因大血管阻塞(large vessel occlusion, LVO)的缺血性中風患者可以得益於盡快地接受血管取栓術(endovascular treatment, EVT)；另一方面，對於那些非大血管阻塞的病患而言，盡早地施打血栓溶解劑(intravenous tissue-type plasminogen activator, IV-tPA)，將會使病患在施打後能有較大的機會恢復到中風前的狀態。由前面這些事實，可以得知這兩種治療方式有其時效性。然而，實際上，一位疑似中風病患的血管狀態是無法在沒有詳細檢查下得知的，所以急救人員需要在現場使用院前中風嚴重程度量表(prehospital stroke severity scale, PSSS)來辨別出這位病患的中風嚴重程度，然後再決定將此病患送至只有提供施打血栓溶解劑診療方案的基本中風病患醫院(primary stroke center, PSC)或者提供血管取栓術及血栓溶解劑的中風病患醫學中心(comprehensive stroke center, CSC)。我們想要處理的問題為建立一個數學規劃模型給急救人員一個建議的醫院來運送病患。

在先前的研究中，兩種接受中風病患的醫院，其院內時間流程是假設為一定值，而這是不實際的。為了解決這個議題，我們考慮院內時間不確定性。也就是把這些時間視為一個機率分布。因此，在此篇論文中我們建立三個基於這種想法的數學規劃模型。藉由模擬在數次的試驗下，我們所提出的模型相較於以往所提出的，大部分都有較佳的表現。我們所使用的資料為台灣台北市中風病患的資訊以及十間位於台北市的醫院，以及由Google Map所估得的病患至這十間醫院的車行時間。

An acute ischemic stroke (AIS) patient with large vessel occlusion (LVO) can benefit from the endovascular treatment (EVT) as soon as possible, and on the other hand, a patient without LVO will have a better outcome when receive the intravenous tissue-type plasminogen activator (IV-tPA) early. Therefore, these facts indicate that both of the treatments are time-sensitive. Nevertheless, in reality, the vessel status of a suspected stroke patient is unknown without a sophisticated inspection, so the Emergency Medical Technicians (EMTs) need to use prehospital stroke severity scale (PSSS) to identify the severity of this stroke patient on the spot and then determine to transport either to primary stroke centers (PSCs), which offer the IV-tPA only, or to comprehensive stroke centers (CSCs), which provide both of the IV-tPA and EVT. The problem we want to handle is to build a mathematical programming model that give a recommended hospital for EMTs to transport the patients.

In the prior research, the in-hospital workflow time in the stroke centers (both PSCs and CSCs) is assumed to be a deterministic value. However, it is not realistic. To address this issue, we take the uncertainty of the workflow time of the hospitals into consideration. That is, we model these intervals of time into a distribution. Thus, in this thesis, we build three mathematical programming models based on this concept to transport patients. We then show that the result of our proposed models is better than the previously proposed strategies in the total number of patients receiving the definitive treatment within a given time by simulating on the numerous number of trials. The data we used is based on the off-peak transport time in the real world from Google Map, the historical performance of the workflow time of ten hospitals, and the real patient’s profiles including the geographic locations, response time, on-scene time and prehospital stroke severity scale scores in the Taipei City, Taiwan.

Contents
Abstract------------------------------------i
中文摘要 ----------------------------------iii
Chapter 1. Introduction --------------------7
Chapter 2. Literature Review ------------9
2.1 Prehospital Stroke Severity Scales ----9
2.2 Time Sensitivity -------------------10
2.3 Optimization Model for Triage ---10
Chapter 3. Model -------------------11
3.1 Model Assumption -------------------12
3.2 Hospital Selection Models -----------13
Chapter 4. Results -------------------18
4.1 Data Source ---------------------------19
4.2 Results of the Model -----------22
4.3 Comparison of Different Strategies ---24
4.3.1 The Setting of Simulation -----------26
4.3.2 The Results of Simulation -----------26
Chapter 5. Conclusions -------------------28
References ---------------------------33

