1 Brief History of Medical Imaging

1895. X-rays discovered accidentally by R¨oentgen. Simple X-ray images, e.g.
bones of hand, produced in early years of 20th Century. Conventional radiography
has been the most widespread medical imaging technique ever since, but the
basic technique has only evolved slowly.

1896. Natural radionuclides studied by Becquerel. Artificial radionuclides first
studied in 1930’s. First uses of radionuclides were for treatment (therapy) and for
metabolic tracer studies, rather than imaging. First gamma-ray imaging by a
rectilinear scanner, 1950’s, replaced by a static array of detectors in the 1960’s.
This design has only evolved slowly to the present day with no dramatic
improvements.

1940’s. Sonar technology from World War 2 (echo location) was readily available,
and the possibilities for adapting this to medical imaging were realized very early.
For various practical reasons, Ultrasound only became widely available in
Medicine in the 1970’s.

20th Century. The mathematical principles behind tomographic reconstruction
have been understood for a very long time, but because of the computing power
needed tomographic imaging techniques had to await the digital revolution. First
practical application in 1960’s for radionuclide imaging, based on rotating and
translating detectors. Then in the 1970’s there was an explosion of activity with
several techniques being developed simultaneously, most notably positron
emission tomography (PET) and X-ray computed tomography (CT). CT is now the
most widespread method, although the ideas were applied first in other areas.

1945. Nuclear Magnetic Resonance discovered by Physicists Bloch and Purcell.
The phenomenon rapidly proved to be more useful to Chemists (1950’s) and later
to Biochemists (1960’s) as a spectroscopic technique to study chemical structure
and metabolic activity. First proposed as an imaging technique by several groups
worldwide around 1973, with developments in the US and the UK. Developed
sufficiently to be used in hospitals by the 1980’s, and hereafter always called
Magnetic Resonance Imaging (MRI) to avoid distressing patients.

21st Century. The ”big 4” of medical imaging, namely X-ray, radionuclide imaging,
ultrasound and MRI continue to dominate, in their many variants, but many other
interesting developments in other techniques are occurring, especially when we
consider ”imaging” to include microscopic as well as macroscopic biological
structures (thermal imaging, electrical impedance tomography, scanned probe
techniques, optical imaging.)
In addition, the emphasis in the future will increasingly be on obtaining functional and
metabolic information simultaneously with structural (image) information (inherent in
PET and now evolving in functional MRI especially at higher fields). This can already
be done to some extent with radioactive tracers (e.g. PET) and magnetic resonance
spectroscopy.
2 Introduction
First of all we examine EM spectrum from DC to cosmic rays, to find a region to do
suitable imaging of tissue. To be useful for imaging EM radiation must have a wavelength
small compared to the resolution desired (< 10 mm) and must be reasonably attenuated
by body tissue. Too much attenuation results in a low signal to noise (S/N) ratio. Too little
attenuation reduces the selectivity or contrast for different structures and tissues. A
transmission curve for EM radiation through soft tissue is shown in Fig 1. In the long
wavelength region at the left, we have excessive attenuation at all but very long
wavelengths where resolution would be extremely poor. In the intermediate regions of the
spectrum corresponding to the infrared, optical, and ultraviolet regions, we have
excessive attenuation due to both absorption and scatter which limits this range to very
thin sections. Hence light transmission is mostly measured on tissue sections removed
from the patient and fixed to glass slides, skin layer imaging and for imaging transparent
tissue like eye layers.
Although absorption is suitable at low frequencies the wavelength is too large for
adequate resolution.
Between 0.5 and 10-2 °A, (°A = 10-10 m), corresponding to photon energies of about 25
KeV to 1:0 MeV, the attenuation is at reasonable levels with a wavelength far shorter than
the resolution of interest. This is desirable since it ensures that diffraction will not in any
way distort the imaging system and the rays will travel in straight lines. This is the most
widely used region and represents diagnostic x-ray spectrum.
At even shorter wavelengths, with energy per photon hν getting increasingly higher, the
attenuation becomes smaller until the body becomes relatively transparent and it ceases
to be a useful measurement. As well, at these shorter wavelengths, the total energy
consists of relatively few quanta, resulting in poor counting statistics and a noisy image.
Ultrasonic waves are acoustic rather than EM waves. Although they are relatively low in
frequency (1-3 MHz) their velocity is low (1500 m/s) so that the wavelength is small and
gives good resolution. Their wavelength is still much greater than that of light, x-rays and
gamma rays so that they are more prone to diffraction and scattering. Thus they are
unsuitable for transmission imaging but images can be derived from reflected waves.
Other differences between ultrasound and x and gamma rays are that ultrasound can be
focused by electronic means whereas x-rays and gamma rays cannot. It appears that
ultrasonic radiation is far less harmful than x-rays and gamma rays in the doses used for
imaging. Ultrasound will be reflected from tissue interfaces that are completely
transparent to x and gamma rays, so some soft tissues can only be imaged by
ultrasound.
Images of the human body are derived from the interaction of energy with human tissue.
The energy can be in the form of radiation, magnetic or electric fields, or acoustic energy.
The energy usually interacts at the molecular or atomic levels, so a clear understanding of
the structure of the atom is necessary.
In addition to understanding the physics of the atom, learning imaging jargon is also
necessary. For example:





