CS代写 BMEN90021, Lecture set 7: Nuclear Medicine ity. Indeed, instead of knowing – cscodehelp代写
Nuclear Medicine / Molecular Imaging
There are three basic subtypes of imaging under the banner of Nuclear Medicine (also called “Molecular Imaging”):
Planar scintigraphy
Chapter 5: Nuclear medicine imaging
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Figure 5.16 A CT and a PET system are linked and integrated into a single gantry and share a common patient bed. Two hybrid PET/CT
There are many different geometries of mechanical
allel hole collimation and in
collimators in SPECT. One example is the cone-
beam collimator. It has a single focal point. Hence,
“Nuclear”: Injection of radioactive tracers (T“imre-aof-dflighito(TOtFr) PaETcers”) into
uction problem is two dimen-
If the uncertainty in measuring the difference in arrival
all the projection lines that arrive at the 2D detector
ve methods can be applied
bone times of a photon pair is limited to 1 ns or less, it
intersect in this point, and exact reconstruction
Combined PET/CT scanner
MBCIU PET/CT
scanners are shown here. (Courtesy of the Department of Nuclear Medicine.)
The differential accumulation of radionuclides in tissue is imaged.
here exist acquisition config- ot allow the problem to be
0.10 0.0960
from cone-beam data requires true 3D methods.
Target organs via different r
diotracers.
x= ct. (5.30) 2
t in measuring the coincidence, that is,
0.1914 0.4350
• 0.0 0.1 0.2 0.3 0.4 0.5
–1 CT attenuation (cm )
y-slice reconstruction without In 3D PET all possible projection lines that inter-
Hospitals typically have a Radiography Department and a
Figure 5.17 Approximate relationship between the linear attenuation coefficient in CT, operating at 140 kV, and PET. The
More specifically, t and x are the FWHM
along the LOR can be calculated from the uncertainty
becomes interesting to use this time difference to local-
ize the position of the annihilation along the line of
response (LOR). The uncertainty x in the position
sect the detector surface (coincidence lines) are
energy spectrum of the X-ray photons is approximated by a single
respectively (Figure 5.18). A coincidence timing
effective energy of 70 keV. The energy of the PET photons is 511
separate Nuclear Medicine Department.
1 BMEN90021, Lecture set 7: Nuclear Medicine ity. Indeed, instead of knowing that the annihilation
keV. Tissue is assumed to be a linear mixture of either air and water,
uncertainty t of 600 ps, for example, yields a posi-
tional uncertainty x of 9 cm along the LOR. Further
reducing t to 100 ps reduces this positional uncer-
or water and bone. The result is a piecewise linear conversion
of the uncertainty distributions in time and space
tainty x to 1.5 cm. This information can be fed to the
reconstruction algorithm to improve the image qual-
with energy 140 keV and lower. To calculate the atten-
took place somewhere along the LOR, the expected
PET attenuation (cm–1)
X-ray vs Nuclear Medicine
Detection based on fraction of X-rays that reach
• There are many different geometries of mechanical In Nuclear Medicine, gamma rays are emitted from
In X-ray imaging and CT, X-rays are produced
outside the body, and are transmitted in beams
through the body.
allel hole collimation and in
collimators in SPECT. One example is the cone-
intersect in this point, and exact reconstruction
within the body, from injection of radiotracers.
here exist acquisition config-
beam collimator. It has a single focal point. Hence, all the projection lines that arrive at the 2D detector
uction problem is two dimen-
ve methodsDecatenctbioenaipspblieadsed on emitted rays moving through the
tissue to the detector.from cone-beam data requires true 3D methods. ot allow the problem to be
y-slice reconstruction without • In 3D PET all possible projection lines that inter- sect the detector surface (coincidence lines) are
2 BMEN90021, Lecture set 7: Nuclear Medicine
Three types of imaging
Planar scintigraphy
Analogous to planar X-ray imaging
Radiotracer emits mono-energetic γ-rays @ 140 keV
Analagous to CT imaging
SPECT = single photon emission computed tomography
• There are many different geometries of mechanical Series of 2-d images of distribution of radiotracer.
allel hole collimation and in
collimators in SPECT. One example is the cone-
Requires image reconstruction like CT
uction problem is two dimen- beam collimator. It has a single focal point. Hence, • all the projection lines that arrive at the 2D detector
Different type of radiotracer that emits positrons =
PET = positron emission tomography
ve methods can be applied
intersect in this point, and exact reconstruction
here exist acquisition config-
ot allow the problem to be
from cone-beam data requires true 3D methods.
positively charged electrons.
y-slice reconstruction without • In 3D PET all possible projection lines that inter- • Positrons annihilate wsiethct lines) are
3 BMEN90021, Lecture set 7: Nuclear Medicine
The EM spectrum (again)
allel hole collimation and in uction problem is two dimen- ve methods can be applied here exist acquisition config- ot allow the problem to be y-slice reconstruction without
There are many different geometries of mechanical collimators in SPECT. One example is the cone- beam collimator. It has a single focal point. Hence, all the projection lines that arrive at the 2D detector intersect in this point, and exact reconstruction from cone-beam data requires true 3D methods.
