Mohs Micrograph Surgery Scheduling 1 Mohs Micrograph Surgery Scheduling Industrial Engineering Honors Research Thesis Patrick Burns University of Florida
Mohs Micrograph Surgery Scheduling 2 Abstract Mohs Micrographic Surgery (MMS) is a layer by layer surgical method used for the excision of skin cancers with each layer being examined for the presence of cancerous cells until a cancer free layer is identified. A stochastic scheduling method and Arena simulation model have been created to make the procedure more feasible in the mainstream by optimizing scheduling since patients often experience long in clinic wait times due to the stochastic nature of iterative layered skin removal process. The research project focus ed on data collection at a local MMS clinic, cleaning and analysis of the data, and verification and testing of the simulation model results using the real clinic data.
Mohs Micrograph Surgery Scheduling 3 Table of Contents Abstract 2 List of Tables 4 List of Figures 5 Introdu ction Motivation 5 Goal, Objective, & Tasks 6 Methodology Data Collection 6 Simulation 8 Results Data Analysis 9 Simulation Model Revisions 10 Simulation Results 1 3 Further Research 1 4 Appendix A 1 6 Appendix B 1 7
Mohs Micrograph Surgery Scheduling 4 List of Tables Table 1: Parameters for Simulation Model 10 Table 2: Objective Function Values for Scheduling Templates 1 4 List of Figures Figure 1: Geometric Structure of MMS 6 Figure 2: Layout of Clinic 7 Figure 3: Arena Simulation Model 8 Figure 4: Pathology Simulation Segment 1 1 Figure 5: Release Simulation Segment 12
Mohs Micrograph Surgery Scheduling 5 Intro duction Motivation Nonmelanoma skin cancers (NMSC) account for the vast majority of skin cancer diagnoses, including 2.8 million basal cell carcinom as and 700,000 squamous cell carcinoma s diagnosed every year . Mohs Micrograph Surgery (MMS) is a layer by layer surgical method used for the excision o f NMSC with each layer being examined for the presence of cancerous cells until a cancer free layer is identified MMS is a cosmetic saving method aiming to minimize scarring on patients It used predominantly on NMSC located on the head and hands and is associated with low recurrence rates [ 3 ]. However, MMS is also heavily associated with long patient w ait times because of the stochastic nature of the reentrance process, meaning patients can sometimes spend a large portion of their day waiting at the clinic for the next layer to be taken. Talking with the UF Shands and VA MMS clinics showed that each cli nic uses their own style of scheduling without factoring in the stochastic nature of iterative layered skin removal process Figure 1 models the process where after the patient has their excision take n to pa thology, they can either have the result s come back positive and have another excision taken or they can move to the repair stage. A patient begins at n ode 1 and as they go through the system th ey can move from their current node n to either no de n+1 or node N. Eac h node n represents the numbered layer being taken and node N represents the repair stage. The process works where after each step, the likelihood of going to n+1 decreases and the likel ihood of going to N increases. Once the patient reaches N, they have completed the system and are ready to be dischar ged.
Mohs Micrograph Surgery Scheduling 6 Figure 1: Geometric Structure of MMS Goal, Objective, & Tasks The goal of the project is to present a more specialized scheduling system for MMS clinics to minimize costs and patient wait times so the procedure will be more accessible. The objective of the project is to create a working simulation model of an MMS clinic populated with real world distributions. The tasks to complete this objective are : Collecting empirical data in MMS clinics Creating distributions for all parameters in the simulation model Populating the simulation model with the distributions Adjusting the simulation model to better reflect actual clinics Running simulation model with various schedules and comparing results Methodology Data Collection Time study o bservations were conducted at the Gainesville VA Dermatology clinic in nine sessions over a thirty day period. The Dermatology clinic has a separate ward for Mohs
Mohs Micrograph Surgery Scheduling 7 Micrograph Surgery consisting of 4 adjacent surgical rooms linked by a hallway and one room for pathology A diagram of the facility is shown in Figure 2. Figure 2 : Layout of Clinic There are two full time physicians at the clinic who work independently of each other one technician working on all sample s in pathology and four nurses with one assigned to each room. Physicians can also be assisted by a physician assistant or resident who is qualified to perform all steps besides the excisions. Patients are schedule at a rate of one per hour for each physician beginning at 8AM and following for 10 to 12 patients. Patients will remain in their room until they are ruled cancer free and finish repair. There are no other patients scheduled at the beginning of the day, so all no show slot s will not be filled. All t imes were collected in integer minute values to track the usage of physicians, patholog y technicians and operation rooms. The data collection sheet used in the study is included in A ppendix A and includes a straightforward list of all important times to be collect ed for analysis.