[1] Ali A, Zachrison KS, Eschenfeldt PC, Schwamm LH, Hur C (2018). Optimization of Prehospital Triage of Patients With Suspected Ischemic Stroke. Results of a Mathematical Model. Stroke, 49(10), 2532-2535.
[2] Benoit JL, Khatri P, Adeoye OM, Broderick JP, McMullan JT, Scheitz JF, et al.(2018). Prehospital Triage of Acute Ischemic Stroke Patients to an Intravenous tPA-Ready versus Endovascular-Ready Hospital: A Decision Analysis. Prehosp Emerg Care, 22(6), 722-733.
[3] Berkhemer OA, Fransen PSS, Beumer D, van den Berg LA, Lingsma HF, et al. (2015). A randomized trial of intraarterial treatment for acute ischemic stroke. N Engl J Med. 372(1), 11–20.
[4] Emberson J, Lees KR, Lyden P, Blackwell L, Albers G, Bluhmki E, Brott T, et al; Stroke Thrombolysis Trialists' Collaborative Group (2014). Effect of treatment delay, age, and stroke severity on the effects of intravenous thrombolysis with alteplase for acute ischaemic stroke: a meta-analysis of individual patient data from randomised trials. Lancet, 384(9958), 1929-1935.
[5] English JD, Yavagal DR, Gupta R, Janardhan V, Zaidat OO, Xavier AR, et al. (2015). Mechanical thrombectomy-ready comprehensive stroke center requirements and endovascular stroke systems of care: recommendations from the Endovascular Stroke Standards Committee of the Society of Vascular and Interventional Neurology (SVIN). Interv Neurol, 4(3-4), 138–150.
[6] Fourer R, Gay DM, Kernighan BW (2002). AMPL: A Modeling Language for Mathematical Programming. 2nd edition. Boston: Cengage Learning
[7] Fransen PS, Berkhemer OA, Lingsma HF, Beumer D, van den Berg LA, Yoo AJ, et al; Multicenter Randomized Clinical Trial of Endovascular Treatment of Acute Ischemic Stroke in the Netherlands Investigators (2016).Time to Reperfusion and Treatment Effect for Acute Ischemic Stroke: A Randomized Clinical Trial. JAMA Neurol, 73(2), 190-196.
[8] Goyal M, Demchuk AM, Menon BK, Eesa M, Rempel JL, Thornton J, et al. (2015). Randomized assessment of rapid endovascular treatment of ischemic stroke. N Engl J Med, 372(11), 1019–1030.
[9] Goyal M, Jadhav AP, Bonafe A, Diener H, Pereira VM, Levy E, Baxter B, et al. SWIFT PRIME investigators (2016). Analysis of workflow and time to treatment and the effects on outcome in endovascular treatment of acute ischemic stroke: results from the SWIFT PRIME randomized controlled trial. Radiology, 279(3), 888-897.
[10] Goyal M, Menon BK, van Zwam WH, Dippel DW, Mitchell PJ, Demchuk AM, Dávalos A, et al; HERMES collaborators (2016). Endovascular thrombectomy after large-vessel ischaemic stroke: a meta-analysis of individual patient data from five randomised trials. Lancet, 387(10029), 1723-1731.
[11] Heldner MR, Hsieh K, Broeg-Morvay A, Mordasini P, Bühlmann M, et al. (2016). Clinical prediction of large vessel occlusion in anterior circulation stroke: mission impossible? J Neurol, 263(8), 1633-40.
[12] Holodinsky JK, Williamson TS, Kamal N, Mayank D, Hill MD, Goyal M (2017). Drip and Ship Versus Direct to Comprehensive Stroke Center. Conditional Probability Modeling. Stroke, 48(1), 233-238.
[13] Holodinsky JK, Williamson TS, Demchuk AM, Zhao H, Zhu L, et al. (2018). Modeling Stroke Patient Transport for All Patients With Suspected Large-Vessel Occlusion. JAMA Neurol, 75(12), 1477-1486.
[14] IBM, 2020 IBM ILOG CPLEX 20.1 User Manual, IBM Corp; 2020.
[15] Jovin TG, Chamorro A, Cobo E, de Miquel MA, Molina CA, Rovira A, et al. (2015). Thrombectomy within 8 hours after symptom onset in ischemic stroke. N Engl J Med, 372(24), 2296–2306.
[16] Jumaa MA, Castonguay AC, Salahuddin H, Schawver J, Saju L, et al. (2020). Long-term implementation of a prehospital severity scale for EMS triage of acute stroke: a real world experience. Journal of NeuroInterventional Surgery, 12(1), 19–24.
