ASSESSING LEAKAGE WORKLOADS OF MEDICAL LINEAR ACCELERATORS FOR IMRT AND TBI TECHNIQUES

Transcription

1 ASSESSING LEAKAGE WORKLOADS OF MEDICAL LINEAR ACCELERATORS FOR AND TBI TECHNIQUES A Thesis submitted to the Faculty of the Graduate School of Arts and Sciences of Georgetown University in partial fulfillment of the requirements for the degree of Master of Science in Health Physics By James R. Jordan, B.S. Washington, DC December 10, 2007

2 Thanks to all people and institutions that provided data for this thesis specifically: Brad Murray of Cross Cancer Institute Ralph Young of Martin Memorial Cancer Center Kathryn Wall and Cara Sullivan of Rock Hill Radiation Therapy Centre Richard Emery and Dr. Anthony Berson of St. Vincent s Comprehensive Cancer Center Julius V. Turian of University of Illinois Medical Center Allan Caggiano of Holy Name Hospital Marc S. Miner of Hughes Cancer Center of Pocono Medical Center St. Joseph Hospital of Orange, California Wolfgang Tomé and Bhudatt Paliwal of University of Wisconsin Hospital And all other people and institutions that wished to remain nameless. Many thanks, James R. Jordan ii

3 ASSESSING LEAKAGE WORKLOADS OF MEDICAL LINEAR ACCELERATORS FOR AND TBI TECHNIQUES James R. Jordan, B.S. Thesis Advisor: James E. Rodgers, Ph.D. ABSTRACT Current estimates for leakage workloads are not well quantified for Intensity Modulated Radiation Therapy () and Total Body Irradiation (TBI) treatments. When analyzed on a large scale, using a large sample, a well defined leakage workload may be established. A database of 17 cancer treatment centers and 73 linear accelerators were used to make the assessment. There were 374,003 total treatments, with 213,757 low energy (4 and 6 MV) treatments, 106,343 of which were and 149,730 high energy (15, 16, 18, and 20 MV) treatments, 64,138 of which were. There were 184 TBI treatments, with 98 being low energy and 86 being high energy. The numbers are too scant to make any statements about the contribution TBI makes to workload, there is more than enough data to estimate the contribution to leakage workload. An factor, C I, of 5.1 may be used for low energy photon calculations, and a C I of 4.4 may be used for high energy photon calculations, where CI is: C = I MU MU conv. iii

4 TABLE OF CONTENTS Introduction... 1 Chapter I: Material and Methods Chapter II: Results... 9 Chapter III: Discussion.. 15 Appendix. 26 Bibliography 122 iv

5 INTRODUCTION Due to its smaller field sizes and the number of segments used per field, Intensity Modulated Radiation Therapy () uses many more monitor units (MU) per delivered dose (usually measured in centigray abbreviated cgy) than does conventional external beam radiation treatment. This does not have an effect on the workload for the primary barrier or for scatter as demonstrated by Rodgers (8), but the increased beam-on time can greatly increase the leakage of radiation from the head of the medical linear accelerator and secondary barrier thickness requirements. Thus, the primary barrier Workload (W ) alone, in dose per week, is not sufficient to determine the contribution of to the total leakage-radiation workload. W must be multiplied by some factor in order to account for its increased MU per cgy in order to calculate its full contribution to the leakage workload (W L ). To find this factor, which the National Council on Radiation Protection and Measurements (NCRP) in NCRP Report Number 151 calls the factor or C I, a ratio is taken of the of the MU per cgy of prescribed dose for and the MU per cgy for conventional treatments (6): MU = i MU ( D pre i ) i so, C = I MU MU conv. 1

