Optimal patient protocols in regional acute stroke care
In acute stroke care two proven reperfusion treatments exist: (1) a blood thinner and (2) an interventional procedure. The interventional procedure can only be given in a stroke centre with specialized facilities. Rapid initiation of either is key to improving the functional outcome (often emphasized by the common phrase in acute stroke care “time=brain”). Delays between the moment the ambulance is called and the initiation of one or both reperfusion treatment(s) should therefore be as short as possible. The speed of the process strongly depends on five factors: patient location, regional patient allocation by emergency medical services (EMS), travel times of EMS, treatment locations, and in-hospital delays. Regional patient allocation by EMS and treatment locations are sub-optimally configured in daily practice. Our aim is to construct a mathematical model for the joint decision of treatment locations and allocation of acute stroke patients in a region, such that the time until treatment is minimized. We describe acute stroke care as a multi-flow two-level hierarchical facility location problem and the model is formulated as a mixed integer linear program. The objective of the model is the minimization of the total time until treatment in a region and it incorporates volume-dependent in-hospital delays. The resulting model is used to gain insight in the performance of practically oriented patient allocation protocols, used by EMS. We observe that the protocol of directly driving to the nearest stroke centre with special facilities (i.e., the mothership protocol) performs closest to optimal, with an average total time delay that is 3.9% above optimal. Driving to the nearest regional stroke centre (i.e., the drip-and-ship protocol) is on average 8.6% worse than optimal. However, drip-and-ship performs better than the mothership protocol in rural areas and when a small fraction of the population (at most 30%) requires the second procedure, assuming sufficient patient volumes per stroke centre. In the experiments, the time until treatment using the optimal model is reduced by at most 18.9 minutes per treated patient. In economical terms, assuming 150 interventional procedures per year, the value of medical intervention in acute stroke can be improved upon up to € 1,800,000 per year.