Physics of Medical Imaging – An Introduction Dove – Physics of Medical Imaging 9222003 Physics of Medical Imaging – An Introduction Edwin L Dove Biomedical Engineering The University of Iowa Table of Contents Physics of Medical Imaging – An Introduction 1 1 Introduction 3 2 X ray Modality 8 2 1 History 8 2 2 X ray physics 9 2 3 Brief review of the structure of the atom 12 3 Interaction between X rays and matter 15 3 1 Coherent (Rayleigh) scattering 15 3 2 Photo disintegration 15 3 3 Photo elec.
Introduction
Images of the human body are produced through the interaction of various forms of energy—such as radiation, magnetic or electric fields, and acoustic energy—with human tissue This interaction typically occurs at the molecular or atomic level, making it essential to have a clear understanding of atomic structure for accurate imaging.
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
Positron Emission Tomography (PET) is a medical imaging technique that relies on the concept of antimatter in the universe When antimatter encounters matter, both are annihilated, resulting in the release of pure energy Understanding this phenomenon is crucial for grasping how PET scans function and their role in modern medical diagnostics.
• 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
Imaging modalities refer to various methods used to acquire images, such as MRI and CT scans These modalities can be classified based on the energy they apply to the body Ionizing radiation modalities, like X-rays, CT, SPECT, and PET, generate enough energy to ionize atoms, which can damage human tissue In contrast, non-ionizing modalities, such as MRI and ultrasound, do not produce ionizing radiation.
Modern medical imaging employs various classification schemes, with radiologists typically identifying four primary methods: X-ray transmission, radionuclide emission, magnetic resonance, and ultrasound Each of these techniques provides distinct categories of information related to anatomical or physiological processes, while additional methods are currently under research A comparison of these four medical imaging techniques can be found in Table 1.1.
Table 1.1 Comparison of medical imaging techniques
Method Parameter measured Medical applications
Density and average atomic number
Anatomy, mineral content, flow and permeability from movement of contrast material
Emission computed tomography (positron and single photon)
Concentration of radionuclides Metabolism, receptor site concentration, flow
Magnetic resonance Concentrations, relaxation parameters T 1 , and T 2 and frequency shifts due to chemical form
Anatomy, edema, flow, and chemical composition
Ultrasound Acoustic impedance mismatches, sound velocity, attenuation, frequency shifts due to motion
Anatomy, tissue structure characteristics, flow
Modern medical imaging encompasses several key modalities, including PET, CT, and MR, which necessitate that patients enter a ring of detectors This can pose challenges for individuals with certain medical conditions, claustrophobia, or other concerns In contrast, ultrasound utilizes a straightforward probe placed directly on the patient's skin, offering a more accessible alternative.
An example of a PET image is shown in Figure 1-2
Figure 1-2 PET scans of a brain tumor (Taken from the Harvard Medical School Nuclear Division web site)
An example of a SPECT scan is shown in Figure 1-3
Figure 1-3 Bottom row - SPECT scans of a brain tumor (Taken from the Harvard Medical School
A schematic diagram of an MR machine is shown in Figure 1-4 A typical MRI image is shown in Figure 1-5
Figure 1-5 Knee study from MRI image
In this class we will only study primarily X-rays and ultrasound The other modalities (and more advanced image processing algorithms) are coved in subsequent elective imaging courses (51:185, 186, 188, and 189).
X-ray Modality
History
On the evening of November 8, 1895, physicist Wilhelm Conrad Röntgen made a groundbreaking discovery of a new type of ray that could penetrate matter, which he named X-rays, with "X" representing the unknown At the time, Röntgen was a 50-year-old professor at Julius Maximilian University in Wurzburg, and his research aimed to explore the properties of cathode rays.
Hermann Ludwig Ferdinand von Helmholtz predicted the existence of "invisible high-frequency rays" based on Maxwell's theory of electromagnetic radiation Wilhelm Röntgen's groundbreaking discovery of these rays was submitted for publication on December 28, 1895, and subsequently published on January 5, 1896.
1896 A portable X-ray unit was available from the Sears catalog in late 1896 The cost was $15
Wilhelm Röntgen pioneered the creation of X-ray images using photographic plates, with human tissue being one of the initial materials examined His most renowned image features the hand of his wife, adorned with a ring, showcasing the groundbreaking potential of X-ray technology.
Figure 2-1 The first reported image of human tissue Mrs Rửntgen’s hand with a ring, taken in 1895
In 1901 Rửntgen received the Nobel Prize for Physics, which was the first Nobel Prize in physics ever awarded Unfortunately, Rửntgen, his wife, and his laboratory workers all
On January 13, 1896, Drs Ratcliffe and Hall-Edwards made history by utilizing X-rays for medical purposes, successfully locating a small needle embedded in a woman's hand This groundbreaking event paved the way for Dr J.H Clayton, who conducted the first X-ray guided surgery just nine days after the announcement of X-rays' discovery.
In 1896, Randolph Hearst, a prominent figure in the Hearst publishing dynasty, challenged scientists to capture an image of the brain Despite numerous attempts and the invention of innovative imaging techniques, such as pneumoencephalography, all efforts to succeed were unsuccessful While test subjects experienced no significant physical discomfort due to the brain's lack of pain receptors, they exhibited unusual behaviors and alterations in mentation, cognition, and motion patterns.
Allan Macleod Cormack and Godfrey Newbold Hounsfield made significant contributions to the development of the CT scanner, with Cormack providing the necessary mathematics in 1962 and Hounsfield creating the first hardware implementation in 1972 that could image the brain This groundbreaking scanner took approximately 24 hours to compute a single CT image In recognition of their work, Cormack and Hounsfield were awarded the Nobel Prize in Physiology and Medicine in 1979, although Hounsfield acknowledged that he did not invent CT, a concept originally published by Radon in 1917.
