ch2_TA.pdf

Physics of Radiotherapy using External Beam Dose distribution Beam dose  Factors Affecting Dose Calculations Essential step in dosimetry Establish measured data tables for each treatment machine Tables prepared as a result of measurements in p...

Physics of Radiotherapy using External Beam Dose distribution Beam dose  Factors Affecting Dose Calculations Essential step in dosimetry Establish measured data tables for each treatment machine Tables prepared as a result of measurements in phantoms (tissue equivalent material) Constancy of the machine must be routinely checked  Dose rate Also referred to as machine output Measured in a water equivalent phantom Amount of radiation exposure produced by a treatment machine or source as specified at a reference field size at a specified reference distance Measured with equipment calibrated according to a national standard (1 MU/cGy in a 10 x 10 at Dmax)  The first major step in determining radiation dose is machine output Output tells us dose delivered at a specified point in a medium, at a specified distance from the target, and in a specified medium The second step is absorbed dose in a medium It is necessary to know the composition of the irradiated material, geometric relationship of the material and radiation beam, and field size  1.1 Phantom Basic dose distribution data are usually measured in a water phantom, which 1. closely approximates the radiation absorption and scattering properties of muscle and other soft tissues. 2. universally available with reproducible radiation properties.  A water phantom, however, poses some practical problems when used in conjunction with ion chambers and other detectors that are affected by water, unless they are designed to be waterproof. In most cases, however, the detector is encased in a thin plastic (water equivalent) sleeve before immersion into the water phantom.  Since it is not always possible to put radiation detectors in water, solid dry phantoms have been developed as substitutes for water. Ideally, for a given material to be tissue or water equivalent, it must have the same effective atomic number, number of electrons per gram, and mass density.  However, since the Compton effect is the most predominant mode of interaction for megavoltage photon beams in the clinical range, the necessary condition for water equivalence for such beams is the same electron density (number of electrons per cubic centimeter) as that of water. The electron density (pe) of a material may be calculated from its mass density (pm) and its atomic composition according to the formula: (1) where Electron densities of various human tissues and body fluids have been calculated according to Equation (1). Table (1) gives the properties of various phantoms that have been frequently used for radiation dosimetry. Table (1) Physical properties of various phantom materials Values for some tissues of dosimetric interest are listed in Table (2). Table (2) Number of electrons per gram of various materials  Synthetic plastic and polystyrene phantom are most frequently used as dosimetry phantoms. In addition to the homogeneous phantoms, anthropomorphic (having human characteristic) phantoms are frequently used for clinical dosimetry. One such commercially available system, known as Alderson Rando Phantom, incorporates materials to simulate various body tissues muscle, bone, lung, and air cavities Rando phantom Solid Phantom (slab phantom) Water phantom  1.2 Depth dose distribution As the beam is incident on a patient (or a phantom), the absorbed dose in the patient varies with depth. This variation depends on many conditions: beam energy, depth, field size, distance from source, and beam collimation system. Thus the calculation of dose in the patient involves considerations in regard to these parameters and others as they affect depth dose distribution.  An essential step in the dose calculation system is to establish depth dose variation along the central axis of the beam. A number of quantities have been defined for this purpose, major among these being percentage depth dose, tissue-air ratios, tissue-phantom ratios and tissue-maximum ratio  These quantities are usually derived from measurements made in water phantoms using small ionization chambers. Although other dosimetry systems such as TLD, diodes, and film are occasionally used, ion chambers are preferred because of their better precision and smaller energy dependence.  1.3 Percentage depth dose One way of characterizing the central axis dose distribution is to normalize dose at depth with respect to dose at a reference depth. The quantity percentage depth dose may be defined as the quotient, expressed as a percentage, of the absorbed dose at any depth d to the absorbed dose at a fixed reference depth do, along the central axis of the beam. Percentage depth dose (P ) is thus: For orthovoltage (up to about 400 kVp) and lower-energy x-rays, the reference depth is usually the surface (do = 0). For higher energies, the reference depth is taken at the position of the peak absorbed dose (do = dm).  Percentage depth dose is (Dd /Ddo) x 100, where d is any depth and do is reference depth of maximum dose.  