This study investigates the bottlenecks in the emergency care chain of cardiac in-patient flow. The primary goal is to determine the optimal bed allocation over the care chain given a maximum number of refused admissions. Another objective is to provide deeper insight in the relation between natural variation in arrivals and length of stay and occupancy rates. The strong focus on raising occupancy rates of hospital management is unrealistic and counterproductive. Economies of scale cannot be neglected. An important result is that refused admissions at the First Cardiac Aid (FCA) are primarily caused by unavailability of beds downstream the care chain. Both variability in LOS and fluctuations in arrivals result in large workload variations. Techniques from operations research were successfully used to describe the complexity and dynamics of emergency in-patient flow.
Capacity decisions in hospitals are made in general without the help of quantitative model-based analyses . Over the past years hospital managers have been stimulated to reduce the number of beds and increase the occupancy rates to improve operational efficiency. This strategy is questionable. Variability in length of stay (LOS) has a major impact on day-to-day hospital operation and capacity requirements. If this variability is disregarded during modeling an unrealistic and static representation of reality will emerge. A model, only based on average numbers, is not capable of describing the complexity and dynamics of the in-patient flow. This is also known as the flaw of averages.
Management does not consider the total care chain from admission to discharge, but mainly focuses on the performance of individual units. Not surprisingly, this has often resulted in diminished patient access without any significant reduction in costs. The suggested solutions are suboptimal.
In this study we investigate the emergency in-patient flow of cardiac patients in a university medical centre. This particular patient flow is characterized by time-varying arrivals at the First Cardiac Aid (FCA), the department where emergency cardiac patients enter the hospital. After initial treatment patients are transferred to the Coronary Care Unit (CCU) before they go to the normal care clinical ward (NC).
Many hospitals have trouble keeping the right resources, such as beds and personnel, available for arriving patients. Measurements show that the CCU in the considered hospital operates at occupancy rates greater than 95%. As a result, it frequently occurs that the CCU has insufficient capacity because the unit is full. Consequently, the number of refused admissions at the FCA is significant and numerous patients are turned away to other referring hospitals.
This is unacceptable and puts a great pressure on the required quality of care. More and more hospitals have to account for their quality of care. An admission guarantee for all patients entering the emergency department is one of the main goals of the hospital. Besides this service requirement, one has to consider the medical emergency aspect. In case of a heart attack, the sooner someone gets to the emergency room, the better his or her chance of not only surviving, but also of minimizing heart damage following the attack. This is often referred to as the ‘Golden Hour’ . This study applies a queuing model to analyze congestion in the emergency care chain. With this model the number of beds in the care chain is determined for several service levels.
In Section 2 the structural model is constructed followed by the data analysis in Section 3. Section 4 describes the impact of fluctuations in arrivals and variation in LOS on capacity requirements. In Section 5 the phenomenon of blocking and the mathematical model are introduced. Section 6 gives the results and the paper ends with the conclusion and discussion in Section 7.
2 Structural model
The first phase of the study is the construction of a structural model (or flowchart) of the patient flow. Such a model describes the different patient routings in a qualitative manner and defines the relations between different hospital units. After expert meetings with cardiologists we decided to identify two different patient flows. The primary patient flow enters the system at the FCA and leaves the hospital after a stay at the CCU and NC. The different departments are defined as follows:
& First Cardiac Aid: A hospital unit intended to provide rapid diagnosis and initiation of treatment for subjects with acute symptoms probably due to cardiac disease (for example chest pain, syncope, palpitations, dyspnea)
Coronary Care Unit:A hospital unit that is specially equipped to provide intensive care of patients with severe acute or chronic heart disease (for example acute coronary syndromes, arrhythmia, heart failure)
Normal Care: A hospital unit equipped to provide nonintensive care to a particular group of patients, in this case patients with cardiac disease.
A secondary patient flow, originating from surrounding hospitals, enters the CCU and returns to other hospitals after treatment, thus bypassing the NC. These patients are hospitalized to have immediate percutaneous (or balloon) angioplasty (PTCA) . This kind of treatment is referred to as top-clinical care. Only certified hospitals are allowed to perform this type of medical procedure.The structural model with the two different patient flows is shown in Fig. 1.
Health care processes are characterized by a great uncertainty. A large variety of possible patient routings can be distinguished. If we investigate the different flows throughout the hospital in great detail the flowchart becomes like the path of a pinball. Therefore, Fig. 1 is not striving for completeness. Nevertheless, it is possible to reduce complexity without losing integrity by focusing on the most critical patient flows. In this study both the primary and secondary patient flow are taken into account.