In 1961, a head phantom was rotated on a gramophone turntable, enabling simultaneous translation using an HO-gauge railway track, which was gradually moved through an X-ray beam directed at a detector This innovative setup allowed Oldendorf to reveal the internal structure of the phantom Notably, earlier reports from Russia in 1957 and 1958 indicated that a functioning CT machine had already been developed during that period.
X-ray physics
An X-ray is electromagnetic (EM) radiation similar to light, radio waves, TV waves, etc shows some of the components of the EM spectrum, their frequency, wavelength, energy, and use
Table 2.1 Electromagnetic Wave Spectrum (from [Enderle et al.])
Figure 2-2 graphically shows the electromagnetic spectrum and the corresponding energy of each component
Figure 2-2 The Electromagnetic Spectrum The photon energies are given in electron volts (eV)
Obviously there is a relationship between frequency and energy The relationship between energy and frequency for EM waves is
The energy of electromagnetic waves can be calculated using the formula E = hf, where E represents energy in kilo electron volts (keV), h is Planck's constant (4.13 x 10^-18 keV s or 6.63 x 10^-34 J s), and f denotes the frequency in hertz (Hz) It's important to note that 1 keV is equivalent to 1.6 x 10^-19 joules In a vacuum, all electromagnetic waves travel at the same speed, commonly referred to as the speed of light.
(c = 3.0x10 8 m s -1 ) The relationship is given by c=λf (2.2) where λ is the wavelength (m)
X-rays are also characterized as particles This is a wonderful example of the duality of nature – energy is simultaneously both a wave and a particle This is the message from
Einstein’s famous equation Viewed as a particle, an X-ray particle with velocity v and mass m has a momentum p given by
E mc= 2 hf h p mv mc = = = Ec = λf = λ (2.3)
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 Diagnostic radiation is typically in the range of 100 nm to about 0.01 nm, or from 12 eV to 125 keV
An electron volt (eV) is defined as the energy needed to move a quantum of charge, equivalent to 1.60 x 10^-19 coulombs, through a potential difference of 1 volt To break chemical bonds, energies ranging from 2 to 10 eV are required, which can be provided by electromagnetic (EM) waves, particularly in the ultraviolet (UV) region or higher Ultraviolet light has the capability to ionize tissue by breaking chemical bonds, posing significant health risks If such bond disruptions occur in the DNA molecule at specific locations, they can lead to skin cancer.
Low-energy electromagnetic (EM) energies, such as those below the ultraviolet level, are unable to break chemical bonds or produce ions The primary concern associated with these low-energy photons is tissue heating For example, infrared light heats objects by inducing vibration, while microwave ovens heat food by causing water molecules to tumble, resulting in an increase in temperature.
A classical experiment that shows the duality of EM energy is the double-slit experiment
In experiments involving photon behavior, when only one slit is open, a single bright spot is detected, indicating particle-like behavior However, when both slits are open, the photons exhibit wave-like characteristics, resulting in an interference pattern This demonstrates that photons do not strictly behave as particles or waves; their behavior is determined by the measurement context Thus, photons act either as particles or waves based on the detection method employed.
Figure 2-3 Classical double-slit experiment used to show dual nature of photons and electrons
Figure 2-4 Results of the double-slit experiment when both slits are open
The double slit experiment demonstrates that both electrons and electromagnetic (EM) radiation exhibit particle-wave duality, indicating that they can behave as both particles and waves While this duality is evident in subatomic particles and EM radiation, it is not perceived in larger objects, such as baseballs, due to their extremely small wavelengths being confined within their size.
Brief review of the structure of the atom
The structure of the atom, typically introduced in high school, plays a crucial role in understanding how electromagnetic (EM) waves or particles interact with human tissue This article will provide a brief review of atomic structure, highlighting its significance in these interactions.
An atom is composed of three fundamental particles: electrons, protons, and neutrons While there are numerous smaller particles that contribute to the atom's structure, their study is typically the domain of sub-atomic physicists specializing in modern physics.
Electrons carry a negative charge, while protons are positively charged, and neutrons are neutral The stability of the atomic nucleus, which contains protons and neutrons, raises questions about how it remains intact despite the repulsive forces between closely packed protons Without neutrons to mediate these forces, the nucleus would be at risk of exploding due to proton repulsion.
Nuclei with insufficient neutrons or an excess of protons and neutrons become unstable and can disintegrate Additionally, there are no stable isotopes for elements heavier than lead (Pb), highlighting the limitations of atomic stability in heavier elements.
• The number of protons is called the atomic number Hydrogen has only one proton, and its atomic number is one
• 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 sizes of the neutron and proton are almost equal (proton rest mass is 1.67x10 -
The atomic mass is defined as the total number of neutrons and protons in an atom, with the neutron rest mass being approximately 1.68 x 10^-27 kg and the electron rest mass significantly smaller at about 9.11 x 10^-31 kg.
• The electron cloud surrounding the nucleus largely determines the volume of space occupied by an atom
Electrons are restricted to specific orbitals with defined energy levels due to their wave-like nature, a concept known as the Bohr model, introduced by Niels Bohr.
• The Bohr model consists of the following (for the first few shells)
Shells Orbitals Number of electrons
• Each shell has a different energy (frequency), and each orbital within the shell has a unique energy
In 1921, Wolfgang Pauli reformulated the Bohr model using quantum mechanical principles, identifying four key quantum numbers that define an atom The principal quantum number (n) is an integer scalar quantity, while the angular momentum quantum number (l) is a vector quantity with integer values ranging from 0 to n-1 Additionally, the magnetic quantum number (mₗ) takes integral values from -l to +l, and the spin magnetic quantum number (mₛ) can have values of -½ or +½.
According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of quantum numbers
In an atom, only two electrons can share the same energy value, but they must possess unique energy states due to their differing spins, one being +½ and the other -½ This means that within a single orbital, each electron must have a distinct energy level Consequently, for any given atom, there can only be one electron at each unique energy level.
