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Positron Emission Tomography (PET) Alisa Govzmann May, 2015 Page 1 Alisa Govzmann Positron Emission Tomography (PET)

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Positron Emission Tomography (PET)

Alisa Govzmann

May, 2015

Page 1 Alisa Govzmann Positron Emission Tomography (PET)

0http:

//sitemaker.umich.edu/pet.chemistry/positron_emission_tomography

Page 2 Alisa Govzmann Positron Emission Tomography (PET)

Idea

I use PET to measure radioactive activity distribution in tissueI use γ ray emission in near opposite directionI connect pair of detectors along coincidence line (Line of response,

LOR)I take line integrals of image function of coincidence linesI line integral the projection or Radon transform of image function

0http://www.turkupetcentre.net/imgproc/documents/radon_in_pet.pdf

Page 3 Alisa Govzmann Positron Emission Tomography (PET)

Setup and Physics

I injection (intravenous, inhalation) of a tracer compound labeled witha positron emitting radionuclide

I radionuclide in tracer decay (β+ deacay:):

p → n + e+ + νe (1)

e.g . 116 C →11

5 B(Boron-11) + e+ + νe (2)

I positrons annihilate on contact with electrons after traveling a shortdistance (ca. 1 mm, dependent on density of tissue)

e+ + e− → 2γ (3)

I each annihilation produces two 511 keV photons traveling in nearopposite directions

I linked detectors surround patient

I detected coincidence events stored in arrays corresponding toprojections through tissue

Page 4 Alisa Govzmann Positron Emission Tomography (PET)

Setup and Physics

Positron emission and annihilation

0https:

//tonygood4.wordpress.com/2012/11/04/a-pets-not-just-for-christmas/

Page 5 Alisa Govzmann Positron Emission Tomography (PET)

e+e− annihilation

I after free path of ca. 1mm positron slowed down at hulls of atomsand cached by electron in hull.

I form positronium (τ ≈ 10−10 s) and decay to two nearly anti-parallel511 keV photons

I the impulses of e+ and e− cause a statistical variance of the angleof ca. 0.3◦

Page 6 Alisa Govzmann Positron Emission Tomography (PET)

Positron emitting substances

Substance half time[min] max/aver free path [mm] production11C (carbon-11) 20.3 4/0.3 cyclotron13N (nitrogen-13) 9.93 5/0.4 cyclotron15O (oxygen-15) 2 8/1.5 cyclotron18F (fluorine-18) 110 2/0.2 cyclotron

Page 7 Alisa Govzmann Positron Emission Tomography (PET)

Coincidence detection

I in PET camera each detector generates a timed pulse when itregisters an incident photon

I pulses are combined in coincidence circuitry

I if they fall within ∆t = 10− 20 ns, they are deemed to be coincident

I coincidence event is assigned to a line of response (LOR) joining thetwo relevant detectors ⇒ position of event

I use collimator to prevent scattered photons not normal to detectorface to hit detector

I image resolution1 in PET: 5-10 mm

1due to: 1.free path, 2.angular distribution,3.detector resolution

Page 8 Alisa Govzmann Positron Emission Tomography (PET)

Coincidence detection

1http://depts.washington.edu/nucmed/IRL/pet_intro/toc.html

Page 9 Alisa Govzmann Positron Emission Tomography (PET)

Types of coincidence

I true coincidence: neither photon undergoes any interaction prior todetection and no other event is detected within the coincidencetime-window

I scattered coincidence: at least one of the detected photons hasundergone at least one Compton scattering ⇒ because of anglechange no more anti parallel ⇒ assigned to the wrong LOR

I random coincidence: two photons not arising from the sameannihilationRandom coincidence is distributed uniformly and corresponds to rateof single events.