Mohs Micrograph Surgery Scheduling 8 Simulation The simulation model was created in Arena Simulation Software, Student Version 14.50.00002  to simulate different scheduling techniques and generate objective function values for comparison. The model was created based off work previously s tarted for Scheduling in Mohs Micrographic Surgery Clinics [ 4 ] Figure 3 : Arena Simulation Model For simplicity, the model will be explained in four parts br oken down in Figure 3 : Part 1 is responsible for creating all the patients and assigning their appointment times and physician assignments based off a .txt input file. All the variables are then initiated, and
Mohs Micrograph Surgery Scheduling 9 In Part 2, the patient entity seizes a room and proceeds into the queue for their first excision. Once their assigned physician is freed, they seize the physician and pass through a delay until their excisions is completed and the physician is released. In Part 3, patient entities pass through pathology, which is divided into two seize delay releases in series. The patho lo gy technician is seized first to prepare the slides and is then released for the physician to be seized to observe the slides. After pathology, the patients reach a decision module that either sends them repair or back for another layer. If patients return for an other layer, the process is nearly identical to passing through Part 2 and pathology except that the delay for secondary excisions is shorter than first excisions. Part 4 handles the completion of patients in the system. A physician is seized and then rel eased to complete repair time on a patient. The patient is then delayed releasing the room for the next patient. Several calculations are then performed to find the optimal value for the system. Results Data Analysis The empirical data collected from the d ata was analyzed to create statistical distributions to populate the Arena simulation model. Parameters are shown in Tab le 1 with th eir respective dist ributions and sample points. Full details can be found in Appendix B. N ormal distributions are represented as Normal(mean, std. dev) and all gamma distributions are represented as Gamma(scale, shape).
Mohs Micrograph Surgery Scheduling 10 Parameters Distributions Sample Points Probability of Showing Up 88.6% N = 70 Probability of Reentrance for Excision n % n 1 N = 54 Patient Time Early for Appointment Norm al (13.2, 13.4) p value = 0.172 N = 26 Time between Room Seize and Physician Seize Gamma(6.18 2.48 ) p value > 0.250 N = 56 Initial Excision Time Gamma( ######### ) P Value = 0.183 N = 29 Secondary Excision Time Gamma( ########## ) p value > 0.250 N = 20 Total Pathology Time Gamma( ########## ) p value > 0.250 N = 30 Patholog y Technician Seize Time Gamma( ########## ) p value > 0.250 N = 23 Repair Time Normal( ########## ) p value = 0.184 N = 45 Discharge Time Normal(16.19, 8.70) p value = 0.425 N = 42 Table 1: Parameters for Simulation Model An alpha of 0.05 was selected for the analysis so we do not reject the null hypothesis for any of the distributions, despite varying sample sizes. For Initial Excisions Time, one physician was shown to perform in a gamma distribution, but the other physician was not significant for any distributions becau se of a high variance is their times despite a lower mean time. It was decided that first excision time would be set as a gamma distribution because of this but using the shape and scale of their 53 combined excisions to have a more meaningful sample size. Simulation Model Revisions As discussed previously, the simulation model for the paper was created based on Mohs surgery literature rather than on clinical observations This meant there was plenty of room to h one the model based on concepts made properly clear in the texts
Mohs Micrograph Surgery Scheduling 11 Figure 4 : Pathology Simulation Segment The first change made to the model as shown in Figure 4, was to m ove the p athology stage from after the reentrance decision to now be before it. Pathology is an important step in deciding whether the patient will reenter for another excision, so the delay cannot be added after the decision without the model missing the delay on the last excision. Moving the delay to before the decision fixes the problem and makes the model more accurate. The pathology stage was also d ivide d into two in series seize delay releas e modules for the patholog y technician and the physician. After they leave the room, excisions go to the pathology lab where the technician prepares them on slides to be viewed under a microscope. Once th is is completed, they go to the physician who examines the slides and determines whether another excision is necessary. The model was adjusted to reflect this with the two modules, so the technician will be utilized for a shorter span and the physician wil l be seized for more time, correctly adjusting both of their usage rates. After pathology is completed, patients will now have the option to reenter the system into the secondary excision stage. Previously, all excisions had been treated as having the same parameter s, but the data analysis shows secondary excision have a mean of #### minutes less than the initial excision. A seize delay release of the physician, which is identical to the initial excision process aside from a different delay time distribution, was add ed for all additional layer calculations.
