Table of Contents
Foreword
Chapter 1. Interactions between Radiation and Matter: Consequences for Detection and Medical Imaging
1.1.The limits of imaging using light
1.2.Imaging with other types of radiation
1.3.X-rays: their interaction with matter
1.4.Radiological imaging relies on the X-ray-matter interaction
1.5.Consequences of interaction modes on detection
1.6.Conclusion
1.7.Bibliography
Chapter 2. Detectors for Medical Imaging
2.1.Radiation-matter interaction and signal formation
2.2.Flux, energy, time and position measurements
2.3.Semi-conductor detectors
2.4.Scintillation and measurement channel
2.5.Pixel detectors
2.6.Bibliography
Chapter 3. Quantitative Digital Radiography Image Processing
3.1.Introduction to flat-panel sensors
3.2.Relation between physical quantities and radiographic acquisition
3.3.Access to linear attenuation coefficients from the attenuation image
3.4.Access to physical dimensions by combining several X-rays of a flat sensor
3.5.Conclusion
3.6.Bibliography
Chapter 4. X-Ray Tomography
4.1.Introduction
4.2.Principle of the first acquisition systems
4.3.Physical aspects and the direct problem
4.4.Principle of tomographic image reconstruction
4.5.Evolution of X-ray scanners and reconstruction algorithms
4.6.Examples of clinical applications
4.7.From tomography to micro-tomography
4.8.Conclusion
4.9.Bibliography
Chapter 5. Positron-Emission Tomography: Principles and Applications
5.1.Introduction
5.2.PET: principle and performance
5.3.PET systems
5.4.PET for cancer staging
5.5.Conclusion
5.6.Bibliography
Chapter 6. Single Photon Imaging
6.1.Introduction
6.2.Overview of single photon imaging
6.3.Conventional detection systems in single photon imaging: the scintillation gamma camera
6.4.Innovative systems: semiconductor detectors
6.5.Tomographic reconstruction and corrections
6.6.Hybrid detectors
6.7.Applications
6.8.Future developments
6.9.Conclusion
6.10.Bibliography
Chapter 7. Optical Imaging
7.1.Introduction
7.2.Physics of luminous propagation in biological tissue
7.3.Different optical imaging techniques for different applications
7.4.Conclusion
7.5.Bibliography
List of Authors
Index
First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Adapted and updated from Imagerie médicale à base de photons : radiologie, tomographie X, tomographie gamma et positons, imagerie optique published 2010 in France by Hermes Science/Lavoisier © LAVOISIER 2010
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
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© ISTE Ltd 2011
The rights of Hervé Fanet to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Cataloging-in-Publication Data
Photon-based medical imagery / edited by Hervé Fanet.
p. ; cm.
Includes bibliographical references and index.
ISBN 978-1-84821-241-1
1. Diagnostic imaging. 2. Photons--Diagnostic use. I. Fanet, Hervé.
[DNLM: 1. Diagnostic Imaging. 2. Photons--diagnostic use. WN 180]
RC78.7.D53P46 2011
616.07'54--dc23
2011012245
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-241-1
After 100 years of latency, medical imaging has been the subject of considerable evolution in the last 30 years. This is mainly the result of the convergence of major innovations in the field of detection, information processing, and instrumentation. This convergence would not have happened without the extraordinary progress of computation power, which is necessary because of the considerable increase in data processing. Previously radiography, nuclear medicine, magnetic resonance imaging (MRI), and ultrasound used to represent “single spectral” methods, independent from one another; however, today emerging techniques called multispectral imaging combine two imaging techniques in the same device, the most accomplished example is positron-emission tomography-computed tomography (PET-CT). This convergence enables us to go beyond the diagnostic stage and reach that of therapy: MRI-based high-energy focused ultrasound is a perfect example.
Information sciences and the development of “physiological” models opened up functional imaging to methods initially used for their physical properties: the extraction of circulation parameters from dynamic scanners or MRI sequences has become an essential tool in the study of tumor response to therapy.
Initially intended for the study of the whole body, high-resolution imaging techniques are starting to emerge: the same can be said for optical imaging, but this is limited because of low sampling. However, its use on man, notably in the endoscopy methods and in the future, probably in imaging-guided biopsy methods, seems very promising.
Imaging is the subject of very intense intrinsic research, and conversely, is considered as an essential tool in physiological and metabolic, or even cognitive, research, because of the integration of physiological signals to imaging data. In this way, magnetic tattoo methods on the cardiac muscle have elucidated the physiology of contraction; the study of aortic stiffness shows that it can presently be considered as an early marker for ageing. In addition, these imaging methods have become vital in preclinical studies in animals: the development of new drugs greatly benefits from these methods. In a more general way, small animal imaging platforms have been developed in a context of multidisciplinarity, and show the interconnection of imaging with physical sciences, information sciences, chemistry, and biology.
