Radioactive decay is arandom process and therefore fluctuations are expected in the radioactivity measurement. That is why measurement of radioactivity must be treated by statistical methods.

In every measurement a deviation from the true value or error is likely to occur. There are two types of errors - systematic and random.   The accuracy of a measurement indicates how closely it agrees with the true value. The precision of a series of measurements describes the reproducibility and indicates the deviation from the average or mean value. The closer the measurement is to the average value, the higher the precision, whereas the closer the measurement is to the true value, the more accurate is the measurement. It is important to keep in mind, that a series of measurements may be quite precise but their value may be far from the true value. Precision can be improved by eliminating the random errors, better accuracy is obtained by removing both the random and systematic errors.

The average or mean value is obtained by adding the values of all measurements divided by the number of measurements. The standard deviation indicates the deviation from the mean value and is a measure of precision. The standard deviation in radioactive measurements indicates the statistical fluctuations in radioactive disintegration. If the number of measurements is large, the distribution can be approximated by a Gaussian distribution even if the radioactive decay follows the Poisson distribution law. For practical reasons, only single measurement is obtained on radioactive sample instead of multiple repeat counts to determine the mean value.  The precision of a count of a radioactive sample can be increased by accumulating a large number of counts in a single measurement because of decreasing the standard deviation.

All radiations may interact with the atoms of the matter during their passage through it producing ionization and excitation of the atoms. These radiations are called ionizing radiation. The mechanism of interaction differ for particulate and electromagnetic type of radiation.

The interaction of beta particles as a charged particles and gamma radiation as an electromagnetic radiation is the most important from the point of view of using them in nuclear medicine.

Beta particles interact primarily with the electrons of the absorber atoms and rarely with the nucleus.

Ionization occurs when beta particle transfers sufficient amount of its energy to the orbital electron and ejects it from the atom. As a result ion pair is formed. This process may rupture chemical bonds in the molecules. Ionization is used namely in the radiation therapy and also serves as a mean of the detection of charged particles in ion chambers.

When energetic beta particles, namely electrons, pass close to the nucleus of the atom, they lose energy as a result of deceleration. This loss of energy appears as an x ray and is called bremsstrahlung. Bremsstrahlung production increases with the kinetic energy of the beta particles and the atomic number of the absorber. That is why high energy beta particles are stored in plastic rather than shielding by lead.

Beta plus particles, positrons, combine with the orbital electrons and produce two 511 keV photons of gamma radiation, so called annihilation radiation, that are emitted in exactly opposite directions. This is the basis of positron emission tomography.

Gamma rays interact with orbital electrons and if their energy is very high they may also interact with the nucleus of the absorber atoms. They travel a long path in the absorber before losing all energy and so they are called penetrating radiations.

There are three mechanisms by which gamma rays interact with absorber atoms from which two are important for nuclear medicine.

Photoelectric effect means transfer of all energy of gamma photon to an orbital electron, called photoelectron, and ejecting it from the atom. The photoelectron then loses its energy by ionization and excitation.

Compton scattering means transfer of only a part of energy of gamma photon to an electron and ejecting it. The gamma photon with less energy is deflected from its original direction. The scattered photon may then undergo further photoelectric or Compton interaction and the Compton electron may cause ionization or excitation.

Depending on the photon energy and the density and thickness of the absorber, some photons may pass through the absorber without any interaction.

Attenuation of gamma radiations by means of their interaction with absorber is an important factor in radiation protection. The term half-value layer is defined as the thickness of the absorber that reduces the intensity of a photon beam by one half. It depends on the energy of the radiation and the atomic number of the absorber.

Interaction of ionizing radiations with the matter is also used for their detection and measurement. There are several principles of radiation detection in nuclear medicine. Some of them are used in radiation protection, others in measurement and imaging.

The oldest principle is darkening of photographic emulsion. This principle is used in the personnel dosimetry. The film badge is most popular and cost-effective for personnel monitoring and gives reasonably accurate readings of exposures from beta, gamma and x radiations. The film badge consists of  a radiation sensitive film held in a plastic holder. Filters of copper and lead are attached to the holder to differentiate exposure from different types and energies of radiation.

