## TDF Plan: Incomplete Courses and Compensating for Treatment Errors

This chapter of the user guide includes examples that illustrate how to use TDFPlan to work the example problems in B. Jones and R.G. Dale, Radiobiological compensation of treatment errors in radiotherapy, The British Journal of Radiology, 81(2008), 323-326.

Perhaps a planned regimen is stopped before its intended completion date due to unforseen circumstances, or a treatment error is detected early in the course and now you want design a revised course to deliver the originally intended biological effect. Lets begin with a really simple example.

- Clear the calculator by clicking New Patient
- Enter the originally intended regimen in IMR course #1. Do NOT check the "include" box for this course. The intended BED for both acute and late effects is, however, displayed in the A(cute) BEDn and L(ate) BEDn columns of course #1 (yellow background) in the IMR spreadsheet. You can optionally click the BEDn cells of the spreadsheet to highlight the intended BED (e.g. A(cute) BEDn = 72.00 in the example below).
- Enter the treatments that have actually been delivered beginning with course #2 (green background) and DO include these courses. The cumulative BED of the delivered fractions will be displayed in the blue BED readout window. In the example below 26 fractions have been delivered as described in course #2.
- Click the Makeup... button.

- The makeup "wizard" dialog analyzes the state of the IMR spreadsheet and configures the Equivalent Single Course (ESC) Calculator for simple makeup calculations. In this case the makeup wizard defaults to matching the intended acute BED for course #1 because spreadsheet cell (course #1,A BEDn) is what is highlighted in the IMR spreadsheet. The BED already delivered is assumed to be the sum of any included courses, which is only course #2 in this example. The BED that needs to be madeup is the intended BED for the applicable reactions (acute or late) minus the corresponding delivered BED. For instance, if the intended BED for acute effects is 72.00 Gy10 and the actually delivered fractions sum to 62.40 Gy10 then the BED that needs to be madeup is 72.00 - 62.40 = 9.60 Gy10. The wizard defaults to putting the makeup course into the first empty course which is course #3 (blue background) in this example, and assumes that you want to keep the original number of fractions, so the number of fractions in the makeup course defaults to 30 - 26 = 4 fractions. You can override these defaults if necessary. Then click the Calculate Makeup Course button. |

- The makeup course is placed in course #3 and automatically included. The total A(cute) BEDn for all included courses is displayed at the bottom of the A BEDn column of the IMR spreadsheet and should match the intended BED (e.g. 72 Gy10).
- The example above was extremely simple but serves to illustrate how the tools operate. Examples of more complex makeup calculations follow. For highly complex problems you will need to directly interact with the ESC Calculator.

Example #1 from B. Jones and R.G. Dale, Radiobiological compensation of treatment errors in radiotherapy, The British Journal of Radiology, 81(2008), 323-326.

1. A prescription of 45 Gy in 25 x 1.8 Gy fractions to the pelvis for squamous cell cancer of the cervix is incorrectly delivered as 1.5 Gy per fraction for 10 fractions. The tissue maximum dose was 105% in small bowel. The aim will be to deliver the same (i.e. prescribed) normal tissue BED in the same overall treatment time. Intended small bowel dose = 45 x 1.05 x (1 + 1.8 X 1.05/3) = 77.0 Gy3.

   To follow this example in TDFPlan start a New Patient. Use the default biology settings. Enter the intended regimen as course #1 as illustrated below. Set the treatment start date in the Calendar window. Label course #1 "Intended dose to small bowel". Set the "Calculate dose to % of the Rx" field for course #1 to 105%. Keep the "Rx to % isodose" field at 100%. Click the cell in the L BEDn column of the IMR spreadsheet for course #1 (77.02 LQ) to mark that as the BED to match in the makeup calculation. Make sure the include control for course #1 is NOT checked.

2. First phase BED = 10 x 1.5 x 1.05 x (1 + 1.5 x 1.05/3) = 24.0 Gy3.

   In TDFPlan enter the erroneously delivered first phase in course #2 as illustrated below. Set the treatment start date in the Calendar window. Label course #2 "1st phase". Again, set the "Calculate dose to % of the Rx" field for course #2 to 105%. Make sure the include control for course #2 IS checked.

