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Physics of nuclear medicine

introductionhistoric and current NM technologies principle of gamma cameraimage quality and gamma camera performance characteristicsgamma camera QCdata acquisition and processing methodsSPECT and SPECT/CTother devices

Physics of nuclear medicine

Cherry SR, Sorenson JA, Phelps ME, “Physics in Nuclear Medicine” 3rd ed (2003)

Chapters 12, 13, 14, 15, and 17

Introduction of nuclear medicine

radiopharmaceutical (a radionuclide attached to a chemical compound) administered to patient, then (hopefully) concentrated to the abnormal sites through interaction between the pharmaceutical and cells or molecules

decay of the radionuclide in the sites: emitting of single or annihilation photons

detection of the emitted photons using gamma camera, PET scanner or other devices


sensitive to functional changes earlier detection of diseases and exclusive diagnostic capability, e.g. perfusion for heart, brain, kidney and lungs, and metabolism for cancers

interaction at cellular or molecular levels bound directly to a target molecule (111In-monoclonal antibody), low sensitivityaccumulated by molecular or cellular activities of the target (18F-FDG, 99mTc-sestamibi, 131I−), high sensitivity


emitted photon energy: 70 to 511 keVmost low-energy photons absorbed by tissues most high-energy photons penetrating the detector charged particles penetrating only mm of tissue

pixel value of the image: concentration of radioactivitymay need post-acquisition data processingpoorer image quality due to limited photon number and poor spatial resolution

History of nuclear medicine

1895 discovery of x-ray by Roentgen1896 discovery of radioactivity by Bequerel1898 production of radium by Curie1927 use of radon to measure the blood

transit time 1930s invention of cyclotron by Lawrence1945 invention of nuclear reactor1951 rectilinear scanner to acquire images

History of nuclear medicine

1958 invention of Anger camera1964 use of Tc-99m (I-131 only prior to 1964)

Tc-99m: metastable (T1/2 = 6.01 hr) pure γ decay (E = 140 keV), flexible for labeling

I-131: electrons and 364 keV photons, thyroid disorders only

1970 derivation of image reconstruction algorithm for tomography (CT, SPECT, PET)1998 rapid spread of PET and PET/CT

The most often used radionuclide: Tc-99m

metastable state of 99Tc43: T1/2 = 6.01 hr long enough for imaging but short for

reduced radiation dose to patient

pure γ decay: less radiation doseE = 140 keV: enough photons to escape from the patient body but most stopped by the detectorflexible for labeling (attached to a pharmaceutical): wide clinical applications

The most often used radionuclide: Tc-99m The first rectilinear scanner (1951)

The first Anger camera (1958) Dual-head gamma camera

SPECT gamma camera

Two detectors mounted on a rotation gantry with different angles (180°, 90°) for tomography

Mobile semiconductor gamma camera

15×20×10 cm CZT detectorbreast imaging sports medicine ER and OR imaging

3000 0.3×0.3 cm discrete crystals48 PSPMT

Planar imaging

Tc-99m sestamibi3 mm lesion detectable

Tc-99m MDP

Dynamical imaging

a series of images with time

SPECT imaging

transaxial coronal sagittal

SPECT imaging

short-axis

verticallong-axis

horizontallong-axis

Pros and cons of nuclear medicine

inherent molecular imaginghigh sensitivity low concentration of

radionuclide ~ pmol/liter

biodistribution depends not only on the specificity of the carrier but also on the route of administration.

noisy and suboptimal resolution

Molecular imaging

ACR definition: Spatially localized and/or temporally resolved sensing of molecular and cellular processes in vivo.SNM definition: Visualization, characterization, and measurement of biological processes at the molecular and cellular levels in human and other living systems.