• In 3D PET all possible projection lines that inter- sect the detector surface (coincidence lines) are
4 BMEN90021, Lecture set 7: Nuclear Medicine
Scintigraphy & SPECT
Basic diagram of image acquisition for scintigraphy & SPECT
Radiotracer injected into patient
γ-rays (f) 140 keV
light 415 nm
allel hole collimation and in uction problem is two dimen- ve methods can be applied here exist acquisition config- ot allow the problem to be
Thereferentgmechanical collimators in SPECT. One example is the cone-
beam collimator. It has a single focal point. Hence, all the projection lines that 2D detector intersect in this point, and exact reconstruction from cone-beam data requires true 3D methods.
In 3D PET all possible projection lines that inter- sect the detector surface (coincidence lines) are
y-slice reconstruction without •
Scintillation crystal
Pulse height
are many dif
Photomultiplier tubes
Positioning
eometries of
arrive at the
5 BMEN90021, Lecture set 7: Nuclear Medicine
Image display
Characteristics of Nuclear Medicine
Relative to X-ray, CT and MRI, nuclear medicine scans have:
Low spatial resolution (~5-10mm)
Slow image acquisition
Extremely high sensitivity
Important and complementary techniques to CT &
No natural radioactivity from body
• There are many different geometries of mechanical can detect nanograms of injected radiotracer
allel hole collimation and in
collimators in SPECT. One example is the cone-
beam collimator. It has a single focal point. Hence,
all the projection lines that arrive at the 2D detector
Very high specificity
uction problem is two dimen- ve methods can be applied
here exist acquisition config-
intersect in this point, and exact reconstruction
from cone-beam data requires true 3D methods. y-slice reconstruction without • In 3D PET all possible projection lines that inter-
ot allow the problem to be
We will consider scintigraphy & SPECT separately to PET
sect the detector surface (coincidence lines) are
6 BMEN90021, Lecture set 7: Nuclear Medicine
estimate will be. Using Eq. (5.7) and replacing t by process is statistical. The larger N is, the better the
s of the to be stochastic.
n a few imaging. Consequently, noise plays a more important
emitted The exact moment at which an atom decays cannot hits an role here, and the imaging process is often considered
Radioactivity
oppo- be predicted. All that is known is its decay probability s of the to be stochastic.
11 keV, per time unit, which is an isotope dependent constant emitted The exact moment at which an atom decays cannot
Radioactive isotope: undergoes spontaneous
ositron. α. Consequently, the decay per time unit is
n oppo- be predicted. All that is known is its decay probability
n emis- -life of
f-life of nucleus
change in nucleus composition = “disintegration”
11 keV, per time unit, which is an isotope dependent constant
ositron ositron.
α. Consequently, the decay per time unit is
For N nuclei of a radioactive isotope at time t,
= −αN (t ), (5.6) = −αN (t ), (5.6)
where N(t) is the number of radioactive isotopes dt
o diag- nucleus
at time t. Solving this differential equation yields
whereN(t)isthenuTmhebrerareomfarnayddioifafecrteinvtegeiosomteotpriesofmechanical whic(hsewehFeignurseo5lv.2e)d gives
allel hole collimation and in
(see Figure 5.2)
all the projection lines that arrive at the 2D detector −α(ti−nte)rsect in this−p(ot−intt,)/aτnd exact reconstruction
ve methods can be applied
here exist acquisition config-
collimators in SPECT. One example is the cone-
at time t. Solving this differential equation yields
to emit N(t) = N(t0)e = N(t0)e . (5.7)
beam collimator. It has a single focal point. Hence, uction problem is two dimen- −α(t−t0) −(t−t0)/τ
τ = 1/α is the time constant of the exponential decay.
to emit N(t)= N(t)e 0 = N(t)e 0
from cone-beam data requires true 3D methods.
ot allow the problem to be
Note that N(t) is the expected value. During a mea-
y-slice reconstruction without
In 3D PET all possible projection lines that inter-
The time constant of exponential decay is τ = 1/α
τ = 1/α is the time constant of the exponential decay.