3. Remaining BED = 77.0 - 24.0 = 53.0 Gy3. As 15 further fractions are to be given, the required fractional dose (d) to match the originally prescribed normal tissue BED is given by the solution of: 15 x d x 1.05 x (1 + 1.05 X d/3) = 53.0, i.e d = 1.98 Gy In TDFPlan click the Makeup... button located just above the IMR spreadsheet. The makeup "wizard" will notice that you marked the cell in the L BEDn column of the IMR spreadsheet for course #1 as the BED to match in the makeup calculation. The wizard will therefore initialize the makeup calculation for late reactions with an intended late BED of 77.02. Thw wizard will the sum the late BED for all included courses in the IMR. Since only course #2 describing the 1st erroneous phase is included, the late BED already delivered will be assumed to be 24.02, and the balance to makeup will be 53.00. The wizard will find the 1st unused course after the last included course for the makeup. In this example the wizard chooses to place the makeup course in IMR course #3. The wizard also assumes that you want to match the calendar of the intended intended course and sets the number of fractions. You can manually override all of these assumptions. If you are satisfied with the makeup settings click the Calculate Makeup Course button to close the dialog. | The Makeup... wizard provides a rapid interface to the ESC Calculator for simple problems involving a single intended course and a single makeup course. For more complex and multi-course regimens you must program the ESC Calculator directly or use the IMR spreadsheet. | The ESC calculator is programed by the Makeup wizard, (e.g. with the result of 198.5 cGy as the new prescribed fraction for the tumor in this example) and the result is automatically copied back into the destination IMR course. You can, of course, program the ESC Calculator directly and copy the results into the IMR using the conventional copy and paste functionality.

4. The makeup wizard adds the makeup course to the IMR and then calls the Auto Sequence Courses function of the Calendar window. The total BED for the applicable (acute or late) BEDn column should match the intended BED.

5. If the tumour involved is squamous cell cancer of the cervix (assumed α/β = 10 Gy), then the BED as originally prescribed (assuming the dose was prescribed to the 100% isodose in the tumour) would have been: BED = 45 x (1 + 1.8/10) = 53.1 Gy10.

   The actual BED delivered in the overall treatment, following correction, is: [1.5 x 10 x (1 + 1.5/10)] + [15 x 1.98 x (1 + 1.98/10)] = 52.8 Gy10.

   Thus, the originally prescribed normal tissue BED has not been exceeded, yet the overall treatment, after correction, has delivered a tumour BED that is only 0.6% less than that originally prescribed. (A tumour repopulation correction is not required in this example as the overall treatment time is kept unaltered.) In practice, both the prescribed and the final tumour BEDs will be less than those calculated and quoted here if repopulation is included, but by the same amount in each case.

   In TDFPlan enter the intended regimen into course #4 and leave the "Calculate dose to % of the Rx" field for course #4 as 100% (this field was set to 105% in course #1 because we were interested in dose to the small bowel, whereas now we are interested in dose to the tumor). Click the cell in the A BEDn column for course #4 to highlight the intended BED. Do NOT "include" the course.

   Enter the 1st phase in course #5, be sure to include course #5 and set the "Calculate dose to % of the Rx" field to 100%.

   Copy the makeup course into course #6, include it and label the course "Makeup to tumor". Round the Rx fraction down to 198 and be sure the "Calculate dose to % of the Rx" field is 100%.

   The cumulative acute BED (e.g. 52.83) to the tumor for the 1st phase and the makeup (ie included courses #5 and #6) is displayed at the bottom of the A BEDn column of the IMR spreadsheet.

Example #2 from B. Jones and R.G. Dale, Radiobiological compensation of treatment errors in radiotherapy, The British Journal of Radiology, 81(2008), 323-326.

A head and neck squamous cell cancer Phase I schedule of 46 Gy in 23 fractions has been delivered at 4 Gy per fraction for 3 fractions. The average spinal cord dose was accepted as 103% of the prescribed tumour dose. Intended BED to cord = 46 x 1.03 x (1 + 1.03 x 2/2) = 96.2 Gy2. "Overdose" of cord BED in the first three fractions = 4 x 3 x 1.03 x (1 + 1.03 x 4/2) = 37.8 Gy2.

To follow this example in TDFPlan start a New Patient. Set α/β = 2 Gy for late reactions in the biology settings. Enter the intended regimen as course #1 and set the treatment start date in the Calendar window. Label course #1 "Intended dose to cord". Set the "Calculate dose to % of the Rx" field for course #1 to 103% for all cord related calculations. Keep the "Rx to % isodose" field at 100%. Click the cell in the L BEDn column of the IMR spreadsheet for course #1 (96.18 LQ) to mark that as the BED to match in the makeup calculation. Make sure the include control for course #1 is NOT checked.