In this context, the setup and development of markers and tracers represent a common issue for all imaging methods; having already been developed in nuclear medicine, contrast materials for molecular and other forms of imaging in animals or man should be the subject of future progress. Substances with diagnostic and therapeutic properties are starting to emerge and are being developed. Imaging progress is also achieved through advances in the field of chemistry.
This book is an attempt to define the progress achieved in the different imaging fields; undoubtedly, the reader will come out with a richer understanding.
Guy FRIJA
The goal of medical imaging is to provide the practitioner with information to reveal, examine, or diagnose disease. Light is absorbed, scattered, or reflected by most types of matter over a very short distance, a few dozen to a few hundred microns for biological tissues, for example.
Medical imaging must provide the practitioner with information on the internal organs to provide a better diagnosis or to direct surgery. Endoscopy provides high-quality visual images of the body's cavities, such as bronchial tubes, the stomach, or the intestine. However, these tests are often complex, requiring preparation and/or anesthesia, and can be risky; therefore, they are usually reserved for cases where visual information provides a real advantage, particularly when surgery can be performed at the same time as the observation (a colonoscopy or an arthroscopy for example). With the aim of extracting information on organs or internal lesions, numerous studies are trying to develop light-scattering techniques in live tissue.
Hemoglobin greatly absorbs wavelengths shorter than 600 nm, and water absorption strongly increases beyond 900 to 1,000 mn. The result is a spectral window between 650 nm and 1 μm for which the absorption of light in animal tissueis minimal. Despite weak transmission, a measurable quantity of light remains in the tissue at a depth of a few centimeters. However, the heterogeneity of the envirormient causes very strong scattering, so much so that there are no longer any direct rays (so-called “ballistic” photons) providing optical imaging.
A digital reconstruction of the three-dimensional structure of the area observed is possible from the distribution of scattered light on the outside surface for different positions of a source located on the other side of the observation. This is the principle of optical tomography.
The use of a fluorescent marker with a specific affinity for the examined object, for example a tumor, makes it possible to detect the object within the tissue. As fluorescence occurs at a different wavelength than excitation, and as it comes completely from the inside, we can use more sensitive detection processes, because direct light does not impede the light to be detected, as in the case of optical tomography. This method is particularly useful for small animal imaging [KOE 07], and for the human body in applications involving superficial organs or areas where endoscopy can be considered.
In order to provide a complete image of the internal organs regardless of distance, we must use penetrating radiation, which is able to traverse 10–30 cm of tissue of low attenuation.
X-rays have this power of penetration through tissue. They have been used for this purpose ever since they were discovered by Röntgen in 1895. At first, they offered projection imaging; the contrast was the result of the absorption differences associated with the composition of organs. y-rays, in the same vein as X-rays, are also used.
True three-dimensional imaging appeared in the mid-1970s with tomographic reconstruction. We can pick up several projections from different angles, and the structure of the object is reconstituted with the help of mathematical transformations from these projections. As with fluorescence imaging, the source can be incorporated into the patient in the form of radio-active markers, which reside in an organ or a lesion; for example in scintigraphy, or positron-emission tomography (PET).
Radiofrequencies are easily transmitted, but the wavelengths are too long to provide sufficient resolution of transmission imaging. An interesting case, however, is that of nuclear magnetic resonance (NMR) imaging.
In NMR, we measure the intensity and frequency of radiation transmitted by the precession of the magnetic moment of the nucleus in a magnetic field, after a brief magnetogenic excitation. Most of the time, we focus on the hydrogen atom nucleus. The radiation wavelength is no longer a limit to resolution, because the size and position of the small volume observed are defined by the characteristics of the applied field, the signal only indicates the quantity of interacting nucleus in that area.
Recently, we have seen the use of terahertz waves emerge. These are submillimetric waves located between the infrared and radio waves. Imaging in this spectral field is still in the exploratory phase. This range of energy corresponds to molecular transitions. This type of imaging can provide specific components for functional imaging, but is hindered by the high absorption of water.
The other particles α,protons, neutrons, do not have an application in imaging in vivo, because of their high absorption, and the associated harmful biological effects.
PET (Positron Emission Tomography) employs a completely different principle: a β+ emission radioisotope is injected into the patient in chemical form making it possible to focus on the target organ or lesion. When a positron (β+) is emitted, it annihilates with the first electron encountered, almost at the point of emission. The annihilation energy is then emitted in the form of two γ rays of 511 keV in the opposite direction. The detection, with the simultaneous location of these two γ photons on the outside of the patient, enables us to trace the line on which the emitter is found. The detection of many annihilations provides the local density of emitters. From an instrumental point of view, a γ detector is used.
