Notes on Modern Physics and Ionizing Radiation

The clinical applications of radiation fall into two primary areas: first, obtaining information about the structure and function of the patient's internal organs, and second, treating (i.e., killing) benign or malignant growths on the surface or within the interior of the patient's body.

A. Diagnostic Uses

Diagnostic uses of radiation can be considered according to the type of detector used as well as according to whether the source of the radiation is outside or within the patient's body. The former case, "passive" investigation, is typified by conventional X-ray imaging: the physical basis of the information is the transmission (or in some cases the scattering) of radiation as it passes through the body. Distinctions among tissues are often enhanced by injection or ingestion of materials that are substantially more or less likely to scatter or transmit the radiation than the tissues themselves (e.g., Barium enemas, air bubbles).

"Active" investigations are typified by the "gamma camera" and "PET" scanner: a radioactive biochemical is introduced into the body and the radiation is detected by position- or direction-sensitive means, so that the site within the body can be established. Like the enhanced contrast studies alluded to above, such studies may be either dynamic (following the initial bolus through the patient's circulatory or digestive systems) or equilibrium (after thorough mixing, which may take minutes, hours, or days, depending on the system involved).

The resolution obviously depends on the body and organs being stationary throughout the measurement period, or on compensation for motion artifacts through recording of additional information. Active studies are a difficult compromise because of the small number of suitably labeled biochemicals that are available, the injury inflicted at the site of introduction (increased if the half-life is too short), the injury inflicted by all radiation that takes place after the examination, (increased if the half-life is too long), and the small probability that the emitted radiation will pass through a detector along its sensitive axis. Despite these difficulties, there are several techniques that provide so much useful information with so little injury (especially compared to exploratory surgery!) that they are in wide clinical use.

Film X-rays

Chapter V includes a discussion of the use of film as a detector of radiation. In medical diagnostic applications the radiation source is typically an X-ray machine (see Chapter III) operating with an accelerating potential between 50 and 150 kV. The material of the anode is chosen so that much of the radiation will be characteristic K radiation of energy perhaps 70 % of the peak energy in the Bremsstrahlung spectrum. Shielding must be provided to protect the operator and to prevent any irradiation of those parts of the patient's body that are not being examined. Often a light bulb inside the x-ray machine provides a clear indication of the region that will be illuminated by X-rays when the machine is energized.

There are two basic types of X-ray film for diagnostic or research uses: "screen" and "no screen." The "screen" in question is a coating of phosphor that will glow with visible light when it absorbs ionizing radiation. This light, in turn, exposes the film. The trade-off here is that the screen provides greater sensitivity but worse resolution, since the light is emitted in a variety of directions, not just straight forward. Both types of film suffer from all of the non-linearities discussed in chapter V. Furthermore, the characteristics of the image will depend in complex ways on the precisetemperature and method of agitation of the chemical baths used in the processing. Mechanized operations can often be more consistent in these than is possible for a small "back office" laboratory.

Film X-rays, as well as the Fluoroscopy and CAT Scanners discussed below, typically use artificial radiation sources. The nature of that radiation influences the information obtained and the damage done. In describing the spectrum of X-radiation, one must specify the Bremsstrahlung end-point and the composition of the anode (to identify the characteristic lines). The usual style is to specify simply the maximum, or peak, accelerating potential, using units of kVp. If the accelerating potential is not constant, but varies, the spectrum will be shifted toward the low-energy end, with fewer photons of near the peak possible energy, since most of the time that energy is impossible.

Such varying accelerating potentials are in fact typicalof medical diagnostic and some crystallographic x-ray generators: they are powered from sinusoidal commercial AC, with transformers to boost the potential from 120 V to the much higher values used for acceleration. There is, however, no energy storage, hence at the instant when the power company gives us 10% of peak power potential, we get 10% of peak accelerating potential, varying smoothly up and down at 60 cycles per second. There are two techniques in common use for producing a more steady accelerating potential, thereby enriching the high energy end of the photon spectrum: multi-phase power and passive energy storage.

