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SPECT

We’ve previously seen how emitted photons as a result of radioactive decay gettransmitted through the body, and interact within a scintillator detector in order to bedetected. In standard nuclear medicine, a 2D projection of the 3D radiotracerdistribution is recorded on the gamma camera. The number of photons detected ateach position on the gamma camera is recorded as a histogram. This is called framemode acquisition.

By accumulating photons over a length oftime, (ie, seconds or minutes), an imagewill build up over time depicting the twodimensional activity distribution within thepatient.

Because of the effect of thecollimator, each location on the camerawill only collect photons from a limitedangle of acceptance (called theacceptance angle). For a parallel holecollimator, photons are only allowed topass through the holes if they originateparallel to the collimator holes.

2

L esionC on trastL esion B ackground

B ackground=

−

The problem with planar imaging is that all activity from a certain ray will besummed together in the final image as planar imaging does not have any provision forthe originating depth of the photon.

For a small lesion in a large organ such as the liver, the overall lesion will be very lowas a result of all the over- and under-lying activity.

Additionally, no information relating to object size, shape, or quantitation isavailable from planar imaging. For these reasons, we use tomography. Tomographyrefers to acquiring multiple images at various angles around the object and performinga mathematical routine called reconstruction in order to determine the threedimensional distribution within the object.

Advantages of Tomographic Imaging1. Improved image contrast due to the removal of over- and under-lying activities.2. Improved 3D visualization allows size, shape and extent of lesions to be determined.3. Improved quantitation by being able to determine volumes.

Disadvantages of Tomographic Imaging1. Reduced spatial resolution due to process of data acquisition and reconstruction.2. Increased noise present.

Single photon emission computed tomography (SPECT) is a 3D imaging methodused in nuclear medicine in order to determine the 3D distribution ofradiopharmaceutical within the body within small volume elements (voxels). It uses aseries of projection images acquired at regular intervals around the object inconjunction with mathematical image reconstruction algorithms. The fact that a threedimensional object can be represented as a series of projection angles is known as theRadon Transform.

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Data Acquisition in SPECT1. Linear sampling - pixel size, û

In order to maintain a high spatial resolution (ie, ability to resolve small features),we must sample at a high enough spatial frequency, or else we will suffer from aliasing.In order to resolve an object with a particular size (ie, a FWHM), we must sample with apixel size of at least ∆ ≤ ≤1 22 0 52. .σ F W H MThe problem is if each image pixel is too small, very few counts will be collected withinthem. The uncertainty in the number of counts collected in each pixel is equal to

. So,C ounts

û�, error �, aliasing �, spatial resolution �û�, error �, aliasing �, spatial resolution �

2. Angular sampling - number of projection anglesIn x-ray CT, the high flux rate of x-rays allows many, many projection angles to

be acquired quickly (ie, limited by gantry rotation time). In SPECT, the photon flux isorders of magnitude less, therefore large numbers of projection measurements notpossible. In order to maintain the same pixel sampling size at the periphery of the fieldof view, as at the centre, we must have the number of projection measurements equalto:

4

A ng lesD

N= =π

π∆

Circumference of periphery at edge of FOV = �D

over 360( rotation, we need to sample the circumference with a pixel size û. Thus, thenumber of angles required is:

where N = number of object voxels across the FOV.

In general, most objects under interest in SPECT are closer to the center of the FOV(ie, heart, lungs, brain), and as such, the angular sampling can be less. Typically, over180(, the angular sampling is equal to N or even N/2.

3. Acquisition contoursBecause of the depth dependent response of the collimators, objects further

from the camera face will be blurred more than objects close to camera. In order tokeep resolution high at all projection angles, the camera must be kept close to thepatient. This is often done using an elliptical orbit of the camera around the patient. Alternatively, sensors placed on the detector heads can detect the outline of the bodyand follow the contours closely.

However, unless the camera response is isotropic, additional corrections mustbe performed in order to account for the different source/detector distances at eachangle.