Enter the erroneously delivered first 3 fractions in course #2 as illustrated below. Set the same treatment start date (as course #1) in the Calendar window. Label course #2 "Initial overdose to cord". Again, set the "Calculate dose to % of the Rx" field for course #2 to 103%. Make sure the include control for course #2 IS checked.

2. Deficit = 96.2 - 37.8 = 58.4 Gy2. In TDFPlan click the Makeup... button located just above the IMR spreadsheet. The makeup "wizard" will notice that you marked the cell in the L BEDn column of the IMR spreadsheet for course #1 as the BED to match in the makeup calculation. The wizard will therefore initialize the makeup calculation for late reactions with an intended late BED of 96.18. Thw wizard will the sum the late BED for all included courses in the IMR. Since only course #2 describing the 1st erroneous overdose fractions is included, the late BED already delivered will be assumed to be 37.82, and the balance to makeup will be 58.36. The wizard will find the 1st unused course after the last included course for the makeup. In this example the wizard chooses to place the makeup course in IMR course #3. The wizard also assumes that you want to match the calendar of the intended intended course and sets the number of fractions. You can manually override all of these assumptions. If you are satisfied with the makeup settings click the Calculate Makeup Course button to close the dialog. | The Makeup... wizard provides a rapid interface to the ESC Calculator for simple problems involving a single intended course and a single makeup course. For more complex and multi-course regimens you must program the ESC Calculator directly or use the IMR spreadsheet. | The ESC calculator is programed by the Makeup wizard, (e.g. with the result of 156.8 cGy as the new prescribed fraction for the tumor in this example) and the result is automatically copied back into the destination IMR course. You can, of course, program the ESC Calculator directly and copy the results into the IMR using the conventional copy and paste functionality.

3. To complete treatment in the originally prescribed time (in 20 remaining fractions), the dose per fraction required in these remaining fractions is the solution for d of: 20 x d x 1.03 x (1 + 1.03 x d/2) = 58.4, i.e. d is found to be 1.57 Gy.

   In TDFPlan, the ESC Calculator solution of 156.8 cGy is placed in course #3 by the makeup wizard. The cumulative BED for late effects from included courses #2 and #3 appears at the bottom of the L BEDn column of the spreadsheet and matches the intended BED of 96.18.

4. The intended tumour BED (assuming α/β = 10 Gy) was 55.2 Gy10 and the actual tumour BED will be 53.1 Gy10

   In TDFPlan copy the intended regimen into course #4, label it "Intended dose to tumor". Do not include course #4. Click the A BEDn column spreadsheet cell for course #4 to indicate this is now the intended acute BED.

   Copy the overdose course into course #5, include it and label it "Initial overdose to tumor". Copy the makeup course into course #6, include it and label it "Makeup dose to tumor". If you used copy & paste to create these courses be sure to reset the "Calculate dose to % of the Rx" field to 100% for courses #4, #5 and #6 (and all other tumor related courses).

   The cumulative BED for acute reactions to tumor (53.08) appears at the bottom of the A BEDn column of the spreadsheet.

5. a slight reduction that can be gained back by, for example, replacing the final fraction with two fractions each of 1.2 Gy with a 7 h gap between them to ensure near- complete repair. This would result in a final tumour BED of: [4 x 3 x (1 + 4/10)] + [19 x 1.57 x (1 + 1.57/10)] + [2 x 1.2 x (1 + 1.2/10)] = 54.0 Gy10, only 2% less than originally prescribed.

   In TDFDPlan uncheck the include control for course #6 and copy and paste course #6 into course #7. In course #7 check the include control, lock the Rx fraction field and reduce the number of fractions from 20 to 19.

   To complete the example, use course #8 to include the last day's BID regimen of 2 fractions of 120 cGy. The cumulative acute BED (54.00) for the initial overdose (course #5), the revised 19 fraction makeup (course #7) and the final 2 BID fractions (course #8) is found at the bottom of the A BEDn column of the spreadsheet.

