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International Conference on Computational Science, ICCS 2017, 12-14 June 2017, Zurich, Switzerland

Multiscale Modeling of Surgical Flow in a Large Operating Multiscale Modeling of Surgical Flow in a Large Operating RoomModeling Suite: Understanding theinMechanism of Multiscale of Surgical Flow a Large Operating Room Suite: Understanding the Mechanism of Accumulation of Delays in Clinical Practice Room Suite: Understanding the Mechanism Accumulation of Delays in Clinical Practiceof 1,2 1,2 1,3 Marc Garbey , Guillaume Joerger , Juliette RambourgPractice , Brian Dunkin1 , Accumulation of Delays in Clinical 1,2 1,2 1,3 1 1 ∗ Marc Garbey , Guillaume Joerger , Juliette and Barbara Bass Rambourg , Brian Dunkin , ∗ 1,2 1,2 1,3 and Barbara Bass1Rambourg Marc Garbey 1 , Guillaume Joerger , Juliette , Brian Dunkin1 , Houston Methodist Research Institute,1Houston, TX, USA ∗ andResearch Barbara Bassof Houston, 21 LaSIE, CNRS 7356, University la Rochelle, HoustonUMR Methodist Institute, TX,France USA 2 3 Ecole Nationale de l Aviation Civile, Toulouse, France 1 LaSIE, UMR CNRS 7356, University of la Rochelle, France Houston Methodist Research Institute, Houston, TX, USA 3 Ecole Nationale de l Aviation Civile, Toulouse, France 2

LaSIE, UMR CNRS 7356, University of la Rochelle, France 3 Ecole Nationale de l Aviation Civile, Toulouse, France

Abstract Improving operating room (OR) management in large hospitals has been a challenging problem Abstract that remains largely unresolved Fifty percent of hospital income depends on OR activities Improving operating room (OR) [7]. management in large hospitals has been a challenging problem Abstract and among the main concerns in most institutions is to improve efficiency of a large OR suite that remains largely unresolved [7]. Fifty percent of hospital income depends on OR activities Improving operating room (OR) management in large hospitals has been a challenging problem that. We advocate that optimizing surgical flow in large OR suites is a complex multifactorial and among the main concerns in most institutions is to improve efficiency of a large OR suite that remains largely unresolved [7]. Fifty percent of hospital income depends on OR activities problem with an underlying multiscale structure. Numerous components of the system can that. We advocate that optimizing surgical flow in large OR suites is a complex multifactorial and among the main concerns in most institutions is to improve efficiency of a large OR suite combine nonlinearly result in the large accumulated delays observed in daily clinical practice. problem with an underlying multiscale structure. Numerous components of the system can that. We advocate that optimizing surgical flow in large OR suites is a complex multifactorial We propose a multiscale agent-based model (ABM) of surgical flow. We developed a smartOR combine nonlinearly result in the large accumulated delays observed in daily clinical practice. problem with an underlying multiscale structure. Numerous components of the system can system that utilizes aresult dedicated network of non-invasive, wireless sensors automatically track We propose a multiscale agent-based model (ABM) ofdelays surgical flow. We developed a smartOR combine nonlinearly in the large accumulated observed in to daily clinical practice. the state of the OR and accurately computes major indicators of performances such as turnover system that utilizes a dedicated network of non-invasive, wireless sensors to automatically track We propose a multiscale agent-based model (ABM) of surgical flow. We developed a smartOR time between procedures. We show that our model can fit these time measurements and that the state of the OR and accurately computes major indicators of performances such as turnover system that utilizes a dedicated network of non-invasive, wireless sensors to automatically track a multiscale description of the system is possible. We will discuss how this model can be used time between procedures. We show that our model can fit these time measurements and that the state of the OR and accurately computes major indicators of performances such as turnover to quantify and target the main limiting factors in optimizing OR suite efficiency. a multiscale description of the system is possible. We will discuss how this model can be used time between procedures. We show that our model can fit these time measurements and that to quantifySurgery, and target the limiting factors inWe optimizing OR how suite efficiency. a multiscale description of main the system is possible. willOperating discuss this model can be used Keywords: Multiscale Modeling, Agent-based Model, Room Managment