Another principle is thermoluminiscence. Several inorganic crystals (e.g. LiF) can accumulate radiation energy and hold it. If the crystal is heated from 300 to 400 degrees of Celsius, it emits light in amount  proportional to the absorbed energy. Thermoluminiscent dosimeters, so called TLD, are mostly used as a finger dosimeters, so inorganic crystals are held in a plastic holders and plastic rings. It gives an accurate exposure reading and can be reused.

Another principle is converting the energy of radiation to electric current. There are two basic principles based on ionization and excitation.

First is ionization of gas molecules, the second is excitation and ionization of solid, liquid or plastic material, called scintilator,  which emits photons of light after absorbing radiation. Light is then converted to the electric current by means of photomultiplier tube.

Gas-filled detectors collect the ion pairs as a current with the application of a voltage between two electrodes. The measured current is proportional to the aplied voltage and the amount of radiation.

At a lower voltages from 50 to 300 V, only the primary ion pairs formed by the initial radiation are collected. Ionization chambers operate in this region. The detector is a cylindrical chamber with a central wire filled with air or different gases. These detectors are primarily used for measuring high intensity radiation. Dose calibrators and pocket dosimeters are the common ionization chambers used in nuclear medicine.

The dose calibrator is one of the most essential instrument in nuclear medicine for measuring the activity of radionuclides and radiopharmaceuticals. It must be regularly checked for constancy, accuracy, linearity and geometry.

At higher voltages from 1000 to 1200 V, the current becomes identical regardless of how many ion pairs are produced by the incident radiation. Geiger-Müller counters operate in this region. Geiger-Müller counters are used to monitor the radiation level in different work areas and they are called area monitors or survey meters. They are more sensitive than ionization chambers but they cannot discriminate between energies. They are almost 100% efficient for counting alpha and beta particles but have only 1 to 2% efficiency for counting gamma and x rays.

Scintillation detectors consist of scintilator emitting flashes of light after absorbing gamma or x radiation. The light photons produced are then converted to an electrical pulse by means of a photomultiplier tube. The pulse is amplified by a linear amplifier, sorted by a pulse-height analyzer and then registred as a count. Different solid or liquid scintillators are used for different types of radiation. In nuclear medicine, sodium iodide solid crystals with a trace of thallium NaI(Tl) are used for gamma and x ray detection.

The basic solid scintillation counter consists of na NaI(Tl) crystal or detector, a photomultiplier (PM) tube , a preamplifier, a linear amplifier, a pulse-height analyzer (PHA) and a recording device.

NaI(Tl) crystals are hermetically sealed in aluminium containers. They are fragile and must be handled with care. Room temperature should not be changed suddenly because of possibility of cracks in the crystal. In well counters and thyriod probes smaller and thicker crystals are used, whereas larger and thinner crystals are employed in imaging devices like gamma cameras.

PM tube consists of a light-sensitive photocathode facing the crystal, series of dynodes in the middle and an anode at the other end - all enclosed in a vacuum glass tube. A high voltage about 1000 V is applied between the photocathode and the anode of the PM tube. The electron pulse reaching  the anode is delivered to the preamplifier. The amplitude of the pulse is proportional to the number of light photons received by the photocathode and in turn to the energy of gamma ray photon absorbed in the crystal. The applied voltage must be very stable.

A linear amplifier amplifies further the signal from the preamplifier and delivers it to the pulse height analyzer for analysis of its amplitude.

A pulse height analyzer is a device that selects for counting only those pulses falling within preselect voltage intervals and rejects all others. Desired pulses are ultimately delivered to the recording devices such as scalers, computers, films and so on.

In the output of scintillation counter a distribution of pulse heights will be obtained depicting a spectrum of gamma ray energies. In an ideal situation each gamma ray would be seen as a line on the gamma ray spectrum. In reality, the photopeak is broder, which is due to various statistical fluctuations in the process of forming the pulses.