### Example #3

An error in both dose distribution and dose (owing to omission of a wedge filter) has occurred in the first 15 fractions of a course of 64 Gy in 32 fractions in the first phase treatment of a prostate cancer (assumed α/β = 4 Gy). Owing to the error, the isocentre (tumour) dose was increased from 100% to 133%, the maximum rectal dose from 103% to 133%, and the maximum bladder dose from 105% to 140%. Intended tumour BED = 96.0 Gy4. Intended maximum bladder BED = 114.2 Gy3. Intended maximum rectal BED = 111.2 Gy3. The BEDs at the time of discovering the error are: Tumour BED = 2 x 1.33 x 15 x (1 + 2 x 1.33/4) = 66.4 Gy4 Bladder BED = 2 x 1.4 x 15 x (1 + 2 x 1.4/3) = 81.2 Gy3 Rectal BED = 2 x 1.33 x 15 x (1 + 2 x 1.33/3) = 75.3 Gy3. The remaining BEDs that should be delivered are, respectively: Tumour = 96.0 - 66.4 = 29.6 Gy4 Bladder = 114.2 - 81.2 = 33.0 Gy3 Rectum = 111.2 - 75.3 = 35.9 Gy3. To complete the treatment without changing the number of remaining fractions (17), the required dose per fraction (d) to restore the prescribed tumour BED is the solution of: Tumour: 17 x d x (1 + d/4) = 29.6Gy4 i.e. d = 1.31 Gy. The dose gradient caused by the original omission of the wedges must also be corrected for in the compensatory phase of treatment. Let the new percentage isodoses (normalized to the new tumour dose) be gB and gR for bladder and rectum, respectively. Consequently, gB and gR may be assessed from the following equations: Bladder: 17 x 1.31 x gB x (1 + gB x 1.31/3) = 33.0 Gy3. Rectum: 17 x 1.31 x gR x (1 + gR x 1.31/3) = 35.9 Gy3. The solutions for gB and gR are 1.025 and 1.09, respectively. The planning team can then attempt to match the revised isodose distributions to meet these requirements and allow the final BEDs to be as close as possible to the prescribed values. In this example, the authors have not assumed a low value of tumour α/β such as 1.5 Gy, which is less than that of normal tissue, because the compensation could produce a potentially dangerous result if such an assumption is incorrect.

TDFPlan solution: work in progress

### Example #4

Owing to a treatment set-up error, the superior half of a tonsillar carcinoma was out of the treatment field for the first eight fractions. The intended dose for the whole tumour was 70 Gy in 35 fractions. Intended tumour BED = 70 x (1 + 2/10) = 84.0 Gy10. In the first eight fractions, the inferior half of the tumour received a BED of 8 x 2 x (1 + 2/10) = 19.2 Gy10. It was decided to open the field to cover the originally intended volume and continue with 2 Gy per day. Additionally, on 14 of the treatment days, a boost to the superior half was added using non-divergent beam edge matching. A gap of at least 6 h was allowed between the two fractions delivered on each of those 14 days. The 27 X 2 Gy fractions to the upper half would deliver a BED of 54 x (1 + 2/10) = 64.8 Gy10. This leaves 84.0 - 64.8 = 19.2 Gy10 to be given by the additional 14 (second daily) fractions to the reduced field. The dose per fraction thus required is given by d in: 14 x d x (1 + d/10) = 19.2, for which d = 1.22 Gy. The BED to the initially untreated half of the tumour will thus be restored to be 64.8 + 19.2 = 84 Gy10, as originally intended. Normal tissues close to the upper half of the tumour receive: [27 x 2 x (1 + 2/3)] + [14 x 1.22 x (1 + 1.22/3)] = 114.0 Gy3. This compares favourably with the originally prescribed normal tissue BED of: 70 x (1 + 2/3) = 116.7 Gy3, although no allowance has been made in the compensatory treatment for the possible effects of incomplete repair from the second dose per day, because the interval is kept as long as >= 6 h.