© 2017 The Authors. Published by Elsevier B.V. Peer-review under the scientific committee International Conference on Computational Science to quantify andresponsibility target the ofmain limiting factors ofinthe optimizing OR suite efficiency. Keywords: Surgery, Multiscale Modeling, Agent-based Model, Operating Room Managment Keywords: Surgery, Multiscale Modeling, Agent-based Model, Operating Room Managment

1 Introduction 1 Introduction Surgical flow is a highly complex process involving multiple scales across the hospital sys1 Introduction tem.Someflow of the maneuvers that affectmultiple patient outcomes should set in conSurgical is acritical highlysurgical complex process involving scales across the be hospital systext of the management and organization of surgerical and performance. tem.Some ofoverall the maneuvers that affect patientstaff outcomes should setAinsingle conSurgical flow is acritical highlysurgical complex process involving multiple scales across the be hospital sysevent in the OR can negatively affect other steps and the combination of otherwise benign text of the overall management and organization of surgerical staff and performance. A single tem.Some of the critical surgical maneuvers that affect patient outcomes should be set in conevent theoverall OR can negativelyand affect other steps the combination of otherwiseAbenign text ofinthe management organization of and surgerical staff and performance. single

∗ This work was supported in part by NSF 106022 - Full Center Grant: I/UCRC for Cyber-Physical Systems event inwork the was OR can negatively affect106022 other steps and Grant: the combination of otherwise benign ∗the for Operating to all the Center surgical staff of Dunn OR suite especiallySystems Wendy ThisHospital supportedRoom. in partThanks by NSFalso - Full I/UCRC for Cyber-Physical Smith, director of the suite.Room. Thanks to Michael Garcia and Cathystaff Williamson for their involvement in the for the Hospital Operating Thanks also to all the surgical of Dunn OR suite especially Wendy ∗ This work was supported in part by NSF 106022 - Full Center Grant: I/UCRC for Cyber-Physical Systems project and its implementation in the clinical world. Smith, director of the suite. Thanks to Michael Garcia and Cathy Williamson for their involvement in the for the and Hospital Operating Room. Thanks to all the surgical staff of Dunn OR suite especially Wendy project its implementation in the clinicalalso world. Smith, director of the suite. Thanks to Michael Garcia and Cathy Williamson for their involvement in the 1 project and its implementation in the clinical world.

1 1877-0509 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the International Conference on Computational Science 10.1016/j.procs.2017.05.228

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events can cascade and result in adverse outcomes for the patient. Fig. 1 shows the different scales that can be impacted by adverse events. The figure must be read from the center to the edge of the circle for the impacts on space scale and following the unit circle for the impacts on time scale. We show, for example, that OR awareness delay of the order of minutes may affect the global time scale with case cancellation. Similar results can be seen at the space scale when missing instruments affect the whole OR suite workflow.

Figure 1: Symbolic representation of the multiscale distribution of surgical flow ranging from the smallest scale, OR awareness, to the hospital system level involving hundreds of staff.

Current optimization techniques to schedule surgery [4, 5] have limited capability because of uncertainty with regard to procedural time, lack of detailed information on the state of the system and a large number of last minute emergency cases added to the schedule. Consequently, continuous real-time rescheduling is done by the staff based on their expertise and one-toone communication with other staff members [13]. Common sources of frustration for OR management include [15]: • Turnover time between surgeries above the hospitals management policy [2]. • Delays in the start time of the first case of the day [6]. • Surgeries that run longer than anticipated and lead to cancellation of other cases [1]. Standard techniques commonly employed, such as check lists and team work protocols [11], cannot maintain satisfactory performance in such a stressful and uncertain environment. We propose that staff and patients would greatly benefit from a user-friendly, cyber-physical infrastructure [10] that constantly monitors events and uses a sophisticated model of surgical flow to anticipate difficulties and efficiently assists rescheduling efforts of the OR team. To establish the necessary infrastructure we first designed and tested an automated system called ”smartOR” in the clinical environment, see figure 2. The system tracks the processes 2