Multi-phase power may be available from the power company, or may be produced on-site with a motor-generator. Conventional power is supplied with two phases, each varying sinusoidally with time, and instant by instant each with oppositepotential with respect to ground. From this two-phase, 3-wire, power, it is easy to deliver 220 VAC and 110 VAC, depending on whether the potential used is between one hot wire and the other, or between one hot wire and ground. Multi-phase power has three or more hot wires, plus a ground wire. Each hot wire's potential varies sinusoidally with respect to ground, and the phases of the several hot wires are set equally spaced, so that one will peak positively, and then the next, and so on. Contemplation of the complex number plane technique for describing phases of sinusoidally varying quantities should suffice to support the assertion that transformers can be designed to change between any two sorts of multi-phase power with morethan two phases, but that two-phase power cannot be transformed into multi-phase.

If the power supply for an X-ray generator is designed to operate with multi-phase power, it is simple to design the circuitry so that it uses the phase that is providing the instantaneously greatest potential. With three or four phases, then, we can see that the potential used to accelerate the electrons will vary from the maximum down to perhaps 2/3 of the maximum, instead of down to zero.

Using two-phase power, the method to reduce the variation in accelerating potential is to use passive energy storage in capacitors or inductors. This is accomplished with low-pass RC or RL filters, which produce an accelerating potential output with much less variation than their rectified potential input. The major disadvantage is that considerable complexity must be added to the circuitry attempting to ensure that X-rays are never generated when the power is off. Capacitors, in particular, that can operate at 40 kV or more, will be able to store dangerous charges for weeks. This can produce shock hazards for technicians, as well as radiation hazards. There may also be electromagnetic radiation at microwave or radio frequencies that interferes with other elecronic equipment, such as computers.

The reason that we seek to shift the photon energy spectrum away from the low and toward the high-energy end is that in medical diagnosis and in crystallography it is rarely possible to learn much from the low energy, long wavelength photons. As discussed in chapter IV, the photoelectric effect displays very large probability of interaction (short average penetration depth) for low photon energies. In this region, then, the distinction between soft tissue and bone vanishes -- all photons are absorbed. Only at higher photon energies does the increased penetration depth for soft tissue permit enough radiation to penetrate so that it can be distinguished from bone. At sufficiently high photon energies, even bone becomes nearly transparant to photons, so there is an optimumaccelerating potential for diagnosic X-ray generators, whether the detection of that radiation will be by film or more exotic means.

A LINAC, another type of X-ray generator, is more commonly used for therapeutic applications, but its design also overcomes the variation of electron kinetic energy upon impact. Conventional X-ray generators, as discussed above and in chapter III, accelerate a continuous stream of electrons to high kinetic energy by using the static electric field created between two electrodes by maintaining a large potential difference between them. A LINAC, on the other hand, accelerates groups of electrons to high kinetic energy by using the electric fields created by imposing a high frequency alternating potential difference between many pairs of electrodes, as shown in Fig. 1.






Figure 1: Simplified LINAC X-ray Generator; compare to Fig. III-1.


The filament, cathode, and grid form a conventional electron gun, producing a beam with energy of perhaps 50 keV. The odd numbered plates are connected together to one side of the oscillator output and the even numbered plates are connected together to the other side. Finally, the anode (or "target") is connected to ground to complete the circuit for the electrons. If the oscillator frequency and the spacing of the plates is properly coordinated to the speed of the electrons as they accelerate, then the kinetic energy of the electrons in each bunch will be increased as they pass through the space between electrodes. What is required is that the half-period of the oscillation be equal to the time of flight from one electrode to the next, and that the electrons are moving with the correct phase relationship to the oscillation. LINACs are commonly used to accelerate electrons to highly relativistic speeds (kinetic energy perhaps one order of magnitude greater than rest energy). Therefore, the spacing of the last several sets of plates will be essentially uniform, since the electrons are already moving at nearly the speed of light.

Consider first the outcome if the plates are connected to a DC power supply, instead of to an oscillator. Each electron will be alternately speeded up and slowed down as it passes through the gaps between plates: speeding up when the plate ahead of it is positive, slowing down when the plate ahead of it is negative. The kinetic energy of impact upon the anode will be equal to the kinetic energy of exit from the electron gun.

