean energy = 0.83 MeV.

Specific activity = 0.98 Ci/g

¹³⁷Cs

Half life = 30 yrs

Decays by beta and gamma emission.

Rate = 3.26 R-cm²/mCi-hr.

Energy = 0.663 MeV.

Specific activity = 50 Ci/g.

Produced as a by-product of fission process in nuclear reactor.

¹⁹²Ir

Half life 74 d.

Gamma rate constant = 4.69 R-cm²/mCi-hr.

Decays by beta and gamma emission

Energy = 0.38 MeV.

Produced in a nuclear reactor with neutron bombardment.

¹²⁵I

Half life 60 d.

Gamma rate constant = 1.45 R-cm²/mCi-hr.

Decays by electron capture and internal conversion.

Energy 27-35 keV

Produced in a nuclear reactor

³²P

Unsealed source

Decays by negatron emission

Short half life of 14 days.

⁸⁹Sr

Unsealed source.

Produced in a nuclear reactor as a by-product of the fission process.

Decays by negatron emission

Half life of 50 days.

Unsealed source (quadrimet)

Decays via negatron emission.

Half life of 2 days (47 hours).

2cm above and 2cm lateral to the cervix.

Typical dose rate to pt A is 50 cGy/hr.

Point B is 3cm lateral to point A

I-125

Pd-103

Dose rates for...

LDR

MDR

HDR

Low dose rate <2 Gy/hr

High dose rate >12 Gy/hr

As photon energy increases, skin dose decreases.

As tray to skin distance increases, skin dose decreases.

As field size increases, skin dose increases.

As obliquity increases, skin dose increases.

Consists of low atomic number plate (usually Lucite) placed in front of the patient, causing low-energy contaminants to strike the patient, causing increases skin dose.

A beam spoiler is opposite of a beam filter.

Quantatative scale describing radiodensity.

HU = 1000 * (μ_x - μ_water) / μ_water

where μ_x is linear attenuation coefficient of substance x.

Air -1000

Fat -120

Water 0

Blood +30

Contrast +130

Bone +400

GTV

CTV

PTV

Gross tumor volume (GTV) = volume containing visible (gross) tumor.

Clinical target volume (CTV) = GTV plus any margins for sub-clinical or microscopic disease.

Planning target volume (PTV) = expansion to account for setup error.

[image]

D_90% = E/4.

D_80% = E/3.

Max range = E/2.

Surface dose increases with increasing energy.

High dose occurs before the high Z material (like metal implant) due to backscatter.

Low dose occurs after the high Z material.

Used in radiation protection (similar to RBE). Take into account the radiobiologic effect of different types of radiation.

Radiation type: quality factor

X-ray, γ-ray, electron: 1

Neutrons (thermal): 5

Neutrons (fast): 20

Random in nature and possess no threshold,

such as cancer.

H = D*Q*N

where H is the dose equivalent

D is the absorbed dose

Q is the radiation quality factor

N is the product of all other factors

Seivert (Sv)

1 Sv = 1 Gy (for photons and electrons)

100 rem = 1 Sv.

Because whole-body exposure is not usually uniform, the effective dose equivalent is defined as "the sum of the weighted dose equivalents for irradiated tissues".

Measured in Sievert (Sv).

Tissue weighting factors

Gonads = 0.2???

Bone marrow, breast, colon, lung, stomach = 0.12

Bladder, esophagus, gonads, liver, thyroid = 0.05

Bone surface, brain, kidneys, salivary glands, skin = 0.01

Remainder tissues = 0.10

Chest x-ray: 8 0.1mSv

CT: 10 mSv

Coast-to-coast airplane trip: 0.05 mSv

As Low As Reasonably Achievable

This principle states that radiation risks should be kept as low as reasonably achievable, taking into account the current state of technology and economics of improvement in relation to public health safety.

