Personnel costs were calculated as follows: the monthly cost of a radiation oncologist is € 6518.41 (based on TV-Ärzte 2022, Ä2/1), the monthly cost of a first-year resident is € 4938.79 (based on TV‑Ä Ä1/1), the monthly cost of a medical physicist is € 4188.28 (based on TV-Länder 2022, E13/1), the hourly cost of a student assistant is € 12.29 per hour according to their contract, and the cost of a precision mechanic (PM) who manufactures the in-house breast models is € 2946.46 (based on TV-Länder 2022, E8/1). The calculation for each working hour is as follows:

$$x=\frac\,per\,\textit\,x12\,\textit}}$$

resulting in one-hour (h) costs of € 37.6 per ROh, € 28.49 per REh, € 24.96 per MPEh, and € 16.99 per PMh.

First, a series of brainstorming sessions was conducted by three radiation oncologists (ROs) involved in interstitial brachytherapy. These sessions lasted for a total of three half-hour meetings, resulting in 4.5 radiation oncologist hours (ROh). Two radiation oncologists spent 2 h each, totaling 4 ROh, working on the PowerPoint® presentation, as well as the student assistant (SA) for 5 h (5 SAh). The student assistant and the precision mechanic collaborated for a total of 6 h to create the first silicone breast model. After completing the presentation and the silicone breast models, a dummy run was conducted for a total of 1.5 h, involving 3 ROh and 1.5 SAh to assess the feasibility of the scheduled 90-minute workshop duration. The student assistant also took on the responsibility of designing flyers for promotional purposes and an evaluation sheet. This activity accounted for 30 SAh (Table 1).

In a subsequent analysis, we endeavored to calculate the hourly costs for the primary hardware and software used in the course. This included a computed tomography (CT) scanner with associated software licenses (SyngoVia®, Siemens®, Erlangen, Germany). The initial purchase price of the CT scanner was € 400,000, and it was depreciated linearly over 8 years at a rate of 12%, resulting in an annual cost of € 48,000 [29]. Upon reaching out to the accountant responsible, it was determined that the operational lifespan of the CT scanner could be extended to 10 years, with an additional cost of € 10,000 per year for the service contract, bringing the total to € 420,000 over 10 years. In daily practice, the planning CT that was used operates in a sharing mode with the institute for radiology, so it was assumed that the CT is also in running mode for 2080 working hours a year, which is a very conservative point of view from the costs. This would result in:

$$x=\frac420.000}\mathrm10\,\text}=\text20.19/\text\left(\mathrm\right).$$

In general, electric energy costs are typically considered as overhead costs. These overhead costs can be allocated to specific cost units and translated into individual costs. One method of allocation is to use calculation rates, such as square meters, for assigning heating costs [30]. Since CTs consume a significant amount of energy, we attempted to estimate the costs of electric energy for the CT by using a 100-kWh usage over 24 h [31]. The price for 1 kWh was € 0.2565 for commercial customers and € 0.2251 per kilowatt hour for industrial customers in 2022 [32]. For our calculation, we chose a conservative rate of € 0.20 per kilowatt hour, resulting in € 20 in electric energy costs per day, equivalent to € 0.83 per hour. Therefore, 1 CT hour was valued at € 21. It should be noted that this assumption is conservative because we did not account for costs associated with water supply (machine cooling) and electric energy for lighting, among other factors. Additionally, the costs for the radiation therapy planning system (TPS) were not included in the calculation. Typically, the price of the TPS is included in the purchase or leasing contract for linear accelerators or afterloader devices, making it difficult to estimate an accurate quota (Table 2).

During each workshop session, six silicone breast models are used. Based on our experience, these need to be replaced every fifth workshop. We calculated the cost for one silicone breast model by considering the materials required for manufacturing 10 models in one production cycle. These materials include two packages of 2 kg silicone (totaling € 129.50), 1 l of silicone oil (€ 29.75), 0.5 kg of Protesil® (€ 7.50), 3 g of colors (€ 7.75), salt and gritty substances (€ 4), and silicone spray (€ 15). This sums up to a total of € 193.50 for 10 models, resulting in a wear and tear cost of approximately € 19.35 per breast model. The production of 10 breast models takes approximately 4 h of work (4 PMh), amounting to a cost of € 67.96 or approximately € 6.79 per breast model.

Therefore, costs for breast models for one workshop were

$$x=\frac19.35\;\textit+\text6.76\;\textit)\,x\,6\,\textit}}=\text31.33.$$

After each production cycle of 10 models, there are unused models, since only 6 breast models are used per course. With three production cycles, a total of 18 breast models are used across three additional courses. Therefore, the three production cycles would provide breast models for 25 teaching courses. However, this would not result in significant cost reduction due to the low material requirements and the limited impact of increased purchase quantity.

Additional costs are incurred due to the wear and tear of brachytherapy hollow needles and single leader catheters. Three single leader catheters are implanted in each silicone breast model, and they need to be replaced after each use. Therefore, a total of 18 catheters and needles are used in each session. These catheters were supplied in a package by the manufacturer (Varian®, Palo Alto, CA), which contains five interstitial needles, five single leader catheters, and five half-moon buttons for catheter fixation. The cost of one package was assumed to be € 400 for the purpose of cost calculation, which is a conservative estimate. Based on our experience from over 10 workshops, all 20 needles and catheters (four packages) need to be used in a single workshop due to the inexperienced handling by students and residents. Although needles can theoretically be reused for teaching purposes, the combination of catheters and needles in one delivery unit renders reusability not useful. It should be noted that in our case, we received outdated sterile needles and catheters from the manufacturer specifically for the teaching course, so these costs did not apply to us. Without sponsorship, the cost of needles and catheters would have been € 1600/course at minimum, making it financially impractical to offer this workshop. Figure 2 provides a representative image of the breast models with catheters and buttons, illustrating the realistic simulation setup.