Radiological imaging based on X-rays is widely known, and the goal of this chapter is to provide information on the physical principles involved in order to understand its strengths and weaknesses, and to make a comparison with the other internal organ imaging methods.
X- or γ-rays are electromagnetic radiation, the same as light and radio waves. We traditionally call X-rays radiation produced by electrons, during transitions between the levels of an atom, or during an acceleration, and γ-rays those coming from a transition in the nucleus. γ-rays are often found in a higher range of energy than X-rays, but all energy being equal, both designate exactly the same radiation.
The acceleration responsible for the emission of X-rays may be a transverse acceleration, as in a synchrotron, or simply braking when electrons hit a target. In this case we often speak of braking radiation or Bremsstrahlung.
The most classic production X-ray mode is an electron beam emitted by a filament, accelerated by high voltage, and focused on a heavy target material such as molybdenum or tungsten.
As the emission performance is weak, about 1%, a significant power is needed, which can reach 50 kW for the sources used in tomography. The anode (target) must be vigorously cooled down, and it is usually rotated rapidly during emission to distribute the enormous thermal load of the focus. Finally, the X-ray tube, illustrated in Figure 1.1, has become a complex system, even though the basic concept is extremely simple.
As a radiofrequency wave, X-rays obviously interact with the charged particles, first with the electrons, as their small mass make them able to follow the electric field oscillating at a very high frequency (lO17-lO19 Hz).
The undulatory character of X-rays only appears when we handle much bigger objects than their wavelength, between 1 and 0.01 nm. It almost never occurs in radiological imaging. Conversely, in crystallne matter, where the frequency of the arrangement atoms is of approximately 0.1 nm, the diffraction and interference effects become very significant. They are widely used to determine the structure of crystals, molecules, and especially biological molecules.
A detailed examination of the mechanisms of interaction with matter is important, as they will guide the experimenter in his choice of spectrum, the appropriate choice of source in accordance with the nature of the object under study, and the choice of detector, which must first absorb the radiation.
As with any radiation, X-rays follow Beer-Lambert's law, i.e. in a homogeneous envirormient, the intensity after a length l path equals:
where μ is the absorption factor, expressed in reciprocal length.
We often use the mass absorption factorμ/ρ, since ρ is the density of envirormient. μ/ρ is given in length2/mass. We can interpret it as the opposite of the surface density of the matter, in g/cm2, transmitting 1/e of the incident power.
What is true for absorption must be generalized for the other phenomena preventing the radiation from continuing its course. For example, the scattering deviating radiation attenuates the rays in the initial propagation direction. This point will be discussed in detail later.
The total absorption of a photon occurs by photoelectric effect, i.e. separation of an electron from the matter, achieved by consuming incident photon energy.
The energy of the X-ray photons falls in the range of deep layer electrons binding energy:
– the K layer that is closest to the nucleus for which the binding energy ranges from a few hundred electron volts for light atoms (284 eV for carbon) to a hundred kiloelectron volts for heavier atoms (88 keV for lead);
– the shallower heavy atom L and M layers;
– X-rays therefore interact with the different elements regardless of their chemical state (bound in a molecule or not), as only outer electrons are involved in chemical bonds. This explains the fact that mass absorptions are added independently, as we will see in section 1.3.3.2.;
– the effective photoelectric effect absorption section varies according toZ3/E3, where Z is the atomic number of the element involved, and E is the energy of the photons (empirical distribution valid for E<500 keV). We can easily deduce that heavy elements, such as lead, can easily stop average X-rays, whereas these same rays go through several dozen centimeters of tissue: [319]
The evolution of absorption with energy is complex, as we can see in the example in Figure 1.2 describing the mass absorption coefficient of iodine on a logarithmic scale. We find the dependence on E-3, which results in a transparency very quickly increasing with energy; this explains the problem of effective protection from high-energy X-rays.
We also observe clear discontinuities, between 4.5 and 5.2 keV, where the absorption abruptly increases in three steps, and 33.16 keV, where the increase occurs at one instance.
The threshold is easy to understand: the binding energy of the iodine's K electrons is 33.16 keV. When the energy of incident photons is lower than this value, they cannot extract these electrons. We are then in an E-3 variation. When the energy exceeds 33.16 keV, two additional electrons per atom can interact with the radiation. The absorption therefore increases greatly, and we then find the dependence onE-3.
The same mechanism explains the discontinuities with 5 keV, corresponding to the binding energy of the L electrons. As L electrons have three possible sub-levels, we find three close steps in the decrease of the absorption with E.
All the elements have the same behavior, which is associated with the decrease of the E-3 absorption coefficient and discontinuities at thresholds K, L and M, which are characteristic of the element.
The variation of the transmission of energy through a matter's given thickness with energy is huge, as the absorption coefficient varies over four decades when the energy goes from 1 to 100 keV, and the transmission itself varies exponentially with the absorption coefficient.