Marc GarbeyRoom et al. /Suite Procedia Science 108C (2017) 1863–1872Dunkin and Bass Multiscale Modeling of Large Operating . . . ComputerGarbey, Joerger, Rambourg,

Figure 2: Left: Symbolic representation of the OR suite lay out and traffic: a white board is used to control all OR scheduling of the bloc in combination with the electronic patient record from EPIC. Right: Low cost wireless sensors are used to acquire room state: a camera detects the motion of the anesthesia ventilator, the door has an array of sensors including an accelerometer to register entry/exit events, a simple IR sensor can detect an empty OR

within the OR in real time and automatically identifies and informs the OR team of the room state [8]. To complement the smartOR we developed a BoardProbe, an electronic whiteboard which supports organizational and collaborative activities within the surgical suite and emulates the familiar dry-erase white board traditionally used the OR suite managment [12]. Combining SmartOR and BoardProbe efficiently delivers real-time information and alerts about OR activity to the surgical staff [9] improving resource utilization and communication. Nevertheless, root cause analysis of surgical flow inefficiencies in any given hospital and identification of factors that need to be adjusted requires a rational analytical model. Here, we propose a multiscale, agent-based, theorectical mathematical model that we successfully compared to the smartOR data and allows management to address problems and inefficiencies.

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Mathematical Modeling

We propose a staff-specific ABM intended to retain the key features we observed in daily clinical practice. The proposed model specifically takes into account the contributions of each staff member in the team necessary to advance the task. Some staff, for example the anesthesiologist and the cleaning team,is assigned to several ORs and the model accounts for delays in awareness of events and time to circulate around the OR suite. The theoretical framework has been kept as general as possible to be able to apply it to any hospital system, and calibrate and adapt the modular structure to the detail of clinical data specific to the hospital. To summarize, the model computes the time evolution of two sets of unknowns: • State of task k for agent i is denoted as vector Tki , • Trajectory and state of agent i denoted Si We start here with a simplified graph showing the macro steps such preparation for anesthesia, access, surgerical procedure (open or minimally invasive), closing time, time to awake the patient and OR exit - see figure 3. The system was deployed in five pluridisciplinary ORs and provides accurate measurements of the duration of each of these steps [8]. We use six main categories of agents: A for surgeons, B for surgeons assistants, C for anesthesiologists, R for Certified Registred Nurse Anesthesit (CRNA), D for scrub nurses, E 3

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for cleaning crew. For simplicity, we assume that a surgical team, denoted S, in any given OR consists of one agent in each category. Most importantly each agent is associated with a level of technical skill and a level of communication skill. For example, a team of N surgeons noted {A(j, n)} working in the ORs suite is represented by a N × 2 matrix of performance level. The first index is the ID of the agent in the set {1 ... N }, the second is for the performance type. n=1 corresponds to the technical performance and is denoted by pA t ; n=2 is for the communication performance index denoted pA c . Initially, we set up individual technical skills as a function of the number of years of experience in the current position, and communication skills as a function of the time spent working with the current team, since frequency in team composition change is negatively correlated to information sharing [3]. We use an estimate of the duration for each macro step, such as patient intubation, access time, surgerical procedure itself, patient extubation, or time to move the patients out of the OR - see figure 3. This estimate is a statistical distribution that depends on the patient s medical conditions and reflects the ideal time that a perfect surgical team should achieve. As we will see later on, our model is stochastic and accounts for delays due team members lack of timely availability, poor coordination between tasks, or suboptimal performance of the surgical team. For any given OR only one task can be in process at any given time,as reflected on the flowchart - see figure 3. The progression T˜ of the task k for the agent i, noted Tki , from 0 to 1 is described by an ordinary differential equation with the right hand side depending on the team skills. T˜ is set to 0 if the task is not completed, i.e. 0 ≤ Tki < 1, and 1 otherwise. M is a sparse matrix that corresponds to the directed graph of Fig 3 . The master equation that provides the time evolution of the state of the graph of tasks {Tki } handled by the team Si that advances the task Tq at time step q is: T˜(tq+1 ) = [M × (T˜(tq ))] ◦ [(G(tq − t0 ))Si .Ek ].

