Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
CHAPTER 8. PHYSICAL BASIS OF MEDICAL IMAGING
8.1. X-rays - properties and effects. Generation of X-rays by means of X-ray tube.
Bremsstrahlung and characteristic X-ray radiation. X-ray luminescence and X-ray structural
analysis.
Roentgen rays, designated as Ro-rays and X-rays were discovered by the German professor in
Physics Wilhelm Roentgen in 1895. They soon found diagnostic application in medicine because they
have three useful properties: they can pass through tissues, they cause blackening of photoplates and
shining of some substances (roentgen luminisence). A soon later their cytotoxic effect was discovered and
used for the purpose of radiation therapy.
X-rays are short-wave electromagnetic radiation. They have too short wavelength, , (and too
higher frequency, ) and, hence, they exhibit strong corpuscular properties. X-rays are photons with 
between 0.01 and 10 nm, i.e., less than that of the UV radiation, and greater than that of gamma -rays.
Unlike the light rays, they can penetrate deeply into tissues. The high penetration ability of X-rays is used
in medical diagnostics. Their photons have too much energy (E = h) and cause ionization and
dissociation of molecules, as well as a variety of chemical transformations. This stipulates the cytotoxicity
of Ro-rays and their application in radiotherapy of tumors. Depending on the energy of their photons, Rorays are divided into soft radiation (beams with greater  and low energy photons) and hard radiation
(beams with shorter  and high energy photons).
Fig. 8.1.1. Structure of X-ray tube (left) and the spectrum of the emitted X-ray photons
(right).
X-ray tube (Fig. 8.1.1) is used in medicine as the main source of Ro-radiation. It represents a glass
vessel, evacuated to deep vacuum, with two side protrusions in which two electrodes, a cathode and an
anode, are attached. Strong electrical voltage, Uac, known as anode or accelerating voltage, which creates a
strong electric field, is imposed between the electrodes. The negatively charged electrode, cathode, is a
thin filament, heated by an auxiliary electric current from a separate electric source. Due to its high
temperature the filament emits electrons (thermoelectron emission). The emitted electrons have low
velocity and are further accelerated by the electric field. They reach the positive electrode, anode, at high
speed, respectively, with a great kinetic energy, Ekin = e.Uac. This energy, expressed in electronvolts (eV),
is equal to the accelerating voltage, Uac in volts. The flow of electrons moving from the cathode to the
anode represents an electric current (anode current) with magnitude, Ian. The anode is made of suitable
metal and serves as a target that attracts the projectile electrons.
The collision of electrons, accelerated by tens to hundreds of kilovolts, to the atoms of anode
causes an emission of X-rays based on the following two physical mechanisms:
1) The first mechanism relys on the interaction of the projectile electrons with the electric field of
the nuclei of the atoms. A part of projectile electrons pass very close to these nuclei and decelerating emit
Ro-rays, called bremsstrahlung (breaking) radiation. This emission is explained by the fact that when an
electrically charged particle moves at high speed, it converts a part of its kinetic energy into
electromagnetic radiation upon sharp change of the value and direction of its velocity. In the
bremsstrahlung radiation each projectile electron emits several Ro-photons with a total energy equal to the
final kinetic energy of the electron, e.Uac. Apparently, the energy of the individual photons may have a
value ranging from zero to a maximum value equal to the e.Uac. Accordingly, the wavelength, , of the
these photons can take values from infinity to a minimum, min, which corresponds to the maximum
energy of photons, e.Uac (Fig. 8.1.1, curve 1). The relationship between min (measured in nm) and Uac
(measured in kV) is min = 12,3 / Uac. Thus, the bremsstrahlung (braking) radiation has a continuous
spectrum and is independent of the type of target atoms (material of the anode).
Ussually 80-90 % of the X-rays, emitted by X-ray tubes, are generated by the bremsstrahlung
mechanism. The bremsstrahlung X-rays increase with the accelerating voltage, Uac, and the atomic
number, Z, of anode.