sect the detector surface (coincidence lines) are
surement a different value may be found because the Note that N(t) is the expected value. During a mea-
process is statistical. The larger N is, the better the surement a different value may be found because the
7 BMEN90021, Lecture set 7: Nuclear Medicine
Measures of radioactivity
allel hole collimation and in
1 Curie [Ci] = 3.7×1010 decays per second = 37 GBq
Radioactivity is typically denoted by the rate of disintegrations:
1 Becquerel [Bq] = 1 decay per second
uction problem is two dimen-
beam collimator. It has a single focal point. Hence, all the projection lines that arrive at the 2D detector
intersect in this point, and exact reconstruction
1 MBq = 1,000,000 disintegrations per second (106 s-1)
Becquerel (1852-1908) French physicist. 1903 in Physics with & .
There are many different geometries of mechanical collimators in SPECT. One example is the cone-
1 Ci is a large amount of radiation
ve methods can be applied here exist acquisition config-
(Approximate) measure of radioactivity of 1g of 226Ra
ot allow the problem to be
from cone-beam data requires true 3D methods.
• In 3D PET all possible projection lines that inter- sect the detector surface (coincidence lines) are
y-slice reconstruction without
8 BMEN90021, Lecture set 7: Nuclear Medicine
α(t t) (t t)/τ
ht atoms tend to emit N(t)= N(t)e− −0 = N(t)e− −0 . (5.7) = τ
Depending on the isot τ = 1/α is the time constant of the exponential decay.
d to prefer other modes, 0 0
depends not only on th process is statistical. The larger N is, the better the
Radiotracer half-life
vemethodscanl
n photons when r pho tions of seconds and billions of years.
here exist acquis ot allow the pro
intersect in this point, and exact reconstruction
of a positron–electron
ends not only on the radioactive decay but also on pr (
uctionproblemisen-
all the projection lines that arrive at the 2D detector
fractions of seconds an Note that N(t) is the expected value. During a mea-
Note that the prese surement a different value may be found because the
Figure 5.1 Schematic representation of a positron–electron annihilation. When a positron comes in the neighborhood of an
Half-life is the time taken for the radiotracer to drop
the number of detected
estimate will be. Using Eq. (5.7) and replacing t by
electron, the two particles are converted into a pair of photons,
biological excretion.
to one half of the original value.
T , the effective half-li B
each of 511 keV, which travel in opposite directions.
smaller than in X-ray
allel hole collimation and in
−T /τ 1 N(0)e 1/2 = 2N(0)
the half-life T1/2 and t0 by 0 yields
N(T1/2) = −T1/2/τ =
Currently the prefe
becquerel (Bq). The cu
Bq means one expecte
There are many different geometries of mechanical
37 MBq. Typical doses T1/2= τln2= 0.69τ. (5.8)
collimators in SPECT. One example is the cone-
beam collimator. It has a single focal point. Hence,
It can be shown th Depending on the isotope the half-life varies between
Note that the presence of radioactivity in the body
from cone-beam data requires true 3D methods.
in the neighborhood of an t •
y-slice reconstruction withTout In3DPETallpossibleprojectionlinesthatinter-
ed into a pair of photons,
site directions.
T , the effective half-life T can be calculated as Figure 5.2 Exponential decay. τ is the time constant and T the
half-life.
be app ition con
biological excretion. Assuming a biological half-life
sect the detector surface (coincidence lines) are
1/2 ∗ Marie and an Prize in 1903 for their disco
9 1 1 BMEN910021, Lecture set 7: Nuclear Medicine . (5.9)
−T /τ= ln1= −ln2
1/2 Effective half-life
the story.
T1/2= τln2= 0.69τ. (5.8)
Note that the presence of radioactivity in the body
TheDinetpreindsincghoanlft-hleifeisotofpthe etherahdalifo-ltirfaecvearieisboentweeesnide of fractions of seconds and billions of years.
Biological excretion of radiotracer from tissue is a
ctron dofan otons,
uction problem is two dimen-
biological excretion. Assuming a biological half-life TB, the effective half-life TE can be calculated as
depends not only on the radioactive decay but also on
factor also, and follows an exponential decay.
Therefore can define an effective half-life:
There are many different geometries of mechanical
= + . (5.9)
collimators in SPECT. One example is the cone-
allel hole collimation and in TE TB
Example: Two patients undergo nuclear medicine scans. One receives a dose of radiotracer A Currently the preferred unit of radioactivity is the
ve methods can be applied
all the projection lines that arrive at the 2D detector
beam collimator. It has a single focal point. Hence,
and the other radiotracer B. The half-life of A is 6 hours and of B is 24 hours. Initially, there is three timesasmuchoftracerAasthereisofBin.tTehresebciotloignicatlhiaslf-lpivoesinotf,AandBeaxreac6tanrdec1o2nhostursu,ction
becquerel (Bq). The curie (Ci) is the older unit.∗ One
here exist acquisition config-
respectively. At what time is the radioactivity in the body the same for the two patients?
from cone-beam data requires true 3D methods.