(1)

Here × denotes the sparse matrix vector product, and ◦ the vector product component-wise, and . the product of a vector by a scalar. This model has three components: • M × (T˜(tq )) where M is a sparse matrix that expresses the dependency on previous tasks. • G(tq − t0 )Si reflects the time-dependent progression of the individual task. • 0 ≤ Ek ≤ 1 is a positive factor representing a penalty for the environment conditions. It may be the limitation resulting from shared equipment or specific overload of the hospital system due to epidemic or crisis. Conceptually we can represent the ABM computing kernel for each node of the flow graph as in Figure 3. The advancement of task provide by G(t) is not linear in time, i.e. G˙ = constant, but instead depends on team performance and coordination. We conveniently use an ordinary set of differential equations to integrate that progression in time: G˙ = βFk (S)f (t) + Ho

(2)

The initial condition is zero, and β is a normalizing constant such that G reaches 1 at completion of the task in the optimal configuration. Time integration starts only when all staff required for that specific task are present in the OR. More precisely, we define the optimum performance of a team as one that (i) has full awareness on the case, (ii) does not show any sign of fatigue or stress, and (iii) has best technical and communication skills. We represent mathematically each of these elements (i) to (iii) below. In equation (2), 1 ≥ Fk (S) ≥ 0 stands for the team efficiency at the task Tk . 4



Multiscale Modeling of Large Operating . . . ComputerGarbey, Joerger, Rambourg, Marc GarbeyRoom et al. /Suite Procedia Science 108C (2017) 1863–1872Dunkin and Bass

Figure 3: Illustration of our simplified flow chart on the left and its impact on the conceptual Model of process advancement corresponding to each node of the flow chart

The team performance component of the surgeon and his assistant for a specific task of the graph of nodes described at the high level is additive on technical skills, impacted by the worst skill in communication on the team, factored by a function f(t) that takes into account fatigue, as well as efficiency as a correlation of repetition of the same surgery. Overall performance cannot go below a given threshold Ho corresponding to a minimum processing rate, since the team has been granted surgical privileges. For simplicity we assume that the same surgical team operates in the same OR the entire day. Nurse shift is modeled as a time penalty for which the ODE integration is on hold. We have applied these basic principles to the team performance description of each task in figure 3 and used the following example in our simulations, with A for surgeons, B for surgeon s assistants, C for anesthesiologists, R for CRNA, D for scrub nurses, E for cleaning crews: • task T1 placing the patient under anesthesia (α31 + α41 = 1, 0 ≤ β1 ≤ 1): F1 (t) =

1 1 R C R β1 [α31 pC t + α4 pt ] min(pc .pc )] + (1 − β1 ). 9

(3)

• task T2 preparation for laparoscopy procedure to provide access (α22 +α52 = 1, 0 ≤ β2 ≤ 1): F2 (t) =

1 2 D B D β2 [α22 pB t + α5 pt ] min(pc .pc )] + (1 − β2 ). 9

(4)

• task T3 preparation for open surgical procedure to provide access (α13 + α23 + α53 = 1, 0 ≤ β3 ≤ 1): F3 (t) =

1 3 B 3 D A B D β3 [α13 pA t + α2 pt + α5 pt ] min(pc , pc .pc )] + (1 − β3 ). 9

(5)

• task T4 laparoscopic procedure (α14 + α24 = 1, 0 ≤ α34 ≤ 1, 0 ≤ α54 ≤ 1, 0 ≤ β4 ≤ 1): F4 (t) =

1 4 B 4 D 4 R A B R D β4 [α34 [α54 [α14 pA t + α2 pt ] + (1 − α5 )pt ] + (1 − α3 )pt ] min(pc , pc , pc , pc )] 9 + (1 − β4 ).

