The Positron Emission Tomography Computer Science Essay

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Positron emission tomography (PET) is a powerful diagnostic tool that is having a major impact on the diagnosis and treatment of disease. It is a nuclear medical imaging technique which produces a 3-d map of functional processes in the body, which was first developed at the Washington University School of Medicine in1975. Disease is a biological process and while x-ray or CT scans show only structural details of tissues and organs, a PET scan is a biological imaging examination which gives physicians important early information about cancer, heart disease and many neurological disorders like Alzheimer's.

Figure 2: Schematic of a PET acquisition process

How it operates:

A PET scan measures the vital functions of the tissues and organs of the body, such as blood sugar (glucose) metabolism, blood flow and oxygen use. This imaging can be used to help distinguish between normally functioning and malfunctioning tissues. A tracer is injected into a patient, as different tissues in the body function differently they absorb different radionuclides; therefore the radionuclide administered depends on the organ that is to be investigated. The number positrons emitted by an organ or tissue indicates how much radioactive substance was absorbed by that area of tissue and is therefore indicative of how chemically active it is.

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For example, areas that absorb more glucose are more metabolically active and appear brighter on a PET scan. Areas that don't use as much energy or that are damaged in some way do not absorb as much glucose and therefore appear dimmer on the PET scan.

Radionuclides, also referred to as radioisotopes, are atoms with an unstable nucleus, which is a nucleus characterised by excess energy. Such radioisotopes of familiar elements such as carbon, nitrogen, and oxygen can serve as tracers because they are very similar to the non-radioactive nuclides, so most chemical, biological processes treat them in a near identical way. These radioisotopes can be used in medicine for diagnosis and research. Radioactive chemical tracers emitting gamma rays or positrons can provide diagnostic information about a person's internal anatomy and the functioning of their organs. It is on this principle that PET operates.

Figure 3: Electron-positron collision producing annihilation gamma rays

To conduct a scan, a short-lived radioactive isotope which has been chemically incorporated into a metabolically active molecule, is injected into a patient, this radioactive isotope undergoes positron emission decay (also known as positive beta decay). A positron is the antimatter counterpart of the electron, and when matter collides with its corresponding antimatter, both are annihilated. Therefore after travelling up to a few millimetres the positron encounters an electron, and the collision produces a pair of annihilation gamma rays (photons). These gamma rays have the same energy and have almost opposite directions. The gamma rays leave the patient and are detected when they reach a scintillator material in the scanning device.

Figure 4: Schematic of a photomultiplier tube coupled to a scintillator

A scintillator is a substance (inorganic crystals, organic plastics and liquids) that absorbs high energy (ionising) electromagnetic or charged particle radiation, converts the energy to light of a wavelength which can be detected by inexpensive detectors, such as photomultiplier tubes (PMTs). PMTs are extremely sensitive detectors of light in the ultraviolet, visible and near infrared. These detectors multiply the signal produced by incident light by up to 108, from which single photons can be resolved. These devices have high gain, low noise and a high frequency response. Photomultipliers are constructed from a glass vacuum tube which houses a photocathode (a negatively charged electrode coated with a photosensitive compound (a compound which reacts upon receiving photons of light)), several dynodes and an anode (a positively charged electrode). Incident photons strike the photocathode material which is present as a thin deposit where the photon enters the device, with electrons being produced as a consequence of the photoelectric effect. These electrons are directed by the focusing electrode towards the electron multiplier, where electrons are multiplied by the process of secondary emission. The electron multiplier consists of a number of electrodes, called dynodes. Each dynode is held at a more positive voltage than the previous one. The electrons leave the photocathode equal in energy with the incident photon minus the workfunction of the photocathode. As they move towards the first dynode they are accelerated by the electric field and arrive with a much greater energy. On striking the first dynode more lower energy electrons are emitted and are in turn accelerated towards the second dynode. The layout of the dynodes is such that a cascade occurs with an ever increasing number of electrons being produced at each stage. Finally the accumulation of charge arrives at the anode resulting in a current pulse indicating the arrival of a photon at the photocathode. If used in a location with high magnetic fields (which will curve the electron paths), they are usually shielded by a layer of mu-metal (a nickel-iron alloy (75% nickel, 15% iron, with copper and molybdenum) that has very high magnetic permeability). Avalanche photodiodes are sometimes used. They can be considered the semiconductor analog to photomultipliers.

