Modeling the Emergency Cardiac in-patient Flow

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Introduction The primary goal is to determine the optimal bed allocation and decrease

the number of refused admissions.

The major problem in planning the day to day operations in a hospital is thevariable length of stay of a patient.

If this variability is disregarded a unrealistic picture of the reality will

emerge.

A model just based on the average numbers is not capable of describing thecomplexity of the patient flow at the hospital. This is also known as the flawof averages.

This case is about the inflow of cardiac patients into a hospital.

This particular patient inflow goes through 3 stages :

1) FCA (first cardiac aid)

2) CCU (coronary care unit)

3) NC (normal care unit)


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What is the problem?

In most of the hospitals the CCU works at a 95% capacity, as a result it

frequently occurs that the CCU has insufficient capacity, as the unit is full.

Consequently the number of refused admissions is significant and numerouspatients are turned away to other hospitals.

An admission guarantee to all the patients getting into the emergency

department is one of their main goal, so they cant keep on refusing patients.

In case of a heart attack, the sooner someone gets into the emergency room thebetter the chance of his survival. This period is referred to as the GOLDENHOUR

This study applies a queuing model to analyze congestion in the emergencycare unit.

With this model the number of beds and equipment is determined at differentservice levels.


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Structural model

The first phase of this study is about constructing a flowchart of the patientflow.

The primary flow of a heart patient is :

The different departments are defined as followed:

FCA (first cardiac aid) a hospital unit intended to provide quick diagnosis andinitiation of treatment.

CCU (coronary care unit) a hospital unit specially equipped to provideintensive care to heart patients with severe or chronic heart disease.

NC (normal care) hospital unit equipped to give non-intensive care to theheart patients.

Enters at

FCA

Stays at

CCU

Goes out

to NC


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The secondary flow accounts for the direct entrance into the CCU,and returns back after treatment bypassing the NC.

Here the patients are admitted for immediate intensive care.


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Data Analysis

Arrivals Total number of arrivals in 2003 2838

The average number of patients arriving per day 7.78


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The FCA is characterized by time-varying arrivals during the day

with arrival pattern over 24-hour period. 14%, 55% and 31% of all patients arrive in the intervals 00.00-

08.00, 08.00-16.00 and 16.00-24.00.

The secondary patient flow is also unscheduled and modeled as a

Poisson process with parameter


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Routings

There is an alarming

amount of refusedadmissions.

Its not uncommon and soorganization of emergencycare is a hot topic for

hospital professionals

Length of Stay (LOS) distributions

The real LOS is generally not equal to the LOS indicated by

hospital professionals the difference of which is caused bycongestion or chain effects.

A certain part of the total LOS consists of additional time

which is around 20-30% of total LOS.


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First Cardiac Aid (FCA) For 2401 (85%) of all arrivals the LOS was registered. The

ALOS at the FCA is 6.4 hours and patients never stay longerthan 24 hours. The median is 5 hours and the CV equals 0.7.

Coronary Care Unit (CCU)

For primary patient flow ALOS is 67 hours, median 48hours and CV 0.99.

For secondary patient flow ALOS is 18 hours, median 5 and

CV 2.6.

About 80% of all patients leave within 12 hours and 80%have prolonged stay. Paretos 80/20 principle applicable

here emphasizing on 20% that matters.


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Normal Clinical Ward (NC)

ALOS at the ward is 164

hours, median 113 hours, andCV is 1.07.

Group with LOS smaller than10 days has 81% of thepatients and consumes 47%of resources while group with

remaining 19% consumes53% of resources.

These numbers cannot be seen as constants as the processes have largely variable LOS.


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Impact of variation on capacity requirements

To demonstrate the effects we assume Poisson arrivals, exponentialservice times and an infinite number of beds.

The queuing system under investigation is referred to as M\M\ in

Kendalls notation.