When gamma rays interact with the scintillation crystal by means of Compton scattering, the Compton electrons of variable energies result in a pulse height smaller than that of photopeak. Thus the gamma ray spectrum will show a continuum of pulses corresponding to Compton electron energies between zero and photopeak, so called Compton continuous spectrum. The relative hights of the photopeak and the Compton scattering depend on the photon energy as well as the size of the crystal.

There are several basic characteristics of counters important from the point of view of using them in nuclear medicine procedures.

Background of the detector  means registered count rate without presence of any measured specimen. It is caused namely by cosmic radiation, natural radioactivity, radioactivity of building material and of the material the detecting system consists of. It can be minimized by shielding detector in lead cover, by using special material for its construction or by means of pulse-height analyzer to exclude inappropriate radiation energy from detection.

The energy resolution simply means the width or the sharpness of the photopeak or the ability to discriminate  the gamma ray photons of similar energies.

The detection efficiency is given by the observed count rate divided by the disintegration rate of a radioactive sample. It depends on the type and energy of  the detected radiation, size and thickness of the detector crystal and geometric efficiency of the measuring.

The dead time is the time period during which the counter is insensitive for the radiation detection. This time enclosed time needed to process a radiation event starting from interaction in the crystal all the way up to forming and recording pulse. Dead time for Geiger-Müller detectors is from 100 to 500 microseconds, for NaI(Tl) crystal from 0,5 to 5 microseconds. Dead time loss of counts is a serious problem at high count rates. Either count rates must be lowered or corrections must be made to the observed count rates.

Scintillation detectors can be used as a part of both nonimaging and imaging devices. From the nonimaging devices, scintillation well counters and thyroid probes are used.

The gamma well counter consists of a scintillation detector with a hole in the center, for a sample to be placed inside for increasing the geometric efficiency and hence the counting efficiency of the counter, and other associated electronics. Well counters are used namely for in vitro measurements of different samples. They are usually available with automatic sample changers and are mostly programmable with computers. Their major advantage is high detection efficiency which is from 50% to 70%  for 140 keV gamma photons.

The thyroid probe is a scintillation counter used for measuring radioacitivity above the thyroid gland to assess the uptake of 131I after its oral administration. In contrast to well counter the thyroid probe must be equipped with collimator, which limits the field of view. This is a cylindrical barrel made of lead and it covers all the detector including PM tube. It prevents the gamma radiations from other organs to reach the detector.

Radionuclide imaging is based on the ability to detect electromagnetic radiation emitted from an injected radioactive tracer that has been taken up by the organ to be studied. The electromagnetic radiation used is in the form of gamma rays or x rays. The radiation absorbed by the detector is used to generate a digital image by the computer, which is then interpreted by the physician.  This imaging device is called scintillation camera or gamma camera. It also employs sodium iodide scintillation detector and the associated electronics like nonimaging systems do.

The most frequently used scintillation camera is of Anger type (Hal O. Anger invented it in the 1960), it means it has a large scintillation crystal which makes possible to detect radiation from the entire field of view simultaneously and therefore it is capable of recording dynamic as well as static images of the area of interest in the patient. Many sophisticated improvements have been made of the cameras over the years, but the basic principles of the operation are essentially the same.

Like nonimaging probe also scintillation camera consists of  a collimator, a scintillation crystal, PM tubes, a preamplifier, an amplifier, a pulse-height analyser and recording or display devices. In addition it must have an X,Y positioning circuit to localize the point of interaction of gamma ray with the crystal. The operation of a camera is performed by a computer built in it and is very convenient for the staff. The detector head (collimator, scintillation crystal, PM tubes and amplifiers) is mounted on a stand called gantry, which moves the head to the appropriate position for patient imaging.

Detectors have usually large (about 50 cm in diameter) circular or rectangular NaI(Tl) crystal with about 1 cm thickness. In front of the crystal, a collimator is attached to limit the field of view so that gamma radiations from outside the field of view cannot reach the crystal.