Mohs Micrograph Surgery Scheduling 12 A Lateness Delay was added to the system to account for some patients arriving late to their appointments. The delay is based on the Time Early for Appointment distribution and only delays patients who have a negat assigned number of minutes and then will proceed into the rest of the system. The model was also updated so it can handle and track different numbers of physicians and rooms. In the duplication loop at the beginning of the model, patients now have a physician assigned to them alongside their appointment time. In the clinic, patients will be treated by the same physician through the extent of their stay. To reflect this, physician seizes were changed from seizing the first free physician to now always wait to seiz e the physician re accurate to the real world and adds further control over parameters in the simulation. Delay module of the new room resource was added to the model. There is a certain amount of time spe nt by the nurse running vitals on the patient and reviewing their medical history before the physician enters and that delay is now added to make the results more accurate. The room is seized by the patient through the entirety of their treatment and is re Figure 5 : Release Simulation Segment
Mohs Micrograph Surgery Scheduling 13 A is a Seize Delay Release module show n in Figure 5, of the physician resource added after the patient is ruled clear. In this case, repair time is solely conducted by the physician and all other work by the nurse is factored into the is a Delay Release of the r oom r esource after the to show the nurses spend discharging patients in the room after the physician is finished This releases the room and allows the patient to be disposed of and another patient to be seized. Simulation Results Although the simulation wa sn t run using calculated optimal scheduling template due to time constraints several templates were passed through the simulation to observe the output results. The templates were designed to evaluate different clustering and spacing options for the scheduled patient appointments. The key focus of the outputs is the Objective Function Value because it is the one aiming to be improved. The Objective Function = [1000 (Patients Served) + 100 ( Total Wait Time) / 60 + 800 (Overtime) / 60] The simulation ran with 2 physicians one pathology technician and 12 patients created to arrive through the day. Overtime is set to 8 hours after the clinic opens
Mohs Micrograph Surgery Scheduling 14 Scheduling Template Objective Function Value Equally Spaced 75 Minutes 10163 Alternating 30 and 60 Minute Spacing 9819.9 10 Minute Waves 9065.2 Two Patients at a Time 8903.9 Equally Spaced 90 Minutes 8415.6 Equally Spaced Hourly (Current VA Strategy) 7434.4 Equally Spaced Every 2 Hours 5924.1 Table 2 : Objective Function Values for Scheduling Templates The results of the simulation in Table 2 show that under the set conditions, scheduling patients every 75 minutes would be more effective than the current VA strategy of scheduling on the hour. However, simply increasing the indefinitely as shown in the drop that comes with the increase to 90 and 120 minutes between patients. Other strategies including two waves of patients every 10 minutes and alternating between 30 and 60 minute spacing proved effective as well but not as meaningful as the 75 minute spacing. Further Research Going forward, there are several directions this project could go in the future to be more successful. First, observations at other MMS clinics will be important to further refine distributions while also observing other necessary distinctions in MMS clini cs to add to the simulation model. Alongside this, the simulation model should be run using the optimized scheduling templates from the paper to determine the objective function value and confirm it is the optimal value. The model should also be run in mul tiple clinical setups with changing
Mohs Micrograph Surgery Scheduling 15 numbers of physicians, rooms, technicians, and patients to observe how the affect the objective function value. Nurses may also need to be added to this list of resources to t rack to more effectively minimize costs at th e clinics
Mohs Micrograph Surgery Scheduling 16 Appendix A VA Dermatology Clinical Observations Date: ____________________ Patient:____ Room: __________ Complete/Incomplete Physician:________________________ Arrival Time Patient Entry Time in Room Doctor Entry Completion of Layer 1 Slides Leave Pathology to Doctor Doctor Reentry Time Completion of Layer 2 Doctor Reentry Time Completion of Layer 3 Doctor Reentry Time Repair Time (Doctor/Resident/Nurse) Notes: ______________________________________________________________________________
Mohs Micrograph Surgery Scheduling 17 Appendix B Probability of Showing Up: At the clinic, 6 of the 70 patients did not show up to their scheduled appointment, resulting in an 88.6% probability of a patient showing up to their appointment. Probability of Reentrance: The reentrance probability is a geometric distribution around 0. ### p ## of 54 ( #### %) Mohs patients required a second layer to be performed and # of ## ( #### %) required a third layer. 0. ### 2 = 0. #### ~ 0. ### probability of reentering for another excision will serve as geometric.
Mohs Micrograph Surgery Scheduling 18 Time Early for Appointment N ormal distribution with a mean of 13.15 minutes and standard deviation of 13.42. This time does not system.
Mohs Micrograph Surgery Scheduling 19 Time between Initial Room Seize and Physician Seize Gamma distribution with shape=2.48 and scale=6.18. This is the time the nurse spends doing initial vital and medical history checks with the patient while they wait for the physician to be free to enter.
Mohs Micrograph Surgery Scheduling 20 Initial Excision Time
Mohs Micrograph Surgery Scheduling 21 The initial excision time is not significant for a gamma distribution when the two physician s have their times combined. However, one of the physician s was significant for a gamma distribution when viewed independently and secondary excision time also foll ows a gamma distribution, so it was decided to use the gamma distribution for all first excisions. With combined excisions between the two physician ##### and scale= #### Secondary Excision Time G amma distributio n with shape= #### and scale= #### All excisions performed after the initial excision fall into this distribution.
Mohs Micrograph Surgery Scheduling 22 Total Pathology Time G amma distribution with alpha = # ###### and beta = #######
Mohs Micrograph Surgery Scheduling 23 Patholog y Technician Seize Time Gamma distribution with shape = ######## and scale = ####### Physician Pathology Seize Time D erived in simulation by subtracting technician distribution from total distribution by nature of gamma distributions
Mohs Micrograph Surgery Scheduling 24 Repair Time Normal distribution with mean= ##### and std. dev= #####
Mohs Micrograph Surgery Scheduling 25 Discharge Time Normal Distribution with mean= 16.2 and std. dev= 8.7
Mohs Micrograph Surgery Scheduling 26 References  J. Paoli, S. Daryoni, A.M. Wennberg, L. Molne, M. Gillstedt, M. Miocic, and B. Stenquist. 5 year recurrence rates of mohs micrographic surgery for aggressive and recurrent facial basal cell carcinoma. Acta dermato venereologica, 91(6):689 693, 2011.  Rockwell Automation Co. (n.d.). Arena Simulation Software ( Student Version 14.50.00002) [Computer soft ware]. [ 3 ] Skin Cancer Foundation. Skin cancer facts. http://www.skincancer.org /skin cancer information/skin cancerfacts#melanoma, 2012. Accessed August 8, 2012. [ 4 ] Steidle, S. V. (2013). Scheduling in Mohs Micrographic Surgery Clinics (Doctoral dissertation, Purdue University) [Abstract]. Purdue E Pubs.