The binding energy of electrons in various energy levels is crucial for understanding how much energy is required to dislodge an electron from an atom Typically, electron binding energies range from 1 to 100 keV, indicating that electromagnetic (EM) waves with X-ray frequencies are necessary to alter an atom's electronic structure For instance, to determine if an EM signal with a wavelength of 1 nm is ionizing, we must calculate its energy If this energy exceeds 1-2 keV, the wave is classified as ionizing and poses potential risks to human health.
X-rays are classified as ionizing radiation because they have the ability to dislodge electrons from atoms, resulting in ion formation This process can alter the chemical bonds of crucial substances, including DNA Typically, the radiation emitted during diagnostic X-ray procedures falls within a specific energy range.
100 nm to about 0.01 nm, or from 12 keV to 125 keV
Higher energies are necessary to alter the nuclear structure of atoms, and gamma rays deliver the required energy to induce ionization Additionally, gamma rays can transform atoms from one type to another by changing their atomic mass and number.
Radio frequencies lack the energy needed to interact directly with atoms; instead, they influence the spin of electrons This unique property is essential for the creation of MRI images.
Interaction between X-rays and matter
Coherent (Rayleigh) scattering
Coherent scattering occurs when a photon collides with an electron, resulting in the photon being deflected into a new direction In this process, the low-energy photon experiences minimal energy loss and does not possess enough energy to ionize the atom, making it a non-ionizing interaction.
While scattering is generally not significant in medical imaging, it plays a notable role in the case of 125 I, which is utilized in nuclear thyroid scans The resolution of these scans is adversely affected by coherent scattering of the emitted photons.
Photo-disintegration
Nuclear reactions involve the interaction of high-energy photons with the nuclei of target atoms, leading to the ejection of nuclear particles and transforming one element into another This process can cause significant damage to human tissue, especially when the photon energy exceeds 1 MeV.
Photo-electric effect
Albert Einstein was awarded the Nobel Prize in Physics for his explanation of a particular modality, which, despite its basis in quantum mechanics, aligns with the qualitative understanding of the relationship between energy, frequency, particles, and waves that we have previously discussed.
According to quantum theory, electromagnetic radiation is composed of discrete packets known as photons The energy of each photon, denoted as E, is directly related to its frequency, f, through the equation E = hf, where h represents Planck's constant.
A photon possesses a single frequency and energy state, allowing it to interact with only one electron at a time, as it cannot share its energy with multiple electrons Traveling at the speed of light, a photon has zero rest mass, meaning its energy is entirely kinetic When a photon interacts with an electron, it transfers its total energy, causing the photon to vanish If the energy imparted exceeds the binding energy required to keep the electron within the atom, the electron can escape, resulting in the creation of a photoelectron The kinetic energy of this photoelectron is determined by the excess energy above the binding energy provided by the incident photon.
When a photon with energy equal to or greater than the binding energy of an atom's K shell interacts with an electron, it can eject a K-shell electron Atoms prefer not to leave their lowest energy levels vacant, prompting an electron from a higher energy level to fill the vacancy This process can occur through the direct movement of an outer shell electron to the lower energy level or via a cascading effect, where electrons shift from higher shells to lower ones sequentially, such as an L-shell electron filling the K-shell and an M-shell electron moving to the L-shell.
When an electron transitions from a higher energy shell to a lower one, it releases excess energy, which can result in the emission of photons or the liberation of other electrons from their shells The energy of the emitted photons during this process is referred to as fluorescent or characteristic energy, and the resulting radiation is known as characteristic radiation Additionally, the photoelectron generated in this process is termed an Auger electron.
Figure 3-1 Drawing of photoelectric effect (from [Sung et al.])
When a photon with energy E interacts with a K-shell electron, it transfers its entire energy to the electron If the binding energy of the electron is Eb, which is the energy needed to free it from its shell, then when E exceeds Eb, the excess energy is converted into kinetic energy This resulting moving electron is known as a photoelectron.
E hf= = m v +E where m 0 is the resting mass of the electron
When an electron transitions from a higher-energy shell to the K shell, it releases excess energy in the form of a photon The energy of this photon corresponds to the difference in binding energies between the two shells If the released energy is sufficient to overcome the binding energy of another electron, it can liberate that electron, resulting in what is known as an Auger electron.
As a quantitative example, consider the following The binding energies for Iodine are:
A photon with a frequency of 9.86 x 10^18 Hz ejects an electron from the K-shell, leading to the transition of an M-shell electron to fill the vacancy This process results in a change in energy of 32.6 keV, consequently emitting characteristic radiation with a photon energy of 32.6 keV.
Compton scattering
In Compton scattering, a photon interacts with an electron, transferring only a portion of its energy to the electron while continuing its path with reduced energy and frequency This results in a decrease in the photon’s momentum, and the electron is emitted from its shell This phenomenon is visually represented in Figure 3-2.
Figure 3-2 Illustration of the Compton scattering phenomenon
The momentum of a photon is given by the following equation
Thus the momentum of an EM wave depends on its frequency The direction of the momentum is along the direction of propagation of the wave
Considering a particle nature of a photon, one can use conservation of energy and momentum to describe the collision between a photon and a charged particle This interaction is graphically illustrated in Figure 3.3
Figure 3-3 Illustration of the interaction between a photon and a charged particle
The momentum of the incident photon is represented as hf, while the momentum of the resulting photon is denoted as hf' The momentum of the electron is given by mv By applying the Law of Cosines to the triangle illustrated in Figure 3-3, we can formulate an equation that reflects the principle of momentum conservation.
This equation can be solved for the change in wavelength (or energy) as
From this the energy of the scattered photon is
The wavelength of a scattered photon is longer than that of the incident photon, resulting in a decrease in energy This energy and wavelength change is determined solely by the electron's rest mass, the speed of light, Planck's constant, and the angle of scattering This fundamental value, which is consistently observed, is equivalent to 511 keV.
High-energy photons exhibit more Compton scattering than low energy photons
Compton scattering is a significant contributor to background noise in X-ray images and is also the primary cause of tissue damage from X-rays, making it an undesirable phenomenon in medical imaging.