6 Where MU is measured in MU/cGy, and C I is a dimensionless quantity. Since MU conv is conservatively defined as 1 MU/cGy, in most cases C I is the same value as MU. Just as disproportionately affects W L, Total Body Irradiation (TBI) does as well, due to the inverse square law. Conventional workloads (W conv ) are calculated at a distance of one meter from x-ray target to the patient, and TBI is treated at much greater distances, up to five meters, with the TBI workload (W TBI ) normalized to one meter (6). This will greatly increase the leakage radiation contribution of TBI, since the amount of MU per delivered dose is increased by a power of two for any increase in distance between the x-ray target and patient. Followill et al. calculated an factor of 3.4 MU/cGy for Varian Multi-leaf Collimators (MLC) at 6 Megavolts (MV) and 2.8 MU/cGy at 18 and 25 MV. For Nomos Tomotherapy an factor of 9.7 MU/cGy at 6 MV and 8.1 MU/cGy at 18 and 25 MV was calculated. These calculations fall in line with the NCRP value of 2 to 10 (1, 6); however, their study was limited to four patients using conventional unwedged treatments, who were also planned using the MLC and tomotherapy techniques. Mechalakos et al. also examined the workload for. They found an increase in MU per week on their Varian 2100C machine with photon energies of 6 and 18 MV using compared to two other machines (a Siemens Mevatron KD with photon energies of 6 and 15 MV and a Varian 600C with photon energy of 6 MV), which were limited to conventional treatments only. Their factor was between 2.2 to 2.5 (4). 2

7 This study was conducted with one year of data, but was limited in scope with only a single machine performing. Since an increased W L may translate into an increased amount of secondary shielding needed to protect radiation workers and the public, it is very important to carefully ascertain the C I and find the increase in leakage due to. Other studies have found increases in workload from and TBI, but the scope of these studies was not very broad. In this study, with a wide range of accelerators and treatment types, I hope to more firmly establish the contributions of and TBI to the total leakage workload. This paper will set values for the C I contribution to the W L for the increased leakage radiation in and TBI. I hypothesize that current estimates for leakage workloads are not well quantified for and TBI treatments, but when analyzed on a large scale, using a large sample, a well defined C I may be established. 3

8 CHAPTER I: MATERIALS AND METHODS In this study, data was collected from seventeen radiation treatment centers, which included 71 Varian accelerators (which included CL 6/100, 600C, 600C/D, CL 1800, 2100C, 2100C/D, 21EX, 2300C/D, and 23EX) and almost 375,000 treatment fields of a combination of conventional unwedged, conventional wedged,, and TBI treatments at energies of 4, 6, 15, 16, 18, and 20MV. The data was organized by Varian using an InfoMaker report to collect the data from the treatment planning systems and entered into Excel spreadsheets where it could be analyzed. The data that was collected included the field, treatment time, gantry angle, energy mode, MU, dose, and accessory used (wedge, cone, etc.). The collected data was separated by hospital system and by individual machine. Individual treatments that were or TBI were identified. It was then analyzed by energy mode for the conventional MU per cgy, MU per cgy, TBI MU per cgy, and the fraction of treatments that were was noted. The data was analyzed by multiple methods. First, for all categories a simple mean was computed by: with the standard deviation being: n = i 1 i µ = µ n 4

9 ( µ µ ) n 2 i = 1 i σ =. For an unbiased estimator of the standard deviation for a small sample n-1 is used in the denominator. However, with the large sample sizes involved in this study, n-1 is not significantly different than n. The mean MU/cGy was calculated for each gantry angle used in the treatment for conventional treatments with and without wedges,, and TBI at each individual energy for all 73 machines in which the treatment applied. This was done simply by summing all MU/cGy and dividing by the total number of occurrences. The, TBI, and conventional (which includes wedges) means are displayed in Tables 2.46 through 2.58 in the appendix for machines that conducted or TBI treatments. Machines that were not used for or TBI had means calculated for their individual energies treated, but they are not represented in this report. Second, the MU/cGy data for treatments was placed into value bins in order to be able to graph the results. To do this, bins of different MU/cGy values were created. The total number of these occurrences were created and then normalized to 100. The width of each bin was charted for its relative weight, and the mid-point of each bin was noted. An example of the collected data is shown in Table 1.1. n 5