As an example, since the density of iodine is 4.9, a thickness of 1 μm only permits 0.7% of incident radiation at 1 keV to pass through, whereas 1 mm of iodine still transmits 40% at 100 keV.
Therefore, in X-ray imaging, the contrast between the Z values for different matters is wide. This is the principle of radiology, which enables the differentiation of bones (calcium phosphate, Z=20, 15, 8) from soft tissue (hydrogen, carbon, nitrogen, oxygen, Z=2, 6, 7, 8).
Now that we have seen that X-rays interact with atoms, regardless of their chemical state, we can use heavy atoms “hidden” in complex and relatively inert molecules or in highly insoluble compounds. As a result, the patient can be shielded from the strong chemical aggressiveness or toxicity of these elements.
This is the principle of contrast agents. Iodine is widely used, often in the form of iopromide, the formula (given below) effectively wraps the iodine atoms, which would be too reactive and toxic if injected in its elemental form.
Similarly, BaS04, which is particularly insoluble, is used in gastrointestinal imaging, despite the toxicity of barium.
Other more sophisticated imaging methods use the abrupt variation of threshold absorption: iodine is injected into the patient, and two single energy images, one at 33.15 keV and the other at 33.17 keV, are compared, on both sides of the iodine's K threshold. The absorption of everything that does not contain iodine is then almost identical in both images, and their difference is almost nil. Only the areas containing iodine have a different absorption at these two very close energies, and thus appear with good contrast.
Unfortunately, the production of a monochromatic X-ray flux with these energies that would be sufficient for imaging is only possible with a synchrotron today! This possibility explains the activity in the field of new X-ray sources for the research of accessible monochromatic sources.
The absorption of X-rays by photoelectric effect in a chemical compound depends on the elements present, and their mass proportions. It is therefore very simple to calculate the absorption of any mix or compound from mass absorption coefficients:
where μPE/ρ is the mass absorption coefficient caused by the photoelectric effect for the compound involved, αI is the mass fraction of each constituting element, μPE/ρI is the mass absorption coefficient of each element.
This law is valid for elements in the form of chemical compounds (for example tungsten carbide) or mixtures (carbon and tungsten mixed powders), or even in the form of consecutive sheets (a sheet of carbon and a sheet of tungsten).
It is the same as having a layer of a mix or several layers of the same surface density of separate components: a sheet of bronze (70% Cu and 30% Sn) with a weight of I g/cm2 has exactly the same absorption as a sheet of pure copper weighing 0.7 g/cm2 superimposed over a 0.3 g/cm2 sheet of tin.
Strictly speaking, if we take into account the other attenuating phenomena such as scattering, the disposition (mixed or superimposed sheets) is no longer exactly the same.
For example, we will calculate the absorption of calcium phosphate Ca3(P04)2 bones at 50 keV (this is an approximation as the true composition is a basic form, hydroxy apatite Ca5(P04)3(OH)).
The mass composition is 38.7% Ca, 20% P, and 41.3% oxygen. Mass absorption coefficients can be found, for example, in the NIST tables1: 0.78 cm2/g for calcium, 0.296 cm2/g for phosphorus, and 0.044 cm2/g for oxygen. The mass absorption coefficient of Ca3(P04)2 then equals: 0.387×0.78+0.2×0.296+0.413×0.044 = 0.379 cm2/g.
The density of bone is approximately 1 g/cm3, taking into account porosity. Its absorption coefficient is therefore approximately 0.4/cm, which means that 2 cm of bone absorbs l-e-0.4×2 = 55% of incident radiation at 50 keV. Comparatively, 2 cm of soft tissue only absorbs 20% of the same radiation. Here we can see the quantitative contrast between the skeleton and muscles, which makes radiography interesting.
In a large spectrum, it is relatively simple to delete low-energy X-rays without greatly affecting high-energy rays: we simply need to place a layer of a matter corresponding to the target attenuation ratio on the X-ray course.
We still practice this filtering in radiology: a traditional X-ray tube, fed for example with 100 kV emits a wide spectrum of X-rays that spreads by approximately 15 keV and up to 100 keV. Energy radiation lower than 25 keV is absorbed at over 99% by 10 cm of soft tissue, whereas 15 to 20% of 60 keV photons are transmitted. Low-energy radiation subjects the patient to a significant superficial dose (called the “skin dose"), and hardly reaches the detector. It provides very little information.
That is why we should cancel this radiation and reduce the patient's dose. We usually place a 20 mm thick aluminum plate between the X-ray tube and the patient, which transmits approximately 50% of the higher energy X-rays at 50 keV, compared with less than 1% for energy lower than 25 keV.
In certain cases, we want to isolate a spectral band, limited to low and high energy. We can then choose a matter with a K threshold that is located at the higher desired limit, and we adjust the thickness for the desired ratio.