4. Rotation acquisitionsTypical data acquisition procedures involve the camera stopping at a number of

angles around the patient in order to acquire projection data. This is known as a stepand shoot method. Such acquisitions will capture the activity distribution at individualangles, but time is required for the camera to stop and rotate to the next angle. Thetime required for this may range from 1 s to 5 s for older cameras.

Newer cameras can perform a continuous rotation acquisition whereby thecamera is always moving and acquiring projection data. Rotation speed is quite slowwith a 3( rotation taking as long as 1 min. Projection data acquired over each smallangular interval is binned together in order to create a projection image at a singleangle. While no extra time is required for the camera rotation, the fact that data isblurred out over a few degrees, may introduce complications in the reconstructionprocedure.

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Image ReconstructionAfter a series of projection images is acquired around the patient, image

reconstruction must then take place. Image reconstruction algorithms typically fall intotwo categories:

i) AnalyticalThese methods make use of mathematical properties in order to reconstruct the

exact 3D distribution within the object. These methods ideally require noise-freeprojection data sets, and infinite numbers of projection measurements. Realisticallysuch acquisitions are not possible, so these methods are then called approximatemethods. The most common analytical reconstruction algorithm is filteredbackprojeecction.

ii) IterativeThese methods are typically based on probability theory and attempt to arrive at

the best estimate of the object distribution, given the particular projection data that wasacquired. They typically can account for a lot more physical effects that occur within thebody than can iterative methods. The most common algorithms of this type aremaximum likelihood-expectation maximization (MLEM), or algebraic reconstructiontechnique (ART).

Consider a collection of projection measurements around an object. Eachprojection measurement is a 2D image consisting of X (camera bins) vs Y (cameraslice). Each element of each image is called a picture element, or pixel.

We can now stack all the 2D projection data together and take out a single slice worthof data. This data will consist of profile measurements of a single transaxial objectslice, at a variety of angles. When plotted as a function of camera bin vs angle, this iscalled a sinogram.

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Reconstruction Methods

Simple Backprojection:When using a parallel hole collimator, we know that all the photons passing

through a hole came from the same direction, but we don’t know the depth of eachoriginating decay. As a result, the best we can do is to say that the original photon hadan equal probability of originating at each object depth along the ray. Thus, for eachprofile measurement, if we smear back the counts collected within each camera bin, thisis process of backprojection.

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( )f x yN

p x yi i ii

N

' ( , ) cos s in ,= +=

∑1

1

φ φ φ

f x y f x yr

' ( , ) ( , )= ∗1

The process of backprojection can be written mathematically as:

Where f’(x,y) is the approximate image of the true object distribution f(x,y). Therelationship between f’(x,y) and f(x,y) can be shown to be,

where * represents the process of convolution.

The fact that an image reconstructed with simple backprojection is blurry results fromthis 1/r factor and is called 1/r blurring. It results from the fact that backprojection tendsto blur data out evenly along the projection rays. As much of this data is inevitably putin the wrong place, no provision is made to correct the backprojections at other angleshowever. The result is an overall blurring.

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Filtered BackprojectionThe 1/r blurring that we’ve just seen, reduced the accuracy of simple

backprojection. In order to improve reconstructed data, it is common practice to modifythe simple backprojection method to eliminate the 1/r blurring. This is most commonlydone through filtered backprojection.

In the Fourier Domain, projection imaging corresponds to sampling the 2DFourier Transform of the image along spokes of a wheel. That is, each projectionprofile, when 1D Fourier Transformed, correponds to a spoke of a wheel in the 2DFourier Transform of the object. This is due to the Fourier Slice Theorem.

Whenmultiple projection angles are acquired and the profiles Fourier Transformed, the alloverlap at the centre. This region corresponds to the low spatial frequencies of theobject (ie, the large, smooth structures in the body). As all profiles overlap at thecentre, this region of space is oversampled in proportion to the outer, higher frequencyareas. These high frequency areas carry information related to image edges and

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boundaries. Recall that 1/r blurring, a result of simple backprojection, didn’t have welldefined boundaries. This is because the low frequencies are oversampled and the highfrequencies are undersampled. This results in more low frequency object in theresultant reconstruction -> blurred image.