Tomography: a cross-sectional image formed from a set of projection images. The
Greek word tomo means cut. CT: Computed (or Computerized) Tomography
MR, or MRI: Magnetic Resonance Imaging. This was first called nuclear magnetic
resonance (NMR), but the mention of anything nuclear scared patients, so the N
was dropped.
PET: Positron Emission Tomography. Understanding this phenomenon requires
acceptance of the theory that there is antimatter in the universe, and when
antimatter meets matter, then both kinds of matter are annihilated, and pure
energy is formed.
SPECT: Single Photon Emission Tomography
Ultrasound: Sonar in the body

OCT: Optical Coherent Tomography the use of infrared light to image
(particularity) the walls of an artery.
A modality is a method for acquiring an image. MR, CT, etc. are all imaging modalities.
Modalities are often categorized based on the amount of energy applied to the body. For
example, the x-ray modality produces energy that is sufficient to ionize atoms (i.e., eject
an electron from an orbit of an atom, thereby creating a positively charged ion that
damages human tissue). The modalities that cause ionizing radiation are x-rays, CT,
SPECT, and PET. Non-ionizing modalities include MR and ultrasound.
3 X-ray Imaging
3.1 Historical Overview
IN 1895, Wilhelm R¨ontgen (sometimes spelled as Roentgen) discovered a ”new kind of
ray” that penetrated matter. He named them x-strahlen ”x-ray” (”x” for unknown).
R¨ontgen was looking for the ”invisible high-frequency rays” that Helmholtz had predicted
the Maxwell theory of electromagnetic radiation.
R¨ontgen developed the first x-ray pictures on photographic plates, and one of the first
materials tested was human tissue. The most famous picture was an image of his wife’s
hand with ring on her finger.
In 1901 R¨ontgen received the Nobel Prize for Physics, which was the first Nobel Prize in
physics ever awarded. Unfortunately, R¨ontgen, his wife, and his laboratory workers all
died prematurely of cancer. The first medical use of the x-ray was in 1896 by Drs.
Ratcliffe and Hall-Edwards, in which they showed the location of a small need in a
woman’s hand. Dr. J. Clayton then performed the first x-ray guided surgery nine days
later.
3.2 X-ray Physics
An x-ray is an electromagnetic (EM) radiation similar to light, radio waves. The
relationship between energy and frequency for EM field is given by the Planck’s
relationship
E = hf
where E is energy in Kilo electron volts (KeV, 1keV = 1.6 x 10-19 joules), h is Planck’s
constant 4.13 x 10-18 KeC s or 6.63 x 10-34 Js), and f is the frequency (Hz). At least in a
vacuum, all EM waves propagate at the same speed, which is known as the speed of light
(c = 3.0 x108 m/s). The relationship is given by
c =λf
The quantum mechanical interpretation of x-rays is that of particles with velocity ν, mass
m and a momentum p and using Einstein’s famous relationship E = mc2 we have that
p = mν = mc =E/c=h/λ
These x-ray particles are called photons, and these photons are delivered in packets
called quanta. If the particle energy is greater than about 2-3 eV, then the photons are
capable of ionizing atoms (for example x-ray, SPECT and PET). Diagnostic radiation is
typically in the wavelength range of 100 nm to about 0.01 nm or from 12 eV to 125KeV.
An electron volt is the energy required to move a quantum of charge through 1 volt of
potential. A quantum of charge is 1.60x10-19 coulombs, or the charge of one single
electron. To break bond, one requires energies in the order of 2-10 eV, which can be
delivered by EM waves in the ultraviolet region or above. Ultraviolet light breaks chemical
bonds in tissue (i.e. ionizes tissue), thus it can be a danger to health. If the broken
chemical bond breaks are located on the DNA molecule and in just the right place, skin
cancer results.
The EM energies below the ultraviolet level cannot break chemical bonds, or produce
ions. The most dangerous event from these low-energy photons is tissue heating. For
instance, infrared light can heat objects by making them vibrate. Microwave oven is the
kitchen cause water molecules to tumble, which excitement in turn cause the temperature
of the food to increase.
3.3 Brief Review of the Structure of the Atom
The interaction of EM waves or particles with the human tissue depends quite heavily on
the structure of the atom. Here we outline key atomic concepts relevant to contrast in
imaging systems.