For example, in the very specific case of mammography, we most often use a molybdenum anode X-ray tube, which emits the K line of the molybdenum at 17.5 keV, superimposed on to the usual continuous spectrum. We want to eliminate the very low energy part of the spectrum (<15 keV) bringing the dose without information, and high energy for which the contrast is low.
A molybdenum sheet of 30 μm with a K threshold at 20 keV transmits 15% at 15 keV, 60% at 17.5 keV, and only 9% at 20 keV. We then improve the intensity ratio between the K line of the molybdenum and continuous background by a factor of approximately 10 via a loss of only 40% of photons that we compensate for by increasing the power of the tube. In this case, heavy matter paradoxically has a window of transmission at a very low energy.
Thresholds in absorption by photoelectric effects therefore induce properties that seem surprising at first glance, both in the object under observation and in the detector material.
A 50 keV photon, typical in radiology, is easily able to extract K or L electrons from all the elements present in the tissue. The conservation of energy mandates that the excess (between 45 and 49.5 keV) is transported in the form of kinetic energy by the electron being expelled from the deep layer. The mean free path of such an electron in tissue does not exceed a few microns.
It will separate K, L, or M electrons, which will in turn take the excess energy in the form of kinetic energy and will trigger other ionizations in chain. At the end of this chain, there are a large number of electrons-positive ion pairs. The electrons have reached an energy that will not enable them to ionize other atoms. They will then recombine quickly and the corresponding energy is finally transformed into heat.
Some of these ions can be very reactive and combine chemically with neighboring molecules. Sub-products are then formed, which can be harmful. When this chemical modification reaches nucleic acid, the result is a mutation that can persist in the cell when it does not kill it. This mechanism can induce cancer, which can occur a long time after the irradiation. If germ cells were affected malformations may occur in their descendants.
Some of these electrons can also recombine with light transmission, called radioluminescence, which lead to the discovery of X-rays, and this principle has been used since the development of X-rays to enable their detection.
The charges created by the ionization of a large number of atoms are often stuck for long periods of time (years!) if the matter involved is a semiconductor with a wide forbidden band, as with many oxides or halides, as impurity levels are located in the forbidden band. These trapped charges constitute a memory of the received irradiation: the latent image. This can be chemically “revealed” (development of the photographic plate). We can also read this memory thermally with the help of simple heating, which releases the charges as in thermoluminescent dosimeters, or optically by applying a short wavelength laser to extract the trapped electrons. This principle is applied in detectors called the “image plate", as described in Figure 1.3.
If the matter is a semiconductor, or a gas, it is also possible to separate the electron-hole or electron-ion pairs created by an electric field, in order to count them and measure the intensity of radiation. This is the principle of the measurement of dose by an ionization chamber: the ions created in the air between the plates are collected in an electric field weak enough so as not to multiply the charges by collisions. We simply measure the corresponding current.
For a given matter, the creation of these pairs requires an average characteristic energy. For example, with silicon, 3.6 eV is needed per pair created. A sensitive amplifier can measure the charge resulting from a single photon, because it corresponds to hundreds or thousands of electrons. We can thus find the energy of the photon: this is non-dispersive spectroscopy, which is possible with a single photon.
The ions resulting from the separation of deep electrons evolve quickly: a missing electron in the K layer is immediately replaced by an electron of a higher layer experiencing a transition, radiative or not. If the transition is radiative, a photon with Ek-El or Ek-Em energy, called the fluorescence photon, is emitted. Fluorescence is the predominant mechanism for heavy elements. Its probability exceeds 80% for Z>50.
We have seen that the absorption of X-rays for a given matter abruptly increases when the energy of the incident X photons exceeds the K or L threshold. Its energy being naturally lower than the threshold, the fluorescence photon experiences a relatively low absorption. It can cover a long distance before being reabsorbed. It may even exit the matter: this is the escape phenomenon. Finally, in this last case, an Ei energy photon will only have left energy (Ei-Ek+El) in the matter.
Here again, the escape is the basis of misleading phenomena in detection:
– the fluorescence photon can escape without being detected. If we measure the total energy in the detector, the incident flux will be underestimated;
– the fluorescence photon can be detected somewhere other than the point of impact of the incident photon. If we are in a photon counting mode, there are two impacts for a single incident photon.
For an ion created, the return to the complete K layer can also occur by loss of energy of an electron of a higher layer and the expulsion of another electron taking away the difference of energy between levels. This is the Auger effect, which particularly occurs with light elements. The energy of the ejected electron is transformed into heat by a cascade of collisions in the matter. Figure 1.4 summarizes the possible situations.
