PET Flashcards
What is an Atomic mass unit?
a unit of mass equal to one-twelfth of the mass of an atom of carbon-12. 1 u = 931.5 MeV/c2
What is proton rest mass?
mp= 1.0073 u = 938.27 MeV/c2
What is electron rest mass?
me= 0.00055 u = 0.511 MeV/c2
Equation of radioactive decay?
If we start with N0 atoms of an element with some decay constant lambda, we’ll have N atoms of the original element at time t.
What is activity?
While N is the number of atoms, A is the activity- the rate of decays occurring. We can combine this with the previous formula to model how activity changes in time.
What is half life?
We often characterize an element by its half-life, the time it takes to decay to ½ its original amount. This is just the first formula, setting N=½N0 and solving for t.
Determine the radius of a nucleus given atomic number A.
Where r0 = 1.4 fm
What is the nuclear volume given A?
What is nuclear charge density?
Knowing volume, and the number of nucleons present, A, we can calculate the proton density of a nucleus. Note that since volume has a linear dependence on A, nuclear charge density is actually pretty much constant for all mass numbers.
What is skin density?
Charge density falls off as r extends outside the nucleus. We call skin thickness the width it takes to drop from 90 to 10 percent. Oddly, it’s roughly constant at ~2.3fm.
What is nuclear binding energy?
The energy input it takes to free a nucleon.
Nuclear binding energy varies over A, peaking at Iron. Generally, lower A has lower BE.
How can nuclei transition to another type of nucleus?
Through fusion. fission or nuclear decay.
Describe gamma decay.
Gamma decay results in no alteration to nuclear composition- Z, A, and N all are unchanged by gamma decay. Instead, a nucleus drops from an excited state (typically denoted as E*) to a lower energy state through the emission of a characteristic photon. These excited states are often very short-lived (~10ns), and those that aren’t are called Metastable (Em).
For what are photons from gamma decay often used?
Often used in SPECT and gamma cameras.
Describe alpha decay.
Alpha decay sees a nucleus emit an alpha particle, which is effectively a Helium nucleus (two protons and two neutrons). This happens as a results of probabilistic quantum tunneling through the nuclear strong(?) force potential barrier, followed by coulomb repulsion.
The emitted alpha particles bear a specific kinetic energy (~4-8 MeV), varying on parent nucleus. Generally, faster decay makes for more energy. This type of decay only naturally happens for high Z materials (Z>83).
An alpha particle (4He) is emitted due to it’s oddly high binding energy relative to other similar nuclei (like Hydrogen or other Helium isotopes), making it more stable than the alternatives.
What are the kinetic energies of daughter nucleus and alpha particle in alpha decay?
Which one has the majority of the kinetic energy?
We can expect the emitted alpha to have a majority of the kinetic energy. A predictable amount, depending on the parent nucleus.
Is kinetic energy for beta decay characteristic?
No. We get a spectrum of emitted KEs for the beta particle.
Why is a neutrino emitted during beta decay?
Since an electron (with lepton number 1) is created, an antineutrino is also emitted to conserve lepton number.
Q for beta plus decay?
What’s the difference in energy spectrums for beta minus and beta plus decay?
Describe Electron capture and QEC equation.
In electron capture, a nucleus may catch an electron, and use it to convert one of its protons into a neutron. This actually results in the same daughter as Beta Plus decay does, but the changes in energy are different. Emits a neutrino too.
EB refers to the binding energy of the captured electron. Often, this will be one of the atom’s k-shell (closest) orbital electrons. When this happens, the atom will then emit photons as the shell vacancy is filled by higher-energy orbital electrons dropping down to fill in.
The emitted neutrino gets all the Q energy, making it monoenergetic for these ‘decays’.
What is internal conversion?
Internal conversion, a competing process to gamma decay, in which the excited nucleus uses its energy to eject an orbital electron WITHOUT emitting a photon. These electrons are known as conversion electrons.
The vacancy left behind is filled by a higher electron dropping down leading to a potential auger electron cascade finishing with gamma emission.
How does kinetic energy spectrum look for internal conversion?
In a mixed process decay (beta minus + internal conversion) how does the spectrum look?
Conversion electrons can take on discrete kinetic energy values based on which shell the electrons were emitted from (lower shell = higher energy).
In the event of Beta Minus decay and IC happening as a mixed process, we’ll see a Beta Minus Spectrum with certain peaks corresponding to the IC energy values.
What is decay correction?