Photographic images (a) and CT scans of the breast model in axial (b) and sagittal view (c). The imitation of the “tumor bed” appears hypointense on CT. The catheter positions (d) within the breast model are visualized by CT scan (e–f)

As per the calculations provided above, the total cost of each workshop consists of the initial setup costs as well as the recurring costs for each session. In the first year, the course was held 11 times, with some sessions aimed at promoting the course and compensating for the deficits caused by the COVID-19 pandemic. Due to positive feedback from participants, the course is planned to be held regularly six times a year for the coming years. For the purpose of calculation, the duration of the course is assumed to be 5 years. This would result in a total of 30 courses conducted, bringing the nascence costs of each workshop to € 35.22 (€ 1056.6 total nascence costs divided by 30 courses).

The remaining costs comprise the personnel and hardware costs per course, which include estimated overhead costs (Table 2, € 169.67). Additionally, there are costs for the breast models per course (€ 31.33) and the theoretical brachytherapy implantation equipment (€ 1600), as summarized in Table 3. The table presents two variants: a) with the brachytherapy equipment sponsored by the manufacturer, and b) with the equipment purchased by the faculty.

The total cost of one hands-on teaching session is approximately € 235.55, based on conservative assumptions. This amounts to an average cost of € 39.25 per participant, considering a course with six participants. However, it is not realistic to expect that the real workshop expenses, which would include the specialized brachytherapy equipment, could have been covered by this amount.

Before and immediately after the course, participants were asked to complete a questionnaire to assess their knowledge level and evaluate the quality of the course. The results of this assessment can be found in a separate publication [19]. Participants used a six-point Likert scale consisting of nine items to self-assess their knowledge of breast brachytherapy. The sum scores of all items were calculated for statistical analysis using a non-parametric paired t-test. A significance level of p < 0.05 was considered significant. In the first year of course implementation, 70 trainees participated in 11 sessions, with 62 participants completing the questionnaires. The course participants reported significant improvements in their theoretical and practical skills as a result of the workshop. Sum scores based on Likert confidence scores were calculated for all survey statements. Prior to the workshop, the average value for the Likert confidence score was 4.7. After the workshop, the average value improved to 1.8 (p < 0.001), representing a 2.9-point improvement. This improvement can be seen as a benefit-to-cost ratio (bfr). The bfr, taking into account the sponsored equipment, can be calculated as follows [33, 34]:

$$bfr=\frac\,\textit\,}\,per\,\textit\,\left(\text39.25\right)}=0.073\,\text/\text.$$

We performed a modulating calculation with the theoretical assumption of reduced billing for the brachytherapy equipment of 25% of the retail price for teaching purposes. In our case, we would have needed four packages needles, catheters and buttons, € 100 each, resulting in € 400 for the brachy material plus the above mentioned € 235.55 (personnel/hardware/breast model/nascence) summing up to € 635.55 per course. This would translate into 0.027 points/€. As Likert points per cash-unit is somewhat counterintuitive, we used the reciprocal of bfr, which can simply be seen as a cost-to-benefit ratio, CBFR:

$$CBFR=\frac\,per\,\textit\,\left(\text39.25\right)}\,\textit\,}$$

CBFR would be € 13.53 for each Likert point increment.

One way to evaluate the effectiveness and cost-effectiveness of a workshop or training program is through use of the transfer effectiveness ratio (TER), which was initially developed for assessing aircraft pilot training [35]. The TER measures the extent to which training translates into improved performance in real-world tasks. It is calculated as follows:

Where Tc represents the time or number of trials needed for a control or baseline group to achieve criterion performance (in this case, the conventional teaching time in the operating room); Tx represents the time or number of trials needed for an experimental group (in this case, the participants) to achieve criterion performance after x amount of time or number trials using simulation or another instructional approach of interest; X represents the time or number of trials spent by the experimental group using simulation (in our case, 30 min of catheter implantation time per participant). The TER indicates how many trials or units of time are saved for every unit of simulation-based training, in order to reach the desired objective experience [36]. In our case, the TER indicates how many trials (or how much time) are saved in achieving breast brachytherapy performance for every unit of workshop training invested. Calculation of the TER was based on the assumption and experience that conventional training needs to be conducted during a real brachytherapy catheter implantation in the operating room. Tc was considered as the learning time required for the first safe catheter implantation and estimated to be 30 min. Tx represents the time for the same routine handling after the initial workshop training with residents, and was estimated to be 10 min. By teaching six workshop participants at a time and providing them with an understanding of the implantation procedure, the initial 30-min teaching time could be reduced to 10 min:

The TER is 0.66, meaning that for every 10 h of simulation-based teaching, there is a saving of 6.6 h. The TER is calculated based on the cost savings achieved by using simulation training instead of expensive real-time training in the operating room. The specific TER threshold depends on the subject being investigated [37]. To approximate costs associated with training in the operating room and thereby to calculate the saved 6.6 h per 10 h of training is far beyond the scope of this article. Therefore, the advantage of our simulation-based approach should be viewed in terms of the widespread dissemination of brachytherapy knowledge per time, the motivation of the participants, and the possibility to give the participants some self-confidence for their first breast brachytherapy under supervision.