Collimator is usually a plate of lead with many holes. Most frequently used are parallel-hole colimators with holes parallel to each others and perpendicular to the detector face. They are of different types according to energy of radionuclides used for imaging and according to their spatial resolution. Thus we can distinguish high resolution, high sensitivity and all purpose (with compromise parameters) types or low, medium and high energy types. The spatial resolution of the parallel-hole collimators decreases with the increasing distance of the object from the front of the collimator but the sensitivity is the same. That is why every data collection must be performed with the minimal space between collimator forhead and the patient body surface.

The collimator of conical shape with one up to three holes on the top is called pinhole and is used for imaging of small and near to the surface lying organs, such as a thyroid gland, tight join or infant kidneys. It has very good resolution but very poor sensitivity. Nowadays also collimators with special converging holes called fan-beam are made for small organs imaging, such as a brain. Also collimators with diverging holes can be used, namely in cameras with small crystal to make possible imaging of large organs. Collimators designed for higher energy are thicker with thicker septa between holes to prevent penetration of photons through them.

Gamma cameras have many photomultiplier tubes (up to 90) mounted to the back of the crystal with optical grease. They are used to be of hexagonal shape and the output from each is used to define the X and Y coordinate of the point of interaction of the gamma ray in the crystal by the use of an X,Y positioning circuit. The X and Y pulses are than projected on a cathode ray tube or oscilloscope to create image or can be stored in the computer in a square matrix for further processing.  The larger the number of PM tubes, the better the spatial resolution on the image.

The use of digital computers in nuclear medicine has considerably increased and today all nuclear medicine studies are being analyzed by the computers. Data from a gamma camera must be digitized by the analog-to-digital converter. The computer memory approximates the area of the detector as a square matrix from 32x32 up to 1024x1024 size. Each element of this matrix is called pixel and corresponds to a specific X and Y location in the detector. The number in each pixel corresponds to the number of pulses detected in this specific location of the crystal. In this manner of storing data in computer memory, called frame mode (the most common mode in nuclear medicine), we must preset the matrix size, the number of images (frames) in the study, and the time of collection of data per frame or total counts to be collected per frame.

Computers are very important part of imaging devices, current cameras cannot operate without it, namely ECT is impossible without computers. The basic function of computers during image construction is to correct and maintain cameras performance parameters, such as high voltage in the PM tubes and photopeak setting in pulse-height analyzer.

Another improvement of image quality is achieved by images smoothing and filtering, mathematical operation with images, background subtraction, creation of parametric and tomographic images, regions of interest (ROI) creation, dynamic curves creation and their mathematical processing with computing quantitative data of physiological processes, by using of  interpolation to reduce digital raster effect on matrix image, smoothing images by means of temporal and spatial filters or by color coding according to number of counts in each pixel.

Very important camera parameter, field of view uniformity, can be effectively improved by means of computers. Detector uniformity means a uniform response throughout the field of view. Even properly tuned and adjusted gamma cameras produce nonuniform images with count density variation of up to 10%.  There are several possibilities of using computer for nonuniformity correction. These are: correction of number of counts in each pixel of image matrix to an average value, setting of the own photopeak for each pixel in image matrix, different gain of high voltage for each photomultiplier tube and spatial distortion correction.

To ensure a high quality of images, quality control tests must be performed routinely on these devices. The most common tests are the positioning of the photopeak, field of view uniformity and background check, which must be performed daily. The spatial resolution of the camera should be checked weekly.

This type of Anger gamma camera provide two dimensional images and that is why it is also called planar camera. According to the type of metabolic processes and the type of data recording we can distinguish two basal type of collecting data.

During static acquisition ofimages we can evaluate distribution of radiopharmaceuticals in the organs, which does not change in time. To achieve good information density of images, we must preset proper acquisition time according to registered count rate or we must preset needed number of collected counts. Except acquiring images with the same size and shape as detector has we can also acquire a so called whole body images. In this type of data collection patient on the examining table passes under or over the detector and the image of radioactivity distribution in the whole body can be obtained. The velocity of the patient movement is again done by the registered count rate to ensure good image information density. Since radioactivity distribution does not change significantly, we can collect data for a longer time period and thus high resolution collimator should be used.