One method used to compensate for the lack of high frequency components inthe sampled data is to artificially accentuate the high frequencies. This is done throughthe use of appying a ramp filter to the projection data prior to backprojecting.

Thus,the

steps involved in filtered backprojection:

1. 1D Fourier transform profile data at a specific angle.2. Apply “ramp filter” to each Fourier Transformed projection profile.3. 1D inverse Fourier Transform back to data space.4. Simple backprojection.

When projection datagets ramp filtered, the highspatial frequencies are amplifiedand the low frequencies areattenuated. The result of this isthe upon inverse transformingthe data, negative lobes are nowpresent in the profile adjacent toareas of increased counts. Backprojecting this dataintroduces negative values tocertain object voxels that tend tocancel backprojected activities atother angles

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One of the problems with FBP using only a ramp filter is that the addition ofstatistical noise in the projection data is a high frequency phenomenon. By applying aramp filter to projection data, it accentuates this noise content, thereby producing noisyreconstructed activity distributions.

total # of photons collected %noisex-ray CT 1016 0.00025%SPECT 107 6%

In order to reduce this noise content, it is common to modify the ramp filter by alow pass filter in order to reduce the high frequency noise. Common filters includeButterworth, Hann and Shepp-Logan.

Direct Matrix InversionThe acquisition of activity projection measurements can be thought of as a

matrix-vector product. Consider a 2x2 object. When ordering these voxelsconsecutively, the activity present within each voxel is denoted as f1, f2, f3 and f4. Letthe number of counts collected along each ray be equal to g1, g2, g3 ang g4. Thus, theacquisition of the g’s can be thought of as consisting of:

g1 = f1+f2

g2 = f3+f4

g3 = f1+f3

g4 = f2+f4

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& &f H g= −1

or,

g

g

g

g

f

f

f

f

O r

g H f

1

2

3

4

1 1 0 0

0 0 1 1

1 0 1 0

0 1 0 1

1

2

3

4

=

=& &

g = projection data,H = system matrixf = object activity

Given g, we wish to find f. Notice that H is simply a property of the acquisition geometry(ie, number of angles, number of camera bins, etc).

So, a direct inversion would give us,

The problem is that, even for simple matrices like the above, H-1 does not exist in manycases. The problem is compounded because of:

1. Size - the system matrix, H, may contain as many as 1283 x 1283 elements for atypical 3D SPECT reconstruction. 2. Singularity - System matrix H may not be invertable (ie, determinate = 0).3. Nonuniqueness - H-1 may not be unique, will give different answers for each case.4. Ill-conditioned - Inverse may exist, but no account is made for image noise.

Iterative ReconstructionMore commonly now, analytical methods are falling out of favour and iterative

reconstruction methods are becoming much more prevalent. These methods are usefulas they are able to better model the transport of photons through the object and in thecamera. Generally speaking, iterative methods start with an estimate of the objectactivity distribution, and constantly refine that guess by comparing it with the actualmeasured data.

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Algebraic reconstruction technique (ART)Again, let g represent our measured data, and f represent the object activity that wewish to determine.

Additive ART:

Multiplicative ART:

Here N is the number of voxels along the ray that leads to the data g.

Example:

Step 1: Vertical rays

� � .

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13

Step 2: Horizontal Rays

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Step 3: Diagonal Rays

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At the end of 1 complete iteration:

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Generally speaking, the more reconstruction iterations performed, the closer theestimate will get to the correct answer. One caveat however. As more and moreiterations are performed, the algorithm will being matching the estimate to the noise inthe data, thereby producing noisier images. In order to control this, modifications havebeen made to the common iterative algorithms in order to preserve image smoothness. These are called maximum a posteriori (MAP) reconstructions.