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The PET technique depends on the simultaneous detection of photons. Photons which do not arrive in pairs, within a few nanoseconds of each other, are ignored. The most significant fraction of electron positron decays result in gamma photons being emitted of equal energy (511 keV) and at almost 180°to each other; therefore it is possible to localise their point of origin along a straight line of coincidence, known as the line of response (LOR). If the recovery time is in the picosecond (10-12) range rather than the nanosecond (10-9) range, it is possible to calculate the single point on the LOR at which the annihilation event originated, by measuring the time of flight of the photons. Using statistics from tens-of-thousands of coincident events, a set of simultaneous equations for the total activity of each section of tissue along numerous LORs can be solved by a number of techniques, and hence a map of radioactivities as a function of location for sections of tissue may be constructed and plotted. The resulting map shows the tissues in which the tracer has become concentrated.

PET scans are increasingly read alongside CT or MRI scans, the combination (co-registration) gives both the anatomic and metabolic information about the body (what the structure is, and how it is functioning biochemically). Because PET imaging is most useful in combination with anatomical imaging, such as CT, modern PET scanners are now available with integrated CT scanners. Because the two scans can be performed simultaneously during the same session, without the movement of the patient, the two sets of images are more precisely registered, so that areas of abnormality on the PET scan can be more perfectly correlated with the anatomical images produced from the CT images.

Figure 5: CT data top left, PET data top right. Overlaying the top two images produces the bottom image allowing for precise location of tumors.

Image Reconstruction:

The raw data collected by a PET scanner are a list of coincidence events representing near simultaneous detection of annihilation photons by a pair of detectors. Each coincidence event represents a line in space connecting the two detectors along which the annihilation event occurred. Filtered back projection (FBP) and the iterative expectation-maximisation algorithm are both frequently used to reconstruct images from the projections.

FBP is based on the Radon transform, which is closely related to the Fourier transform. The Radon transform in two dimensions, is the integral of a function over straight lines. It is the inverse of the Radon transform that is used to reconstruct images from medical computed tomography scans. We define the Radon transform of a function f on the plane (where it is assumed to be continuous) by:

In the context of tomography, the Radon transform is often called a sinogram because the Radon transform of a Dirac delta function (an approximation for a tall narrow spike, an impulse) is a measure, with support on a graph, of a sine wave. Therefore the Radon transform of a number of small objects appears graphically as a number of blurred waves with different amplitudes and phases. The original image f can be recovered from the sinogram data g using the equation:

where,

is commonly called the back-projection and

is defined as a ramp filter.

As the filtering step can be performed efficiently (e.g. using digital signal processing techniques) and the back projection step is simply an accumulation of values in the pixels of the image, this results in a highly efficient, and hence widely used algorithm.

An expectation-maximisation (EM) algorithm is used in statistics for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on the unobserved latent variables. Latent variables are variables that are not directly observed but are rather inferred (through a mathematical model) from other variables that are observed and directly measured. EM alternates between performing an expectation (E) step, which computes an expectation of the likelihood by including the latent variables as if they were observed, and a maximisation (M) step which computes the maximum likelihood estimates of the parameters by maximising the expected likelihood found on the E step. The parameters found on the M step are then used to begin another E step, and the process is repeated. The EM algorithm is widely used in medical image reconstruction, especially positron emission tomography and single photon computed tomography.

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The FBP algorithm has the advantage of being simpler while having a low requirement for computing resources. However, noise is prominent in the raw data in reconstructed images and areas of high radioisotope absorption tend to have streaks across the image. Iterative expectation-maximisation algorithms are now the preferred method of reconstruction. The advantage is a better noise profile and resistance to the streaking across the image with is a common occurrence in FBP, however the disadvantage is higher computer resource requirement.

Attenuation Correction:

As different LORs must traverse different thicknesses of tissue, the photons are attenuated differentially. The result is that structures deep in the body are reconstructed as having incorrectly low tracer absorption. Modern scanners can estimate attenuation using integrated x-ray CT equipment. While corrected images are generally more accurate representations, the correction process itself is susceptible to significant inaccuracies. As a result, both corrected and uncorrected images are always reconstructed and read together.

Radioisotopes used in PET:

Radioisotopes used in PET scanning are typically isotopes with short half lives.