TDFPlan solution: work in progress

### Example #5

A solitary plasmacytoma of the L2 vertebral body was to be treated by a single posterior field and prescribed a dose of 45 Gy in 25 fractions at spinal cord depth, the distal tumour region receiving 93% of the prescribed dose. Owing to an error, the distal tumour is actually treated to 113% of the prescribed cord dose for the first seven fractions. The plasmacytoma α/β is assumed to be 10 Gy. The intended spinal cord BED = 45 x (1 + 1.8/2) = 85.5 Gy2. The intended minimum tumour BED = 0.93 x 45 x (1 + 0.93 x 1.8/10) = 48.9 Gy10. Following seven fractions of 1.13 x 1.8 Gy (i.e. 2.03 Gy per fraction), the BED to the tumour is 7 x 2.03 x (1 + 2.03/10) = 17.1 Gy10. The spinal cord BED has been initially delivered as 1.8 x 113/93 = 2.19 Gy per fraction, so that the spinal BED in the first seven fractions is: 7 x 2.19 x (1 + 2.19/2) = 32.1 Gy2. The difference between the intended and already given spinal cord BED is thus 85.5 - 32.1 = 53.4 Gy2. To deliver the originally prescribed spinal cord BED, the remaining treatments, if completed using the same intended number of fractions, will be given at a spinal cord dose per fraction given by d in: 18 x d x (1 + d/2) = 53.4, i.e. d = 1.63 Gy. The minimum tumour BED will then be 17.1 + 18 x 0.93 x 1.63 x (1 + 0.93 x 1.63/10) = 48.5 Gy10.

TDFPlan solution: work in progress

### Example #6

A radical course of radiotherapy (prescribed as 55 Gy in 20 fractions) is intended for a stage TINOMO squamous cell lung cancer. 5 Gy per fraction is delivered in error for the first seven fractions. The spinal cord was not directly irradiated. Intended BED = 55 x (1 + 2.75/10) = 70.1 Gy10. Tumour BED in first seven fractions = 35 x (l + 5/lO) = 52.5 Gy10. The intended lung BED to PTV = 7 x 5 x (l + 2.75/3) = 105.4 Gy3. Lung BED in first seven fractions = 7 x 5 x (1 + 5/3) = 93.3 Gy3. In the 13 remaining treatments, in order to preserve lung tolerance, the required fractional dose to give a BED of 105.4 - 93.3 = 12.1 Gy3 is given by d in 13 x d d (1 + d/3) = 12.1, i.e. d is 0.74 Gy. The dose per fraction is small and in the range where the LQ model is considered to be less reliable owing to the possibility of low-dose hypersensitivity effects [7]. It was therefore decided to give fewer than 13 fractions in order to deliberately increase the fractional dose size. To find the required fractional dose in (for example) eight fractions, solve for d in: 8 x d x (1 + d/3) = 12.1 i.e. d = 1.1 Gy. The relevant BED to the PTV (planning target volume) is then: 93.3 + [8 x 1.1 x (1 + 1.1/3)] = 105.3 Gy3. The resultant tumour BED is 52.5 + [8 x 1.1 x (1 + 1.1/10)] = 62.3 Gy10; this is considerably (11%) lower than intended (70.1 Gy10), but the treatment has been delivered in a shorter overall time. However, if the repopulation BED equivalent (K) is between 0.2 Gy and 0.5 Gy per day by the fourth week of treatment, a time saving of 5-7 days would, at best, restore approximately 3.5 Gy10 of the deficit, which is insufficient. As a result, the clinician has the option of accepting a higher PTV dose in order to preserve adequate tumour dose; there is also the option of making the field sizes smaller if tumour shrinkage has occurred. For example, by using field sizes 0.7 cm smaller in each direction, it might be decided to give the final phase of treatment by means of 10 fractions of 1.4 Gy. Thus, the BED to the smaller PTV would be 93.3 + [10 x 1.4 x (1 + 1.4/3)] = 113.8 Gy3, which is 8% higher than the prescribed dose of 105.4 Gy3. The tumour BED would be 52.5 + [10 x 1.4 X (1 + 1.4/10)] = 68.5 Gy10, which is 2.3% lower than the prescribed dose of 70.1 Gy10. This is a compromise solution to the problem.

TDFPlan solution: work in progress

You can use the ESC calculator to explore alternative methods of delivering missing BED, such as by fewer fractions, BID, concomitant, or brachytherapy. For example, using the case above, lets say you want to makeup for the 800 cGy deficit that resulted from the patient missing 4 treatments, but the patient is leaving on vacation and there are only 3 days available. In the ESC window, uncheck the Match IMR BED box and enter a Target BED of 9.60. Set the number of ESC fractions to 3. The result of 765 cGy delivered in 3 fractions of 255 cGy will deliver the required BED of 9.6 Gy(10.0) Another option is to mark missed treatment days on the course calendar (select course #1 and shift-click on the missed dates). The "Auto Sequence Courses" button in the Course Calendar window will automatically reconfigure all included IMR courses and display the updated BED. To get the most benefit from this calculation tumor repopulation should be included in the calculation. You can explore the biological effect of additional fractions to compensate for tumor repopulation by enabling repopulation in the biology group. |

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