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) = e1t e2t

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 e1t e2t⇥ 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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