2) The secong mechanism relys on the interaction of the projectile electrons with the electrons
orbiting around the nucreus of the atoms of the anode. A part of the projectile electrons hit such electrons
causing their ejection (knocking out) from the targeted atoms of anode. Thus the targeted atoms become
ionized or exited. The electrons orbiting around the nucreus of each atom are positioned in different shells
(layers, orbitals), depending on their distance to the nucleus. Accordingly, the binding energy of these
electrons can have only certain quantized, negative values: - EK (for the lowest, K-shell) < -EL (for the Lshell) < - EM (for the M-shell), etc. The shell with one electron ejected is called vacancy (a gap). A
projectile electron can knock out some inner electron if its kinetic energy is greater than the binding
energy of the targeted electron. The formed vacancy is immediately occupied by another electron from a
higher shell and, therefore, having greater energy (the binding energy of electrons is negative !). The
excess energy is emitted (with certain probability) in the form of Ro-photon, and the vacation moves to
the upper shell. The process of filling the newly formed vacancies is repeated. Thus, once formed each
vacancy moves to the highest shell of the atom, and this movement is accompanied by emission of
different Ro-photons, called characteristic X-rays (Fig. 8.1.1).
Fig. 8.1.2. Structure and operation principle of an X-ray tube with a rotating anode (left).
Rightward, illustrated is the method for narrowing the outflow of Ro-rays by placing the target at
an angle to the flow of projectile electrons.
The energy of the characteristic photon is always equal to the difference in the binding energy of
nearby shells; EK - EL, EK - EM, etc. X-rays produced by the transitions from L shell to K shell are called
K-alpha X-rays, and those by the transition from M shell to K shell are called K-beta X-rays. The K-alpha,
K-beta, ect, rays form the K-series. Accordingly, the characteristic radiation due to the transitions from the
above shells to the L-shell is designated as L-alpha, L-beta, L-gamma rays and so on. The latters form the
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
L-series. So, the characteristic X-rays contain several portions of photons, each having the same energy,
called spectral lines. The structure of spectral lines corresponds to the type of atoms, making up the anode,
hence the term characteristic X-ray radiation.
In the X-ray tube, the characteristic radiation is emitted simultaneously with the bremsstrahlung
radition and both are superimposed (Fig. 8.1.1, curve 2).
The power of the anode current flowing through the X-ray tube is given by the product of Ian and
Uac and is usually very large - several tens of kW. Only a few percent of this energy is converted into Ro
radiation. The remaining energy is spent for the exitation and ionization of atoms and finally it is
converted into heat at the anode. This requires the anode to be made up of high-melting metal and the Xray tube to be continuously cooled down by a stream of air or oil.
The most important part of the X-ray tube is this portion of the anode surface, which is
bombarded by the highly accelerated electrons. This site, designated as focal spot (focus) of the X-ray
tube, accepts all the power of the anode current and emitts the X-ray photons. In case this focal spot has a
large area the X-rays will come from different points and will not be parallel, deteriorating the X-ray
image. Therefore, the focal spot of X-ray tubes is minimized to the area of several mm2. In addition, the
forehead surface of anode is inclined at an angle of about 30° to the cathode-anode axis. This is called a
line focus principle yiealding the crossection of the emitted Ro beam to be less than the crossection of the
stream of accelerated electrons (Fig.8.1.2). To avoid overheating of the focal spot, the anode of modern Xray tubes is made rotating about its longitudinal axis. So the electron beam bombards different areas of the
anode while the remaining part of the anode is cooled down (Fig. 8.1.2).
The anode voltage, accelerating the electrons in X-ray tube, can reach a maximum value of about
300 kv. In recent days, instead of X-ray tube a linear accelerators of electrons is frequently used in order
to obtain electrons with much higher energy and, respectively, to generate much harder Ro-photons. The
linear accelerator generates Ro-rays using the same physicsl principle, bombarding a high-melting metal
target with electrons accelerated by a voltage of several thousand kv.
Fig. 3.8.1. Diffraction of Xrays scattered by a crystalline
lattice.
X-rays are also used to
study the composition and structure
of various substances. In atoms, the
binding energy of electrons to
nucleus is greater when the atomic
number, Z, is greater. Hence, the
energy of
the
photons
of
characteristic radiation has greater values in atoms with higher atomic number, Z. It is experimentally
determined that the frequency, , of each series of characteristic radiation is related with the atomic
number, Z, according to the Mosley plot as expressed by the relation: ()1/2 = k.(Z - b). The parameters k
and b are constants, depending on the type of chemical element. This relationship is used to assay the
elemental composition of different samples. For this purpose the characteristic Ro-radiation is induced
irradiating the sample with hard Ro-rays which knock out inner electrons of atoms. Based on the
frequencies of the registered K, L, M etc. series the type of the atoms can be established. This method is
known as X-ray luminescence analysis.