(6) 5

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• task T5 open surgery procedure (α15 + α25 = 1, 0 ≤ α35 ≤ 1, 0 ≤ α55 ≤ 1, 0 ≤ β5 ≤ 1): F5 (t) =

1 5 B 5 D 5 R A B R D β5 [α35 [α55 [α15 pA t + α2 pt ] + (1 − α5 )pt ] + (1 − α3 )pt ] min(pc , pc , pc , pc )] 9 + (1 − β5 ).

(7)

• task T6 closing laparoscopic procedure: similar to T2 . • task T7 closing open surgery procedure: similar to the above. • task T8 waking up procedure (α38 + α48 = 1, 0 ≤ β8 ≤ 1): F8 (t) =

1 8 R A C R β8 [α38 pC t + α4 pt ] min(pc , pc , pc )] + (1 − β8 ). 9

(8)

• task T9 cleaning the OR (0 ≤ β9 ≤ 1): E F9 (t) = β9 pE t pc + (1 − β9 ).

(9)

Overall the team performance impact on task advancement are provided by the matrix α:   0 0 0.6 0.4 0  0 0.5 0 0 0.5     0.5 0.3 0 0 0.2     0.6 0.4 0 0.8 0.8     0.8 0.2 0 0.8 0.8     0 0.6 0 0 0.4     0.3 0.5 0 0 0.2  0 0 0.6 0.4 0 and the vector:

β = [0.7 0.6 0.3 0.5 0.5 0.3 0.3 0.7]t This matrix is largely the result of a heuristic effort based on a priori knowledge. However our plan is to eventually retrieve these values from clinical data provided for example by the black box system [14] that has the ability to report most of these parameters.

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Results

Starting from the general model described above and, we simplified it according to the data that we have collected in the clinic. Without an extensive electronic patient record input into the model, we assume a normal distribution of patient conditions. Similarly, we will assume a normal distribution of the individual team performances of staff to keep the probabilistic nature of the model without adding additional complexity. The resulting model has 13 key parameters describing the overall infrastructure, see Table 1. A nonlinear sensitivity has been done utilizing a partial rank correlation method based on the exploration of the hypercube of the parameter space. Table 1 provides this list of parameters and their impact on segments of surgical flow time known for their value as efficiency indicators. The ranking in each row increases starting from one for the most influential parameters, including only the parameters 6



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macrostep/parameters anesthesia waking up turnover

q1

q2 2

q3

q4

q5

q6

q7

2

5

4

q8

2

q9 1 3 4

q10

q11

3

1

q12

q13 1 5

Table 1: Ranking the Influence of the Parameters on key factors of OR efficiency, such as anesthesia time, wake up time and turnover that have significant impact. Given parameters • q1 is the maximum length of time it takes the patient to arrive from the pre-operative area, • q2 is the ideal length of time to put the patient under anesthesia. • q3 is the shortest lenght of time achievable for minimally invasive surgery that would correspond to the simplest case, and q4 the largest length of time that would correspond to the most complex patient condition. • q5 and q6 are equivalent time length estimates to q3 and q4, applied to open surgery. • q7 is the ideal length of time for the patient to wake up from anesthesia. • q8 is the ideal length of time to clean and disinfect the OR according to best practices. • q9 is the ratio of anesthesiologists to the number of ORs. • q10 is the ratio of janitorial teams to the number of ORs. • q11 is the awareness and communication delay until a janitorial team arrives at the OR, expressed in seconds per each OR in the surgical suite. • q12 is the awareness delay for anesthesiologists to come to the OR expressed in seconds per each OR in the surgical suite. • q13 is the average recovery time in the post-operative area after surgery. We ran our simulation over a period of one year for which we have clinical data, and use a genetic algorithm to get the best fit. We present our data as a normalized histogram of time distribution for anesthesia, surgical time for open and minimally invasive procedures, awaking time and turnover time. The large pluridisciplanry suite we use for our analysis has roughly an equal number of open and minimally invasive procedures. The curves in red in Figure 4 and Figure 5 are for the clinical data and in black are the simulation result. In this process, we retrieved the unknown parameters q1 to q13 as the solution of the best-fit optimization problem and compare some of them with additional observations or knowledge of the organization of the staff that has not been entered in the model. The first conclusion is that the simulation cannot fit the clinical data if we zero parameters characteristics of the multiscale nature of the model such as q9 to q13 . For example, instead of a lognormal distribution of surgical time as it can be demonstrated by analyzing our data, it would result in normal curves, and instead of a turnover time distribution with slow decay 7