When the incident energy (E) is low, the scattered energy (E′) remains relatively constant regardless of the scattering angle (θ) Conversely, at high incident energy levels, the scattered energy increases at smaller angles, suggesting that higher-energy scattered photons tend to maintain a similar trajectory.
Pair production
Pair production occurs when high-energy photons interact with a nucleus, resulting in the emission of a positron and an electron This phenomenon is rare in diagnostic radiology due to the significant energy requirements However, pair production plays a crucial role in the formation of antimatter, which is utilized in positron emission tomography (PET) scanning.
Summary
The primary modes of interaction are
1 Photoelectric in which a photon is absorbed, characteristic radiation is emitted along with photo-electrons, and possibly Auger electrons
2 Compton scatter in which a photon is not absorbed but rather scattered The photon energy is reduced, and an electron is ejected This is the major source of noise in X-ray (and CT) images
3 Pair production in which a photon is absorbed by the nucleus, a positron is emitted, and an electron is ejected
The occurrence probability of X-ray absorption mechanisms in human tissue is influenced by factors such as incident energy, electron configuration, atomic number, and tissue mass A key understanding of medical X-ray physics reveals that at energy levels between 50 keV and 200 keV, the majority of energy absorbed by tissue is due to the photoelectric effect, while Compton scattering contributes to image noise Pair production, however, typically occurs at energy levels outside the range used in medical X-rays.
Low energy photons are mainly absorbed through the photoelectric effect, while high energy photons are absorbed via pair production Mid-level energy photons are primarily absorbed through Compton scattering.
Dose and Exposure
Dose equivalent
The dose equivalent is measured in sieverts (Sv) and represents the amount of radiation that poses an equivalent risk of health damage, regardless of the radiation type.
The radiation weighting factor is a constant that varies based on the type of radiation Additionally, the rem, an older unit of measurement, is still in use and is connected to the sievert through a specific relationship.
1 rem = 0.01 Sv = 0.01 J kg -1 tissue x constant The dose equivalent in Sv is obtained by multiplying the dose in Gy by a constant: dose in Sv = dose in Gy x constant
The radiation weighting factors indicate that X-rays and γ-rays have a factor of 1, neutrons have a factor of 10, and α particles have a factor of 20, suggesting that exposure to X-rays is preferable to that of α particles For a clearer understanding of radiation doses, refer to Table 4.1, which illustrates the various unit sizes.
Table 4.1 Typical figures for X-ray doses for five different conditions
Dose due to background radiation in 1 year (in Iowa) 1 mSv=0.1 rem
Level set as the maximum dose to the general population in 1 year (a larger dose is sometimes allowed in 1 year provided the 5-year average does not exceed 1 mSv)
Level set as the maximum dose to people who work with radiation (50 mSv is the maximum any one year) 20 mSv = 2 rem
Dose exposure that will cause nausea, sickness, diarrhea in most people 0.5 Gy = 50 rad
Dose exposure that will kill many people in a few months following exposure 6 Gy = 500 rad
Maximum permissible levels
The maximum permitted doses in various codes of practice are measured in dose equivalent units The International Commission on Radiological Protection (ICRP) advises that radiation workers should not exceed an annual dose equivalent of 50 mSv (5 rem), with a five-year average below 20 mSv per year Specific body parts may tolerate higher doses, while for the general public, the recommended whole-body dose is limited to 1 mSv (0.1 rem) averaged over five years.
Table 4.2 Maximum permitted doses from ICRP
Radiation worker 50 mSv = 5 rem (5-yr average < 20 mSv = 2 rem)
Public 1 mSv = 0.1 rem over 5 years
The US Nuclear Regulatory Commission has established exposure limits for the general public at a maximum of 0.5 rem per year, while occupational exposure limits are set at 1.25 rem per three months for the whole body and 18.75 rem per three months for extremities To ensure safety, routine personal monitoring is conducted using film badges and ring-type finger badges.
Over the past 70 years, the maximum permitted dose levels for ionizing radiation have significantly decreased, from 15 mSv (1.5 rem) per week in 1931, with potential for further reductions due to the long-term effects of even small doses These effects contribute to ongoing debates about establishing "safe" exposure limits, as the biological impacts can only be quantified statistically, indicating the likelihood of conditions such as leukemia or other cancers developing over time Assessing risk is further complicated by natural causes of such changes Young individuals, particularly unborn fetuses, face the highest risk from ionizing radiation, leading to specific maximum exposure levels for them For instance, the "10 day rule" advises that women should only undergo diagnostic X-ray procedures during the 10 days post-menstruation when the chance of pregnancy is low.
Environmental dose
Throughout our lives, we encounter radiation from various sources, both natural and man-made It is essential to quantify the body's exposure to these different radiation sources and compare the results with the maximum allowable dose.
Table 4.3 The doses correspond to six different situations (values are approximate)
Cosmic radiation 200 àSv (20 mrem) over 1 year
Natural radioactive materials (e.g., 238 U) 300 àSv (30 mrem) over 1 year
Naturally occurring radioactive materials in the body (e.g., 40 K)
Chest X-ray 500 àSv (50 mrem) skin dose for one X-ray
Coronary angiogram 20 mSv (2 rem) skin dose for one procedure Nuclear power station < 1mSv (100 mrem) over 1 year 1 km from the station
Body parts – whole body dose
Radiation safety regulations establish a maximum dose of 20 mSv (2 rem) for radiation workers and 1 mSv (0.1 rem) for the general public, based on the potential risk of biological damage However, some experts argue that radiation hazards are often overstated when compared to other life risks For instance, Table 4.4 presents data illustrating the equivalent risk of death over one year from various hazards.