Page 10 Alisa Govzmann Positron Emission Tomography (PET)

Types of coincidence

1http://depts.washington.edu/nucmed/IRL/pet_intro/toc.html

Page 11 Alisa Govzmann Positron Emission Tomography (PET)

Random coincidence

I The random coincidence rate Rij can be calculated as follows

I t = coincidence window, ri = single event rate on detector i

Rij = 2tri rj (4)

I time window has to be small

I correct random coincidence: because of uniform distributionsubtract measurement with time window slightly shifted

Page 12 Alisa Govzmann Positron Emission Tomography (PET)

Compton scattering and photoelectric absorption

I Compton scattering: large deflections with small energy loss occuri.e. for 511 keV photons 10% of the photon energy loss correspondto scattering angle of 25◦

I use collimator to prevent scattered photons from hitting detector

I use small time window because scattered photons need longer toreach detector due to longer path

I photoelectric absorption: photon is absorbed by an atom and inthe process an electron is ejected from one of its bound shells

I probability increases with increasing atomic number of the absorberatom and decreases with increasing photon energy

Page 13 Alisa Govzmann Positron Emission Tomography (PET)

Correction for gamma-ray attenuation

I total probability that a photon will undergo interaction with matterwhen traveling unit distance through a substance is:

I (x) = I0e−

∫ x0µ(x)dx , (5)

where µ is linear attenuation coefficient of substance, I0 initialintensity of photon beam and x the distance.

I if two detectors joined along a line are separated and an annihilationtakes place at position x the probability of the photons reaching thedetectors is

P1 = I0e−

∫ x0µ(x)dx (6)

P2 = I0e−

∫ txµ(x)dx (7)

and the probability for coincidence it is the same all along the line:

Pc = P1P2 = I0e−

∫ t0µ(x)dx (8)

Page 14 Alisa Govzmann Positron Emission Tomography (PET)

Correction for gamma-ray attenuation

Figure : major advantage of PET: attenuation correction can be determinedexactly if attenuation coefficient µ uniform throughout object, the attenuationis independent of the depth x in the object, but depends only on the totalthickness t

1http://www.medizinphysik.uni-wuppertal.de/download_home/Pietrzyk_

habil_final_corrected.pdf

Page 15 Alisa Govzmann Positron Emission Tomography (PET)

Image reconstruction

I number of counts assigned to an LOR joining a pair of crystalsproportional to a line integral of the activity along that LOR

I Parallel sets of such line integrals are projections

I get and analyze Filtered Back-projection (FBP) using methodsdiscussed in first talk

The explanation of Radon transformation and Filtered Back-projection isdone on the blackboard.

Page 16 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Function of detectorThe task of the detector is to convert energetic photons into visible light.This is done as follows

I photon incident on the scintillator detector creates energeticelectron, by Compton scatter or by photoelectric absorption

I electron passes through the scintillator detector and excites otherelectrons

I excited electrons decay back to their ground state giving off light

I photons strike the photocathode material in photomultiplier tube(PMT) behind behind scintillator

I electrons are ejected as consequence of the photoelectric effect

I electrons directed by focusing electrode toward the electronmultiplier, get multiplied secondary emission

Page 17 Alisa Govzmann Positron Emission Tomography (PET)

Figure : photomultiplier tube coupled to a scintillator

1http://en.wikipedia.org/wiki/Photomultiplier

Page 18 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Properties of scintillation detectors

I need many geometrically equal detectors close to each other

I most efficient and cheap: take one big detector and subdivide it inmany small ones by sawing in such a manner, that the incidentbeam hits the PMT spot exactly behind it.

I need high density material to absorb the gamma ray energyi.e.Bismuth germanate(BGO)

I PET detectors work at high count-rates2 ⇒ use scintillator withshort decay time3

I to improve the statistical quality of the signal from PMT: increasenumber of scintillation photons incident upon its face

2rate of counts per unit time registered by a radiation monitoring instrument3time after which the intensity of the light pulse has returned to 1/e of its

maximum

Page 19 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Energy distribution and coincidence

I Compton scatter and photo-electric absorption generate electrons ofdiffering energy distributions

I in photo-electric absorption all photon energy is transferred to theelectron ⇒ sharp peak close to energy of the incident photon