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Problems in SPECT1. Depth dependent detector response

Recall that since collimator septa are a finite length, they will inevitably acceptphotons that do not come strictly from angles parallel to the holes. As the source tocamera distance increases, the acceptance angle also increases. The result of thiseffect is that object voxels further away from the camera are blurred over more camerapixels than object voxels closer to the camera.

In order to correct for this effect, it is possible to model the effect of detector response inan iterative reconstruction algorithm. This is done by altering the system matrix toreflect the true ray integral, rather than ideal strips.

2. Photon attenuation.As photons are emitted

from the location of radioactivedecay, some of these photons willinteract with the tissues of thebody. These interactions willtypically consist of coherentscattering, photoelectric effect andCompton scattering. No pairproduction will occur as photonenergies used in nuclear medicineare < 1 MeV.

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( )I I x y d l= − ∫0 exp ( , )µ

The deeper within the object the photon originates, the more likely it is to undergo aninteraction on it’s way to the detector. As a result, fewer photons are detected fromlocations deep within the object. When reconstructed, the object will not be uniformacross the field of view, but will rather have a higher activity on the periphery of theobject.

In order to correct for the effects of photon attenuation, object specificattenuation coefficients must be determined for each object voxel. One determined,these coefficients can be included in the reconstruction algorithm in order to account forthe attenuation. Recall from x-ray CT, that the total attenuation of an externalradioactive source is equal to:

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In order to determine these coefficients, several methods have been proposed, thatmainly focus on using an externally mounted radionuclide source (eg, Gd-153, Tc99m,Ba-133).

By measuring the photon flux both with and without the object present, it is possible todetermine the various patient specific attenuation factors. Once determined, thesefactors are included as additional modeling terms in an iterative algorithm.

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3. Photon ScatterAs we’ve seen previously, a large

fraction of the photons emitted from withinsoft tissue will undergo Comptonscattering on their way to the detector. These scattered photons affect thereconstructed image quality as they will beincorrectly positioned during thereconstruction process. Thus, it would bedesirable to remove these photons fromthe measured data, thereby reducing theirimpact on the reconstructed image quality.

Recall that the output data from the PMT’s goes through a multi-channelanalyzer in order to determine the total photon energy. Recall that Compton scatteredphotons have a decreased energy upon scattering, thus, it is possible to remove a largenumber of scattered photons from the measured data strictly by restricting the energiesof photons that we record. Thus, when imaging Tc-99m, we may choose to discard anyphoton with a detected energy less than 126 keV (140 - 10%). This will eliminate manyscattered photons from the photopeak acquisition window, but due to the relatively largeenergy resolution of NaI,(~ 10%), there will still be some scattered photons appearingwithin the photopeak window of 126-154 keV. In order to reduce these photons, we cansubtract off a proportional number of photons from the photopeak window that wouldcorrespond to the number of scattered photons. One method to do this is to use the

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( )Scatter P ho topeakW id thSca tterW indow C oun ts

Sca tterW indow W id th=

1

2

two energy window method (TEW).

By acquiring data in a narrow width energy window lower than that of thephotopeak, it can be assumed that only scattered photons are present within thiswindow. As the width of this window is known, and the width of the photopeak windowis also known, the number of counts within the photopeak window as a result of scattercan be found by:

For the case of scatter on both sides of the photopeak (eg, from imaging a dual energyemitter) , we can estimate the scatter within the photopeak by using narrow windows onboth side of the photopeak and using the triple energy window method (TEW). Thescatter can be estimated as:

( )Sca tter P ho topeakW id thL ow erW indow C oun ts

L ow erW indow W id th

U pperW indo w C oun ts

U pperW indo w W id th= +

1

2

Once the scatter is known, these photons can be subtracted from the photopeak data. Note however, that the true scattered photons are not subtracted, but rather, just aproportional number of photons that would be due to scatter.