10 Delta 0.5 Unit 1 6X Bin Unit 1 6X 0 n Ni wi b'i Ni*wi*b'i Ni*wi Ni*wi*(b'i-mean(0-15))^ Table 1.1. Chart of collected data. The first bin is all occurrences that are greater than or equal to 0 MU/cGy through all occurrences less than 0.5 MU/cGy. The second bin is from 0.5 to less than 1.0. Delta is the smallest bin size. The number of occurrences is denoted by n. N i is the number of occurrences normalized to 100 total occurences. The bin weight calculated by subtracting the bottom of the bin from the top of the bin and dividing by the smallest bin width is w i. The midpoint of each bin is b i. The unit number (Unit 1 in Table 1.1) is the tracking number for the machine at the facility being analyzed. Each facility has a unique hospital serial number (HSN) and each machine analyzed in a facility has a number assigned as a resource serial number (RSN) starting at one for each facility, e.g., HSN 1, RSN 1. A table on page 12 shows each machine that conducted treatments, the energies at which the machine conducted s, and the page where the data is located. These results were then graphed. The abscissa is the value of mid-point of the bin, and the ordinate is the number of occurrences for that bin. This can be seen in Figure 6

11 1.1. RSN 1 6X 25.0 Number of Occurrences, N RSN 1 6X bins of MU/cGy Figure 1.1. Frequency distribution of MU/cGy plotted versus bin mid-point value. A table was also created of means and standard deviations with differing maximum cutoffs. Since the means and standard deviations are greatly affected by outliers, this will give the ability to disregard higher numbers for anomalous high values. An example of this table is shown in Table 1.2. The mean becomes: µ and the standard deviation becomes: n i= 1 = n Ni * wi * b i i= 1 Ni * wi 7

12 σ n i= 1 = n i= 1 ( b i ) Ni * wi * µ Ni * wi 2. RSN 1 6X mean for indicated range mean(0-15)= 4.23 mean(0-25)= 4.23 mean(0-50)= 4.94 mean(0-200)= 4.94 mean(0-1500)= 4.94 stdev(0-15)= 2.33 stdev(0-25)= 2.33 stdev(0-50)= 4.76 stdev(0-200)= 4.76 stdev(0-1500)= 4.76 Table 1.2. Table of means and standard deviations at different cutoffs of MU/cGy. As mentioned in the introduction, I set out to analyze C I on a large sample group. I believe I have achieved this by using a database of 17 cancer treatment centers and 73 linear accelerators. There were 374,003 total treatments, with 213,757 low energy (4 and 6 MV) treatments, 106,343 of which were and 149,730 high energy (15, 16, 18, and 20 MV) treatments, 64,138 of which were. There were 184 TBI treatments, with 98 being low energy and 86 being high energy. All 374,003 treatments have several data recorded besides MU and dose, these include machine model, accessories used (wedge, cone, et cetera), field identification and name, reference identification and name, gantry angle, energy mode, patient and session serial number, treatment technique, and treatment date and time. 8

13 CHAPTER II: RESULTS Figures 2.1 through 2.44 in the appendix show the graphs of all machines that performed s. Each figure has a corresponding table of means and standard deviations at MU/cGy cutoffs of 15, 25, 50, 200, and 1500 MU/cGy. These cutoffs are useful for determining the most useful data to use. For example, if set-up fields were included with the data, then the extremely low dose (nominally zero assessed to these fields) causes the MU/cGy value to be inordinately high and these numbers may be discarded since they are fictitiously high. The data in the tables below represent the number of MU/cGy of treatments which represents the MU. The factor or C I may be found by dividing the MU by the MU conv. A MU conv of 1 may be used for conservative values of C I which also makes MU equal to C I for conservative estimates. The overwhelming majority of data, before being analyzed whether there is a need to restrict the ranges to lower cutoffs, show an factor within the NCRP suggested value range of between 2 and 10. All values above the range noted in NCRP 151 will be discussed here. The first elevated values, as seen in Tables 2.4 and 2.5, are from HSN 2, a hospital cancer center, RSN 4 at 15 MV and 7 at 6 MV. The computed mean with a cutoff of 1500 MU/cGy was and 9.17 with a standard deviation and 7.71 for RSN 4 and 7 respectively. For RSN 4 these numbers are representative of only three patients, so the numbers are easily skewed, and for RSN 7 the data was for a single 9