Three basic particles of an atom are electron, proton, and neutron. There are of
course many more smaller subparticles that hold everything together but these are
not do affect our understanding of the basic physics of medical imaging systems
and will thus be ignored.

The electron is negatively, the proton is positively charged and the neutron is
neutral.

A nucleus consists of two types of particles collectively known as nucleons,
protons and neutrons. Each proton possesses a positive charge of +1:6 x 1019
coulombs, exactly opposite that of an electron and a mass of 1.6734 x 10-27 kg.
Neutrons, the second type of nucleon, are uncharged particles with a rest mass of
1.6747x 10-27 kg. The rest mass of the electron is much smaller at 9.11 x 10-31 kg.

The number of neutrons in a nucleus is the neutron number N, while the number of
protons is the atomic number Z. For example, Hydrogen has only one proton and
its atomic number is thus one. The mass number A of the nucleus is the number of
nucleons (neutrons and protons) in the nucleus so that A = Z +N.

If the nucleus has too few neutrons, then the nucleus will be unstable, and fall
apart. If the nucleus is too big, or has too many protons and neutrons, the nucleus
will also become unstable. There are no stable isotopes of atoms above lead (Pb208).

To be neutral, an atom must have the same number of protons as electrons. If the
atom is charged, then it is called an ion.

The electron cloud surrounding the nucleus largely determines the volume of
space occupied by an atom.

The electrons cannot go just anywhere, due to their wave nature, electrons are
confined to orbital of specific energies. This notion is called the Bohr named after
Niels Bohr.

The first few shells of the Bohr atom model are:

Each shell has a different energy (frequency), and each orbital within the shell has
a unique energy.

Wolfgang Pauli (1921) later reformulated the Bohr model in terms of quantum
mechanical principles. Pauli observed that an atom can be defined by four
quantum numbers;
– n is the quantum number, which is an integer and scalar quantity;
– l is the angular momentum quantum number, a vector quantity that has integer
values ranging from 0 to n -1;
– mI is the magnetic quantum number with integral values ranging from -1 to 1;
and
– ms is the spin magnetic quantum number, which has value -1/2 to 1/2 . This spin is
the basis of magnetic resonance imaging.
According to the Pauli Exclusion Principle, no two electrons in an atom can have the
same set of quantum numbers.