Positron Emission Tomography

Recall that in SPECT imaging, we use radionuclides that emit a single photon. Individual photons will be detected on the camera. However, in order to determine thdirection from which the photon originated, we relied on a large lead collimator in orderto limit the photons collected. In PET imaging, as we will see, the collimator is notrequired because we use electronic collimation.

PET imaging relies on using radionuclides that decay via + decay. With this type ofdecay, a positron is produced that is emitted from the nucleus of the atom undergoingdecay. Recall that the energy of the decay reaction is shared between the positron andthe neutrino. Depending on the energy of the emitted positron, it will travel a shortdistance in the medium prior to coming to rest and colliding with an electron andundergoing a process known as annihilation. When this occurs, the positron andelectron are converted into two photons that have energy equal to the rest mass of theparticles (ie, 511 keV each) and are emitted in opposite directions.

The distance from the location of the +decay, to the point of annihilation is known asthe positron range.

In order to determine the location of the initialdecay, it is necessary to detect both emittedphotons resulting from the annihilation. Thisis possible by using two detectors placed180

�

apart.

1

When both photons are detected within a very short time interval (called the coincidencewindow, ~12 ns), it can be assumed that the initial decay event occurred somewherealong the line connecting the two detectors. We don’t know exactly where along the linethe event occurred, but we leave it to the reconstruction algorithm to find out.

With the detector geometry described, we will only ever be able to detect events alongone line. In order to perform tomography, we either have to rotate this detector array, oruse a lot more detectors. This is the approach takenin most PET scanners. Most PET scanners todayuse a ring of scintillationdetectors surrounding theobject under study.

Within each ring, eachdetector is free to work inconjunction with a numberof detectors on theopposite side of the ring. That is, when a photonenters one detector, all

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detectors opposite it are free to detect the coincident photon. Once detected, a line isdrawn connecting the two detectors that were in coincidence thereby creating what isreferred to as a line of response (LOR).

Each line of response in the scanner has a unique angle and offset from the origin,. This means that each line of response can be mapped to a specific location in asinogram. Thus for each coincidence pair detected in coincidence, a single location inthe sinogram will be increased by 1.

After a number of coincidence pairs have been detected, a full sinogram will have beencreated. At this point, tomographic image reconstruction can be done using either ananalytical method such as filtered backprojection or iterative methods.

Event types1. True coincidence

A true coincident event is when both emission photonsare detected by opposing detectors within a specified timewindow (typically 6-12 ns). These are also called promptevents.

2. Scattered coincidenceRemember in SPECT, it is possible that a photon will

undergo a Compton scatter within the object being imaged priorto being detected by the camera. When this occurs, the point ofthe decay emission is incorrectly localized in the reconstruction,resulting in image artifacts. It is possible that in PET, photonscatter will also occur and that the scattered photon will still bedetected. When this occurs, the line of response will beincorrectly identified and reconstructed with artifacts.

3. Random coincidence

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It is important in PET imaging that only the two photons released as a result ofannihilation get detected within the coincidence window.Because of the relatively short transaxial field of view ofmost PET scanners (~15 cm long), most photons will notbe detected as a coincidence pair. It is in fact, more likely,that only one of the coincident photons will be detected. When this occurs, it is called a single event and must bedisregarded from the acquisition process.

Because of the large numbers of photons beingemitted in PET (~ 200 Mbq), there is a large chance thattwo single events will get detected within the coincidencewindow. When this happens, the two events are regardedas a random coincidence as they cannot be discernedfrom a true coincidence. In order to correct for these false events, a certain number ofevent are subtracted off from the measured coincident events. The rate of randomevents being accepted as coincidences is equal to:

Rrandom�Tcoin×R 2singles

where T_coin is the coincidence timing window and R_singles is the rate of single eventbeing detected.

PET detectorsBecause of the higher energy photons (511 keV) emitted in + decay compared

to SPECT imaging, PET scanners require detectors that have much greater probabilityof stopping the incoming photons. For this reason, most PET scanners use either BGOor LSO scintillator.