14 head and neck patient. Two of the three patients for RSN 4 are eight field head and neck patients. The last is an eight field plan with an unrecorded reference point. All contain split fields. Since the dose calculation point is taken from isocenter, if isocenter is blocked off by MLCs then the dose becomes very small, making the MU/cGy become extremely high and really meaningless. In this case it causes RSN 7 to have an outlier at 25.81, which has a dose which is an order of magnitude less than any other field, when all the rest of the field doses are below 10. Using the cutoff of 25 MU/cGy the mean and standard deviation become more acceptable values of 5.85 and As for RSN 4, its values range from to a little over 323 MU/cGy. If the data is analyzed for treatments of less than 46 MU/cGy then the mean becomes 3.14 and the standard deviation In both cases the numbers are now well within the NCRP recommended value range. HSN 3, another hospital center, RSN 5 at 6 MV (Table 2.8) has a mean and standard deviation of 7.36 and This number is a decent value since the treatments performed on the machine are primarily head and necks which call for many small fields with more MU/cGy. As mentioned in the introduction MU conv is usually defined to be 1 MU/cGy, this creates a conservative value for C I, however, vaults are currently shielded for a conventional MU/cGy which exceeds this number due to differing techniques and wedge use. It is then practical, to examine higher MU in this light. Therefore, when the value of the MU mean is divided by the mean of the machine s conventional treatments (Table 2.46) the C I becomes

15 HSN 6, a stand alone cancer center, RSN 2 at 6 MV (Table 2.12) has a mean and standard deviation of 6.29 and Just like the previous machine if the MU mean is divided by the conventional mean, the C I become 5.11, but also like HSN 2 it contains a few fields which contain doses of an order of magnitude less than other fields in a patient s treatment. If these fields are thrown out then a cutoff of 25 MU/cGy may be used to yield a mean and standard deviation of 5.04 and HSN 8, a hospital center, RSN 1 (Table 2.14) has a mean and standard deviation of 8.33 and and RSN 2 has and 18.85, both at 6 MV. When fields are removed that again are less in dose by an order of magnitude than other fields in a patient treatment then values of MU/cGy between 55 and 440 drop out and the 25 MU/cGy cutoff may be used, which brings the mean and standard deviation down to 7.15 and 2.80 for RSN 1 and 7.35 and 2.96 for RSN 2. Table 2.17 for HSN 10, a hospital center, RSN 3 shows its 6 MV mode has a mean and standard deviation of and 7.62 and its 15 MV mode has and The field doses are uniform throughout and there is no reason to use a cutoff. Head and necks and brains are treated with 6MVs driving up the MU/cGy. When both treatment modes are compared to the conventional means, then the C I drops to 5.35 for 6MV and 9.48 for 15MV. The 15 MV is still a little high in comparison to the NCRP recommended value. A lower cutoff may be used for HSN 12, a hospital center, RSN 1 (Table 2.19) at 6 MV which has a mean and standard deviation of 5.87 and When values that are derived from field doses that are an order of magnitude less than the other field doses in a 11

16 patient treatment, then the 25 MU/cGy cutoff may be used and the mean and standard deviation becomes 4.93 and For HSN 13, a hospital cancer center, RSN 1 (Table 2.21) in 6MV mode some MU/cGy are almost as high as 800 MU/cGy due to the low doses assigned to fields where the isocenter is blocked. If these high values are disallowed then the 50 MU/cGy cutoff may be used which brings the mean to When divided by the conventional mean the C I becomes Its 18MV treatment mode has a mean and standard deviation of 7.37 and Since 2% of the treatments are above 25 MU/cGy and these are split fields around critical structures, i.e., with blocked isocenter, a cutoff of 25 MU/cGy may be used for the 18 MV mode. This brings the mean and standard deviation down to 6.49 and HSN 15, a university hospital center, RSN 3 (Table 2.24) at 4 MV has a mean and standard deviation of 8.01 and Again, when divided by the conventional mean, the C I drops to When the 600 MU/cGy setup fields are removed from HSN 16, a university hospital center, RSN 3 (Table 2.28) at 6MV, the mean and standard deviation fall from 4.25 and to 3.96 and This is the same for HSN 17, another university hospital center, RSN 4 (Table 2.31) at 6 MV which sees its mean and standard deviation drop from 6.44 and to 6.43 and 3.05 when the setup fields that are greater than 50 MU/cGy are removed. Unrestricted values for MU/cGy means can be seen in tables 2.46 to 2.51 of the appendix for different photon energies. For these tables the MU/cGy is a 12

17 simple mean. The value, C, is the MU/cGy factor for conventional treatments, which do not include any or TBI treatments, but does include wedges. The value C differs from MU conv in that C is a mean of all conventional treatments, and MU conv is defined as the MU required to deliver the same dose as MU to a phantom at a 10 cm depth at 100 source-to-axis distance with a 10cm by 10cm field (6). F I is the fraction of treatments that are. A conservative value of the factor can be ascertained by simply using the MU/cGy. To get a number that more closely resembles the reality of clinical operation, the MU/cGy can be divided by conventional MU/cGy (C). When tables 2.46 and 2.47 are examined, it can be seen that three out of 44 machines using low energy photons have an MU/cGy value that is above the conservative C I of 2 to 10. When the MU/cGy is divided by the conventional MU/cGy this falls to one out of 44. In four cases the MU/cGy is lower than the conventional MU/cGy. For machines performing at energies greater than 6 MV, only two out of 24 had a value greater than 10 MU/cGy. When MU/cGy was divided by the conventional MU/cGy, one outlier disappeared and the other will disappear when a cutoff is used. The tables were also recreated for only MU/cGy using cutoffs and can be seen in the appendix in Tables 2.52 to Table TBI has been presented the same as. Even with the volume of fields in this study. There were only a total of nine patients divided between four centers using four treatment machines and three different energies. This makes it difficult to draw any 13

18 definitive numbers for a TBI Workload. The treatments may be seen table 2.58 in the appendix. 14

19 CHAPTER III: DISCUSSION AND CONCLUSION The NCRP estimate for the factor of 2-10 is sufficient, based on the data from the reporting centers. These results were independent of energy. For low energy beams, 4 or 6 MV, there were only three deviations from the range suggested in NCRP 151 for 44 different machines. For high energy beam, 10 MV or greater, there were two values of C I above the NCRP range for 24 machines. All of the above mentioned deviations disappear when a reasonable cutoff is applied or the MU/cGy is divided by the conventional MU/cGy. Also, the deviations were almost exclusively from head and neck treatments which usually contain many small fields which cause treatments to have a larger amount of monitor units per centigray. If we look first strictly at only removing outliers at a reasonable cutoff, the only outliers that remain with a combined mean plus one standard deviation over 10 are seen in table 3.1. The cutoffs were established by either removing extraneous high numbers caused either by the insertion of set-up fields or by removing fields with uncharacteristically low dose. The low dose numbers are caused by isocenter being blocked for the majority of the segments delivered in the treatment field. HSN RSN Energy Mean Standard Deviation 3 5 6X X X X X X X Table 3.1. Mean and standard deviations above NCRP suggested range after cutoff. 15

20 If we take these remaining deviations and divide their means by their respective conventional mean, then we see that all of the outliers now disappear. Although using a strict mean gives a more conservative answer, dividing the mean by the conventional mean yields a number that is closer to reality, since secondary shielding in vaults are already designed to handle this conventional workload. The results of performing this operation can be seen in table 3.2. Only HSN 10, RSN 3 still hovers near 10. This machine represents 526 of 34,059 or 1.5% of treatments at 15 MV. HSN RSN Energy Mean Conventional Mean /Conventional 3 5 6X X X X X X X Table 3.2. mean divided by Conventional mean. A chart of the mean values of C I for each MV, in the above table, gives: CI CI /C Linear (/C) MV Figure 3.1. Mean values of CI for each MV. 16

21 If charts are created for all machines the trend appears first without a cutoff as: Total Treatments without Cutoff CI MV Total Treatments without Cutoff Linear (Total Treatments without Cutoff) Figure 3.2. Mean values of CI for each MV for total treatments without cutoff. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table 3.3. mean and standard deviation for total treatments without cutoff. Low energy is defined as 4 or 6 MV x-rays and high energy treatments are any treatments above 10 MV. Next the trend is plotted with the cutoffs discussed in section two: 17

22 Total Treatments CI Total Linear (Total) MV Figure 3.3. Mean values of CI for each MV for total treatments with cutoff. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table 3.4. mean and standard deviation for total treatments with cutoff. It is interesting to note that with or without a cutoff both low and high energy means are very similar. The low energy mean is 5.50 with a standard deviation of 3.06 without a cutoff and 5.09 and 2.16 with a cutoff. The high energy mean and standard deviation without a cutoff are greatly affected by the MU/cGy outlier. Without a cutoff the 18

23 high energy mean and standard deviation are 5.81 and 6.96, with a cutoff they are 4.38 and The remainder of the plots uses the data with the cutoffs. The next couple is for mono and dual energy machines. A mono energy machine is defined as a machine that is used for only one photon energy. Likewise, a dual energy machine uses two photon energies. Mono Energy Machines CI Mono Energy Machines Linear (Mono Energy Machines) MV Figure 3.4. Mean values of CI for each MV for mono energy machines. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table 3.5. mean and standard deviation for mono energy machines. 19

24 Dual Energy Machines CI Dual Energy Machines Linear (Dual Energy Machines) MV Figure 3.5. Mean values of CI for each MV for dual energy machines. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table 3.6. mean and standard deviation for dual energy machines. With a small sample for mono energy machines, five low energy machines and one high energy machine the numbers are easily skewed, and are very similar to the numbers without a cutoff. The dual energy machine results are very close to the mean and standard deviation of the total with cutoff. 20

25 The next pair is for mono and dual use machines. Use refers to how the machine treats. A mono use machine only uses one energy for, and a dual use machine treats patients at both of its photon energies. Mono Use Machines CI Mono Use Machines Linear (Mono Use Machines) MV Figure 3.6. Mean values of CI for each MV for mono use machines. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table 3.7. mean and standard deviation for mono use machines. 21

26 Dual Use Machines CI Dual Use Machines Linear (Dual Use Machines) MV Figure 3.7. Mean values of CI for each MV for dual use machines. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table 3.8. mean and standard deviation for dual use machines. In this case the low energy sample was almost evenly split with 24 mono use and 20 dual use and it can be seen that their numbers are very close and well within a standard deviation of the total. The high energy sample has only three for mono energy and 21 for dual energy, yet the results are still within a standard deviation of the total. 22

27 The next two plots divide the data between large and small facilities. A small facility is defined as only having one or two machines. A large facility has three or more and would thus require a larger staff with more than a single doctor. Large Facilities CI Large Facilities Linear (Large Facilities) MV Figure 3.8. Mean values of CI for each MV for large facilities. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table 3.9. mean and standard deviation for large facilities. 23

28 Small Facilities CI Small Facilities Linear (Small Facilities) MV Figure 3.9. Mean values of CI for each MV for small facilities. Energy Sample Size Mean Standard Deviation Low Energy High Energy Table mean and standard deviation for small facilities. The large facility sample group is much larger than the small facility group, with 35 low energy and 20 high energy samples. The small facility group has 9 low energy and 4 high energy samples. The trend of interest is that in all cases, besides the group computed without a cutoff where a single point was greatly skewing the results, is that the numbers are 24

29 consistently lower, in MU/cGy, for high energy treatments, but still close (within a standard deviation). Also there is no significant difference for machine type or use or facility size. For low energy calculations for W L a C I of 5.1 may be used, this number may be increased by its standard deviation if the facility engages in procedures such as head and necks which use many more MU/cGy than other procedures. For high energy calculations of W L a C I of 4.4 may be used. Again this number may be increased if a machine is specialized in procedures that use more MU/cGy. It is interesting to note that in both cases the mean plus two standard deviations for the calculated value of the C I, are less than the maximum value of ten for the range discussed in NCRP Report 151. The low amount of TBI treatments, a total of nine patients for 184 out of 374,003 total exposures, makes any conclusions drawn tenuous at best. In all cases the workload in MU/cGy was much higher than conventional treatments, as would be expected. For 6 and 15 MV treatments the mean MU/cGy hovered around 20, and for 18 MV TBI treatments the number increased to a little over 30. In conclusion, although the numbers are too scant to make any statements about the contribution TBI makes to workload, there is more than enough data to estimate the contribution to leakage workload. An factor, C I, of 5.1 may be used for low energy photon calculations, and a C I of 4.4 may be used for high energy photon calculations. These numbers are higher than the studies of Followill and Mechalakos, but except in the case of low energy for Mechalakos are within a standard deviation. 25