Dose limit:

radiation worker

Annual: 50 mSv/yr

Cumulative: 10 mSv x age

Dose limit:

general public (infrequent & continuous)

Infrequent exposure: 5 mSv/yr

Continuous of frequent exposure: 1 mSv/yr

Extremities, skin, lens of eye 50 mSv/yr

Dose limit:

Students under age 18

Dose limit:

Embryo-fetus

Total: 5 mSv

Monthly: 0.5 mSv

To abdomen survace: 2 mSv

Dose limit:

Lens of eye

Dose limit:

skin, hands, feet

dose below which further efforts to reduce radiation exposure are unwarranted

0.01 mSv/yr

Radiopharmaceutical dose >10% different from prescribed dose.

Weekly teletherapy dose >15% off

Brachytherapy dose >10% off

Dose delivered without prescription

Dose delivered without daily record

Radiopharmaceutical differs by >20%

Total teletherapy dose off by >20%

Weekly teletherapy dose off by >30%

SRS dose off by >10%

Brachytherapy dose off by >20%

Wrong patient treated

Wrong treatment site

When total effective dose equivalent to any other individual is less than 5 mSv for adults,

or 1 mSv for children.

Type        Surface dose   Dose rate at 1m

White       0-0.5 mR/hr      N/A

Yellow II   0.5-50 mR/hr    0-1 mR/hr

Yellow III  50-200 mR/hr   1-10 mR/hr

Treatment room design:

Radiation rate max for

Controlled area

and

Uncontrolled area

Controlled area = 1 mSv/wk

Uncontrolled area = 0.1 mSv/wk

Primary barrier: attenuates the direct beam.

Seconday barrier: attenuates scatter radiation.

Workload (W) gives the amout of beam-on time.

Defined in terms of Gy at 1m from the source

Use (U) factor is the fraction of operating time during which radiation is striking a particular barrier.

Walls = 1/4

Floor = 1

 Ceiling = 1/4-1/2

D = B*(WUT)/d².

where D is the dose,

B is the barrier transmission factor,

W the workload,

U the use factor,

T the occupancy factor,

and d the distance

At 90 degrees it's 0.09% for Co-60,

and 0.06% for 6MV.

Concrete good because of high hydrogen content.

Borated polyethylene also good, but the neutron interaction will create a high energy photon, so you need lead shielding behind borated poly (in door construction).

good choice for qualitative measurements of radiation.

Bad for quantitative measurements

...based on the principle that when an excited or ionized ion undergoes de-excitation or recombination, energy is released. In some materials this energy is released as visible light (called scintillation). The radiation detectors that they are used to detect this light are called scintillation detectors.

Very sensitive to small amounts of radiation.

Based on the following rection

[image]

the alpha particle from this rxn is detected.

TLD badge

Film badge

Electronic dosimeter

Improves resolution in diagnostic imaging.

Placed over the film to block scattered x-rays (scattered x-rays come from the Compton effect)

In diagnostic imaging, a screen amplies/intensifies the energey of an incident x-ray, by converting the x-ray energy (inefficient detection by film) into visible light which interacts with radiographic film (efficiently).

Less dose to patient, but sacrifices image quality.

Single Photon Emission Computed Tomography

Most commonly uses ^99mTc, which emits a 104 KeV photon.

Basic idea is that your body emits the photons, which are then projected onto a collimator which absorbs any scattered radiation. The gamma rays then causes scintillation (generating a light ray) which is then detected.

positron emission tomography (PET)

¹⁸F decays and emits a positron that travels a short distance before it interacts with an electron and annihilates, creating two 0.511 MeV photons that travel in opposite directions.

¹⁰³Pd

Half life = 17 days

Decays by electron capture and emits characteristic x-rays.

Energy 20-23 keV

Brachytherapy dosing system:

Non-uniform source distributions resulting in a uniform dose distribution.

Brachytherapy dosing system:

Uniform distribution and uniform strength of sources.

Results in a non-uniform dose distribution.

Dose specified 3mm beyond periphery of volumes.

Brachytherapy dosing system:

Uniform distribution and uniform strength of sources.

Results in a non-uniform dose distribution (like Quimby).

Dose specified at the edges of the volume (Quimby uses 3mm beyond periphery of volume).

Brachytherapy dosing system:

Uniformly spaced source lines of equal length and strength.

Dose prescriptions are  to 85% ofthe average of the local dose minima between neighboring needles.