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A mathematical model for simulating daily bed occupancy in an intensive care unit

Julio Barado¹, Juan María Guergué, Laida Esparza

¹Hospital of Navarra, Pamplona, Spain. jbaradoh@navarra.es

Critical Care Medicine

|November 10, 2011

Abstract

Objectives:

To develop a mathematical model for simulating the daily bed occupancy in an intensive care unit.

Design:

Data collection and retrospective analysis to develop a mathematical model for simulating daily bed occupancy in an intensive care unit.

Setting:

We studied all admissions to the intensive care unit at the Hospital of Navarra over a 9-yr period.

Patients:

Six-thousand three-hundred adult patients consecutively admitted to intensive care units at a tertiary care hospital.

Interventions:

None.

Measurements And Main Results:

The large set of data collected comprises an arrivals file, a patient file, and a bed occupancy file. The arrival file records the number of patients admitted to the intensive care unit each day, by admission type, and by day of the week. The patient file contains records for all patients admitted to the intensive care unit during the study period: Admission type, admission and discharge dates, age, sex, Acute Physiology and Chronic Health Evaluation II score within the first 24 hrs, infections during hospitalization, and mortality. We used these two files to fit appropriate statistical models of arrival rates and length of stay by patient type. Based on this statistical analysis and the representation of the intensive care unit as a queuing problem, we built a simulation model. The bed occupancy file records the number of occupied beds at 4:00 PM each day. We used this file to validate the simulation model by testing the similarity of the real and simulated output data. The simulation model also includes bed management decisions related to patient discharge.

Results:

We obtained a valid simulation model that reproduced on a computer the patient flow through the intensive care unit at the Hospital of Navarra. This computerized simulation model can be used to study the intensive care unit bed occupancy profile and can be used as a reliable sizing and capacity analysis tool. As an example, we present the problem of estimating the number of beds needed to meet an increase in patient arrivals at the intensive care unit because of different causes.

Conclusions:

It is possible to develop simulation models that can be used to predict future intensive care unit resource needs.

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