Decay correction is applied to measured decay curves because concertation of radioactivity changes due to biological effects in the body.
we can ‘correct’ the decay to isolate only the biological component of the decay. With N = N0e-∧t , the exponential term is the radioactive decay. We can then simply multiply the measured curve by e∧t to correct it to biological decay
What is specific activity?
Specific activity is the amount of activity present in some amount of material. Amount may be mass, or molarity. Often could be units of Bq/g, or mCi/nmol, or whatever. It’s inherent to each individual radionuclide. Hence, ‘specific’.
What are decay chains?
As one parent nucleus decays into another, it is often that the daughter, too, will decay into some third, granddaughter nucleus (and on until stable). We can use Bateman Equations to model the amount of atoms of parent, daughter, and so on, provided we known initial conditions, and the decay constants of each. We can have forms of equilibrium between parents and daughters over time.
What is secular equilibrium?
If the parent has a much longer half-life than the daughter (~100-1000x), the daughter will essentially catch up to, and then match the parent. This makes them appear to have the same half lives.
What is transient equilibrium?
If the parent has a not-much longer half-life than the daughter (~10x), the daughter will slightly exceed the parent, but then both will decay. This also makes them appear to have the same half lives.
Equation f binomial distribution, mean and variance?
Poisson distribution equations?
Error propagation for addition?
Error propagation for multiplying by a constant?
Error propagation for multiplication or division?
Error propagation for averaging?
At what angle and energy does the Compton edge occur?
At max energy transfer (𝛳=180 degrees), we get the Compton Edge, which terminates the Compton shelf.
What is energy resolution?
Equation for detector absolute efficiency?
What is a paralyzable detector?
Paralyzable detector is a detector that tracks the end of a second pulse that occurs while the first pulse is displayed, effectively lengthening the original pulse.
If we know what model it is, and what the dead time (tau) is, we can solve for the number of true counts (n) given some amount of measured counts (m).
Must be solved iteratively (not that easy)
What is a non-paralyzable detector?
Non-Paralyzable: If a new pulse comes in while an old one is still being displayed, it just ignores the second pulse.
If we know what model it is, and what the dead time (tau) is, we can solve for the number of true counts (n) given some amount of measured counts (m).
Easy to solve
How does spatial encoding work in gamma cameras?
Spatial encoding occurs via Anger Logic- the array of PMTs (and amplifiers) correlate charge collected across dimensional bins, with some resistors for weighting.
Z is the total charge collected. Can be used for pulse height investigations.
What is gamma camera collimation used for?
Collimating grids are used in Gamma Cameras to improve spatial resolution by collimating out scattered photons (since they will be at oblique angles to the grid).
Obviously, collimation results in some loss of signal, too. Modeled as collimator efficiency, g, we see a loss in efficiency proportional to the square of the improvement in resolution. As resolution gets smaller (good), so too does efficiency (bad).
SEE PICTURE- In this way, we can see that narrower holes (d) lead to more fine resolution, as do some other factors.
Describe image contrast in PET.
Image contrast arises from differences in the amount of signal received between two different spatial locations.
In imaging via photon detection, this typically correlates to differences either in source emission rate (emission imaging), or material attenuation (x-ray imaging). In practice, both can be quantified the same way- number of photons detected (as either a rate or raw count).
The presence of any background signal will reduce contrast, (it increases Rl and Rb such that it cancels in the numerator, but not the denominator).
Where does the noise come from ?
What is CNR?
have many sources of noise, such as from unavoidable stochastic variations in photon emission. We can characterize some noise through and equation, and the define Contrast-to-Noise-Ratio (CNR) via another (picture)
Generally, via the Rose Crietrion, we need a CNR > 3-5 or so in order to really make out some sort of contrast-based image feature.
What is a sinogram?
Sinogram is h is simply the 2-D array of data containing the projections.
Of note are the sinographic representations of a point (becomes a sine wave), a line (becomes a point), and an angular array (becomes line).
What are the most common detectors made of ?
LaBr3(Ce), NaI (Ti) and HPGe
What’s the difference between 2D and 3D mode in PET?
Septa.
We can use septa on the PET Detector ring to collimate out undesirable incidence orientations. Historically, this was done such that all collected signal was in a series of axial planes (2D mode).
Removing the septa allows for far more lines of response, and makes the system no longer strictly axial (3D Mode). While this does allow in more noise, it also increases the true signal by a sufficient amount to be worth the change.
What is radiotracer compartment model?
We model the flow between compartments using a first order differential equation like:
