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214   PART III    Therapeutic Modalities for the Cancer Patient


         tolerated, because without the treatment, patients may not live   10 1
         long enough to develop late effects; however, for structures such                  S   e     2
                                                                                                  ( D    D )
         as the spinal cord, where a late effect such as paralysis is viewed as
  VetBooks.ir  unacceptable, a 1% probability of effects is used. Conversely, for   10 0  S    S at D    /



         procedures like SRT limb-sparing for canine osteosarcoma (OSA),
                                                                                                       D
                                                                                               S    e

         the risk of fracture is affected by the region and condition of lytic                 for     0.15 Gy  1
         bone at the time of treatment. Owners may choose to accept a
         higher risk of fracture to maintain limb function, because a future
                                                                                                            D
         amputation can be used as a salvage procedure. 101        Surviving fraction  10  1        S    e  2

            It is not within the scope of this chapter to prescribe specific                           for       2
         radiation doses or fractionation schedules, because many factors                              0.03 Gy
         must be considered. Rather, referring veterinarians must know    2


         what to expect when sending patients to a radiation oncology   10             S        S • S

         center and should be able to explain the fundamental principles                           2
                                                                                                D    D
         to clients. The radiation oncologist should inform the referring                    e
         veterinarian and owner of the probabilities of tumor control,   10  3
         acute effects, and late effects expected with a specific protocol.   0  2  4    6    8    10    12   14
         The goal of RT is to destroy the reproductive capacity of the                   Dose (Gy)
         tumor without excessive damage to surrounding normal tissues.
         The relationship of three parameters (overall treatment time,   • Fig. 13.2  Illustration of the alpha/beta model in which cell killing occurs
                                                               by either a single-event process or a double-event process such that the
         total dose, and fraction size) as well as other factors, such as che-  overall killing by either process is the product of the two, and the alpha/
         motherapy, previous surgery, and underlying medical conditions   beta ratio is the dose at which both processes contribute equally to the
         such as diabetes, must be carefully considered in the develop-  total killing. Note that the upper curve is survival for the alpha component
         ment of an RT plan.                                   only, the middle curve is for the beta component only, and the lower curve
                                                               is for both components. (From Wilson PF, Bedford JS. Radiobiological
                                                               principles. In: Hoppe RT, Phillips TL, Roach M, III, eds. Leibel and Phillips
          THE LINEAR QUADRATIC FORMALISM AND                   Textbook of Radiation Oncology. 3rd ed. St. Louis: Elsevier; 2010:3–30.)
          BIOLOGIC EFFECTIVE DOSE
                                                                  Most early-responding tissues and tumors have a high  α/β
         Many mathematical models have been used to describe or predict   ratio,  whereas  late-responding  tissues have a  low  α/β  ratio. 103
         the effect of radiation on cells and tissues. The linear quadratic   Tumors that may have a low α/β ratio can influence the optimal
         formalism has been useful for evaluating the effect of radiation   radiation prescription in terms of total dose, time, and fraction
         in fraction sizes commonly used in RT and has been a tool for   size. Tumors that may have lower α/β ratios include melanoma,
         modifying radiation protocols based on projected effect on late-  prostatic tumors, soft tissue sarcomas, transitional cell carcinomas,
         responding tissues. 102–105  Mechanistically, this model corresponds   and OSA, but these are generalities and the α/β ratio may differ
         radiation injury to chromosome aberrations. 106–108  After a tissue   from tumor to tumor. 110–112
         or population of cells is exposed to any dose of radiation, a frac-  The concept of biologic effective dose (BED) is used to predict
         tion of the cells will be killed. The proportion of remaining cells   how changes in dose prescription may preferentially affect differ-
         is known as the surviving fraction (S). The sensitivity of a tumor   ent cells or tissues based on their α/β ratio in the linear quadratic
         or tissue to radiation can be shown as a graph of the radiation   model of survival. The formula for BED is as follows: BED = nd
         dose (D) versus the surviving fraction (Fig. 13.2). 109  The relation-  [1 + d/(α/β)], where n is the number of fractions and d is the
         ship between a dose of radiation and the surviving fraction of cells   dose per fraction. If the α/β ratio of a tissue is known or can be
         is commonly described by the linear quadratic equation: S(D) =     estimated, the BED can be calculated for any dose prescription.
         e –(αD +  βD 2 ) , where S is the surviving fraction at a dose (D). 103    It is possible to use this formula to assess how dosimetry changes
         Alpha (α) and beta (β) are constants that vary according to the tis-  or errors alter the effective dose of a protocol. It is important to
         sue, with α corresponding to the cell death that increases linearly   note that there are several limitations to the use of this equation,
         with dose, and β corresponding to the cell death that increases in   including that it does not account for differences in the overall
         proportion to the square of the dose (also known as the quadratic   length of time of the radiation protocol or accelerated repopula-
         component). The α/β ratio is a useful number that is the dose in   tion. More complicated additions to the formula can be used to
         Gy when cell kill from the linear and quadratic components of the   take overall treatment time into account. 105  Although experi-
         cell survival curve are equal. Cells with a higher α/β ratio have a   mental and clinical data provide confirmation of α/β ratios for
         more linear appearance when plotted on a log scale, and cells with   most tissues, linear quadratic parameters for tumors are uncer-
         a low α/β ratio have a parabolic shape. The α/β ratio is also an   tain; therefore calculations made with this model for tumor con-
         important description of the radiosensitivity of a cell. At low dose   trol prediction may not be valid. 113  Nevertheless, this formula
         fractions, tissues or cells with low α/β ratio are relatively radia-  is a useful tool when considering hyperfractionating a standard
         tion resistant compared with tissues or cells with high α/β ratio.   radiation protocol to create a new protocol that increases nor-
         It has been suggested that tissues and cells with low α/β ratios   mal tissue tolerance, which could allow increased total dose, or
         have a greater capacity for repair of sublethal radiation damage. 110    to adjust a protocol when there has been an extensive delay in
         Sublethal radiation damage is defined as damage that can become   treatment. The validity of BED for SRT is unclear. It has been
         lethal if it interacts with additional damage. 29,30  Sublethal damage   useful for estimating late effects based on data from conven-
         repair is the reason that cell survival increases when a radiation   tionally fractionated RT; however, BED-derived constraints for
         dose is split into two fractions separated by a time interval. 29,30  acutely responding tissues may overestimate tolerance of acutely
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