Labelling Agent

Half Life

carbon-11

~20 mins

oxygen-15

~2 mins

fluorine-18

~110 mins

bromine-75

~98 mins

nitrogen-13

~10 mins

Table 1: Common radioisotopes and their half-lives

These radionuclides are incorporated into compounds which are normally used by the body such as, glucose, water, or ammonia and then they are injected into the body where they become distributed. The isotope used is dependant on which body function is being studied. Oxygen-15 can be used to label oxygen gas for the study of oxygen metabolism, carbon monoxide for the study of blood volume, or water for the study of blood flow. Similarly, fluorine-18 can be attached to a glucose molecule to form FDG for use in the study of metabolism. The small size of the radiation dose to the patient is an attractive feature of the use of these radioisotopes. PET scans using radioactive fluorine FDG would result in patients receiving exposures comparable to (or less than) those from other medical procedures, such as x-rays. Other tracers e.g. 6-F-dopa or radioactive water normally result in even less exposure. Many more radionuclides exist and even more are being developed to assist in the observation and exploration of the functioning of the different organs and tissues in the body. For example, dopa, a chemical active in brain cells, is labelled with positron emitting fluorine or carbon and applied in research on the communication between certain brain cells which are diseased, as in Parkinson's disease or schizophrenia.

Applications of PET imaging:

PET is both a medical and research tool.

Cancer:

Pet scans are hugely important in clinical oncology; they are useful in determining the extent of the spread of certain cancers, assessing how the cancer responds to treatment and determining if the cancer has recurred. Cancers may use more energy than surrounding tissues and therefore appear brighter on the PET scan. As can be seen from the table PET scanning has made vast improvements on the diagnostic accuracy of many different types of cancer. PET scanning is also a valuable resource in assessing how certain cancers respond to chemotherapy.

Table 2: Diagnostic accuracy

(Source: The Journal of Nuclear Medicine Supplement, Vol. 42, no. 5, May 2001 & UCLA)

Figure 6: Normal PET scan left, PET scan showing abnormal lymph nodes centre, PET in woman with breast cancer that has spread to bones right

Heart Problems:

Doctors use PET scanning to detect areas of decreased blood flow in the heart. A pet scan may reveal early coronary artery disease and damaged heart muscle due to a heart attack. It can also differentiate nonfunctioning dead heart muscle from poorly functioning heart muscle which would benefit from a procedure such as heart surgery, angioplasty or coronary artery bypass surgery, to increase blood flow to the heart muscle. A PET scan can be particularly important to people who have previously had heart attacks.

Brain Disorders:

A PET scan can detect mild physiological changes in the brain even before any signs or symptoms of Alzheimer's disease are evident and before severe damage to the brain or memory loss can occur. PET scanning can also provide visual images of activity in the brain when a person is asked to read, talk to listen to music, making it a valuable tool in research into how the brain functions and can also be important in differentiating Alzheimer's disease from other types of dementia such as frontal dementia and Huntington's disease. A PET scan can also be used to help locate the origin of abnormal brain activity associated with seizures due to epilepsy and assess brain function after a stroke. In the future, doctors may also use a PET scan to detect memory disorders and certain mental health disorders, such as schizophrenia and depression. Such uses are currently being investigated.

Figure 7: Healthy 70 year old patient top, patient with Alzheimer's centre, patient with brain tumor bottom

Figure 8: PET scan of brain for depression. A PET scan can compare brain activity during periods of depression (left) with normal brain activity (right).

Limitations of PET:

PET scanning is an invaluable diagnostic and research tool that is having a major impact on diagnostic accuracy and on the treatment of a wide range of diseases. Besides its role as a diagnostic technique, PET has an expanding role as a method to assess the response to therapy, in particular, cancer therapy. However there are limitations preventing the widespread use of PET which arise from the need for cyclotrons which are needed to produce the short-lived radionuclides for PET scanning and the need for specially adapted on-site chemical synthesis apparatus to produce the radiopharmaceuticals, which can be prohibitively expense. Few hospitals and universities are capable of maintaining such systems, and most clinical PET is supported by third party suppliers of radiotracers which can supply many sites simultaneously. This limitation can restrict the PET scanning to the use of tracers labelled with radioisotopes with longer half-lives such as fluorine-18 (~110 mins) and bromine-75 (~98 mins) facilitating the transport of the tracers to the PET scan location. Nevertheless, in recent years a few on-site cyclotrons with integrated shielding and hot labs have begun to accompany PET units to remote hospitals. The presence of the small on-site cyclotron promises to expand in the future as the cyclotrons shrink in response to the high cost of isotope transportation to remote PET machines, therefore the importance of PET in diagnostic medicine can only increase.