In clinical practice, the peak absorbed dose on the central axis is sometimes called the maximum dose, the dose maximum or simply the Dmax. Thus, A number of parameters affect the central axis depth dose distribution. These include beam quality or energy, depth, field size and shape, source to surface distance, and beam collimation  1.3.A. Dependence on Beam Quality and Depth The percentage depth dose increases with beam energy (beyond the depth of maximum dose) Higher-energy beams have greater penetrating power and thus deliver a higher percentage depth dose. Central axis depth dose distribution for different quality photon beams. Field size, 10 x 10 cm; SSD = 100 cm for all beams except for 3.0 mm Cu HVL, SSD = 50 cm.  If the effects of inverse square law and scattering are not considered, the percentage depth-dose variation with depth is governed approximately by exponential attenuation. Thus the beam quality affects the percentage depth dose by virtue of the average attenuation coefficient µ. As the µ decreases, the more penetrating the beam becomes, resulting in a higher percentage depth dose at any given depth beyond the build-up region  1.3.A.1 Initial Dose Build-Up The percentage depth dose decreases with depth beyond the depth of maximum dose. However, there is an initial buildup of dose which becomes more and more pronounced as the energy is increased. In the case of the Orthovoltage or lower energy x-rays, the dose builds up to a maximum on or very close to the surface.  But for higher-energy beams, the point of maximum dose lies deeper into the tissue or phantom. The region between the surface and the point of maximum dose is called the dose build-up region.  The dose build-up effect of the higher-energy beams gives rise to what is clinically known as the skin-sparing effect. For megavoltage beams such as cobalt-60 and higher energies the surface dose is much smaller than the Dm , this offers a distinct advantage over the lower- energy beams for which the Dm occurs at the skin surface.  Thus, in the case of the higher energy photon beams, higher doses can be delivered to deep-seated tumors without exceeding the tolerance of the skin. This, of course, is possible because of both the higher percent depth dose at the tumor and the lower surface dose at the skin The physics of dose buildup may be explained as follows: (a) As the high-energy photon beam enters the patient or the phantom, high-speed electrons are ejected from the surface and the subsequent layers; (b) These electrons deposit their energy a significant distance away from their site of origin. Because of (a) and (b), the electron fluence and hence the absorbed dose increase with depth until they reach a maximum. However, the photon energy fluence continuously decreases with depth and, as a result, the production of electrons also decreases with depth. The net effect is that beyond a certain depth the dose eventually begins to decrease with depth.  We can explain the buildup phenomenon in terms of absorbed dose and a quantity known as kerma (kinetic energy released in the medium). The kerma (K) may be defined as "the quotient of dEtr by dm where dEtr : is the sum of the initial kinetic energies of all the charged ionizing particles (electrons) liberated by uncharged ionizing particles (photons) in a material of mass dm.  Because kerma represents the energy transferred from photons to directly ionizing electrons, the kerma is maximum at the surface and decreases with depth because of the decrease in the photon energy fluence. The absorbed dose, on the other hand, first increases with depth as the high-speed electrons ejected at various depths travel downstream.  As a result, there is an electronic build-up with depth. However, as the dose depends on the electron fluence, it reaches a maximum at a depth approximately equal to the range of electrons in the medium. Schematic plot of absorbed dose and kerma as functions of depth.  1.3.B. Effect of Field Size and Shape Field size may be specified either geometrically or dosimetrically. The geometrical field size is defined as "the projection, on a plane perpendicular to the beam axis, of the distal end of the collimator as seen from the front center of the source”.  The dosimetric field size: is the distance intercepted by a given isodose curve (usually 50% isodose) on a plane perpendicular to the beam axis at a stated distance from the source. The field size will be defined at a predetermined distance such as the source surface distance (SSD) or the source- axis distance (SAD).  SAD : is the distance from the source to axis of gantry rotation known as the isocenter. For a sufficiently small field one may assume that the depth dose at a point is effectively the result of the primary radiation, that is, the photons which have traversed the overlying medium without interacting.  The contribution of the scattered photons to the depth dose in this case is negligibly small or 0. But as the field size is increased, the contribution of the scattered radiation to the absorbed dose increases. Because this increase in scattered dose is greater at larger depths than at the depth of Dm. The percent depth dose increases with increasing field size.  The increase in percent depth dose caused by increase in field size depends on beam quality. Since the scattering probability decreases as the energy increase and the higher-energy photons are scattered in the forward direction, the field size dependence of percent depth dose is less pronounced for the higher-energy than for the lower- energy beams.  Percent depth dose data for radiation therapy beams are usually tabulated for square fields. Since the majority of the treatments in clinical practice require rectangular and irregularly shaped (blocked) fields, a system of equating square fields to different field shapes is required.  