In X-ray diffraction analysis the X-rays are used to examine the structure of crystalline bodies,
biomacromolecules, etc. Let a sheaf of Ro-rays is scattered at the angle, , by a crystal, which has crystal
lattice planes spaced at d (Fig. 8.1.3). Because the distance, d, is comparable to the wavelength of the Rorays (), the scattered rays diffract with each other. The resulting patern of diffraction is determined,
allowing the scattered rays to fall on a luminescent screen, which gives a picture of glowing points,
concentrically arranged around a central luminous spot. The shining points are formed by X-rays that have
the same phases, while their dark surrounding corresponds to X-rays with opposite phases. The Figure
8.1.3 shows, that the beams 1 and 1 travel different distance, equal to 2d.sin. When this difference is a
multiple of , the phase difference between these beams will be zero and these rays will give a glowing
dot on the screen. If this difference is a multiple of /2, the rays quench each other. This method allows
measure the distance, d, and determines the type of crystal lattice. If the crystal consists of
biomacromolecules (proteins, nucleic acids), dehydrated and crystallized on a solid support, this method
allows the determination of their tertiary structure and molecular weight.
8.2. Attenuation of monochromatic X-ray radiation by a layer. Physical basis of roentgen
diagnostics. Basic elements of X-ray machine. Radiographic contrast agents
Roentgen diagnostics and X-ray radiation protection are both based on the law which expresses
the absorption of x-ray radiation. Let a beam of monochromatic Ro-photons (photons of the same
wavelength, ) passes through a thin layer (tissue) having a thickness d, a density, , and effective atomic
number, Zef. A part of the incident photons are absorbed or scattered by the atoms of the layer.
The interaction of incident photons with the atoms of the layer depends on the energy (frequency)
of photons (Fig. 8.2.1). Photons with low energy are scattered by atoms elastically (coherently), i.e.,
without changing their energy. Absorption of photons takes place when the energy of photons is sufficient
to eject a valence electron (photoelectric effect) or even an electron from the inner layers; this is an
inelastic, non-coherent scattering, or
Compton effect. At greater energy,
photons are scattered by the nuclei of
atoms.
Fig. 8.2.1. Interacton of photon
radiation with atoms.
As a result of scattering and
absorption, the number, N, of photons
coming out of the layer is smaller than
the number, No, of incident photons: N =
No. exp (- .d), where  is the linear
attenuation coefficient of the layer. This is the law of absorption of Ro-rays. In turn,  = k. . 3. Zеф4.
From the formula for  it follows that
1) The X-ray photons will be stronger absorbed by layers with greater density.
2) The Ro-radiation with shorter wavelength, , (hard radiation) will be less absorbed and will
have greater penetration ability.
3) At the same other conditions, layers with a higher mean effective number, Zef, (containing more
heavy elements) will absorb more Ro-rays.
The personel working with Ro-dagnostic apparatus must be protected from the Ro radiation.
When reducing the time of exposure and increasing the distance to the sourse of Ro-rays may not be
possible and sufficient, one can use a shielding layer to reduce the Ro radiation. A shielding layer with a
thickness (d1/2), which attenuates the Ro radiation twice is called a half value layer. For protection against
X-rays, layers with thickness several (sufficient number of) times greater than that of d1/2 are used. The
protective shields are made from a suitable material with high Zef and greater density, usually from lead.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Classical diagnostic radiology uses the so called X-ray system (unit, machine) (Fig.8.2.1). The
main part of the X-ray system is a Ro-tube inserted into a protective lead casing with a window that
transmits a narrow sheaf of Ro-rays. A part of these rays pass through the patient's body and form
shadow-like image of its internal organs on a screen. The image is created by those rays that have passed
through the tissues of the patient and are weakened according to the law for absorption of X-ray radiation.
The direct current voltage, applied between the anode and cathode of the Ro-tube (anode or
accelerating voltage), has the values typically from 5 to 50 kv. It is created using a step-up transformer,
which increases the mains voltage (220 v, 50 Hz) to a value close to that of the required accelerating
voltage. The high voltage obtained on the transformer output is rectified by diode electronic lamp and
filtered out by means of a high-voltage oil capacitor (Fig. 8.2.2). Most commonly used is the two-way
rectification, carried out by a several pairs of diods, which strongly reduces the pulsation (riple) of the
accelerating voltage and improves image. The console is a part of X-ray machine, where the magnitudes
of anode voltage and anode current are properly chosen, in order to produce image with high quality.