Now consider the situation with the oscillator driving the plates. While moving through a gap between plates, the typical electron will speed up with a positive plate in front of it. As it approaches that plate, that half-cycle of the oscillation completes, hence the electron passes through the plane of the plate during the zero-crossing of the oscillator output. During the entire time of flight to the next plate, the electron will again be exposed to an electric force in its direction of travel, because of the reversed polarity of the plates during the second half of the oscillator's cycle. This increases its kinetic energy, instead of slowing it back down again. As it passes through each plate, the electric fields reverse, so that the electron is accelerated to progressively higher kinetic energy.

This permits exceedingly high kinetic energies to be attained with very limited potential differences between any two parts of the apparatus. This is known as a linear accelerator, or LINAC for short, to distinguish it from cyclotrons and synchrotrons, which use the same key idea of alternating electric fields to increase kinetic energy, but with magnetic fields to bend the path into circles, so that a great many small increments add up to the high final kinetic energy. The LINAC proper is just the device that creates this beam of very high energy electrons (4 MeV is common). The same name is commonly used, however, for the entire X-ray generator that uses this beam. The spectrum of the X-rays generated when such a monoenergetic electron beam lands on a metal anode will be stronger in the high energy, and weaker in the low energy photons, than that generated by a conventional X-ray machine with an unfiltered "DC" supply.

One commonly used technique to remove the low energy photons that can contribute no diagnostically useful information, but can injure the patient, is to interpose an aluminum plate of perhaps one inch thickness between the source and the patient. This should be located as far from the patient as possible, so that any secondary radiation will have spread out to a lesser intensity and perhaps even been slowed down or stopped (beta) or absorbed (gamma) by the intervening air. Such "filtration" of X-rays with aluminum is often legally required.




Fluoroscopy

If the radiation is displayed visibly at the same time it is detected, the clinician can observe dynamic processes, such as the beating heart or a probe moving through a cardiac artery or vein. The original technique for this involved nothing more subtle than interposing a screen of suitable composition between the patient and the observer. The material was chosen on the basis of visible light emission upon bombardment with X-rays, a special case of fluorescence, which generally refers to the emission of longer-wavelength electromagnetic radiation upon bombardment by shorter-wavelength radiation. Fluorescent lights, for example, emit visible light when the ultra-violet light from the mercury arc in the interior strikes the coating on the inside surface of the glass tube.

Direct X-ray fluoroscopy has two major problems: first, the detection is not very efficient, so that a larger dose of radiation to the patient is required. Second, there is often a great deal of scattered radiation, or radiation that is not absorbed in the screen, which will irradiate unintended parts of the patient, or the observer, or both. Both of these problems are addressed by using image intensifiers (see chapter V, section C), to amplify the light from the fluorescent screen so that less radiation is required.




Gamma Cameras

Gamma cameras provide images based on the straight-line propagation of gamma radiation. Labeled biochemicals are administered to the patient, either by mouth or injection, and the radiation examined by a detector that includes a great many individually reporting sensitive regions, each exposed only through collimators that prevent radiation from reaching it unless the source is along a particular line. The set of all such lines covers an area on the patient's body, and the radiation as a function of position provides information comparable to that of a conventional X-ray, except that the signal depends on the local concentration of the labeled biochemical, so it can be relevant to particular metabolic or circulatory processes.

The main problem with gamma cameras is the small fraction of all the radiation emitted that is detected. Thus the information to damage ratio is likely to be low. On the other hand, it may well still be superior to exploratory surgery!

The gamma camera normally records simply the total number of counts in each detector, from which the image is directly constructed. An alternative technique is to record also the timeat which each photon is detected, or at least to accumulate totals separately for different intervals of time. Diagnosis of cardiac patients can be done in this way, using the electrocardiogram signal to synchronize division of the data into consecutive phases of the heartbeat. If the gamma-emitter has been injected into the blood, good images of the heart are readily achieved by accumulating data over many minutes' of heartbeats. If the patient exercises in place (for example, with a bicycle bolted appropriately to the apparatus), the damaged parts of the heart wall are immediately evident: they don't stroke any farther during the stress test than they did during the initial, resting, data collection.