Table 4.4 All of these activities carry the same risk They give a 1 in 20000 chance of
Table 4.4 causing death in 1 year (from E.E Pochin, 1974)
Exposure to 5 mSv (0.5 rem) whole-body radiation
Smoking 75 cigarettes Traveling 2500 miles by motor car Traveling 12 500 miles by air Rock climbing for 75 minutes Canoeing for 5 hours
Working in a typical factory for one year Being a man aged 60 for 16 hours
Being a man aged 30 for 20 days
The information presented is intended to provide perspective on the risks of radiation, rather than downplay its harmful effects It's important to note that these findings are derived from statistical models rather than direct laboratory measurements.
Table 4.5 presents typical radiation doses for various common radiological examinations, highlighting that some doses approach the recommended limit of 0.1 mSv averaged over five years for the general public.
CC = Cranio-caudal view or projection
AP = Anterio-posterior view or projection
The International Commission on Radiological Protection (ICRP) recommends using the effective dose equivalent (EDE) to quantify the potential harm from radiation exposure, reflecting the dose that would produce the same detriment if applied to the entire body Although calculating the EDE is complex and involves Monte Carlo simulations, it ultimately yields a figure indicating the overall radiation risk associated with specific clinical procedures Each procedure is assigned an EDE, prompting the importance of selecting those with lower EDE values for patient safety For reference, Table 4.6 outlines the effective dose equivalents and organ doses for various diagnostic procedures.
Table 4.6 Effective dose equivalent (mSv) and organ doses (mGy) for breast, red bone marrow, lung, thyroid, skin, ovaries, and testes for selected radiological examinations (from [Webb])
EDE Breast RBM Lung Thyroid Skin Ovary Testes
The literature on ionizing radiation hazards is enormous A general qualitative understanding for the situation can be gained, however, by consensus statements such as
The average risk of inducing a fatal malignancy from a tissue dose of 10 mSv is approximately 1 in 10,000, with a similar risk range of 0 to 1 per 1,000 for serious malformations and cancers in developing embryos or early fetuses It is crucial to minimize radiation exposure, particularly for young patients, as current medical imaging practices can result in tissue doses between 0.1 and 100 mSv per examination, with nuclear medicine and CT procedures often exceeding these limits This article will explore the implications of these radiation risks for medical imaging engineers.
Propagation model
Simple transmission imaging
The transmission image, denoted as I(x, y), represents a two-dimensional projection of the three-dimensional distribution of X-ray attenuation properties within tissues When an X-ray beam with an initial intensity I0 strikes a block of uniform tissue, the interaction is influenced by the beam's cross-sectional area A and the cross-sectional area of an atom in the tissue, σ.
Figure 5-1 X-ray beam of cross-section A intersects tissue of thickness x
In a block of tissue, let n denote the number of atoms per unit volume, which results in a total atomic cross-sectional area of nσ per unit volume Given that the beam has a cross-sectional area of A units, the total area of atoms impacted by the beam can be expressed as Anσ Consequently, the likelihood of a photon in the beam interacting with an atom is determined by this relationship.
Assuming that any interaction fully attenuates the X-ray energy beam is an oversimplification, as this is not typically the case Under this assumption, the change in beam intensity within a small thickness of the beam, denoted as dx, can be expressed mathematically as dI = −n Idxσ This relationship indicates that the rate of change of intensity, dI, is proportional to the product of the number of interactions, n, the initial intensity, I, and the attenuation coefficient, σ, leading to the equation dI/nI = −σ.
Solving this simple equation yields the simple by critically important solution given by
I x =I e − à (5.4) where à =nσ is called the linear attenuation coefficient (1/cm), and x is the path length
The linear attenuation coefficient, denoted as à, is a crucial factor in understanding photon intensity, represented by I x at position x, in relation to the initial intensity, I 0, from the X-ray source This concept applies specifically to homogeneous tissue and mono-energetic X-ray photons, highlighting that the coefficient varies with photon energy.
Attenuation coefficient
Normalizing the attenuation coefficient by the tissue's density (ρ) results in a mass-attenuation coefficient, which helps ensure that the coefficient remains consistent regardless of the tissue's physical state For instance, when a 50 keV X-ray beam passes through water, this normalization allows for a more accurate analysis of the tissue's interaction with the X-rays.
Table 5.1 Attenuation coefficients for water in different states
If we compute the mass-attenuation coefficient, then for all states:
2 gm -1 Figure 5-2 depicts the mass-attenuation coefficients for different tissue types and other materials as a function of the energy levels of the X-ray incident photons
Figure 5-2 Mass-attenuation coefficients of several media as functions of X-ray energy
To achieve optimal contrast between bone and muscle in imaging, it is essential to select the appropriate photon energy, such as using a 30 keV beam instead of 100 keV The significant mass-attenuation coefficient of Iodine makes it a preferred choice as a contrast agent in these applications.
Certain materials display "discontinuities" in their mass-attenuation coefficients, notably seen in Iodine, where a significant increase occurs around 35 keV This spike corresponds to the bonding energy of K-shell electrons surrounding the nucleus, a phenomenon known as the K-edge.
The attenuation coefficient is essential for determining the half-value layer (HVL), which represents the thickness needed to reduce the beam intensity by 50% By solving Equation (5.4) for the variable x, we can obtain the required value.
The HVL is sometimes known as the half-value thickness
As an example, water (in liquid state) has an attenuation coefficient à=0.214 cm -1 at 50 keV The HVL is then
So 3 cm into the material the beam intensity is reduced to I 0 /2, 6 cm into the material the intensity is I 0 /4, etc
Representative HVLs for soft tissue are: 22 mm at 30 keV, 35 mm at 60 keV, and 45 mm at 120 keV This indicates that HVLs are a function of the energy of the X-ray beam.