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Attenuation Correction in PETRecall that in SPECT, because of the different depths of decay within the imaged

objects, significant photon attenuation may occur between the point of decay anddetector. Such an effect reduces the number of photons detected vs depth and resultsin artifacts in the reconstructed images unless accurately corrected for during thereconstruction process (a non-trivial correction in SPECT). As we will see, the situationin PET is even worse, but the correction methods are quite easy.

Consider the geometry of a single positron source in a water bath as below:

The point source is at depth x. Photons emitted from the source will be measured incoincidence by detectors 1 and 2. Notice however, that as the photons are emittedtowards the detectors, they will be attenuated by the medium, thereby reducing the

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number actually detected. The probability of each photon being attenuated is:

P1�e � µx and P2�e � µ(T� x)

The total probability of a coincidence pair being attenuated prior to being detected issimply P1*P2 or,

Ptotal�P1P2�e � µT

So, the probability of attenuating photons along a given line of response is simply equalto the total attenuation along that LOR. This means, that if we know the totalattenuation along each LOR, we can rescale the measured data to account for thisdecrease in counts due to attenuation. We can typically determine what the scalingfactor is for each LOR by using an external radioactive source, and finding what thetotal attenuation factor is for each LOR. Once determined, we then rescale themeasured emission data by this factor in order to correct for attenuation.

Common Radiopharmaceuticals used in PETMost radionuclides used in PET imaging are very short lived (ie, half-lives < 2

hours). This means that most of them have to be produced as needed for imaging,typically with an on-site cyclotron. Some nuclides like Rb-82 can be produced via agenerator, thus negating the need for an on-site cyclotron, thereby reducing cost. As

well, F-18 (T1/2 = 110 min) can often be created with a cyclotron and shipped to thelocation needed for imaging, provided it is only a short distance away.

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Clinical Applications of PET Oncology with F-18 labelled Fluoro-deoxy glucose (FDG)

FDG is a sugar analog that behaves in a very similar manner as sugar, being taken upin regions of the body with a higher metabolism (ie, tumours). However, unlike glucose,once metabolised, the F-18 remains fixed in the cells, thus allowing it to be imaged.

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Cardiac viability

In coronary artery disease, the coronary arteries become clogged, thus reducingthe flow of blood to certain regions of the myocardium, and impairing the ability of theheart to pump enough blood to sustain the body. We have already seen in SPECT howTc-99m imaging can be used to determine regions that have reduced blood flow(perfusion).

In regions with impaired perfusion, myocardial infarction (tissue death) with set inif the regions are without blood for too long. Over time, the regions under-perfusedbecome starved for blood and in desperation to remain alive, the myocardial cells switchfrom metabolizing fatty acids (normal myocardial fuel), to metabolizing glucose. If thecells have been starved for blood for too long, the cells will die and will no longermetabolize sugar. Thus, in cardiac viability imaging, we wish to determine which areasof the heart are ischemic (reduced blood flow), but whether these regions are still viablewith tissue if surgical bypass can be performed. That is, we want to look for a mismatchbetween areas that have low perfusion, and those that have high glucose metabolism. For this we use PET imaging with two different radiotracers, N-13 labeled NH3 and F-18FDG. The NH3 image depicts tissue perfusion, while FDG imaging depicts glucosemetabolism.

Low FDG High FDG

Normal NH3 normal normal

Low NH3 infarct (non-viable) viable

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Brain receptors 18F-labeled PET tracers are used in neurology to study metabolism,neurotransmission, and cell processes. L-[18F]DOPA can be used to examine thepresynaptic distribution of stored neurotransmitter. L-DOPA is the precursor for theneurotransmitter dopamine and radiolabeled L-DOPA is taken up by dopaminergicterminals and becomes incorporated into the neurotransmitter. L-[18F]DOPA has beenused clinically in the study of Parkinson's disease.

FDG

FDG

F-DOPA

Normal Parkinson

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