When the energy of the incident photon exceeds the equivalent of the mass of two electrons (1.022 MeV), the probability of materialization in the form of an electron-positron pair becomes significant. At the end of a very short path, the positron recombines with an electron within the environment, and the energy is converted into two opposite 511 keV photons. This process does not involve X-rays used in medicine, which have a lower energy than MeV.
Contrary to low-energy luminous photons, an X-ray photon can lose only part of its energy in an inelastic collision against an electron. This is the Compton effect as mentioned previously. X photons have a marked “particle” behavior, all the more so as their energy is great. 100 keV photons and over can experience consecutive rebounds and lose a small fraction of their energy in many areas along their course.
The conservation of energy and the quantity of movement leads to the classic formula:
where Δλ is the wavelength variation during collision, h is Planck's constant, c is the speed of light, me is the electron mass, and θ is the angle of deviation. The term h/mec is called the Compton wavelength and equals 0.0243 Å.
For low relative variations of wavelengths, the above formula easily provides the loss of energy:
We can thus see that the relative loss of energy during a collision increases proportionally to the energy of the incident photon. For a 100 keV photon deviated by 45°, it is 5.4 keV.
Figure 1.5 shows the relative scattered intensity according to the angle of deviation for different energies. It is evident that low energies (<100 keV, typically used in medicine) are scattered in an isotropic way, whereas high energies are mainly diffused forward.
This explains the harmful role of the radiation scattered by the patient's body in radiological imaging: the diffused radiation causes even masked areas to receive a significant dose, and of course, the surrounding staff members are exposed, even if they are not in the direct path. Protection measures must be taken, even outside of the direct path.
Furthermore, the path of a scattered ray affecting the detector is unknown. Therefore, it provides no information, but adds noise and reduces the contrast. The Compton effect only depends on the electron density in the environment, which does not vary much from one matter to another, because the electron-rich heavy atoms occupy a volume that is more significant then light elements. There is little more than a decade between the extremes in electronic density. Soft tissue, particularly adipose tissue (containing many hydrogen atoms and not much oxygen) absorbs very little and produces Compton scattered radiation proportionately.
Great efforts are being made in medical imaging to eliminate scattered radiation; for example:
– only irradiate the area involved, to reduce the scattering volume;
– place thick grids, in the form of Venetian blinds that only let direct rays through;
– reduce the thickness of the tissue to be traversed by compression (in a mammography).
Exposition by scanning the object using a fan-beam and a linear detector is another method for the almost complete elimination of scatter: this is emitted in space, whereas we only detect scattered photons in the flat beam opening.
We can also attempt to take advantage of the difference between the transmitted radiation spectrum, “hardened” by its passage through the patient, which preferentially absorbs low energies, and the scattered spectrum, which is centered on lower energies. With monochromatic irradiation, we could hope to distinguish the rays scattered by their lower energy without ambiguity. Imaging systems for objects only accessible from one side were developed basis on the analysis of backscattered radiation (around 180°), intense enough for energies <100 keV, as shown in Figure 1.5.
Finally, the Compton effect also occurs in the detector: during the course of an X photon, electrons from the detector are freed by these inelastic collisions, and join those created by the photoelectric effect. Again, this is a source of noise, i.e. a random signal without direct relation to the image, thus creating no useful information. Thankfully, the constituents of the detectors are by definition high Z heavy matters for which the probability of Compton interaction is much lower than that of a photoelectric absorption, as we can see in Figure 1.6.
X-rays are also scattered without an energy change; this is Thomson scattering. It particularly occurs in situations where the electron is sufficiently bound so as not to be ejected from the atom. In this case, the electron cannot acquire kinetic energy after the collision. This type of collision is elastic where the energy of the incident photon is weaker than the binding energy: with low energy X-rays or heavy atoms. In medical imaging (light elements, dozens of keV of energy), Thomson scattering is usually insignificant compared with Compton scattering. Figure 1.6 shows the relative contributions of the different interaction methods between radiation and matter. For light elements (tissue), the Compton effect dominates over traditional radiology energies. Heavy elements mainly absorb by photoelectric effect. The creation of pairs only occurs for high energy, which is greater than the energy required for creating an electron and a positron, or 2x511 keV, and is not involved in radiological imaging.
The refractive index, which is very useful in optics, characterizes the slowdown of the electromagnetic wave by interacting with the envirormient that it passes through. Light wavelengths are such that a photon interacts with a very large number of atoms simultaneously, which translates into a collective phenomenon: we can use the image of propagation in viscous environment.
Conversely, X-rays interact very little with matter, and their wavelength, which is close to atomic dimensions, makes it so that the interaction only involves one electron at a time. The radiation phase is little affected, and the refractive index is very close to 1 (the complex theory even shows an index that is slightly lower than 1 because of the proximity of absorbing regions). Except in very specific cases, no collective deviation of X-ray beams is seen: there are no refractive lenses or prisms that can be used for imaging. Propagation only occurs in a straight line and only projection imaging is possible.