Transmission imaging
The formulation used to derive Equation (5.4) is based on a thin beam passing through a homogeneous block of tissue, and assuming that the attenuation coefficient is constant along x
Consider Figure 5-3 in which the X-ray beam passes through lung, water, soft tissue, and bone In this case, the attenuation coefficient is not constant
Figure 5-3 The geometry of X-ray transmission imaging
The intensity arriving at the film (or detector) is more generally written
∑ ∆ (5.7) where the path is divided into intervals ∆z i
To illustrate the application of Equation (5.7), we can analyze the contrast between a lung tumor and the surrounding normal tissue in a conventional X-ray image In this scenario, X-ray photons travel through approximately 35 cm of the chest, encountering 3 cm of chest wall tissue initially, followed by 29 cm of lung air and tissue, and concluding with another 3 cm of chest wall tissue This process highlights the significant intensity difference that can be measured between the tumor and adjacent healthy tissues.
(if the beam passes through the inter-costal space) The total attenuation is the following:
The attenuation coefficients for chest wall tissue and lung are à 1 =0.14 cm -1 and à 2 =0.05 cm -1 Thus the intensity of the image arriving at the detector is
With a 3 cm round tumor with attenuation coefficient of 0.14, we will need to add attenuation given by e − ( 0.14 3 x ) , which will result in a decrease in intensity by
This is a change in contrast of 23% If photons pass through two 1.5 cm thick ribs with a bone attenuation coefficient of 0.4 cm -1 , then we observe
As the number of photons decreases, the exposure to the film or detector diminishes, resulting in a brighter image in that area Analyzing the logarithm of the ratio between incoming and outgoing intensity can provide valuable insights.
Note that the logarithm of the intensity ratio, which is named the projection , is simply the line integral of attenuation coefficients if the
∆z s approach zero In this case,
This sum is called a ray sum You will work with the ray sum extensively when computing CT images in subsequent courses.
Brief Summary So Far
X-ray imaging is primarily an anatomical procedure that relies on the interaction of energy with body tissues Some energy passes through the body without any interaction, while other energy interacts with the tissues The contrast in the resulting image is determined by the difference between the photons that interact with the tissues and those that do not.
Photons interacting with matter can lead to ionization primarily through the photoelectric effect and Compton scattering The derived equations, particularly Equation (5.4), describe these effects and the intensity of X-ray beams as they pass through the body, but they are applicable only to monochromatic radiation In reality, X-ray photons emitted from sources are typically heterogeneous or polychromatic, meaning that photons of varying energies are attenuated differently This complexity in photon transmission necessitates that the effective energy of a polychromatic beam is defined as the energy of a monochromatic beam with the same half-value layer.
Beam hardening is a significant concept in which a polychromatic beam, after passing through a medium, exhibits a reduction in lower-energy photons, leading to an increase in the effective energy of the beam.
Generation of X-rays
White radiation
When an electron approaches a positively charged nucleus, it experiences attraction, causing it to deviate from its path If the electron retains its energy, this phenomenon is termed elastic scattering, resulting in no X-ray photon emission Conversely, if the electron loses energy during the interaction, it undergoes inelastic scattering, leading to the production of a photon known as white radiation.
Figure 7-2 Deflection of high-energy electron by nucleus produces white radiation
The probability of the electron to lose energy increases as the atomic number of the atom increases In the high-energy limit the probability density is given in E Lohrmann,
The electron may interact with many nuclei, therefore the energies of the X-ray photons generated by this process are distributed over a wide range of values, as shown in
Figure 7-3 X-ray spectrum produced by the tungsten target of an X-ray tube
Characteristic radiation
When high-energy electrons collide with the inner shell of target atoms, they produce characteristic radiation, akin to the photoelectric effect This phenomenon is illustrated in Figure 7.2, which depicts the characteristic radiation emitted when L-shell electrons transition to the K shell at energies of 59.3 keV and 57.9 keV, as well as M and N-shell electrons transitioning to the K shell at energies of 67.2 keV and 69 keV, respectively.
Heavier elements, particularly tungsten, are known for their ability to emit x-rays when bombarded with electrons, primarily through bremsstrahlung While tungsten is preferred due to its high intensity and excellent thermal conductivity, the challenge lies in the engineering aspect, as many electrons fail to produce significant x-ray emissions, resulting in heat generation instead Tungsten's high melting point allows it to endure this electron bombardment effectively.
Bremsstrahlung, or "braking radiation," refers to the electromagnetic radiation produced when charged particles, such as electrons, are decelerated or deflected by other charged particles, typically atomic nuclei This phenomenon is significant in various fields, including astrophysics and medical physics, as it contributes to the energy loss of high-energy particles in matter The intensity and spectrum of Bremsstrahlung radiation depend on several factors, including the charge and velocity of the incoming particle, as well as the atomic number of the target material Understanding Bremsstrahlung is crucial for applications like radiation therapy and the design of particle accelerators.
For the continuous bremsstrahlung spectrum, equate the quantities
The charge on the electron, denoted as e, along with the voltage change (V), Planck's constant (h), and the speed of light (c), are crucial variables in determining the minimum possible wavelength of radiation By rearranging the equation, we can solve for the desired variable, yielding important insights into the relationship between these fundamental constants.
The cross section for an electron to be observed in a solid angle is given by
In the soft-photon limit, the initial and final velocities are denoted as and , while represents the range of wavenumbers For a specific scattering angle, the last two integrals can be expressed as
The first integral can be reduced to
This can be expanded in a series as
(7) in the nonrelativistic limit (Bjorken and Drell 1964, pp 126-127)
X-ray generators
An X-ray tube operates in a vacuum, allowing precise control over the number and speed of electrons striking the anode, which is typically made of tungsten or molybdenum The cathode consists of a tungsten filament and a focusing cup; the filament, a helical coil approximately 0.2 mm in diameter, heats up when current flows through it, energizing the electrons If the temperature reaches a sufficient level, electrons escape from the filament and are accelerated towards the anode by a high-voltage potential applied between the anode and cathode.
Figure 7-4 Basic components of an X-ray source
The energy from electrons is primarily transformed into heat at the focal spot, where the anode angle directs the electron flow into a concentrated area To prevent the formation of a hole in the cathode, the target material continuously rotates.