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Figure 4: Comparison of normalized distributions of cases with respect to elapse time for open surgery, minimally invasive surgery, anesthesia and waking up time between observed (red dots) and simuated (black line) data.

toward the worst performance we would achieve a normal distribution with a very narrow standard deviation. However, we observe a poor fitting of the open surgical time, and a slightly better result for minimally invasive surgery. This result is not surprising since we treated the description of surgery in a very coarse way in our model. Our data set includes very short surgeries such as cholecystectomy or appendectomy as well as much longer one such as organ transplantation. Obviously we need to refine our surgical flow chart by including more specific description of surgery types and acquire estimates of parameter values similar to q3 to q6 for each class of surgery. The prediction of anesthesia time and wake up time seem accurate enough to be of practical value, see figure 4. The prediction of turnover time on figure 5, one of the key targets for improvement in OR suite management, is very good, especially considering the uncertainty of the system and the fact that this is the most non-linear factor. The validation of the multiscale model comes in part from the optimal value of the parameters we retrieved through in the fitting process. For example we found that q9 and q10 , the delay of OR awareness for the cleaning team, is between 6 and 12 min while for anesthesiologist it is between 2.5 and 5 min. This is in agreement with our observation during monitoring of the white board activity over a period of a week [9], with the main reason for the delay being that OR state changes are entered manually and communication is often depending on individual cell phone conversation (call or text message). The model also estimates that the optimal proportion of anesthesiologists q9 is 1 to 5, while it is in reality about 1 to 4. Other results from this a posteriori analysis cannot be provided in this short paper. From the many lessons we learned from this study we retain three key elements of the capability of multiscale modeling to test various hypotheses on OR management improvement: • The OR performance is limited by the shortage of shared personal such as anesthesiologists who circulate from one OR to another in order to assist the Certified Registered Nurse Anesthesists (CRNA). If this ratio was as large as 1/2, the model predicts a significant improvement of performance. 8



Marc GarbeyRoom et al. /Suite Procedia Science 108C (2017) 1863–1872Dunkin and Bass Multiscale Modeling of Large Operating . . . ComputerGarbey, Joerger, Rambourg,

Figure 5: Comparison of normalized distribution of cases with respect to turnover time between observed (red dots) and simuated (black line) data.

• The overall OR system is very sensitive to OR awareness time, i.e. how much time it takes for an anesthesiologist or the cleaning staff to realize that their presence is needed. This would advocate in favor of installing a cyber-physical infrastructure including our BoardProbe design [12] that shorten that critical communication time. • The inability to free the OR because there is no bed available in the recovery area is another important cause of suboptimal efficiency. In our simulation, accumulation of delays resulting of these three factors can result in turnover time about an hour; this seems to be congruent with our observation. However, a solution that would increase the infrastructure size and staff support without reason would increase health care costs and eventually impact the patient. We are confident that modeling with a concept like ours should be sufficiently accurate to predict optimum ratio of resources that would significantly improve the efficiency, improve the budget, and increase patient satisfaction.

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Future Work

Our multiscale modeling of surgical flow of a large OR suite brings new light and rational to improve organizational and infrastructure costs positively. There is additional effort needed to gather accurate information on surgical time according to a pertinent classification of procedures, as well as to systematic use of the electronic patient record in order to condition those estimates with patient comorbidities. As the health industry becomes closer and closer to other industries standard such as civil aviation that has precise protocol and worldwide standards for each procedure, it is only a matter of time that a multiscale model could be calibrated precisely. However, there are still wide open questions on how surgical team performs and how we can really quantify such organization as a function of individual skills. We found this topic fascinating and intend to devote significant effort in future work to tackle that challenge. 9

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