2-D or 3-D imaging and variation over time

Including NM, PET, MRI, MRS, optical, US and CT with contrast

Molecular imaging modalities

resolution ____modality sensitivity spatial temporal contrast

MRI + 10-100µm msec +++MRS + 1 cm min-h +PET +++ 3-4 mm min ++SPECT ++ 8-12 mm min +optical +++ 1-2 mm msec +++US +++ 1 mm msec ++

+++: high, ++: medium, +: low

Probes for molecular imaging

bound directly to a target molecule

accumulated by molecular or cellular activities of the target

activated by the target enzyme in vivo

Smart NIR agents

With specific enzyme cleavage, fluorophores are separated from the backbone and each other so as to markedly increase their fluorescence.

Gamma camera

pat ient

collimat ordet ect or

PMT

pre- amp

amp & sum

posit ionPHA

comput er

display

X Y Z

Major components

collimatorto establish position relationship between γ photon source and detector (projection imaging)

scintillation detector (NaI(Tl))to convert x or γ photons to blue light photons

photomultiplier tube (PMT)to convert blue photons to electrons and to increase the number of electrons

electronicsto amplify and discriminate electrical signals

displayto display the image acquired by gamma camera

Collimator

to establish position relationship between the source and detectorpoor spatial resolution (abilityto see details) and low detection efficiency (ability to count photons)The weak link of a gammacamera: The collimatordetermines the resolutionand sensitivity of a gammacamera.

Collimator

design principle:to optimize the trade-off between resolutionR and sensitivity ηhole size d and hole length l

smaller (or longer) holeshigher R but lower η

septal thickness tpenetration < 5%hole orientation:parallel-hole, converging, divergingpinhole: single hole

d

t

Parallel-hole collimator

increasing source-to-detectordistance leads to

same sensitivitysame FOVsame image sizelower R

Converging beam collimator


decreasing FOVincreasing image sizelower Rhigher sensitivity

FOV

Ffan cone

Pinhole collimator


increasing FOVdecreasing image sizelower Rlower sensitivity

FOV

NaI (Tl) detector energy spectrum

scintillation process to convert γ photons to blue photons (E ≈ 3 ev or λ ≈ 415 nm)theoretical deposited energy spectrum in detector

photopeak:completely absorbedcompton edge:Ee = E0 – Es (at 180º)above the edge: multiple scatterbelow the edge:single + multiple


photopeak single scatter double scatter

p.e p.e c.sc.s

Compton edge

c.s c.sc.s

c.s


actual deposited energy spectrum in detectorspread photopeak caused by imperfect energy resolution (random fluctuation of blue photon number in detector)backscatter peak due to photon penetrating the detector, backscattered by surrounding material, reentering detector, and absorbed by the detector:Eb + Ee = E0

iodine escape peak 30 keV K-shell x-rays following p.e. absorption of iodine: Ee ≅ E0 – 30 keVlead K-shell x-ray (80 – 90 keV) following p.e. in lead


backscatter iodine escape lead x-rays

p.e

c.s

p.e

p.e

NaIx-ray

x-rayp.e

e

x

γ


Hg-197 w.o. scatter I-131 w/w.o. scatter

Advantages of NaI (Tl) detector

good stopping power for low-energy γ(ρ = 3.67 g/cm3, Zeff = 50, PE dominant)

µ = 16.58 cm-1 @ 69 keV, t = 0.95 cm, T ≅ 0%µ = 2.57 cm-1 @ 140 keV, t = 0.95 cm, T = 7.7%µ = 0.72 cm-1 @ 247 keV, t = 0.95 cm, T = 48.5%

good detector linearity over 20 - 2000 keV good conversion efficiency: ~ 26 eV/blue photongood transparent to blue photonsblue photons matched with the performance of PM tubeeasy to manufacture

Disadvantages of NaI (Tl) detector

poor stopping power at Eγ > 200 keV

slow scintillation decay (230 ns)low counting rate

Compton scatter dominated at Eγ > 250 keV poor spatial resolutionfragilemust keep dry

Photomultiplier tube

to create and amplify e-pulse

photocathode (CsSb): blue light to electrons

9 - 12 dynodes: each increasing electrons3 – 6 times

anode: collect electrons: 610 ≅ 6 × 107 NaI(Tl) 0

+ 3 0 0 v+ 4 0 0 v

+ 5 0 0 v+ 6 0 0 v

+ 7 0 0 v

cathod

anode

dynode

To preamplifier


stable high voltage1200 V needed for 10 dynodes1% increase of high voltage 10 % increase of current at anode

sealed in glass and evacuatedwrapped in ‘Mu-metal’(alloy of Fe, Ni, Cu) to shield magnetic fieldmagnetic field affecting focusing of electron beam