Due to the different attenuation of the rays passing through different tissues, images of various
internal organs can be distinguished on the screen. A portion of the X-rays, passing through the body,
however, becomes scattered, i.e., they change their direction. When falling on the screen, scattered rays
create background and decrease the contrast of image. To obtain a clear and sharp image an anti diffusion
grid is placed between the screen and the body (Fig. 8.2.3). It transmits predominantly those rays that pass
through the body without deviation and absorbs most of the rays that are scattered. This method of
improving the quality of the Ro-rays image is known as collimation. The outside aspect of the screen (Fig.
8.2.2) is coated with a layer of proper fluorescent luminophore (zinc sulfide, cadmium tungstate). Under
the impact of the incident Ro-rays the luminophore shines, creating a visible image of the internal organs
of the body (roentgenoscopy). The observation of the image is carried through a transparent layer of lead
glass to protect the personel from the Ro-rays. In roentgenography (radiography), the screen represents
photoplate which imprints the image.
Fig. 8. 2. 2. Classical scheme of Xray radiology system.
An image of high quality,
i.e., having good brightness and
contrast, could be obtained in case the
tissues of a given organ strongly
differ in their absorption coefficients,
. Most tissues including the soft
tissues, however, have almost the
same Zef varying between 6.5 and 7.5
and density close to that of water. Hence, they practically can not be distinguished on the screen. Clearly
distinguishable on screen are only the bones and the lung. Bones strongly absorb Ro-rays because they
contain a significant amount of heavy elements (calcium and phosphorus) yielding significantly greater Zef
(14 - 15). By contrast, the lung tissues absorb Ro-rays weakly due to their low density.
When the soft tissues are preliminary incorporated with salts, containing elements with high
atomic number, their absorbtion of X-rays strongly increases making them visible on screen. Such salts
are called contrast substances and usually contain barium, calcium, iodine and the like. This method
(contrasting X-ray imaging) allows several soft tissues; stomach, blood vessels, kidneys, to become
discernable. Depending on the observed tissues this technique is called angiography, gastrography and so
on. Contrast agents, however, are harmful to the patient and their application is allowed only at strictly
controlled conditions. If possible, it is desirable to use other, non-harmful methods and techniques for
imaging such as ultrasound, MRI imaging, thermography.
In diagnostic radiology the X-ray beams contain polychromatic photons with different energies.
This affects the ability of photons to penetrate the patient, i.e., the quality of imaging which depends on
the effective photon energy of X-rays. The effective photon energy is taken to be between one third and
one half of the maximum photon energy.
The quality of diagnostic radiology depends heavily on the intensity and spectral composition of
the X-rays. These characterictics heavily depend on the following three principal parameters of Ro-tube:
the magnitude of anode current, Ia, the magnitude of anode voltage Uac and the atomic number of the
anode material, Z. The intensity of Ro radiation, J, (the number of photons emitted by the tube per 1 s) is J
= k. Ia. Uac2. Z. In order to reduce the exposure time of the patient, required for the preparation of its X-ray
image, the radiation intensity, J, should be increased. To achiev this, the aforementioned parameters - Z, Ia
and Uac should have higher values. For example, the anode is typically made of metal with higher Z
(tungsten with Z = 74, molybdenum Z = 42, rhodium Z = 45). When selecting suitable values of Ia and Uac
several preconditions must be taken into consideration. First, increasing the Ia the number of emitted
photons linearly increases, however, the energy of the individual photons does not change (Fig.8.2.4).
Second, increasing Uac, the intensity of photon emission increases even more (because of the quadratic
dependence), in addition, the energy of the individual photons sharpy rises (beam hardening).
Furthermore, at greater Uac, the characteristic radiation of K-series lines may apper (Fig. 8.2.4). Usually,
the L-series lines are too weak and have no practical importance.
In conlusion, increasing the Uac, the x-ray tube output and the average photon energy both
increase. As a result, the beam quality arises as the X-ray penetrating power increases.
Fig. 8. 2. 3. Collimation of X-rays using anti
diffusion grid.