Figure 7-5 Drawing of a typical X-ray tube
The X-ray tube electrical diagram is schematically shown in Figure 7-6 The tube voltage V t can be dc or ac The intensity of the X-ray beam is proportional to the power delivered to the tube from the supply voltage; thus, the beam intensity is proportional to the tube voltage V t squared Typical tube voltages range from a few kilovolts to about
Figure 7-6 Electrical circuits associated with an X-ray generator
The production of X-ray photons in the tube is directly influenced by the number of electrons hitting the target material, making it dependent on the tube current Experimental findings indicate that the emitted photon count is linearly proportional to the tube current, which typically varies from a few milliamperes to several hundred milliamperes.
As the tube voltage rises with a constant filament current, the tube current initially increases; however, after reaching a certain voltage, further increases in potential difference do not affect the tube current, a phenomenon known as saturation current In this saturation region, the tube current is constrained by the filament temperature, which is directly related to the filament current, typically ranging from a few amperes.
In normal operating conditions, when the tube is saturated, the intensity of the beam is directly proportional to the tube current, commonly referred to as mA by radiology technicians.
The intensity of the X-ray beam is theoretically proportional to the tube current and the square of the tube voltage In practice, the beam intensity is primarily adjusted by modifying the tube current, typically achieved by altering the filament current Consequently, adjusting the filament current directly influences the intensity of the emitted X-ray photons.
The X-ray beam coming off the cathode material is polychromatic Usually only a portion of the beam spectrum is desirable Filtering out the undesired portion of the X-ray spectrum can substantially reduce the radiation dose delivered to the patient Remember, the low-energy photons don’t have enough energy to make it through the body (see
) As a result, the body absorbs almost all of the low energy photons, and no energy reaches the detector This situation increases the chances of iatrogenic effects Figure 5-2
The glass encasing the X-ray tube plays a crucial role in filtering the X-ray beam, with a sheet of aluminum positioned directly beneath the tube to enhance this filtration This aluminum layer effectively reduces the lower energy components of the beam, with a 3 mm thickness capable of attenuating over 90% of X-ray energy at 20 keV Additionally, copper is utilized in the filter sheet, serving as an efficient filter for the higher energy portions of the beam's spectrum.
Grids
X-rays are scattered, primarily by photoelectric effect and/or Compton scattering effects The scattered photons appear on the X-ray image as noise that degrades image quality and increases patient exposure Therefore, great efforts are expended in minimizing scattering The most effective method is to place an X-ray grid under the patient and before the detector as shown in Figure 7-7
Figure 7-7 Scattered X-ray photons can be removed from the image by positioning a grid between the patient and the detector (or film)
Grid strips, typically made of lead due to its excellent X-ray absorption properties, can be designed to minimize their visibility on detectors by using thinner strips However, when thicker lead strips are required for image quality, the grid may be repositioned during exposure to obscure the grid line image The grid referenced is known as a linear grid, while other variations exist, such as the focused grid, which aligns the strips towards the X-ray source.
Detectors
The human eye is unable to detect X-ray photons because our rods and cones are sensitive only to lower frequency electromagnetic waves As a result, the energy transmitted by X-rays must be transformed into a visible format that we can perceive.
“see.” This conversion is usually done by
1 exposing a photographic film: the X-ray energy excites the silver halide crystals, which are washed off leaving a viewable film;
2 estimating the photon density by measuring the ionization in a gas;
3 converting the X-ray photons to visible light, amplify this light with a photomultiplier tube, and view; or
4 building a solid state detector with current flow proportional to incident photon density
The resulting images suffer from the non-ideal nature of the X-ray source and detectors These non-deal qualities are due to geometric unsharpness, beam size, and object magnification
The finite aperture of an X-ray source leads to image blurring, known as geometric unsharpness or penumbra When the X-ray beam has a width of 'f', a point in the patient appears smeared with a width of 'd' To minimize this blurring effect, one can increase the source-to-patient distance (S), decrease the patient-to-detector distance (t), or install a point collimator near the tube to reduce the beam width (f).
Figure 7-9 demonstrates how beam size divergence impacts photon trajectories, leading to an increase in beam size as the distance from the source increases To mitigate this divergence effect, it is recommended to reduce the distance between the source and the patient.
Of course, this solution exacerbates the penumbra blurring effect Oh well
Figure 7-9 Effect of diverging X-ray beam size
Figure 7-10 X-ray image of object magnified by ratio ( f f )
The magnification effect, represented by S − t, demonstrates that an object's apparent size is influenced by its position within the scanner's field of view Specifically, objects positioned closer to the source appear larger than those that are the same size but located further away To reduce this magnification effect, it is advisable to increase the distance between the patient and the source.
The human eye cannot directly perceive X-ray information, necessitating the conversion of X-ray images into a visualizable format, typically initiated by an intensifying screen This screen consists of a phosphor layer, ranging from 0.05 to 0.3 mm thick, that emits light photons when exposed to X-ray photons Common phosphors include calcium tungstate (CaWO4) and terbium-activated rare-earth oxysulfide, with newer phosphors like gadolinium (Gd2O2S) offering improved efficiency While CaWO4 has an efficiency of only 5%, newer phosphors can exceed 15% efficiency and emit light in specific narrow bands, predominantly green or blue.
Many electronic imaging systems use image intensifiers (show schematically in
X-ray photons that pass through a patient are absorbed by a fluorescent screen, typically ranging from 15 to 35 cm in diameter, which then emits light photons These light photons hit a photocathode at ground potential, resulting in the emission of electrons proportional to the screen's brightness The photocathode is generally composed of antimony or cesium compounds An anode, set approximately 25 kV higher than the cathode, accelerates and focuses the electron beam onto a smaller output fluorescent screen, usually measuring 1.5 to 2.5 cm in diameter.
Figure 7-11 Physical construction of an image intensifier
There are two primary types of radiation detectors utilized for X-ray detection: scintillation detectors and ionization chamber detectors A scintillation detector typically features a scintillation crystal, often made of sodium iodide doped with thallium, paired with a photomultiplier tube to enhance detection capabilities.