The very low deviations observed by refraction resulting from index variations between the envirormients (of approximately 10-6) can, however, enable projection imaging with edge enhancement, even without absorption, if the source is almost a point source, and the image detector is very far from the subject. This is phase contrast imaging [GID 05] for the observation of objects with very little absorption contrast.
As of now, in laboratory, phase contrast imaging could create better quality images of soft tissue using a lower radiation dose administered to the patient than the dose necessary for absorption imaging. Mammography would be the first beneficiary of this technique. The problem comes from luminance (power emitted by unit of surface) required by the source, which greatly exceeds what is accessible for a tube, and a geometry that imposes a great distance between the subject and the detector.
Two different attenuation coefficients of X-rays are noted in the literature called the mass attenuation and mass absorption. The significance of these two values is as follows: for an observer located far from the subject, the attenuation is the same whether the photons are absorbed or deflected by scattering; scattering with or without energy change makes it so the photon does not reach the observer, exactly as if it was absorbed.
Mass attenuation includes attenuation by absorption and by scattering, mainly Compton. In order to calculate the effect of a subject in an imaging system where the sensor is far from the subject, we should use mass attenuation.
Conversely, if we are close to the subject and for example, we focus on the dose received without considering the point of impact, the absorption coefficient will provide a better evaluation (somewhat excessively pessimistic, because the backscattered rays are still lost). The diagram in Figure 1.7 illustrates these situations. The difference is mostly sensitive for high energies.
The cascade of ionizations described previously terminates with the generation of heat, or by the rearrangement of the matter at the molecular level. We can even observe movements of atoms in crystal networks. The separation of electrons has a significant chemical effect. An ionized atom will attempt to fill its lack of electrons by capturing a neighboring electron, thus creating a new connection. The many secondary electrons freed by the cascade ionizations have a strong reducing effect. The result is a modification of the chemical nature of the exposed matter. It is well known, for example, that all types of glass become dark under the effect of X-rays: this is the reduction of oxides constituting the glass, in the form of metal that is very light absorbent. It is visible on the glass of the X-ray tube in Figure 1.1.
Another major chemical effect is that on living material, and especially on nucleic acid, which contains our gene pool. The energies of molecular bonds present in the tissue are approximately of 1 to 10 eV. The cascade of ionizations following the absorption of a 50 keV photon, common in radiology, is therefore able to break thousands of bonds. Damage to DNA is especially dangerous, because it translates into errors in the coding of the genetic information. As our cells are constantly submitted to the many aggressions of ultraviolet rays and natural radioactivity, mechanisms of repair or destruction have developed over time (apoptosis). These mechanisms are not perfect, and cannot handle massive irradiation. In addition, even in the case of moderate irradiation, certain unrepaired cells survive with faulty operation. This can lead to cancer. The hazard of X-rays comes directly from their chemical effects.
The chemical effect has been used for detection since the discovery of X-rays: the local reduction of a silver halide crystal provides a beginning for the reduction of the crystal by a chemical developer. This is detection by photographic film.
We define the dose as the quantity of energy deposited (in all its forms: heat, chemical, etc.) by unit of mass. The SI (International System of Units) unit is gray:
It is a very large unit: I J corresponds to approximately lO14 absorbed photons. A few gray constitute a lethal dose for man is most cases. The doses received in a radiological examination are only of hundreds of microgray per image.
For a given incident flux, the dose does not depend on the density of the matter, only on its nature. In fact, for a given element, the energy absorbed is proportional to the matter quantity, but it is also distributed over this same quantity. The energy deposited by unit of mass is therefore independent of density. In this way, the air in front of a patient receives approximately the same dose as the patient, because the air is made up of nitrogen and oxygen, of average atomic numbers that are very close to that of tissue (C, N, O, H). Thus it is justifiable to evaluate the dose received by the patient by monitoring the dose measured in the air right in front of the patient.
In order to characterize physiological effects, we use the sievert, which corresponds to gray multiphed by an experimental factor of biological efficiency, which depends on the tissue. For X-rays and for an average effect on the human body, I Sv = I Gy. Dosimetry is very important in radiology for the patient as well as for the staff [BAU OO].
The different modes of interaction between X-rays and matter described above have a major influence on the result in imaging. This section uses the interaction modes described previously and their consequences in medical imaging. These effects are visible for the object studied, but also for the detector, detailed in section 1.5.
In most cases, X-ray imaging is an image created by projection. The contrast is the result of the transmission difference between the areas of the object. In medical imaging, the goal is to distinguish different tissues with thicknesses between 1 and 30 cm. The field of usable energy is then important: above l5 to 20 keV for an acceptable transmission, and not beyond 150 keV, because the absorption then becomes too little dependent on the tissue traversed. The Compton effect and the photoelectric effect compete in this area of the spectrum.