Scanners

Although the physical principles underlying their operation are not the same, CAT, PET, and NMR (or MRI) scanners have much in common: they provide an image, typically of a cross-section through the patient's body, limb, or head, presented either on a video display or on film made from a video display, based on computationfrom a multitude of measurements, of the same property, made for successive, adjacent or overlapping, segments of the patient's body. Usually the varying quantitative results will be displayed as a range of colors (a "false color image").

Computed Axial Tomography was the first of these techniques to be widely used. The "axial" refers to the fact that the segments measured all pass through the same axis, in different directions. In the CAT scanner, the measurement made is of X-ray transmission along these "diameters" through the patient. The information presented is a picture of a cross-section through that part of the patient, typically showing X-ray transparency levels by different colors or by shades of gray. There are two significant advantages of CAT scanners over conventional X-rays. First, they permit direct imaging of a cross-section, presenting the clinician with a point of view not available from conventional techniques. Second, they typically employ a small diameter beam of radiation aimed through the patient directly toward a detector that will respond to a virtually every X-ray photon that reaches it. Thus, the information to damage ratio can be several orders of magnitude better with the CAT scanner. It is still invasive, but much less so.

Positron Emission Tomography, a more recent innovation, may be viewed as an exotic sort of Gamma Camera. A radioactive material that emits low-energy positive beta rays is introduced into the patient's body. The decay positrons travel a modest distance through the tissues in a random direction before coming to rest, where they annihilate with electrons from the atoms present there. This produces two annihilation photons, each of energy 511 keV, travelling in opposite directions, therefore the point of annihilation (which will be quite close to the point of decay, where the radioactive substance was located) must lie along the line connecting the two detectors that registered the events "simultaneously" on opposite sides of the patient. The most sophisticated PET scanners use the slight difference in time of flight of the photons to estimate wherealong that line they started from, but since the speed of light is one foot per nanosecond, very precise measurement of the relative time of arrival at the detectors is required to improve the picture significantly. The annihilation photons are of an energy that is highly penetrating, so much of the dose to the patient will come from the initial kinetic energy of the positron and from any X-rays emitted as the atomic electrons rearrange themselves following the nuclear transformation. Unlike gamma cameras, most of the photons are detected, so the information to damage ratio can be reasonably good.

Nuclear Magnetic Resonance scanners are the most recent of these devices. Their invention was the basis of one of the 2003 Nobel Prizes. Unlike the CAT and PET scanners, they are truly non-invasive, since they subject the patient to noionizing radiation. Because some people recoil at the mention of the word "nuclear," they are now being called "Magnetic Resonance Imaging" (or "MRI") scanners, but the physics is the same benign thing. Another of their major advantages clinically, besides being non-invasive, is that they produce images based on different chemical conditions, so the combination of PET scan or gamma camera images with MRI scans may permit a much more confident diagnosis and treatment planning than would be possible based on any one technique alone.

B. Therapeutic Uses

Therapeutic uses of ionizing radiation are now limited almost exclusively to the treatment of cancer. Prior to 1960 irradiation was used as an alternative to surgery for the removal of such tissues as tonsils and adenoids. Consequently, there are now many middle-aged people at greatly increased risk of thyroid cancer, because of the exposure that organ received from scattered radiation or from radiation that had passed through the target tissues and on into the thyroid. Such radiation treatments work by killing the target cells without killing the individual. This is possible by combining several techniques: first, administering the radiation over a period of a few weeks, so that the body's healing mechanisms can help. Second, the rapidly growing cancer cells are more vulnerable to radiation. Third, by irradiating from several directions the dose to the surrounding tissue can be kept much smaller than the dose to the tumor, which is in the beam every time, and each region of healthy tissue will have more healing time between doses than the tumor, which gets hit every time.