In X-ray diagnostics, the iradiation of
human tissues by Ro-rays has always a
detrimental effect which, therefore should be
minimized. This is achieved by:
1) The X-ray system uses hard Ro-rays,
which readily pass through the tissues of the
human body. Besides the necessary hard
radiation, the Ro-tubes emits, however, lowenergy radiation, which is absorbed almost
entirely by the superficial tissues (especially the skin) and does not contribute to the formation of X-ray
image. The low energy radiation of Ro-systems it removed by a filter (Fig. 8.2.3), a thin metal plate that
entirely absorbs the low energy photons, transmitting the high energy photons. Some of the very low
energy X-rays are stopped by the X-ray tube window, which acts as inherent X-ray beam filter. Beryllium
does not absorb low energy photons and is often used as a window in mammography X-ray tubes, which
uses low-energy photons.
2) The crossection of the sheaf of X-ray beams is made sufficiently narrow in order the beams to
pass only through the observed organ. Consequently, the sheaf is passed through a metal diaphragm (Fig.
8.2.3). To protect personnel, the entire Ro-tube is enhoused in a lead casing that absorbs all of the side
radiation.
3) Classical radiography uses sensitive screens and photopates for the detection of radiation
transmitted through the patient. This reduces both the intensity of X-ray radiation and exposure time
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
needed to form a quality image. Used are special radiographic plates containing additional fluorescent
foils (layers of calcium tungstate). Under the impact of X-ray these foils emit light with blue color that
increases the blackening of photoplates. Fluorography uses a special optical system to project and
photograph the image on a highly sensitive photographic film. The developed X-ray film is then observed
under an optical apparatus with great magnification. This gives the opportunity to explore a large number
of patients. The X-ray machines in fluoroscopy use low anode current and there is no danger of
overheating the focal spot.
The most sensitive X-ray machines use television cameras (electron-optical converters), which
strongly enhance the brightness of the image.
4) In most recent X-ray apparatus the image of the observed organs is digitized, allowing for its
further processing with specialized computer programs. The so called computer digitization uses the
existing classic X-ray machines in which the classic photographic plate is replaced by a charged phosphor
plate. The phosphor plate serves as a memorable luminophor which retains the image for a sufficient time.
The digitalization of the image is carried out using a special scanner with an infrared laser, which
consequtively activates different points of luminophor plate and transmits the data for their charge in the
computer memory. This method is cheap and convenient because it uses the available conventional analog
X-ray machines.
Direct digitization requires entirely new type of X-ray machines. The image is formed on a wide
scale screen (43 x 43cm), containing a large number of thin-film transistors. Each transistor converts the
stream of incident Ro-photons in so called pixel values (numbers). The image is digitized quickly, which
greatly reduces the radiation dose absorbed by the patient.
Fig. 8. 2. 4. Spectrum of the X-ray emission of a Ro – tube at different magnitudes of anode
current (in right) and anode voltage (in left).
The hard Ro-rays effectively interact with the atoms and molecules of tissues causing their
ionization and dissociation and producing free radicals. This has cytotoxic effect on cells and tissues.
Relatedly, the hard X-rays with high intensity are used for radiation therapy - killing of cancer cells and
tissues by irradiation. Radiotherapy of tumors with X-rays uses an X-ray tube with high anode voltage
(150 kV - 300 kV). This tube generates predominantly hard Ro-rays albeit a small fraction of soft Ro-rays
is also emitted which has no therapeutic effect. The emitted radiation is directed to the therapeutic zone of
the body where the tumor is localized. If the tumor is localized in the deep tissues, the skin must be
protected from the passing therapeutic radiation beems. The protection is based on:
(1) In general, the soft rays are absorbed by the skin. To reduce the radiation load of skin, the soft
rays are absorbed by a thin metal filter (an aluminum plate with thickness of 2 mm).
(2) The X-ray machines contain X-ray tubes which rotate convergently. The X-ray beem crosses
the skin at the periphery of a circle and, at the same time, it is always directed to the therapeutic zone.
The time for exposure to Ro radiation and the total dose that is needed to kill the tumor mass are
preliminary calculated and experimentally measured using a model (phantom). The models are made of
materials similar by its chemical content and absorption properties to the human tissues. In radiation
therapy of tumors, the X-rays are frequently replaced by the harder -rays, emitted by proper radioactive
sources (60Co, cobalt-60). This method is known as a telegamma radiation therapy.