Figure 7-12 Physical construction of a scintillation detector with a photomultiplier tube
A photocathode generates electrons upon exposure to light, which are then accelerated by dynodes coated with materials that emit secondary electrons when hit by an electron This process effectively multiplies the number of electrons as the beam travels through each dynode Consequently, the output current correlates directly with the number of electrons impacting at voltage Vn, achieving an impressive efficiency exceeding 85%.
The ionization chamber, depicted in Figure 7-13, is a cost-effective radiation detector that features a gas-filled chamber, typically with xenon When X-ray photons enter the chamber, they ionize the gas molecules, creating ions that are subsequently drawn to the electrodes due to a voltage difference This compact device is known for its small size and affordability, making it a practical choice for various applications.
Figure 7-13 Physical construction of a radiation detector: ionization chamber
Miscellaneous X-ray procedures
There are many X-ray based procedures used in medical diagnosis Some are fluoroscopy, mammography, and Xeroradiography
X-rays can be captured on film, or viewed directly on a fluorescent screen Figure 7-14 illustrates a conventional fluoroscope In a typical fluoroscopic procedure for examining the GI tract, a contrast medium (usually barium sulfate) is taken orally or by enema shows a colon radiograph where colon containing the contrast medium appears darker than the surrounding tissues Because the patient is being continuously exposed to X-ray radiation, the radiation dose can be very high
Figure 7-14 Basic components of fluoroscopy
Figure 7-15 X-ray radiogram of the colon following air-barium double-contrast enema
X-ray mammography is usually performed without contrast injection Mammography has a couple of special requirements For example, low energy (typically 20 keV) X-rays are used since the tissues are soft As a result, the anode in the X-ray tube is made of molybdenum Modern mammography units can achieve spatial resolution of better than 0.1 mm with very low radiation dose
Xeroradiography is an innovative X-ray technique created by the Xerox Corporation, utilizing X-ray energies ranging from 35 to 45 keV This method employs an electrostatic process akin to that of a Xerox photocopy machine A typical xeroradiographic image, such as one of a breast, is illustrated in Figure 7-16, showcasing the unique physical attributes of this technology.
Figure 7-16 Physical construction of Xeroradiographic system
Figure 7-17 Xeroradiogram of breast where ribs and breast vasculature are seen
Summary and history
Before the discovery of X-rays by Dr Röntgen, physicians primarily relied on patient history and their questioning skills to diagnose illnesses, as accurate diagnosis was crucial for effective treatment They utilized their senses—sight, touch, hearing, smell, and even taste—to detect abnormalities in patients.
Figure 8-1 The Grecian- Roman era of medical diagnosis
Hippocrates revolutionized medicine by emphasizing patient observation and disease progression, focusing on the patient's appearance, temperature, and even the smell of their vomit While physicians excelled in external examinations of injuries and ailments, internal investigations were infrequent Notably, Hippocrates innovated techniques like the Hippocratic Succussion Splash, where he would shake patients with pleurisy to identify fluid in the pleural space.
Observations are considered to be more scientific if measurement of them can be made
In ancient Alexandria around 300 BCE, Herophilus pioneered the practice of pulse assessment using a water clock, laying the groundwork for future medical diagnostics By 129 ACE, Galen advanced medical techniques by emphasizing the importance of touch and palpation for diagnosing conditions, which proved crucial for evaluating wounds and injuries His experience in sports medicine, particularly with gladiators, further enriched his understanding of physical trauma and healing.
Galen assessed patients by observing their general appearance, tasting sweat for signs of jaundice, and listening to the sounds of the abdomen He gained valuable insights from feeling the pulse at both wrists with three fingers, as it was believed to indicate organ disorders This understanding of the pulse shares similarities with concepts in Chinese medicine, suggesting a possible exchange of ideas along the Silk Road While the Chinese did not measure the pulse, they were known to derive significant information from its characteristics.
Figure 8-2 Methods of feeling the pulse, and interpreting the information gained
In 1583, a medical student, distracted by a sermon, noticed the consistent swinging of an altar lamp, which inspired him to realize that this motion could be used as a method for measuring time.
Galileo (1564-1642) who, as we know, gave up medicine for astronomy fame and ill fortune at the hands of the Catholic Church Galileo's pendulum clock was adapted by
Sanctorius (1561-1636) significantly contributed to physiology by introducing the use of a thermometer for temperature measurement and a weighing chair to assess food and fluid intake and output Despite these innovations, the limited understanding of bodily functions at the time meant that his measurements did not advance medical knowledge However, the Italian Renaissance brought about a transformative shift, as anatomists began to accurately identify the state of the body's organs, paving the way for a deeper understanding of their functions.
William Harvey (1575-1657), an English physician who studied in Italy, is renowned for his groundbreaking work on blood circulation; however, he did not contribute to disease diagnosis He believed that the heart was responsible for distributing the body's humours and spirits Following him, in 1707, Sir John Floyer (1649-1734) further explored the complexities of the circulatory system.
1743) introduced the pulse watch and thought it of more value than Harvey's work
In 1731, Stephen Hales introduced a groundbreaking method for measuring blood pressure by inserting a cannula into arteries and veins to assess the height of the blood column This advancement in understanding the body's functions marked a significant shift in medical practice, as it paved the way for recognizing that many diseases stem from structural or functional abnormalities in organs.
Figure 8-3 Schematic of Harvey’s blood pressure measurement system
Dr Röntgen's discovery of X-rays revolutionized medicine, significantly impacting diagnostic practices alongside other advancements like anesthesia and the understanding of sepsis This innovation enabled medical professionals to examine the knee and hip, among other areas, without the need for invasive surgery, as demonstrated in the accompanying images.
Figure 8-4 Anatomic information obtained from a modern X-ray study
Figure 8-5 Acetabular fracture on the left posterior lip