Surface lesions, of course, will be treated best with radiation that penetrates only as far as the other side of the tumor. Internal tumors, on the other hand, should be treated with highly penetrating radiation, so that as little as possible of the incident beam is absorbed by the overlying tissues. Such penetrating radiation, typically photons of energy between 250 keV and 4 MeV, will surely also penetrate the tumor and irradiate the underlying tissue. Treatment planning in such cases requires careful consideration of the absorption, in different tissue types, of both the incident radiation and the secondary radiation (typically ejected electrons, beta radiation).

The calculation of irradiation patterns (dose as a function of position throughout the irradiated volume within the body) is routinely done by computer modeling. Such modeling will be more easily made accurate if the incident radiation is "monochromatic," i.e., all of the quanta having the same energy. This will occur with gamma-emitting radioisotopes, such as Co-60, but not with machine generated X-rays, including LINAC machines; see the discussion of kVp and LINAC's in part 1 of section A earlier in this chapter, under the title " Film X-rays ."

The balance between desirable irradiation of the tumor and undesirable irradiation of healthy tissue will depend particularly on the intensity of the radiation in the tumor, compared to its intensity in the overlying tissue. As is implicit in Eq. IV-13, there are two factors that reduce the intensity at the tumor: the absorption in the overlying tissues, which for incident photons will approximate an exponential in the thickness, and the spreading of the radiation from its source, which will follow an inverse square law at distances large compared to the size of the source. The absorption in the overlying tissues is reduced by using penetrating radiation. For photons, this means an energy of roughly 1 MeV. The effects of the spreading of the radiation are reduced by increasing the separation from source to skin. The radiation is unchanged, but the skin to body ratio is reduced so it acts like it is "more penetrating." For this to be effective, the intrinsic brightness of the X-ray generator must be increased, so that the same dose rate will occur at the tumor. Otherwise the treatment would have to be prolonged, imposing a potentially intolerable burden on the patient. The increased source strength in turn will require more shielding to protect the patient and staff.

The trade-off between Co-60 radioactive gamma sources and very high energy X-ray machines (typically 4 MeV LINAC's) can be summarized simply: first, you can turn off the X-ray machine, but not the radioactive decay process. Second, the broad spectrum of X-ray photon energies will include many that are less penetrating than the Co-60 gamma radiation, which has photons of two characteristic energies, 1.17 and 1.33 MeV.

When a beam of high energy photons strikes a solid or liquid, the photons interact with the target material in a variety of ways, as discussed in chapter IV. Many of these interactions produce secondary beta radiation whose initial energy is a large fraction of the photon energy. Thus, the energy of the photon is not delivered to the material at the point of interaction, but rather is spread out along the path of the secondary beta ray as it is slowed down and stopped. Therefore the ratio of the delivered dose rate (Grays/second) to the intensity of the radiation (Watts/square meter) will rise as the radiation penetrates from the skin inward until a depth approximately equal to the range in that tissue of beta radiation of energy equal to that of the incident photons, typically several mm. The clinical effect is described simply as "skin-sparing," since the damage to the skin is reduced for any given dose to the tumor.

When a surface lesion is being treated, it is necessary to place a suitable "phantom" in contact with the surface. The phantom is often just a flexible plastic bag filled with water; its function is to produce secondary beta radiation, so that an equilibrium mixture of photons and betas is incident upon the lesion. Thus the dose to the tumor will be increased for any given dose to the underlying tissues.

Problems

1. Consider the design of a 2 MeV LINAC. Calculate the ratio of relativistic total energy to rest energy for an electron with kinetic energy equal to 2 MeV. What will be the speed of that electron? What frequency should the oscillator operate at if the largest spacing between the plates is to be 20 cm? If the smallest spacing between plates is to be 1 cm, what kinetic energy must the electron gun provide to the electrons starting through the LINAC (the potential difference between cathode and grid as shown in Fig. 1)?

Dick Piccard revised this file ( https://people.ohio.edu/piccard/radnotes/clinical.html ) on March 29, 2005.

Please E-mail comments or suggestions to piccard@ohio.edu .