8. 3. Physical foundations of X-ray computed tomography
In classical X-ray diagnostics the Ro-beams passing through the tissues form shadow image on a
luminescent screen. An ideal image would be formed if the rays, passing through a given point of the
irradiated tissue, collect in a single point on the screen. In reality, any point on the screen collects either
rays, passing without deviation through the given point of irradiated tissue, and rays scattered from other
points of the tissue. The overlay of both the transmitted and scattered rays on the screen reduces the
contrast and deteriorates the quality of image. Collimation of the rays does not solve the problem as it is
incomplete and the image quality is far from that typical for the visible optics.
Another disadvantage of the classical Ro-diagnostics is the space characteristics of the image. The
image is two-dimensional (flat) so that all internal inhomogeneities of the observed tissues, lying on a
single Ro-beam, are superimposed on the screen. For example, the image of the ribs located in front of the
lung, as well as the image of the rear ribs are superimposed on the image of the lung. Thus, different
projection effects are produced; the summation effect, the effect of overlapping, border effect, etc. All
these effects hinder the diagnosis of tumors and other abnormalities.
A third drawback comes from the fact that the focus of the X-ray tube is not a point but has the
form of a small spot. Any point of the focal spot emits a sheaf of divergent beams that form its own image
on the screen. The wider is the focal spot, the greater will be the displacement of these images from one
another, hence, the image contrast will be poor.
Fig. 8. 3. 1. Simplified model of an irradiated by Ro-rays crossection, consisting of 16 pixels.
In the left - an indication of the absorption coefficients for each pixel. On the right - the calculated
absorption coefficients (CT-numbers) for each pixel are represented as various degrees of gray.
Fourth drawback is the inability to differentiate soft tissue without special contrasting agents.
These disadvantages are avoided in modern computer axial tomography (CT). It is based on the
mathematical theory allowing the three-dimention image of an object to be constructed using great
number of side projections of this object. In CT the projections of the observed object (internal organ) are
prepared transmitting a thin sheaf of Ro-rays through a thin crossection of the object and coming from
different angles. To achiev this the Ro-tube and the opposed detectors rotate rapidly around the center of
the object. Measured is the absorbtion (weakening) of the rays intersecting the object in each direction.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Next, all these measurments are carried out for the nearby crossection and so on, until the entire object is
scanned. All data, obtained for different projections and crossections, are collected in a computer, and a
video image of the inside of the object is finally synthesized.
In X-ray computer tomography a narrow, strongly collimated Ro-ray is used, thus the scattered
light is removed. The beam passes through the patient in a plane (imaginary crossection or slice), which
gives rise to the term tomography, meaning “a record of a slice”. After combining the images of all slices
the three dimentional image of the inner organs is reconstructed, in which the soft tissues, such as brain,
liver and kidneys can be differentiated.
To obtain a synthesized image of the irradiated slice, it is divided into a large number of square
picture elements (abbreviated to pixels), each with an area of about 1 mm2. For this purpose, small cubic
volume elements, called voxels, are also used. Each pixel is characterized by his own linear absorption
coefficient of Ro-rays (absorption coefficient, ), which depends on the type of tissue (bone, muscle,
blood vessel, etc.). Assume a given pixel is irradiated by X-ray photons and the No and N denote the
numbers of incident and transmitted photons, respectively. The incident photons are emitted by a Ro-tube
and the transmitted photons are measured by a proper detector of Ro-radiation. According to the law for
Ro-ray absorption, obviously N = No. exp (-.d), where d is the thickness of the irradiated pixel. To
synthesize the image of the entire crossection (slice) we need to determine the absorbtion coefficients of
all the pixels of this crossection. This task is solved irradiating the crossection with a narrow, strongly
collimated Ro-beam across a large number of directions and measuring the total attenuation of the beam
for each direction (Fig. 8.3.2). For each line of irradiation an equation is draun expressing the physical law
that the total absorption of one row of pixels is equal to the sum of the absorptions of all pixels included in
this row. This yields a system of equations, which contains sufficient number of equations neaded to
determine the unknown quantities - the absorption numbers of pixels.
Fig. 8. 3. 2. Transmission of collimated
Ro-beam across different directions of the
irradiated section. With 16 pixels in the
section, tottaly required are 16 directions
of irradiation to compute all the
absorption coefficients. Shown are a total
of 8 lines of irradiation, four horizontal
and four vertical. The remaining 8
diagonal directions are not shown.
For simplicity, assume the cross
section contains only sixteen pixels (Fig.