30 APPENDIX: FIGURES AND TABLES FROM RESULTS HSN RSN MV of Table Number page and and and and and and and and and and and

31 and and and and and and and and and Table 2.1. Page location of machines by HSN, RSN, and MV combination. 27

32 RSN 1 6X RSN 1 6X RSN 1 18X RSN 1 18X RSN 1 All RSN 1 All Energies 50.0 N MU/cGy Figure 2.1. HSN 1, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 28

33 RSN 1 6X RSN 1 6X RSN 1 18X RSN 1 18X RSN 1 All RSN 1 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.2. HSN 1, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 29

34 RSN 2 6X RSN 2 6X N MU/cGy Figure 2.2. HSN 1, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 30

35 RSN 2 6X RSN 2 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.3. HSN 1, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 31

36 60.0 RSN 4 15X RSN 4 15X N MU/cGy Figure 2.3. HSN 2, RSN 4 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 32

37 RSN 4 15X RSN 4 15X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.4. HSN 2, RSN 4 mean and standard deviation at different cutoffs of MU/cGy. 33

38 RSN 7 6X RSN 7 6X RSN 7 15X RSN 7 15X RSN 7 All RSN 7 All Energies 40.0 N MU/cGy Figure 2.4. HSN 2, RSN 7 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 34

39 RSN 7 6X RSN 7 6X RSN 7 15X RSN 7 15X RSN 7 All RSN 7 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.5. HSN 2, RSN 7 mean and standard deviation at different cutoffs of MU/cGy. 35

40 RSN 2 6X RSN 2 6X N MU/cGy Figure 2.5. HSN 3, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 36

41 RSN 2 6X RSN 2 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.6. HSN 3, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 37

42 RSN 4 6X RSN 4 6X 20.0 N MU/cGy Figure 2.6. HSN 3, RSN 4 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 38

43 RSN 4 6X RSN 4 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.7. HSN 3, RSN 4 mean and standard deviation at different cutoffs of MU/cGy. 39

44 RSN 5 6X RSN 5 6X N MU/cGy Figure 2.7. HSN 3, RSN 5 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 40

45 RSN 5 6X RSN 5 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.8. HSN 3, RSN 5 mean and standard deviation at different cutoffs of MU/cGy. 41

46 RSN 6 6X RSN 6 6X N MU/cGy Figure 2.8. HSN 3, RSN 6 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 42

47 RSN 6 6X RSN 6 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table 2.9. HSN 3, RSN 6 mean and standard deviation at different cutoffs of MU/cGy. 43

48 RSN 2 6X RSN 2 6X RSN 2 18X RSN 2 18X RSN 2 All RSN 2 All Energies 40.0 N MU/cGy Figure 2.9. HSN 5, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 44

49 RSN 2 6X RSN 2 6X RSN 2 18X RSN 2 18X RSN 2 All RSN 2 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 5, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 45

50 RSN 3 6X RSN 3 6X RSN 3 20X RSN 3 20X RSN 3 All RSN 3 All Energies 40.0 N MU/cGy Figure HSN 5, RSN 3 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 46

51 RSN 3 6X RSN 3 6X RSN 3 20X RSN 3 20X RSN 3 All RSN 3 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 5, RSN 3 mean and standard deviation at different cutoffs of MU/cGy. 47

52 RSN 2 6X RSN 2 6X N MU/cGy Figure HSN 6, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 48

53 RSN 2 6X RSN 2 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 6, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 49

54 RSN 1 6X RSN 1 6X RSN 1 15X RSN 1 15X RSN 1 All RSN 1 All Energies N MU/cGy Figure HSN 7, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 50

55 RSN 1 6X RSN 1 6X RSN 1 15X RSN 1 15X RSN 1 All RSN 1 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 7, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 51

56 RSN 1 6X RSN 1 6X RSN 2 6X RSN 2 6X 8.0 N MU/cGy Figure HSN 8, RSN 1 and 2 Frequency distribution of MU/cGy, plotted versus bin mid-point value. The different x-ray beams and combinations are indicated on the graph. 52

