modeling of head injuries facilities in london

8/13/2019 Modeling of Head Injuries Facilities in London

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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


INJURIES IN LONDON

INTRODUCTION


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


INJURIES IN LONDON

INTRODUCTION


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


INJURIES IN LONDON

INTRODUCTION


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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INJURIES IN LONDON

INTRODUCTION

RESULTS

PROBLEM FORMULATION

PROBLEM DESCRIPTION


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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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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.

modeling of head injuries facilities in london

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