The second type of collecting data, during which we can evaluate differently fast metabolic or functioning processes in the body (blood flow), is called dynamic study. According to velocity of assessing processes we must preset number of images (frames) and duration of one image. Because distribution of radiopharmaceuticals changes rapidly and duration of one frame acquisition is limited (up to split second), high sensitivity collimators should be used to achieve sufficient image information density.

A special kind of collecting data is gated or synchronized method. It is used for acquiring a periodical organ activity, such as heart mechanical function. In this example ECG signal is used for synchonization and by this way to collect data with very high temporal resolution is possible. In principle, computer divides each R to R interval into several intervals, for example twenty. Each interval has its own number, in this example from one to twenty, is presented as a frame in the computer memory and its duration is of tens miliseconds. After R interval detection by computer, data are stored into the frame number one, after the time of one frame duration is over data are stored into frame number two and so forth till the further R wave is detected. From this point all the process is repeated and by this way several hundreds heart cycles are summed into one, so image information density is sufficient for further processing.

On planar images, the third dimension of displayed objects is obscured by superimposition of data. Therefore tomographic devices have been developed. Primarily, so called longitudinal tomography was used, which display sharply only one slice parallel to the face of detector. The images was not of good quality and thus nowadays only transversal tomography is used. In this technique multiple views are obtained at many agles around the long axis of the patient and images in the slices perpendicular to the detector face, transversal slices (each element of this slice is in the form of cube in the computer memory and is called voxel), are constructed by the computer. Since in nuclear medicine the source of radioactivity is in the patient body, and the gamma photons or x rays are emitted from it,  we talk about emission computed tomography (ECT). This technique improves images quality and by this way physician interpretation by means of a better contrast between target organ and background,  better topography of pathological sites and higher detection efficiency of pathological lesions, which is done by better spatial resolution predominantly.

According to the type of radionuclide used we can distinguish two types of ECT. Single photon emission computed tomography (SPECT), which uses gamma emitting radionuclides (most of today used) and positron emission tomography (PET), which uses positron emitting radionuclides.

The SPECT cameras have in principle the same detector as planar cameras have, but the gantry makes possible to rotate the detector around the patient. The minimal angle of rotation is 180 degrees at small angle incremets. The path around the patient can be circular or eliptical and current cameras have the possibility of so-called body contouring pathway to minimize the distance between detector forhead and patient body surface. The data are stored in the computer for further processing and image reconstruction in the form of slices in three perpendicullar planes of transverse, coronal (frontal) and sagittal direction. There are different designs of SPECT cameras with one, two or three detectors. SPECT image is a type of static image, so sufficient image information density must be achieved. That is why about 20 to 30 minutes of time is needed to collect sufficient data. We must preset angle of rotation, angular step and time for one frame acquisition according to count rate detected.

There are several mathematical algorithms to reconstruct images from acquired data. The most frequently used is so called filtered back projection. Filters are mathematical functions, which increase image quality and suppress artefacts. Various types of filters are commercially available in the form of software packages. Another methods for image reconstruction are Fourier transform or iterative methods.

PET is based on the detection of coincidence of the two annihilation gamma photons that are emitted after interaction of positron with electron in the patient body. These two photons, which arise at the same time, have the same energy of 511 keV and are emitted in the angle of 180 degrees, are detected by the two detectors connected in coincidence. Data collected around the body axis are then used for image reconstruction.

In current PET systems, many detectors (hundreds to thousands) are arranged in circular rings. The number of rings can be up to sixteen and are arranged in arrays. Each detector is connected to the opposite detector in the same ring by a coincidence circuit. The field of view is defined by the width of the array of detectors. For this device no collimator is needed. Data are collected in the computer in the frame mode.  Image reconstruction is accomplished by the same method as in the SPECT does.