57 RSN 1 6X RSN 1 6X RSN 2 6X RSN 2 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 8, RSN 1 and 2 mean and standard deviation at different cutoffs of MU/cGy. 53

58 RSN 1 6X RSN 1 6X N MU/cGy Figure HSN 9, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 54

59 RSN 1 6X RSN 1 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 9, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 55

60 RSN 2 15X RSN 2 15X N MU/cGy Figure HSN 10, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 56

61 RSN 2 15X RSN 2 15X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 10, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 57

62 RSN 3 6X RSN 3 6X RSN 3 15X RSN 3 All RSN 3 All Energies RSN 3 15X N MU/cGy Figure HSN 10, RSN 3 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 58

63 RSN 3 6X RSN 3 6X RSN 3 15X RSN 3 15X RSN 3 All RSN 3 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 10, RSN 3 mean and standard deviation at different cutoffs of MU/cGy. 59

64 RSN 1 6X RSN 1 6X RSN 1 18X RSN 1 18X RSN 1 All RSN 1 All Energies N MU/cGy Figure HSN 11, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 60

65 RSN 1 6X RSN 1 6X RSN 1 18X RSN 1 18X RSN 1 All RSN 1 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 11, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 61

66 40.0 RSN 1 6X RSN 1 6X N MU/cGy Figure HSN 12, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 62

67 RSN 1 6X RSN 1 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 12, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 63

68 RSN 2 6X RSN 2 6X RSN 2 18X RSN 2 18X RSN 2 All RSN 2 All Energies N MU/cGy Figure HSN 12, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 64

69 RSN 2 6X RSN 2 6X RSN 2 18X RSN 2 18X RSN 2 All RSN 2 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 12, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 65

70 RSN 1 6X RSN 1 6X RSN 1 18X RSN 1 18X RSN 1 All RSN 1 All Energies N MU/cGy Figure HSN 13, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 66

71 RSN 1 6X RSN 1 6X RSN 1 18X RSN 1 18X RSN 1 All RSN 1 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 13, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 67

72 60.0 RSN 1 6X RSN 1 6X N MU/cGy Figure HSN 14, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 68

73 RSN 1 6X RSN 1 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 14, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 69

74 RSN 2 6X RSN 2 6X RSN 2 15X RSN 2 15X RSN 2 All RSN 2 All Energies 40.0 N MU/cGy Figure HSN 15, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 70

75 RSN 2 6X RSN 2 6X RSN 2 15X RSN 2 15X RSN 2 All RSN 2 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 15, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 71

76 RSN 3 4X RSN 3 4X N MU/cGy Figure HSN 15, RSN 3 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 72

77 RSN 3 4X RSN 3 4X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 15, RSN 3 mean and standard deviation at different cutoffs of MU/cGy. 73

78 RSN 4 6X RSN 4 6X RSN 4 15X RSN 4 15X RSN 4 All RSN 4 All Energies 40.0 N MU/cGy Figure HSN 15, RSN 4 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 74

79 RSN 4 6X RSN 4 6X RSN 4 15X RSN 4 15X RSN 4 All RSN 4 All Energies mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 15, RSN 4 mean and standard deviation at different cutoffs of MU/cGy. 75

80 RSN 1 6X RSN 1 6X N MU/cGy Figure HSN 16, RSN 1 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 76

81 RSN 1 6X RSN 1 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 16, RSN 1 mean and standard deviation at different cutoffs of MU/cGy. 77

82 RSN 2 6X RSN 2 6X N MU/cGy Figure HSN 16, RSN 2 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 78

83 RSN 2 6X RSN 2 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 16, RSN 2 mean and standard deviation at different cutoffs of MU/cGy. 79

84 30.0 RSN 3 6X RSN 3 6X N MU/cGy Figure HSN 16, RSN 3 Frequency distribution of MU/cGy, plotted versus bin midpoint value. The different x-ray beams and combinations are indicated on the graph. 80

85 RSN 3 6X RSN 3 6X mean(0-15)= mean(0-25)= mean(0-50)= mean(0-200)= mean(0-1500)= stdev(0-15)= stdev(0-25)= stdev(0-50)= stdev(0-200)= stdev(0-1500)= Table HSN 16, RSN 3 mean and standard deviation at different cutoffs of MU/cGy. 81