Semi-empirical methods have been developed to relate central axis depth dose data for square, rectangular, circular, and irregularly shaped fields. Equivalent squares of rectangular fields  Data for equivalent squares, taken from Hospital Physicists' Association are given in previous table. As an example, consider a 10 x 20-cm field. from table the equivalent square is 13.0 x 13.0 cm. Thus the percent depth dose data for a 13x13 cm field (obtained from standard tables) may be applied as an approximation to the given 10x20cm field.  A simple rule of thumb method has been developed by Sterling et al. for equating rectangular and square fields. According to this rule, a rectangular field is equivalent to a square field if they have the same area/perimeter (A/P).  For example, the 10 x 20-cm field has an A/P of 3.33. The square field which has the same A/P is 13.3 x 13.3 cm, a value very close to that given in Table. The following formulas are useful for quick calculation of the equivalent field parameters: For rectangular fields, where a is field width and b is field length. For square fields, since a = b,  1.3.C. Dependence on Source-Surface Distance Photon fluence emitted by a point source of radiation varies inversely as a square of the distance from the source. Although the clinical source for external beam therapy has a finite size, the source-surface distance is usually chosen to be large so that the source dimensions become unimportant in relation to the variation of photon fluence with distance. In other words, the source can be considered as a point at large source-surface distances.  Thus the exposure rate or "dose rate in free space" from such a source varies inversely as the square of the distance. Of course, the inverse square law dependence of dose rate assumes that we are dealing with a primary beam, without scatter. In a given clinical situation, however, collimation or other scattering material in the beam may cause deviation from the inverse square law.  Percent depth dose increases with SSD because of the effects of the inverse square law. Although the actual dose rate at a point decreases with increase in distance from the source, the percent depth dose, which is a relative dose with respect to a reference point, increases with SSD.  This is shown in the figure. in which relative dose rate from a point source of radiation is plotted as a function of distance from the source, following the inverse square law.  The plot shows that the drop in dose rate between two points is much greater at smaller distances from the source than at large distances. This means that the percent depth dose, which represents depth dose relative to a reference point, decreases more rapidly near the source than far away from the source. In clinical radiation therapy, SSD is a very important parameter. Because percent depth dose determines how much dose can be delivered at depth relative to the surface dose or Dm , the SSD needs to be as large as possible. However, because dose rate decreases with distance, the SSD, in practice, is set at a distance which provides a compromise between dose rate and percent depth dose.  For the treatment of deep-seated lesions with megavoltage beams, the minimum recommended SSD is 80 cm. Tables of percent depth dose for clinical use are usually measured at a standard SSD (80 or 100 cm for megavoltage units).  In a given clinical situation, however, the SSD set on a patient may be different from the standard SSD, For example, larger SSDs are required for treatment techniques that involve field sizes larger than the ones available at the standard SSDs  Thus the percent depth doses for a standard SSD must be converted to those applicable to the actual treatment SSD. The Mayneord (F) Factor, this method is based on a strict application of the inverse square law, without considering changes in scattering, as the SSD is changed.  Figure below shows two irradiation conditions, which differ only in regard to SSD. Let P(d,r,f) be the percent depth dose at depth d for SSD = f and a field size r (e.g., a square field of dimensions r x r). Since the variation in dose with depth is governed by three effects-inverse square law, exponential attenuation and scattering. Change of percent depth dose with SSD. Irradiation condition (a) has SSD = f1 and condition (b) has SSD = f2. For both conditions, field size on the phantom surface, r x r, and depth d are the same. where µ is the linear attenuation coefficient for the primary and Ki is a function which accounts for the change in scattered dose. Ignoring the change in the value of Ki from one SSD to another, Dividing the two equations The terms on the right-hand side of the last equation are called the Mayneord F factor. Thus, It can be shown that the F factor is greater than 1 for f2 > f1 and less than 1 for f2 < f1. Thus itmay be restated that the percent depth dose increases with increase in SSD. Example 1 The percent depth dose for a 15 x 15 field size, 10-cm depth, and 80- cm SSD is 58.4 (60CO beam). Find the percent depth dose for the same field size and depth for a 100-cm SSD. Assuming dm= 0.5 cm for 60CO γ-rays: From the above equation the desired percent depth dose is:  1.4 TISSUE-AIR RATIO Tissue-air ratio (TAR) was first introduced by Johns et al. in 1953 and was originally called the "tumor-air ratio." At that time, this quantity was intended specifically for rotation therapy calculations. In rotation therapy, the radiation source moves in a circle around the axis of rotation which is usually placed in the tumor.  