40 to 100 PM tubes (d = 5 cm) in a modern gamma cameraphotocathod directly coupled to detector or connected using plastic light guidesanode connectedto electronics inthe tube baseultrasensitive to magnetic field

Electronics

preamplifierto amplify pulses from the PM tubeto match impedances between the detector and subsequent componentsto shape pulses for subsequent processingvoltage- and charge-sensitive circuits

amplifier to amplify pulses from mV to Vto reshape slow decay pulses to narrow ones using resistor-capacitor circuitbaseline restoration circuit

Electronics

pulse height analyzer: selecting the pulses of certain voltage amplitudes (channel) to discriminate against unwanted γ photon

lower-level discriminatorupper-level discriminatoranticoincidence circuit

1 2 3

V2 (154 keV)

V1 (126 keV)

Electronics

position circuit

x

y

Z

YYky

Z

XXkx

YYXXZ

ii

ii

y

ii

ii

x

ii

ii

ii

ii

∑∑

∑∑

∑∑∑∑

−+

−+

−+−+

−=

−=

+++=

Display

cathode ray tube (CRT)

linearity

dynamic range contrastbrightness

LCD: thin film transistor (TFT)

plasma display

e- source

anode

def lect ion plates

screen

z

y x

Detection of a γ-photon

1 γ-photon 1 electrical pulse (1 count)The photon may experience p.e in the detector (A), c.s in the detector (B), or c.s in the patient (C).energy deposited on the detector # blue photons pulse height

entire energy maximum pulse height (A)partial energy reduced pulse height (B, C)

A B C BA C

Image quality

main factors of image quality: 1. contrast: the difference in count density

between two objects (or background)

C = (Imax-Imin)/(Imax+Imin), MTF (k) = Cout(k)/Cin(k)

2. resolution: ability to distinguish between two objects in close distance, measured by full width at half maximum (FWHM) of PSF

image sharpness and details3. artifacts

Factors determining image quality

camera performance characteristics

detection efficiency count rate image noise contrast, resolution

collimator performance resolutionpatient-to-detector distance resolution

energy resolution width of energy window scatter counts contrast

non-uniform FOV artifactsdead time artifacts or count loss at high count rates

Factors determining image quality

patient motion contrast, resolution, artifacts photon attenuation and scatter contrastlow-pass filter in the reconstructionresolutionwrong energy window contrast, artifacts

Non-uniform FOV

collimator defect defected PMTs

Image noise and off-peak effects

50,000 500,000

1,000,000 2,000,000

Collimator performance

low-energy all purpose (LEAP) collimator better efficiency but worse resolution

low-energy high resolution (LEHR) better resolution but worse efficiency

low-energy fan-beam (LEFB) collimatorlow-energy cone-beam (LECB) collimatormedium-energy all purpose (MEAP) high-energy all purpose (HEAP) collimator

Patient-to-detector distance

system resolution Rsys

intrinsic resolution Rint

collimator resolution Rcol

at d > 5 cm, Rcol >> Rint

larger d poorer Rcol

poorer Rsys

R R R 2col

2intsys +=

Detection efficiency Energy resolution and energy window

energy spread due mainly to fluctuation of the blue photon number in the detector and of electric signal in the subsequent electronicsenergy resolution: 8 – 10% for NaI

~ 20% for BGOenergy window: ±10% for NaI

±30% for BGObetter energy resolution smaller energy window fewer scatter counts

Multiple energy window

summing images to increase count rate Tl-201: 70±10% keV + 167±10% keV

In-111: 171 keV + 245 keV

Ga-67: 93 keV + 185 keV + 300 keV

dual energy window simultaneous acquisition to accelerate studye.g. cardiac perfusion: Tc-99m and Tl-201140±10% keV and 70 keV + 167 keV

Down scatter contamination must be corrected.

