# Maths and Choppers from Norway to New South Wales

There are a bunch of ways to figure out where to put your resources. Dr Alan Garner found a guy who can crunch the big numbers to look at it a little differently.

What’s the answer for optimal locations? First ask what is the question.

We have just had a new study published in BMC Emergency Medicine on modelling techniques to determine optimal base locations for helicopter emergency medical services (HEMS).  There is always more to say than can be covered in a publication so I thought I might have a look at some of those issues here.

First up is a big thank you to my co-author Pieter van den Berg from the Rotterdam School of Management in the Netherlands.  Pieter is the real brain behind the study and the mathematician behind the advanced modelling techniques we utilised.  Pieter has looked at HEMS base location optimisation previously in Norway and has done some modelling for Russel McDonald’s service Ornge in Ontario, Canada as well.  Without him the study would not have been possible.

So what did we do and why?

As already noted Pieter had recently done a similar exercise in Norway where the government has a requirement that 90% of the population should be accessible by physician staffed ambulances within 45mins.  Pieter and his co-authors were able to demonstrate that the network of 12 HEMS bases easily accomplishes this – indeed it could be done with just four optimally positioned bases.  They also modelled adding and moving bases to determine if the coverage percentage could be optimised with some small adjustments.

As it happens New South Wales (NSW) and Norway have very similar population densities and both are developed, first world jurisdictions.  Hence this previous study seemed a good place to start for a similar exercise in NSW.  Both jurisdictions also have geographical challenges; Norway is long and thin with population concentrated at the southern end whereas NSW has almost all the population of the state along the eastern coastal fringe with high concentration along the Newcastle – Sydney – Wollongong axis.

We were interested in population coverage but we also wanted to look at response times as this also is a key performance indicator for EMS systems.  It is certainly reported as a key indicator by NSW Ambulance.  Response times were not modelled in the Norwegian system so we were interested in seeing how the optimum base locations varied depending on the question that was asked, particularly in a jurisdiction such as NSW where the population is so concentrated to a non-central part of the state.

If you look at the study you will note from Figure 1 the existing arrangements in NSW. You’ll be shocked to know these arrangements weren’t planned in advance with the aid of a Dutch maths guru. These things happen organically. Nevertheless it provides a reasonable balance of response times and coverage although the gap on the north coast is immediately evident.

If you start with a clean slate and optimally position bases for either population coverage or average response time, both models place bases to cover that part of the coast (see Figure 2).  Hardly surprising.  When we modelled to optimise the existing base structure by adding or moving one or two bases, the mid north coast was either first or second location chosen by either model too.

This seems an obvious outcome from even a glance at the population distribution and current coverage in Figure 1.  What is surprising is that the 2012 review of the HEMS system in NSW (not publically released) which utilised the same census data in demand modelling did not come to the same conclusion when two previous reviews in the 1990s and 2000s had recommended just such a change.  Certainly the Reform plan for helicopter services which was released the following year did not make any changes or additions to base locations leaving this significant gap still uncovered.

Wagga Wagga was the other location identified for a HEMS base in the 2004 review.  Interestingly it is favoured as the first relocated base when the existing structure is optimised for average response time by moving Canberra to this location.  But a Wagga Wagga base also was not mentioned in the reform plan.

When the green field modelling was done it is clear that the current NSW system mostly closely resembles the model optimised for average response time, rather than coverage.  The Wollongong base really justifies its location on this basis as it contributes to a better overall average response time.  Its population coverage falls entirely within the overlapping circles of the Sydney and Canberra bases so it makes no contribution here, at least if a 45min response time is used as the standard.

There was another aspect that interested us compared with Norway.  In Norway all aircraft have the same capability and this is also true for the recently tendered services in NSW.  The unusual feature in NSW though (unique to Australia although common in Europe in particular) is a dedicated urban prehospital service operating from a base near to the demographic centre of the largest population density – Sydney.  The performance characteristics of this service have been well described (by us, because I’m talking about the CareFlight service which I think does serve a useful function) previously and when it was operating with its own dispatch system was the fastest service of its kind in the world to our knowledge.

Like the Wollongong service it operates entirely within the population coverage circles of other bases, but it makes an enormous contribution to average response time.  When this rapid response urban service is added to the network of large multirole helicopters in NSW the average response time across the entire state falls by more than 3.5mins because that service is able to access more than 70% of the state population within its catchment zone, and significantly faster than the multirole machines.

This modelling only takes into account the response time benefit of the specialisation afforded by such as service.  We have previously been able to demonstrate that the service is also much faster in almost every other aspect of care delivering patients to the major trauma services in Sydney only a few minutes slower than the road paramedic system but with much higher rates of intervention and ultimately passage through the ED to CT scan faster than either the road paramedic or multirole retrieval systems in NSW.  At least this was the case when it had its own specialised dispatch system but that is a story we have discussed previously too.

There are recurrent themes here.  The Rapid Response Helicopter service adds significantly to the response capability in NSW whether you model it using advanced mathematical techniques or whether look at the actual response data compared with the alternative models of care.  Indeed the real data is much stronger than the modelling.  It seems that at least in large population centres in Australia there is a role for European style HEMS in parallel with the more traditional multirole Australian HEMS models that service the great distances of rural and remote Australia.  Different options can work alongside one another to strengthen the whole system and better deliver stuff that is good for patients – timely responses when they really need them. The capability differences however need to be reflected in dispatch systems that maximise the benefits which come with specialisation rather than a one size fits all tasking model that takes no account of those significant differences.

Every version of the numbers I look at tell the same story.

Notes and References:

While this post covers a few ways of looking at a tricky sort of problem, there are lots of clever people out there with insights into how these things work. If you have ideas or examples from your own area, drop into the comments and help people learn.

Now, the paper that’s just been published is this one:

Garner AA, van den Berg PL. Locating helicopter emergency medical service bases to optimise population coverage versus average response times. BMC Emerg Med. 2017;17:31.

The paper on optimal base locations in Norway is this one:

Røislien J, van den Berg PL, Lindner T, et al. Exploring optimal air ambulance base locations in Norway using advanced mathematical modelling. Injury Prevention. 2017;23:10-15.

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