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MODELING OF
FACILITIES FOR
HEAD INJURIES
IN LONDON
- A CASE STUDY
PRESENTED BY:MOHSIN DALVI
M.TECH (INDL. ENGG.)
SEM 1
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INTRODUCTION
MODELING OF FACILITIES FOR HEAD
INJURIES IN LONDON
PROBLEM DESCRIPTION
CONCLUSIONS AND RECOMMENDATIONS
RESULTS
PROBLEM FORMULATION
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INTRODUCTION
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Throughout England and Wales, injury is the main
single cause of death and disability in both sexes in
15- 34 years age group and is the third most common
cause of deaths in all ages.
This study is part of a greater effort of the London
Severe Injury Working Group that is aiming to the
improvement of care, treatment and transfer of
severely injured patients in London
INTRODUCTION
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The aim is to position the minimum number of
trauma centers within a network of existing hospitals
and minimize the total traveling time of patients,
from the place of injury to the hospital of final
treatment in such a way that everyone in the entire
population of London can reach a trauma center
within acceptable time limits.
Location Set Covering Type of Problem.
INTRODUCTION
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Location problems have been attracting the attention
of academics and practitioners since 17 th century
when Fermat and Torricelli posed the Euclidean
minisum problem (given a set of existing points,locate a point X in a way that the sum of distances
from existing points to point X is minimized)
Since late 1950's, location problems began to beviewed in a mathematical programming and
optimization context.
INTRODUCTION
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INTRODUCTION
x1
x2
x3
x4
x5
x6
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PROBLEM DESCRIPTION
MODELING OF FACILITIES FOR HEAD
INJURIES IN LONDON
INTRODUCTION
CONCLUSIONS AND RECOMMENDATIONS
RESULTS
PROBLEM FORMULATION
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London has 26 hospital sites with full Accident and
Emergency Departments that can offer initial
treatment to severely injured patients.
Statistics show only one third of the patients are
transferred directly to a hospital that can provide
them with neurosurgical care.
The remaining patients after initial care are latertransferred to a hospital that has the facilities
required for their treatment.
PROBLEM DESCRIPTION
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PROBLEM DESCRIPTION
PATIENT TREATMENT
PROCESS FLOW CHART
SHOWING EXISTING
CONDITION
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The time spent before the patient receives the first
help and the inter-hospital transportation time are of
great risk and extremely critical for the survival and full
recovery of the severely injured patients.
The average time between injury and admission to the
proper hospital is approximately 4-6 hours.
PROBLEM DESCRIPTION
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The Royal College of Surgeons Commission on the
Provision of Surgical Services reports that above 30%
fatalities could have been prevented and were the
result of failure to stop bleeding and absence of, ordelay in surgical treatment.
PROBLEM DESCRIPTION
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In the United States trauma systems are well
developed since the 1980's, but are not so in Europe.
Current services in London are neither well located nor
well coordinated to provide the best care to patients.
The initial goal set was to improve the current
situation, but it had to be translated to criteria.
PROBLEM DESCRIPTION
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Three criteria were selected to improve accident
response system:
All patients should be able to reach a hospital with A&E
facilities within acceptable time limits.
The time patients have to travel to the hospital of their
final treatment should be minimized.
Cost should be reduced by minimizing the number of
hospitals that will retain their A&E Centres consideringthe political aspects of closing down the A&E Centres.
PROBLEM DESCRIPTION
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26 hospitals have been included in the analysis.
7 hospitals having neurosurgery facilities are called main
hospitals.
The remaining 19 hospitals that cannot treat traumapatients are called local hospitals.
Only head injured patients were considered in view ofthe fact that more than 50% of the severely injured
patients suffer from head injury and the relevant data
was available.
PROBLEM DESCRIPTION
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PROBLEM DESCRIPTION
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PROBLEM DESCRIPTION
PROPOSED PATIENT
TREATMENT PROCESS
FLOW CHART
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PROBLEM FORMULATION
MODELING OF FACILITIES FOR HEAD
INJURIES IN LONDON
INTRODUCTION
CONCLUSIONS AND RECOMMENDATIONS
RESULTS
PROBLEM DESCRIPTION
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PROBLEM FORMULATION
Observation sets:
M= set of main hospitals with neurosurgery facilities.
m= index referring to a main hospital.
L = set of local hospitals that cannot treat patients
suffering from severe head injury.
l= index referring to a local hospital.
R= set of regions in the city r= index referring to a region.
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PROBLEM FORMULATION
Time variables:
mtimer,m= time taken to travel from region rto main
hospital m.
ltimer,l= time taken to travel from region rto localhospital l.
c= time spent in lbefore they are transferred to m.
lmtimel,m= time taken to travel from local hospital ltomain hospital m.
Average speed of ambulance is assumed as 30km/h.