Performance at high count rates

pulse pile-up effectsTwo events acquired at different locations but same time are recorded as a single event with summed energy at a location between them.

2 scatter counts possibly accepted as 1 event image quality degradation

rejected if both events in photopeak

count loss

Performance at high count rates

typical dead time in clinic: 4 – 8 µs5 µs dead time 20% count loss at 40,000 cpse.g. first-pass cardiac study: 100,000 cps

very high count rate may paralyze camera.

Camera quality control

uniformity: daily, 256×256, > 4M counts

resolution: weekly, 512×512, > 4M counts

energy and COR: monthly

acquisition of new uniformity maps and possible energy map: quarterly, > 30Mcounts

Uniformity of detector

integral unif = max. count – min. count< 5% max. count + min. count

differential unif = max. count diff. – min. count diff. < 5% max. count diff. + min. count diff.

Bar phantoms

Data acquisition

collimator: LEAP, LEHR, LEFB, LECB, MEAP, HEAPenergy window: match the radioisotope and energy resolutionpixel size: 1/3 ~ 1/2 of spatial resolution

64×64, 128×128 or 256×256, 2 bytes in pixel depthpatient close to the detector, steady, in FOV

size pixelsizedetector size matrix =

Matrix size

64×64 128×128

Data acquisition

static acquisition: recording x and y in a matrixdynamic acquisition: recording a sequence of static images at different time, each image corresponding a certain time periodlist mode acquisition: recording x, y, t (and R-wave trigger for gated list mode), no frames during acquisition and later reframing needed

Data processing

windowing in display: 2 byte image displayed on a 256 gray color monitor 2-D filtering the image: reducing noisetemporal filtering for dynamic images: reducing noiseROI: maximum, minimum, mean counts, s.d.time-activity curve from a dynamic image: renogram, first-pass count profile: often used in camera QC

Time-activity curve SPECT

eliminate overlaying and underlying activity of a slice better contrastmore accurate lesion localization more demanding technically and longer data acquisitionmore severe image noise

Data acquisition

a sequence of 2-D static images at different angular positions (views)detector rotation range

180º with 2 perpendicular detectors or 360º with 2 opposite detectors

45º RAO

45º LPO

Data acquisition

circular or elliptical orbitcloser to the patient better spatial resolution

step-shoot or continuous acquisition

Data acquisition

energy windowacquisition time or counts per viewmatrix size for each view depending on the spatial resolution (64×64 or 128×128) number of views = matrix size for 360º SPECT (64 or 128) ECG gated for cardiac SPECT

View number

128 views 64 views

43 views 32 views

SPECT camera performance

mechanical center coinciding with COR using software, calibration and testing

all detectors aligned accurately in axial direction to acquire same slice data

uniformity < 1% ~ 41 M for 64×64 image

SPECT reconstruction

filtered backprojection algorithm (FBP)iterative algorithms (OSEM, MLEM)compensation techniques

attenuationscatterpatient motionspatially variant blurring

Filtered backprojection

ramp filter required even for noise-free data to remove 1/r blurring

low-pass filterto suppress noise

Filtered backprojection

Hann filter: 0.5 k (1 + cos(πk/kc))

Butterworth filter:

0

k1 + k / k c

2n

4.25 4.15 8.15

RampHannBW 4.25BW 4.15BW 8.15

frequency

filte

r

1

Iterative algorithm

to assume an initial image and toupdate the image iterativelySteps of one iteration:

1. to project the image2. to compare to the data3. to backproject P - P0

4. to update the imageI1 = I0 + bpj (P - P0)