The following parameters describe the queuing system:

= average arrival rate

= average length of stay

B(t) = number of patients in the system at time t or number of beds

occupied at time t

Following shows the relation between the expected number of

patients in the system, EB(t), and the average length of stay ()


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Multiple State Analysis

The probability distribution of the number of beds occupied at

the FCA is calculated with the use of a M\M\-model.

The average arrival rate ( = 7.78) is assumed to be constant overthe day. The ALOS () equals 6.4/24 = 0.27 days. Thus, theexpected number of beds occupied is 2.1.

The 24-hour period is divided in three intervals of each eighthours.


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The expected number of beds occupied increases from 2.1 to 3.4

(+ 62%). Flexible staffing levels are a possible answer to this

strong variation in workload.


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Modeling the Emergency Cardiac Care Chain

In the previous section we assumed an infinite number ofbeds. In this section capacity is limited.

Phenomena of blocking and economies of scale are

introduced. Both blocking (e.g. refused admissions) andeconomies of scale are important features of health care

processes.

An important model from queuing theory is the Erlang Lossmodel or M\M\c\c in Kendalls notation.


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In this model customers.

Patients arrive according to a Poisson process with

intensity (including refused)= lambda The LOS of arriving patients (independent and

exponentially distributed ) =.

The number of beds = c.

The fraction of patients which is blocked and sent away to other hospitalsin the long run (Pc) can be calculated with the Erlang Loss


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The occupancy rate is related to the real demand and LOS () and

can be defined as,

the product is known as the workload of the system.

In general the unit size varies between 6 and approximately 60

beds. The target occupancy rate 85%.

In order to demonstrate the relation between the size of a

hospital unit, the feasibility of the 85% target and the fraction of

refused admissions two calculations have been made.

1. The percentage of refused admissions (Pc) given an occupancyrate of 85% (2


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Larger hospital units can operate at higher occupancy rates than

smaller ones while attaining the same percentage of refused

admissions.

The 85% target is only attainable for units with more than 5

If we hold the 85% target for a small unit such as the CCU (6

beds) nearly half of all arriving patients is blocked, assuming Pc =

0.05 is acceptable.


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Results of the case study

The primary goal is to determine the optimal bed

allocation over the emergency cardiac care chain, given a

required service level.

The service level requirement is set at a maximum of 2%

refused admissions at the FCA.

In our model the service level requirement is rewritten

into a maximum of 5% blocking at the CCU.


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We varied the number of CCU beds from 5 to 15 and the

number of NC beds from 12 to 19.

The LOS at the CCU is corrected for the additional waiting

time (based on measurements).The additional waiting time

was 27% of the original length of stay.

The ALOS at the CCU now equals 44 0.27 * 44 = 44 -12 = 32hours (1.3 days).

The LOS at the NC is corrected for the additional time at the

CCU. Furthermore a LOS-reductionof 20% is assumed.

The ALOS at the NC now equals 0.80 * (164 + 12) = 141 hours

(5.9 days).


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In order to determine personnel costs for each bed

combination the following conversion rates are used:

2.2 fte (full time equivalent) per CCU bed 0.95 fte per NC bed

The cheapest combination within the solution

area is 8 CCU beds and 16 NC beds (32.8 fte).


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General results

A calculation based on average data, regarding the number

of arrivals and LOS, does not meet the actual capacityrequirements and will most certainly result in frequent

operational difficulties.

The length of stay (LOS) of patients in hospital is highly

variable (Cv>= 1) and congestion or chain effects influence

the average length of stay (ALOS).

The characteristics of arrival patterns and LOS distributions

result in large workload variations at nursing units.

The 85% target is only attainable for units with a minimum

of approximately 50 beds


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The variation in arrival rate at the FCA increases the

workload during office hours with 62%.

For a maximum of 2% refused admissions at the FCA a greatamount of reserve capacity is required at the CCU and NC.

The number of beds required at the NC and CCU is

respectively and 16. The occupancy rate for this optimal

situation is respectively 55% and 78%. For the CCU this

means 2 extra beds are required, a capacity expansion of2/6 = 33%.


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Modeling the Emergency Cardiac in-patient Flow