I in Compton scatter recoil electrons have a range of energiesdepending on the scattering angle

Page 20 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Energy distribution

3http://depts.washington.edu/nucmed/IRL/pet_intro/toc.htmlPage 21 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Energy distribution and coincidence

I energy measured: not that generated by electron at initialinteraction, but total energy deposited by photon in detector

I if detector sufficiently large most Compton-scattered photonsdeposit all energy ⇒ most events in photon energy peak

I set cut for events with low energy

I it more photons interact by photo-electric absorption more eventswith full energy peak ⇒ choose scintillators with a large value ofeffective atomic number(Z)

Page 22 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Time resolution and coincidence time

I important issue is interplay between coincidence time ∆t anddecay time:

I time difference between two timing pulses from coincidence eventdue to the finite time resolution of the detector

I if ∆t small compared to the time resolution of the detector, truecoincidences will be missed

I if ∆t too large more random coincidences counted without increasein true coincidences

I if ∆t sufficiently small then time-of-flight effects may becomeimportant⇐ time for one photon from an annihilation to detector significantlylonger

I another issue is dead time: big overlap in coincident pulsesmeasured as one pulse

Page 23 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Block detectorsI block of up to 8 by 8 BGO

crystals are coupled to 4PMTs with 2 cathodes each

I from relative pulse heightsmeasured by PMTs attachedto crystal calculate locationwhere photon was stopped:

x =B + D − A− C

A + B + C + D(9)

y =A + B − C − D

A + B + C + D(10)

3http://www.medizinphysik.uni-wuppertal.de/download_home/Pietrzyk_

habil_final_corrected.pdf

Page 24 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Up to three or fourdetector rings arecombined in modern PETsystems providing 47 (ormore) image planes

3http://www.medizinphysik.uni-wuppertal.de/download_home/Pietrzyk_

habil_final_corrected.pdf

Page 25 Alisa Govzmann Positron Emission Tomography (PET)

Detection systems in PET

Block detectors

8 by 8 crystal blockdetector. The 64peaks can be clearlydistinguished

3http://www.medizinphysik.uni-wuppertal.de/download_home/Pietrzyk_

habil_final_corrected.pdf

Page 26 Alisa Govzmann Positron Emission Tomography (PET)

The resulting image

Collection of 47PET slices obtainedwith a highresolutiontomograph andFDG as tracer

3http://www.medizinphysik.uni-wuppertal.de/download_home/Pietrzyk_

habil_final_corrected.pdf

Page 27 Alisa Govzmann Positron Emission Tomography (PET)

Application

In oncology

I largest area of clinical use of PET is in oncology

I most widely used tracer in oncology is 18F-fluoro-deoxy-glucose

I tissue absorbs it in similar way as glucose

I proliferating cancer cells have a higher than average rate of glucosemetabolism ⇒ get more enriched with the tracer

Page 28 Alisa Govzmann Positron Emission Tomography (PET)

Application

In cardiology

I 13N (Nitrogen-13) is used as a tracer

I quantitative values of myocardial blood-flow are measured

I distinguish between viable and non-viable tissue in poorly perfusedareas of the heart

I decide about coronary by-pass surgery or not

Page 29 Alisa Govzmann Positron Emission Tomography (PET)

Thank you for your attention

Page 30 Alisa Govzmann Positron Emission Tomography (PET)

references

University of Washington, Division of Nuclear Medicine : Introduction toPET Physicshttp://depts.washington.edu/nucmed/IRL/pet_intro/intro_src/section1.html

http://www.medizinphysik.uni-wuppertal.de/download_home/

Pietrzyk_habil_final_corrected.pdf

Siemens: Bildgebende Systeme fur die medizinische Diagnostik

Dossel: Bildgebende Verfahren in der Medizin

J.Johansson: Radon transdormation in PET,http://www.turkupetcentre.net/imgproc/documents/radon_in_pet.pdf

http://en.wikipedia.org/wiki/Photomultiplier

Page 31 Alisa Govzmann Positron Emission Tomography (PET)