X-ray Penetration: Lecture Notes PDF

INTRODUCTION AND OVERVIEW One of the characteristics of x- and gamma radiations that makes them useful for medical imaging is their penetrating ability. When they are directed into an object, some of the photons are absorbed or scattered, whereas others completely penetrate the object. The penetrat...

INTRODUCTION AND OVERVIEW One of the characteristics of x- and gamma radiations that makes them useful for medical imaging is their penetrating ability. When they are directed into an object, some of the photons are absorbed or scattered, whereas others completely penetrate the object. The penetration can be expressed as the fraction of radiation passing through the object. Penetration is the inverse of attenuation. The amount of penetration depends on the energy of the individual photons and the atomic number, density, and thickness of the object, as illustrated below. Factors That Affect the Penetration of Radiation through a Specific Object The probability of photons interacting, especially with the photoelectric effect, is related to their energy. Increasing photon energy generally decreases the probability of interactions (attenuation) and, therefore, increases penetration. As a rule, high-energy photons are more penetrating than low-energy photons, although there are limits and exceptions to this, which we discuss later. PHOTON RANGE When photons enter an object, they travel some distance before interacting. This distance can be considered the range of the individual photons. 1- A characteristic of radiation is that all photons do not have the same range, even when they have the same energy. 2- In fact, there is no way to predict the range of a specific photon. Some of the photons travel a relatively short distance before interacting, whereas others pass through or penetrate the object. If we count the number of photons penetrating through each thickness of material, we begin to see a fundamental characteristic of photon penetration. The relationship between the number of photons reaching a specific point and the thickness of the material to that point is exponential. Penetration Range of Individual Photons The nature of the exponential relationship is that each thickness of material attenuates the same fraction of photons entering it. This means that the first layer encountered by the radiation beam attenuates many more photons than the succeeding layers. Very few photons travel a distance exactly equal to the average range. The average range of a group of photons is inversely related to the attenuation rate. Increasing the rate of attenuation by changing photon energy or the type of material decreases the average range of photons. Actually, the average photon range is equal to the reciprocal of the attenuation coefficient (µ): Average Range (cm) =1/Attenuation Coefficient (cm-1) Therefore, the average distance (range) that photons penetrate a material is determined by the same factors that affect the rate of attenuation: photon energy, type of material (atomic number), and material density.  HALF VALUE LAYER Half value layer (HVL) is the most frequently used quantity ore factor for describing both the penetrating ability of specific radiations and the penetration through specific objects. HVL is the thickness of material penetrated by one half of the radiation and is expressed in units of distance (mm or cm). Increasing the penetrating ability of a radiation increases its HVL. There is a difference between the two because of the exponential characteristic of x-ray attenuation and penetration. The specific relationship is: HVL = 0.693 X Average Range = 0.693/µ. This shows that the HVL is inversely proportional to the attenuation coefficient. The number, 0.693, is the exponent value that gives a penetration of 0.5: (e-0.693 = 0.5). Any factor that changes the rate of interactions and the value of the attenuation coefficient also changes the HVL. These two quantities are compared for aluminum in the figure below. Aluminum has two significant applications in an x-ray system. It is used as a material to filter x-ray beams and also as a reference material for measuring the penetrating ability (HVL) of x-rays. The value of the attenuation coefficient decreases rather rapidly with increased photon energy and causes the penetrating ability to increase Relationship between Attenuation Coefficient and HVL for Aluminum  Relationship between Attenuation Coefficient and HVL for Aluminum The figure below illustrates an important aspect of the HVL concept. If the penetration through a thickness of 1 HVL is 0.5 (50%), the penetration through a thickness of 2 HVLs will be 0.5 x 0.5 or 25%. Each succeeding layer of material with a thickness of 1 HVL reduces the number of photons by a factor of 0.5. The relationship between penetration (P) and thickness of material that is n half value layers thick is P = (0.5 )n. Relationship between Penetration and Object Thickness Expressed in HVLs An example using this relationship is determining the penetration through lead shielding. Photons of 60 keV have an HVL in lead of 0.125 mm. The problem is to determine the penetration through a lead shield that is 0.5 mm thick. At this particular photon energy, 0.5 mm is 4 HVLs, and the penetration is n = thickness / HVL = 0.5 / 0.125 = 4 P = (0.5)4 = 0.0625. The following figure summarizes two important characteristics of HVL. In a specific material, the HVL is affected by photon energy. On the other hand, for a specific photon energy, the thickness of 1 HVL is related to characteristics of the material, density, and/or atomic number. Factors That Affect the Thickness of 1 HVL to filter out the low-energy photons. In diagnostic x-ray equipment, aluminum is normally used for this purpose. The figure above shows the penetration through a 1-mm thickness of aluminum. Typically, most x- ray machines contain the equivalent of several millimeters of aluminum filtration. This might not always be in the form of aluminum because several objects contribute to x-ray beam filtration: 1- the x-ray tube window, 2- the x-ray beam collimator mirror, 3- and the table top in fluoroscopic equipment. The total amount of filtration in a given x-ray machine is generally specified in terms of an equivalent aluminum thickness. The addition of filtration significantly alters the shape of the x-ray spectrum, as shown below. Since filtration selectively absorbs the lower energy photons, it produces a shift in the effective energy of an x-ray beam. The figure below compares an unfiltered spectrum to spectra that passed through 1-mm and 3-mm filters. It is apparent that increasing the filtration from 1 mm to 3 mm of aluminum produces a noticeable decrease in the number of x-ray photons. It should be observed, however, that most of this decrease is in photons with energies less than approximately 40 keV. These are the photons with a low probability of penetrating a typical patient and contributing to image formation. They do, however, contribute to patient exposure. X-Ray Spectra After Filtration Recommended Minimum Penetration (HVL) for Various KV Values Minimum penetration (HVL) KV for Aluminum (mm) 30 0.3 50 1.2 70 1.5 90 2.5 110 3.0 PENETRATION VALUES We have seen that the amount of radiation that penetrates through a specific thickness of material is determined by the energy of the individual photons and the characteristics (density and atomic number) of the material. HVL values provide useful information about the penetration of a specific radiation in a specific material. When an HVL value is known, the penetration through other thicknesses can be easily determined. The table below gives HVL values for several materials related to diagnostic imaging. HVL Values for Certain Materials HVL (mm) Material 30 keV 60 keV 120 keV Tissue 20.0 35.0 45.0 Aluminum 2.3 9.3 16.6 Lead 0.02 0.13 0.15