Bq means one expected event per second and 1 mCi =
ot allow the problem to be y-slice reconstruction without •
37 MBq. Typical doses in imaging are on the order of • Solution:2Solve for when 3N exp(-tα ) = N exp(-tα ) , giving t = 7.6 hours.
In 3D PET all possible projection lines that inter-
10 MBq. sect the detector surface (coincidence lines) are
It can be shown that the probability of measuring
10 BMEN90021, Lecture set 7: Nuclear Medicine n photons when r photons are expected, equals
Properties of radiotracers
Ideal properties of nuclear medicine radiotracers:
Radiotracer should have high uptake in organ-of-interest, and low
Half-life should be short enough to not require big dose, but long
enough to allow distribution in organs from blood.
Energy of γ-rays should be greater than 100 keV, so that rays emitted deep in tissue can travel through body and reach detector.
Decay should produce mono-energetic γ-rays without alpha- or beta- particles which are absorbed in tissue (and harmful).
• There are many different geometries of mechanical Energy of γ-rays should be less than 200 keV, so that rays don’t
allel hole cpoelnliemtrattieontheancdolliimnator.
uction problem is two dimen-
collimators in SPECT. One example is the cone-
beam collimator. It has a single focal point. Hence,
ve methods can be applied
all the projection lines that arrive at the 2D detector
uptake elsewhere in the body.
here exist acquisition config-
intersect in this point, and exact reconstruction
In scintigraphy and SPECT, most studies use 99mTc.
ot allow the problem to be
from cone-beam data requires true 3D methods.
Formedfrom99Mo,in• metastablestate,half-lifeof6hours.
y-slice reconstruction without In 3D PET all possible projection lines that inter-
sect the detector surface (coincidence lines) are
11 BMEN90021, Lecture set 7: Nuclear Medicine
Technetium generator
The generator lasts about a week before needs replenishing.
“Meta-stable” = Two-step decay process:
• There are many different geometries of mechanical collimators in SPECT. One example is the cone-
99Mo T1/2=66 hours β- + 99mTc T1/2=6 hours 99gTc + γ 42 43 43
(N1) (N2) (N3)
This gives a differential equation,
allel hole collimation and in
uction problem is two dimen- ve methods can be applied here exist acquisition config-
ot allow the problem to be
dNbeam collimator. It has a single focal point. Hence, 2all the projection lines that arrive at the 2D detector
= 1N1 2N2
dtintersect in this point, and exact reconstruction
from cone-beam data requires true 3D methods.
y-slice reconstruction without
with solution:
In 3D PET all possible projection lines that inter-
N2(t) = e 1t e 2t
sect the detector surface (coincidence lines) are
12 BMEN90021, Lecture set 7: Nuclear Medicine
Technetium “milking” Solution for technetium build-up looks like:
N2(t) = 1N0 e 1t e 2t⇥ 2 1 (f)
allel ho in uctionn- vemeed hereexg- ot allow be
y-sliceut•In3DPETallpossibleprojectionlinesthatinter- sect the detector surface (coincidence lines) are
The generator is eluted (“milked”) regularly to extract the technetium ready for injection:
There are many different geometries of mechanical collimators in SPECT. One example is the cone- beam collimator. It has a single focal point. Hence, all the projection lines that arrive at the 2D detector intersect in this point, and exact reconstruction from cone-beam data requires true 3D methods.
le collimation and problem is two dime thods can be appli
ist acquisition confi the problem to
reconstruction witho
“Moly cows” (RMIT/Wiki)
13 BMEN90021, Lecture set 7: Nuclear Medicine
Gamma camera
Detects 10,000’s γ-rays per second.
Imaging equipment for scintigraphy & SPECT
allel hole collimation and in uction problem is two dimen- ve methods can be applied here exist acquisition config- ot allow the problem to be y-slice reconstruction without
There are many different geometries of mechanical
collimators in SPECT. One example is the cone-
beam collimator. It has a single focal point. Hence,
all the projection lines that arrive at the 2D detector
intersect in this point, and exact reconstruction from cone-beam data requires true 3D methods.
• In 3D PET all possible projection lines that inter- sect the detector surface (coincidence lines) are
14 BMEN90021, Lecture set 7: Nuclear Medicine
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