European Nuclear Medicine Guide
In 1917, the Austrian mathematician Radon formulated his theory about the possibility of reconstructing a two-dimensional function starting from its line integrals. It took more than fifty years to get to the first prototype of CT equipment, as we know by Hounsfield. After a first implementation of reconstruction with iterative algebraic algorithms, the filtered back projection (FBP) dominated the scene for 40 years, with some variations introduced to cope with spiral acquisition (interpolation of raw data) and multislice (three dimensional back projection). Since 2009, we have witnessed the introduction and rapid implementation of new iterative algorithms.
In CT equipment, for each angle of the x-ray tube and for each sampling of the detector data, attenuation profiles are acquired. The complete set of attenuation profiles obtained by a complete rotation of the detector tube assembly represented in an image is what is called the sinogram. The superposition of the projections of the attenuation profiles along the acquisition directions can give a rough first approximation of the tomographic plane with evident noise (where constant pixel values are expected they oscillate around an average value), artifacts (presence of signal different from reality), and spread of the signal. In order to partially overcome this problem, a filtering of the attenuation profiles is performed which is a convolution product with a filter function (kernel) accentuating the edges of the profile. In this way, there will be a greater definition of the object in the filtered back projection and a lower dispersion of the signal in the surrounding regions.
An important aspect of the filtered back projection is that the result we obtain depends strongly on the choice of the convolution filter. Depending on the case, we can favour noise reduction at the expense of spatial resolution (with a standard or even smoothing filter) or favour spatial resolution by accepting a higher level of noise (with an edge enhancing filter). With the filtered back-projection we obtain an approximation of the balanced reality in terms of resolution and noise.
From a mathematical point of view, the filtered reconstruction process can also be seen in the Fourier space. In the Fourier formulation of the filtered back projection, the convolution filtering becomes a ramp filtering in the frequency domain.
In the first decade of this century, the technological development of CT scans was mainly aimed at increasing the number of slices that can be acquired simultaneously with a single rotation. This is particularly useful for cardiac examinations. The number of slices progressively increased from 4 to 16, then 64, and further to 256 layers and over a volume of length 16 cm and with rotation times of the detector tube assembly of less than 0.3 s. Some tomographs have 2 x-ray tubes and two arcs of detectors placed at 90° to improve temporal resolution. Once these performances were achieved, the research focused more on the possibilities of improving image quality and reducing the dose.
Figure 1. (a) Schematic view of a third generation tube detector assembly, common to all present CT equipment, with four rows of detectors. The number of detectors along the arc is of the order of one thousand. The nominal slice and radiation beam thickness are defined at the rotational axis distance, that is usually about 0.5 m from the focal spot. As a consequence, a slice thickness of 0.6 mm corresponds to a detector thickness along z axis of about 1.2 mm. (b) Representation of a spiral acquisition with the trajectory of the four banks of detectors around the patient.
Work has been done on increasing the performances of the detectors in terms of efficiency and response times. One manufacturer has developed a double-layer detector that discriminates between the energy of incident photons to create double-energy images. Photon count detectors are also being studied, even if important technological limits still need to be overcome before these can be included in clinical practice. From the point of view of the X-ray tubes, the range of kV available has expanded, which now ranges from 60 to 140 kV with indications on the preferred values to be used for the particular clinical application. Higher filtrations and small focal spots are available, even for high anodic currents.
The two elements that have had the greatest impact on dose reduction in CT diagnostics are the anodic current modulation systems and iterative algorithms, and these will be discussed in the following paragraphs[98].
With regard to the TC equipment used in the hybrid SPECT/CT and PET/CT machines, the number of slices commonly used is between 2 and 64 on a maximum scan length per rotation of 4 cm. A manufacturer offered a CT machine with cone beam for a period of time, but it is currently no longer in production. The kV values are between 80 and 140, and the maximum anode current can exceed 800 mA. In some cases, explicitly “non-diagnostic” CTs are implemented, in the sense that their function is limited to use for attenuation correction, scatter modelling, volume definition, and for the anatomical location of the radiopharmaceutical, although it cannot be used autonomously as CT. In this case the anodic current values are limited to some tens of mA.
Two different dose indicators, specifically defined for computed tomography, are normally used in order to compare different protocols and to assess diagnostic reference levels. The computed tomography dose indicator (CTDI) is a local dose indicator which quantifies the absorbed dose in a standard phantom (with a diameter of 32 cm for body scans and of 16 cm for head scans) for contiguous axial scans or helical scan. It intrinsically accounts for primary beam and scatter contributions. The dose length product (DLP) accounts for both the local absorbed dose and the extension of the acquired volume. It can be obtained in most cases simply by multiplying the CTDI by the scan length[99]. Both CTDI and DLP are displayed together with the other exposure parameters of each selectable acquisition protocols. Typical values of CTDI for diagnostic CT are about 60 mGy in the head region and about 10-15 mGy in the body district. Correspondent DLP values are of the order of 1000 mGy cm for a skull acquisition and of 400-600 mGy cm for a chest or abdominal scan. Regarding the CT acquisitions functional to the nuclear medicine methods, several studies have been published with a wide range of values for the CTDI and DLP indicators, which in any case are typically less than half of the values reported for diagnostic CT[100–103].
It must be clear that the CTDI indicator, despite having an undisputed utility in the definition and comparison of the acquisition protocols and being referred to cylindrical phantoms of standard size, does not correctly represent the absorbed dose of the patient’s irradiated organs which depend greatly on their actual anatomical dimensions[104]. In order to compare the relative radiation risks of the CT acquisition and of the radiopharmaceutical, effective dose is typically employed. Effective dose for CT examinations can be roughly evaluated by means of conversion factors applied to DLP values[105], or more properly with greater accuracy by dedicated software[106–108].
In the latest generation of TC equipment, an automatic modulation system of the x-ray tube current is available which, on the basis of a pre-set quality index or a nominal value of mA, modifies the intensity of the beam during the acquisition so as to maintain the image quality constant with a reduction of the dose to the patient [109,110].
There are several current modulation techniques:
The presence of automatic modulation alters all known relationships between the dose and other exposure parameters in presence of a constant anodic current, so it is important to consider the behaviour of the system when other scanning parameters such as kV, the pitch, or the combinations of multi-bank detectors are modified with respect to the basic protocol. This information is essential for the adoption of optimization strategies that take into account all possible variables[111].
Automatic current modulation is particularly useful in hybrid scanners employed for both paediatric and adult patients, where a proper definition of the needed level of noise for each age class results in a significant dose reduction and image quality optimization[100].