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PROBLEM FORMULATION
Binary variables:
loc_retl= 1 if lretains its trauma centre, else 0.
main_retm= 1 if mretains its trauma centre, else 0.
to_locr,l,m= 1 if patient from region rtravels to lfirst
and then to m, else 0.
to_mainr,m= 1 if patient from region rtravels to m
directly, else 0.Other variables:
patientsr= number of patients coming from region r.
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PROBLEM FORMULATION
Minimise objective function
[loc_retl+ main_retm] +
[(ltimer,l+ lmtimel,m+ c) * to_locr,l,m*patientsr] +[mtimer,m* to_mainr,m*patientsr]
Subject to constraints
to_locr,l,m loc_retl . . . . . (1)
[to_locr,l,m+to_mainr,m] main_retm . . . . . (2)
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PROBLEM FORMULATION
to_locr,l,m+to_mainr,m = 1 . . . . . (3)
ltimer,l* to_locr,l,m 20 . . . . . (4)
lmtimel,m
* to_locr,l,m
60 . . . . . (5)
mtimer,m* to_mainr,m 20 . . . . . (6)
where r R, l L, m M.
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PROBLEM FORMULATION
Two conflicting objectives:
Reduce hospitals thereby increasing travelling time
Reduce travelling time thereby increasing hospitals.
Minimising main_retmmeans closing down a traumaunit in main hospital - political ramifications.
No costs used in objective function - solving the
problem would give fiscally impractical solutions by
suggesting opening of new trauma centres to reduce
travelling times.
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PROBLEM FORMULATION
Decomposition of the problem will allow trading-off
the number of kept trauma centers at main hospitals
against the number of trauma centers at local
hospitals.
The modified algorithm is of an iterative type and
follows the following four steps:
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PROBLEM FORMULATION
STEP 1: Calculate minimum number of local hospitals
retaining their trauma centers if only one main
hospital maintains its trauma center.
Model MINLOCMinimise
loc_retl
subject to
main_retm= 1 . . . . . (7)
and constraints 1 to 6 from original problem.
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PROBLEM FORMULATION
STEP 2: Repeat the calculation for different number of
main hospitals (RHS value in constraint 7) ranging
from 2 to m.
is the minimum number of local hospitals obtained.
STEP 3: Identify the main and local hospitals that
should retain their trauma centers for one main
hospital and local hospitals in order to minimize the
total traveling time weighted by the number of
patients coming from each region.
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PROBLEM FORMULATION
Model MINTIME
Minimise
[(ltimer,l+ lmtimel,m+ c) * to_locr,l,m*patientsr] +[mtimer,m* to_mainr,m*patientsr]
subject to
loc_retl=
and constraints 1 to 7.
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PROBLEM FORMULATION
STEP 4: Repeat the calculation and determine the
main and local hospitals that should retain their
trauma centers for 2to mmain hospitals andlocal
hospitals
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RESULTS
MODELING OF FACILITIES FOR HEAD
INJURIES IN LONDON
INTRODUCTION
CONCLUSIONS AND RECOMMENDATIONS
PROBLEM FORMULATION
PROBLEM DESCRIPTION
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RESULTS
The results from the model MINLOC suggest that we
can achieve full coverage and satisfy all constraints if
we maintain at least 2 trauma centres in main
hospitals and 8 in local hospitals or for more than 2main hospitals retaining their trauma centers 7 local
should maintain theirs.
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RESULTS
The results from the model MINTIME give the specific
hospitals that should retain their trauma centers in
order to minimize the traveling time from the place of
the injury to the hospital of definitive care (weightedby the number of patients that come from each
region).
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RESULTS
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The six different scenarios have been compared.
Figure presents the average traveling time for
reaching a hospital for patients going directly to a
main hospital and going to a local hospital first.
RESULTS
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Since in medical emergencies time is an extremely
critical issue, an important aspect in comparing the
solutions is the number of patients that can go
directly to a main hospital for the different scenarios.
RESULTS
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CONCLUSIONS AND RECOMMENDATIONS
MODELING OF FACILITIES FOR HEAD
INJURIES IN LONDON
INTRODUCTION
RESULTS
PROBLEM FORMULATION
PROBLEM DESCRIPTION
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CONCLUSIONS AND RECOMMENDATIONS
In this paper, an alternative scheme of transferringseverely head injured patients to hospitals that can
offer neurosurgical care was investigated and proposed.
The specific configurations of the network of existing
hospitals that should retain their trauma centers so as
to minimize the traveling time of patients and the
number of trauma centers and achieve full coverage ofthe London population were identified.
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CONCLUSIONS AND RECOMMENDATIONS
The proposition has been included in the LondonSevere Injury Working Group report regarding the
modernization of trauma services in London [London
Severe Injury Working Group (2001)].
Moreover, the assumptions made in the problem
formulation, such as the exclusion of capacity and
workload constraints and the assumed best possible
cooperation between hospitals receiving severely
injured patients, became their recommendations in
order to improve the NHS (National Health System) of
London.
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THANK
YOU.