Thus only two electrons can have the”same” energy value within the atom. In fact,
the model states that two electrons having the”same” energy must have unique
energies. State in a different way, each electron must have a unique energy since
the same energy within a single orbital must have different spins (one being +1/2
and the other being -1/2 ). For any one atom, there can only be one electron for
each unique energy level.

The energy that we are interested in is the binding energy of the electron in each
energy level. This will tell us how much energy we need to impart to the atom in
order to dislodge that electron from the atom. Electron binding energies are high,
usually on the order of 1-100 keV. Thus at least EM waves with the frequency
(energy) of x-rays are necessary to change the electronic structure of an atom. As
an example, is an EM signal with wavelength ¸λ = 1nm ionizing? We need to
calculate the energy of the wave. If it exceeds 1-2 keV, the n the wave is
considered ionizing, and potentially dangerous to human health.

Since x-rays can dislodge electrons and make the atom and ion, x-rays are
ionizing radiation. This radiation can change the chemical bonds of important
substances such as DNA. Diagnostic x-ray radiation is typically in the range of 100
nm to about 0:01 nm, or from 12 keV to 125 keV.

Even higher energies are required to change the nuclear structure of atoms.
Gamma rays provide sufficient energies to not only cause ions, but also cause a
transformation of the atom from one type to another through a change in the
atomic mass and number.

Radio frequencies are not energetic enough to interact with the atom at all.
Instead, radio frequencies interact with the spin of an electron. This property is
used in building MR images.
4 Interaction of x-rays and Matter: Contrast
There are several modes of interaction of x-rays with matter. The study of x-ray
interaction is important for understanding the development of image contrast in medical
images, and in understanding how x-ray detectors work. There are five possible modes of
interaction:
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Coherent (Rayleigh) scattering
Photoelectric effect
Compton scattering
Pair production
Types of Radiation Interactions
There is a finite probability per unit length that the radiation is absorbed. If not, there is no
interaction. The radiation interacts almost continuously giving up a small amount of its
energy at each interaction.
The reduction in the beam intensity should be a property of the object along the line.

 dI
 dx
I
Where
is the linear attenuation coefficient. Integrate along the path for a uniform
material of length, x.
I  I 0 e  x
In general,
  ( x, y )
I ( x, y )  I 0 e 
Consider a sample geometry with only a collimator at the output side:
So the buildup factor, B, can contribute to the signal as well as the noise.
I  I 0 Be  x
Attenuation Mechanisms
(a) Simple Scatter (Rayleigh Scattering)
The incident photon energy is much less than the binding energy of the electron in an
atom. The photo is scattered without change of energy.
(b) Photoelectric effect
The photon, E slightly greater than the binding energy of electron,
Eb gives up all of its energy to a inner shell electron, thereby
ejecting it from the atom. The excited atom retains to the ground
state with the emission of characteristic photons. Most of these are
of relatively low energy and are absorbed by the material.
(c) Compton Scattering
The photon energy is much greater than the binding energy, and only of this is given
up during the interaction with an outer valence electron ( the binding of valence
electrons is relatively weak, hence the “free”). The photon is scattered with reduced
energy and the energy of electron is dissipated through ionizations.
(d) Pair production
A very high energy photon interacts with a nucleus to create an electron/positron pair.
The mass of each particle is 9.11x 10-31 kg. So the minimum photon energy is:
Both the electron and the positron lose energy via ionization until an annihilation event
takes place yielding two photons of 0.51 MeV moving in opposite directions.
Attenuation Mechanisms
The optimum photon energy is about 30 keV (tube voltage 80-100 kV) where the
photoelectric effect dominates. The Z3 dependence leads to good contrast:
Z (fat)= 5.9
Z (muscles)= 7.4
Z (bone)= 13.9
Beam energy is important
This does not include buildup factor or scattering but does include beam hardening. Also
need to consider beam energy even if only photoelectric effect, since absorption rate
depends on the energy. Thus, low energy photons deliver no useful information.