8.3.1), and the individual pixels have
absorption coefficients, indicated by 11, 12,
13, etc., a total of 16 unknown quantities.
These quantities can be found, irradiating the
crossection through multiple number of lines and measuring the total attenuation of the radiation that
passes across each row of pixels. To find out the 16 quantities we need at least 16 different directions, and
they could be, for example, 4 horizontal, 4 vertical and 8 across the two diagonals (Fig. 8.3.2). So we get
the attenuated intensities N1, N2, N3, … , N16 of the transmitted Ro-rays. For each direction of irradiation
an equation is drawn expressing the total attenuation of the irradiated row of pixels as a sum of the
attenuations caused by the pixels included in this line.
For the four horizontal directions we get the equations:
N1 = N0 . exp-(11 + 12 + 13 + 14).d
N2 = N0 . exp-(21 + 22 + 23 + 24).d
N3 = N0 . exp-(31 + 32 + 33 + 34).d
N4 = N0 . exp-(41 + 42 + 43 + 44).d
Four vertical directions, the equations are:
N5 = N0 . exp-(11 + 21 + 31 + 41).d
N6 = N0 . exp-(12 + 22 + 32 + 42).d
N7 = N0 . exp-(13 + 23 + 33 + 43).d
N8 = N0 . exp-(14 + 24 + 34 + 44).d
The remaining eight equations for the diagonal irradiations are obtained in a similar way.
So a system of 16 equations is obtained whose solution allows find out the aquired 16 absorption
coefficients of the individual pixels. In reality, the number of aquired absorption coefficients and of
corresponding equations is much greater. Solving such a complex system of equations is only possible
with the help of a computer, running a special program for calculation (algorithm). Thus, if the first
important part of the computer tomography system is the rotatory X-ray emitting and detection system, the
second important part is the computer and its program for calculation.
Fig. 8. 3. 3. Two ways to
irradiate the patient in
modern
computer
tomography. (A) X-ray
tube together with the
opposite detectors, both
circle around the patient
(in the center); (B) X-ray
tube circles around the
patient while the detectors
are
mounted
on
a
immobile circle whose
center coincides with the
patient.
The third important part of each computer tomograph is the monitor (screen) where the irradiated
crossection is presented with all pixels and their absorbtion coefficients. The absorbtion coefficient, , of
each pixel can be displayed directly but, instead, it is more convenient to use the dimensionless
Houndsfield numbers (CT-numbers), defined by the formule: CT-number = 1000 x ( - H2O)/( H2O - air),
where the  is the linear absorption coefficient of the pixel, H2O is the absorption coefficient of water and
air is the absorption coefficient of air, which is close to zero. The CT-numbers range from -1000 for a
non-absorbing medium (air) to about +1000 for compact, dense bone. The zero value corresponds to the
absorption of water, which is close to the absorption of human tissues. As a third possibility, the CTnumbers can be displayed as different levels of grey, where white means no absorption (air) and black
indicates full absorption (lead plate). Fig.8.3.1 shows an example of arbitrary solution in which the
absorption coefficients are presented in gray levels; a strong absorption area (bone) in the center
surrounded by soft tissues, whose absorption is close to that of water.
In modern tomographs, the number of pixels is 256 x 256 (or 512 x 512 in some cases), and the
irradiation of each crossection is carried out by about 1000 different angles or positions. Therefore, for
each crossection the Ro-tube is rotated at 360° around the patient. At each position of the Ro-tube, the
detector block is rotated occupying about 100 different positions at which it measures the transmitted
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
radiation (Fig. 8.3.3). During this angular scan the patient must be at complete standstill retaining its
breathing, otherwise every movement of the irradiated tissue will degrade the quality of the obtained
image. Therefore, the calculation of the absorption numbers should be performed by a fast computer
within 1 second while the full rotation of the Ro-tube and detectors should complete in a few seconds.
Compared with classical X-ray radiography, the patient receives significantly (5 to 10 times)
greater radiation load (1 to 10 rad) during the computer tomography imaging. However, this
inconvenience is paid by the significantly sharper and more detailed diagnostic image. Furthermore, the
image is digitized, can be saved, some details can be displayed enlarged. Absorbtion numbers are present
in digital form, allowing the diagnosis to be based on quantitative indicators.
The three-dimensional image of the damaged joints of knee, made by X-ray computer
tomography, was recently used to prepare knee prostheses with unsurpassed accuracy of up to 1 mm.