Although the SSD may vary depending on the shape of the surface contour, the source-axis distance remains constant. Since the percent depth dose depends on the SSD, the SSD correction to the percent depth dose will have to be applied to correct for the varying SSD- a procedure that becomes difficult to apply routinely in clinical practice. A simpler quantity namely, TAR has been defined to remove the SSD dependence.  Since the time of its introduction, the concept of TAR has been defined to facilitate calculations not only for rotation therapy but also for stationary isocentric techniques as well as irregular fields. Tissue-air ratio may be defined as: the ratio of the dose (Dd) at a given point in the phantom to the dose in free space (Dfs) at the same point.  The definition of tissue-air ratio. TAR (d, rd) = Dd/Dfs For a given quality beam, TAR depends on beam energy, depth d and field size rd at that depth:  1.4.A. Effect ofDistance One of the most important properties attributed to TAR is that it is independent of the distance from the source. This, however, is an approximation which is usually valid to an accuracy of better than 2% over the range of distances used clinically. 1.4.B. Variation with Energy, Depth, and Field Size Tissue-air ratio varies with energy, depth, and field size very much like the percent depth dose. For the megavoltage beams, the tissue-air ratio builds up to a maximum at the depth of maximum dose (dm) and then decreases with depth more or less exponentially.  For a narrow beam or a 0x0 field size in which scatter contribution to the dose is neglected, the TAR beyond dm varies approximately exponentially with depth  As the field size is increased, the scattered component of the dose increases and the variation of TAR with depth becomes more complex. However, for high-energy megavoltage beams, for which the scatter is minimal and is directed more or less in the forward direction, the TAR variation with depth can still be approximated by an exponential function, provided an effective attenuation coefficient (µeff) for the given field size is used.  1.4.B.1. Backscatter Factor The term backscatter factor (BSF) is simply the tissue-air ratio at the depth of maximum dose on central axis of the beam. It may be defined as: The ratio of the dose on central axis at the depth of maximum dose to the dose at the same point in free space. Mathematically, Or where rdm is the field size at the depth dm of maximum dose.  The backscatter factor, like the tissue-air ratio, is independent of distance from the source and depends only on the beam quality and field size. For the orthovoltage beams with usual filtration, the BSF can be as high as 1.5 for large field sizes. This amounts to a 50% increase in dose near the surface compared with the dose in free space or, in terms of exposure, a 50% increase in exposure on the skin compared with the exposure in air.  For megavoltage beams (60Co and higher energies), the BSF is much smaller. For example, BSF for a 10 × 10-cm field for 60Co is about 1.036. This means that the Dmax will be 3.6% higher than the dose in free space. This increase in dose is the result of radiation scatter reaching the point of Dmax from the overlying and underlying tissues 1.4.C. Relationship between TAR and Percent Depth Dose TAR and PDD are interrelated. The relationship can be derived as follows: Considering Fig. (a), let TAR(d,rd) be the tissue-air ratio at point Q for a field size rd at depth d. Let r be the field size at the surface, f be the SSD, and dm be the reference depth of maximum dose at point P. Let Dfs(P) and Dfs(Q) be the doses in free space at points P and Q, respectively (Fig. B,C). Dfs(P)and Dfs(Q) are related by inverse square law. Relationship between TAR and percent depth dose. 1.4.C.1. Conversion of Percent Depth Dose from One SSD to another-the TAR Method Suppose f1 is the SSD for which the percent depth dose is known and f2 is the SSD for which the percent depth dose is to be determined. Let r be the field size at the surface and d be the depth, for both cases. let rd , f1 and rd, f2 be the field sizes projected at depth d in Fig. above (A,B) respectively. The last term in the brackets is the Mayneord factor. Thus the TAR method corrects the Mayneord F factor by the ratio of TARs for the fields projected at depth for the two SSDs.  1.5 SCATTER-AIR RATIO SARs are used for the purpose of calculating scattered dose in the medium. The computation of the primary and the scattered dose separately is particularly use in the dosimetry of irregular fields. SAR may be defined as the ratio of the scattered dose at a given point in the phantom to the dose in free space at the same point.  The scatter-air ratio like the tissue-air ratio is independent of the source-to-surface distance but depends on the beam energy, depth, and field size Because the scattered dose at a point in the phantom is equal to the total dose minus the primary dose at that point, scatter-air ratio is mathematically given by the difference between the TAR for the given field and the TAR for the 0 x 0 field.  SAR (d,rd ) = TAR (d,rd) – TAR (d,0) TAR(d,0) represents the primary component of the beam. Because SARs are primarily used in calculating scatter in a field of any shape, SARs are tabulated as functions of depth and radius of a circular field at that depth. An example of a mantle irregular field. Two segments out of 36 are highlighted. The first is simple with radius r1, the seventh is composite with three radii: ra , rb and rc.