[17] Kim JT, Fonarow GC, Smith EE, Reeves MJ, Navalkele DD, Grotta JC, et al. (2017). Treatment With Tissue Plasminogen Activator in the Golden Hour and the Shape of the 4.5-Hour Time-Benefit Curve in the National United States Get With The Guidelines-Stroke Population. Circulation, 135(2), 128-139.
[18] Krebs W, Sharkey-Toppen TP, Cheek F, Cortez E, Larrimore A, Keseg D, et al. (2018). Prehospital Stroke Assessment for Large Vessel Occlusions: A Systematic Review. Prehosp Emerg Care, 22(2), 180-188.
[19] Marti K (2005). Stochastic optimization methods (Vol. 2). Berlin: Springer.
[20] Menon BK, Sajobi TT, Zhang Y, Rempel JL, Shuaib A, Thornton J, et al. (2016). Analysis of workflow and time to treatment on thrombectomy outcome in the ESCAPE randomized controlled trial. Circulation, 133(23), 2279-2286.
[21] Milne MS, Holodinsky JK, Hill MD, Nygren A, Qiu C, Goyal M, Kamal N (2017). Drip 'n Ship Versus Mothership for Endovascular Treatment: Modeling the Best Transportation Options for Optimal Outcomes. Stroke, 48(3), 791-794.
[22] Mulder MJHL, Jansen IGH, Goldhoorn RB, Venema E, Chalos V, Compagne KCJ, Roozenbeek B, Lingsma HF, et al; MR CLEAN Registry Investigators (2018). Time to Endovascular Treatment and Outcome in Acute Ischemic Stroke: MR CLEAN Registry Results. Circulation, 138(3), 232-240.
[23] Ng FC, Low E, Andrew E, Smith K, Campbell BC, Hand PJ, et al. (2017). Deconstruction of interhospital transfer workflow in large vessel occlusion: real-world data in the thrombectomy era. Stroke, 48(7), 1976–1979
[24] Powers WJ, Rabinstein AA, Ackerson T, Adeoye OM, Bambakidis NC, et al. (2018). 2018 Guidelines for the Early Management of Patients With Acute Ischemic Stroke: A Guideline for Healthcare Professionals From the American Heart Association/American Stroke Association. Stroke, 49(3), e46-e99.
[25] Pride GL et al. (2017). Prehospital care delivery and triage of stroke with emergent large vessel occlusion (ELVO): report of the Standards and Guidelines Committee of the Society of Neurointerventional Surgery. J Neurointerv Surg, 9(8), 802-812.
[26] Richards CT, Huebinger R, Tataris KL, Weber JM, Eggers L, Markul E, et al. (2018). Cincinnati Prehospital Stroke Scale Can Identify Large Vessel Occlusion Stroke. Prehospital Emergency Care, 22(3), 312-318.
[27] Saver JL, Fonarow GC, Smith EE, Reeves MJ, Navalkele D, Grotta JC, et al. (2015). Abstract 50: Shape of the tPA time – benefit curve: insights from the national US Get With The Guidelines – stroke population. Stroke, 46(suppl_1)
[28] Saver JL, Goyal M, van der Lugt A, Menon BK, Majoie CLM, et al. (2016). Time to treatment with endovascular thrombectomy and outcomes from ischemic stroke: a meta-analysis. JAMA, 316(12), 1279-1289.
[29] Scheitz JF, Abdul-Rahim AH, MacIsaac RL, Cooray C, Sucharew H, et al. (2017). Clinical Selection Strategies to Identify Ischemic Stroke Patients With Large Anterior Vessel Occlusion. Stroke, 48(2), 290–297.
[30] Schlemm E, Ebinger M, Nolte CH, Endres M, Schlemm L (2017). Optimal Transport Destination for Ischemic Stroke Patients With Unknown Vessel Status. Use of Prehospital Triage Scores. Stroke, 48(8), 2184-2191.
[31] Sheth SA, Jahan R, Gralla J, Pereira V M, Nogueira RG, Levy EI, Zaidat OO, Saver JL & SWIFT‐STAR Trialists (2015). Time to endovascular reperfusion and degree of disability in acute stroke. Annals of neurology, 78(4), 584-593.
[32] Venema E, Lingsma HF, Chalos V, Mulder MJHL, Lahr MMH, et al. (2019). Personalized Prehospital Triage in Acute Ischemic Stroke. Stroke, 50(2), 313-320.
[33] Xu Y, Parikh NS, Jiao B, Willey JZ, Boehme AK, Elkind MS (2019). Decision Analysis Model for Prehospital Triage of Patients With Acute Stroke. Stroke, 50(4), 970-977.
[34] Yu-Chen Chang (2020). A prehospital-stroke-scale parameterized hospital selection protocol for suspected stroke patients. Thesis (Master). National Tsing Hua University.