The other modes of interaction have a marginal effect in the area involved, as seen in Figure 1.8. For soft tissue, over 30 keV, the Compton effect becomes dominant, i.e. there are more X photons scattered than absorbed. As the density of these tissues is close to 1 g/cm3, their mass attenuation is approximately 0.2/cm, and the average attenuation length at 1/e corresponds to approximately 5 cm.
The average energy will obviously be adapted to the area of the body observed. Mass attenuation of the tissue involved will guide the choice of the optimal spectrum. Figure 1.9, for example, shows the evolution of mass attenuation (photoelectric and Compton effects) according to the energy of incident photons for muscles and bones.
They differ by a decade around 20 keV, and only by a factor of two around 100 keV.
In order to obtain very fine details on the skeleton in a thin area, such as the hand, the energy applied should be 20 to 30 keV, where the transmission is between 20 and 50% for 25 mm of muscle, and 2 and 10% only for a few mm of bone.
Conversely, for a transverse X-ray of the. pelvis where we must traverse 30 cm of tissue, the highest energy is required (150 kV on the X-ray tube, or an average energy of 90 keV), and even in this case, the transmission will not exceed a few percent.
The case of chest X-rays is particular: chest X-rays are used to search for areas where possible inflammation, tumors, or lesions reduce the volume of air in the lungs. The image of the thorax is obviously superimposed onto the lungs. In order to limit the disruption, we use a high average energy (60 keV, obtained with a tension of 125 kV on the generator tube). Absorption by the patient is then of approximately 10 to 30%), and scattering is approximately 40%) of incident photons. The contrast between the bone and the soft tissue is low because of the high energy, which is an advantage for the Compton effect, as it is not very dependent on the average Z as shown in Figure 1.6, and we mainly see the tissue/air contrast that contains the medical information. The scattered radiation constitutes a generally uniform cloud on which the useful information is superimposed.
Another particular case is that of the mammography. In mammography we look for, among others, hydroxyapatite calcifications (composition similar to the bone) of a few hundred microns, in a lightly absorbent soft tissue (fat, glandular tissue). For maximum contrast, we will use the lowest energy possible, leading to low transmission above approximately 30 mm of tissue. We generally use a molybdenum anode tube as the source, which mainly emits the Kα line of molybdenum at 17 keV, possibly filtered by 30 μm of molybdenum, as explained in section 1.3.3.3.
Compressing the breast between two plates is necessary in order to limit the maximum thickness traversed, and also to make the transmission uniform for the correct exposition of the detector over its surface. Scattered radiation (Compton) is once more a severe limitation.
Scattered radiation is always the basis of a loss of contrast. Appropriate image processing can help us achieve a good level of contrast, but an irreversible deterioration of the information is inevitable: even if we could, by different methods, subtract the average level of scattered radiation, it is by nature marred by statistical fluctuations equal to the root of the number of photons received, which can neither be predicted nor corrected.
Several methods make reducing its influence possible:
– moving the detector farther from the patient (air gap). This is an inefficient method, because the scattered flux/transmitted flux ratio in the detector slowly decreases with distance. In addition, the footprint and especially the need for a greater detector decrease the advantage of this solution,
– placing a “'Venetian blind” grid in very absorbent material in front of the detector (sometimes called a Bucky grid after the name of its inventor). This type of grid is achieved by stacking thin sheets of lead and thick paper sheets or a material that is not absorbent as shown in Figure 1.10. The transmission is approximately 70% for direct radiation, and 5 to 10% for scattered radiation. The thickness of lead walls and the height of the grid are determined so that the loss of signal in the grid and the decrease of the noise resulting from the scattered attenuation combine to improve the S/N (signal-to-noise) ratio. The grid can be moved during exposition with an oscillating movement of several steps, so as not appear in the image. There are even “focused” grids where the absorbent walls are directed toward the tube's source point,
– creating the image by scanning a slot in front of the X-ray tube and using a linear detector to receive the transmitted beam. Scattered radiation is dispersed in all directions and the fraction falling on the detector is very low. This method has the advantage of not losing signal as all useful photons exiting the patient reach the sensor. However, we must implement a complex mechanism that will guarantee the aligrmient of the slot and detector during movement. The power required by the generator is a major drawback of this principle: the consecutive exposition of n lines requires that the generator works n times longer than in a simultaneous exposition of the whole sensor with the same power. The thermal charge on the anode is thus n times greater, necessitating a much more complex tube.
Detection obviously relies on an interaction between the detector's material and radiation to detect. As the mode of interaction has a significant influence on the information contained in the image, the physical phenomena used for the detection condition the qualities and faults of the final image.
Almost all effects were used to detect X-rays. We should mention:
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