I0 P0

P

I1

P-P0

Photon attenuation and scatter

attenuation decreased photon number on AB due to absorption and scatter, half of 140 keV photons absorbed over ~ 5 cm inwaterscatter and downscatter

misplaced source position C instead of A

det ect or

A

B

C

D

pat ient

θ

Photon attenuation effect Attenuation compensation

geometric meanP = (p1× p2)1/2

exact compensation for a pointsource in uniform medium

analytical method: uniform attenuation built in FBP, magnifying image noise

Chang’s method, for uniform µ (brain SPECT)

transmission images attenuation map used in iterative algorithm, most accurate and best noise control

p1

p2

Transmission image

Gd-153 (97-103 keV, 8 mo)moving line source for parallel-hole collimatorsstationary line source for fan-beam collimatorsstationary point source for cone-beam collimators

x-ray source and detector (SPECT/CT)p = p0 exp(-Σµi∆xi): Σµi∆xi= ln(p0/p) µi

Transmission image

scaling µ to the photon energy of emission image downscatter contamination

Photon scatter and compensation

reduced contrast

spill of counts from a hot spotscatter model built in iterative algorithmdeconvolution dual energy window method prior to image

reconstructiondata P acquired from 126 - 154 keVdata S acquired from 91 - 125 keVcompensated data = P - S/W, e.g. W = 2

Photon scatter and compensation

Partial volume effects

occurring for small sources Vs

resolution volume VR = π.FWHMT2.FWHMA

when Vs < VR, pixel value < concentration

Partial volume effects

reducing contrast and error in quantitaion, ‘spillover’recovery coefficient RC = Capparent/Ctrue

RC used to correct PV with known Vsand VR , but not feasible in clinic

Compensation for movement

patient motion1. a Tc point source with Tl patient2. fast, repeated acquisition 3. software correction

physiological organ movementgated cardiac imaging

SPECT/CT scanner

A gamma camera and a multi-slice spiral CT scanner on the same gantry with a single patient table

SPECT/CT scanner

CT: to create attenuation map for SPECT attenuation correction with any radioisotopesImage fusion for SPECT and CT to better localize the diseaseSPECT/CT advantage over PET/CT: possible to label the imaging agent with a therapeutic isotope to highly-specifically treat the disease

SPECT/CT scanner

GE Infinia Hawkeyehelical CT, 140 keV, 2.5 mA, 4 rows × 384Elements, 16 slice/min, in-plane res = 4 lp/cm,sw = 0.5 mm

Siemens Symbia T, T2, T6, T16

Philips Precedence 6, 16 slice

SPECT/CT image fusion

Cardiology

SPECT/CT image fusion

Oncology

Gas-filled detectors

to measure activity onlyionization chamber: dose calibrator and survey meterGeiger-Muller counter(quenching gas): sensitive survey meter,area monitor

γh

e

+

_

.

Dose calibrator

high pressure (12 a.p.) Ar-filled ion chamber to assay activity only

sample volume effect

linearity of response versus sample activity

Dose calibrator quality control

constancy: daily, Cs-137 (660 keV, 30 y) and Co-57 (122 keV, 9 mo): ±10%linearity: quarterly, 10 µCi - 300 mCi

Tc-99m, long-term decay or lineator: ±10%accuracy: yearly, Cs-137 and Co-57: ±5%geometry: upon installation, Tc-99m: ±10%

Well counter

detecting in-vitro x- and γ-raysmain components

single NaI crystal (4.5×5 cm or 1.6×3.8 cm) with a hole for samplea PM tubepreamplifier amplifierSCA or MCAreadout device

Well counter

detection efficiencyintrinsic: 100% for Eγ < 150 keV geometry: for < 1 mL sample at bottom: 93%absolute activity: Asam= Astd× [Csam/Cstd]shieldingenergy calibrationdead time ~ 4 µsA < 10 kBqfor 50 kBq, 18% loss

Thyroid probe

measuring thyroid uptake of I-131 in-vivo

5×5 cm NaI(Tl) with 15 cm long conical collimatorpointing to neck, thigh bkgcalibration phantom with

known activity for calculatinguptake1 – 2 cm diff. in depth

10 – 40% diff. in count rate

Miniature γ probe

used in surgerydetecting sentinel lymph nodes with Tc-colloiddetecting radioactive monoclonal antibodies of In-111, I-131, I-125

5×10 mm, high directional sensitivity, light, easyto use, no hazard