Can our emergency department crisis be averted with a shift to the left?

Focusing on the ‘patient dissociation curve’ and the median hour of discharge could solve the overcrowding in emergency departments, writes CAREFUL CEO Dr DJ Hamblin-Brown

Inpatients die more frequently when hospital emergency departments (ED) are overcrowded. Long stays undoubtedly cause excess deaths in the ED itself.

The Royal College of Emergency Medicine [full disclosure: I am a fellow] has argued this for years.

And the harrowing result of this, in the UK, has been brutally exposed this week by Channel 4.

We all know that overcrowding at the front of the hospital is caused by poor patient flow and bed availability inside the hospital.

We also know that this causes ambulances to queue outside the hospital; the entire system of care deteriorates when hospital flow fails.

This is the emergency department (A&E) crisis with which we are now becoming familiar, which is also the most visible part of the ‘winter crisis’.

At the time of writing in late June, this may seem a long way off. But it’s not, as the C4 documentary shows. We need to think about patient flow even while the sun shines.

This is my small contribution.

A detour via the magic of haemoglobin

But before we head, metaphorically, to the ward or the ED, let me take you on a quick detour via one of my favourite pieces of biological magic.

Below is a graph, familiar to anyone who has studied respiratory physiology. In my view, this may be key to understanding how we should measure and manage hospital flow.

Bear with me.

Let me briefly explain the magic. (If you’re already familiar with oxygen dissociation, feel free to skip to the next section).

Haemoglobin (Hb) – as I’m sure you know – is the red pigment of the blood, concentrated exclusively in the tiny red corpuscles that make up around 40% of our blood volume. The molecule has been beautifully crafted though millions of years of evolution to carry four molecules of oxygen (O2) from lungs to tissues. We can measure the percentage of the Hb molecules which have this full complement of four O2 molecules using clever lighting. This give us the common measure of oxygen saturation. It tells how much the Hb is ‘holding on’ to the O2.

The graph shows how this saturation varies with the amount of oxygen dissolved in the plasma in the blood which surrounds the red blood cells (measured in this case in a slightly old fashioned unit of mmHg).

The graph therefore shows how much the Hb ‘holds on’ to the O2 as the oxygen in the blood plasma varies.

The shape of this graph tells us four things:

  1. Hb grabs oxygen in the lungs
    Where there is plentiful oxygen dissolved in the blood – i.e. in the lungs and arteries – the haemoglobin hangs on to the oxygen like crazy, scooping up the O2 from the surrounding plasma (top right of the graph).
  2. Hb gives up its oxygen in the tissues
    Where there is little oxygen dissolved in the blood – i.e. in the tissues, where O2 is being consumed – the Hb dumps the O2 allowing it to dissolve out to where it’s needed (bottom left of the graph).
  3. The transition is sudden
    In the middle of the graph, there is a steep curve, not a straight line. This means there is a rapid transition between ‘hanging on’ and ‘letting go’ in the midpoint, around the time the blood enters the tissues, at the point in its journey when it’s going to be most needed.
  4. The transition changes according to circumstances
    Note that this shape changes – moves to the right or left – depending on conditions. The dotted lines either side of the main line indicate that the ‘falling off point’ can move under different circumstances.

All of this is controlled biochemically by tiny shifts in the shape of the haemoglobin protein as the red blood corpuscles move from the lungs to the tissues and as the circumstances of the individual change, such as during exercise or infection.

It is beautiful. A truly exquisite – magical – example of molecular evolution.

The power of S-shapes

What, you may ask, is the relevance to hospital and healthcare patient flow management? The answer is in studying the dramatic effect of the S-shape when the curve shifts left or right.

To demonstrate, let’s go back to the graph and trace a line vertically at a PO2 of 30mmHg on the horizontal axis and see what happens when the curve shifts left and right.

At the level of 30mmHg, the saturations are different in the left-hand curve (70%) compared to the right (20%) – as indicated by the top and bottom of the red line. This is because the ‘dropping off point’ – indicated by the green circles – moves from 35mmHg to 15mmHg on the horizontal axis.

In summary, a small shift in the position of the curve can have an outsized effect on what happens at a particular point in the middle of the graph.

The patient dissociation curve

Now let’s think about hospitals. Patient flow throughout the hospital – and, I would assert, across an entire local health system – is similarly affected by an S-shaped curve, which we can call the ‘patient dissociation curve’.

Instead of the stickiness of oxygen to haemoglobin, we can think of this as the stickiness of patients to their hospital beds.

If we take a hypothetical hospital and map the discharge time of a patient, across 24 hours against the percentage of discharges that have taken place in that day, we get a shape that looks remarkably similar.

This shows that:

  • Almost no one goes home before about 10am.
  • The bulk of patients leave between 10am and 5pm.
  • The midpoint – when exactly half the patients have gone home i.e. the median hour of discharge (MHD) – is about 3pm. This is the average time at which patients come ‘unstuck’ from their beds.

Now let’s superimpose another S-shaped curve on top of this.

Oh dear.

The number of available beds is fixed by the number of discharges. And because admissions tend to arrive in the middle of the day, by 12pm there are now wwaaaaayyy too many patients in the hospital – all queuing in the emergency department and in admissions units all over the hospital.

This problem is not confined to the UK (from where I am writing) or to socialised medicine. A hospital administrator in a private hospital in India told me recently that his hospital regularly runs at 140% capacity in the middle of the day.

The usual reason given for this state of affairs is that ‘there are no beds’.

But this is demonstrably not true. The total number of beds is largely fixed. The problem – as we know – is that many of them are housing patients who are well enough to go home.

Anyone working hard to discharge patients on a ward will recognise the paradox that, despite all the work on discharging patients as rapidly as possible, there are still no available beds.

Shifting the patient dissociation curve to the left

Let’s see what happens if we shift the discharge curve to the left?

Let’s say that we have 100 discharges during this 24 hours. (To be clear this is 100 discharges not 100 total beds). This creates a time-series map of the patients going home.

If the median hour of discharge moves from 1330 to 1000, just like in our haemoglobin example, there is an outsized difference at 12pm, when most unscheduled patients are arriving and needing beds.

In this example, by midday, instead of only 30, there are now 80 available beds.

Think about that.

By making a relatively small shift in the median hour of discharge, you can magically ‘create’ 50 beds in your hospital available at the most pressing time of day.

That doesn’t mean that every patient has to go home by 10am. No – only that half of your patients need to be gone by 10am.

Consider what that will do to the patient experience; to the safety of patients in the emergency department; to the impact on the ambulance service; to the stress on your junior nurses and doctors.

It would be transformational.

Measuring it right

This – you may say – is stating the bleedin’ obvious. Early discharge has been a mantra of patient flow for years ….

Of course, but thinking about this curve tells us what we should be measuring.

Are we measuring the right thing to get early discharges? I would hazard a guess that we are not.

When was the last time that anyone told you the median hour of discharge in your hospital?

In my experience, most hospitals concentrate on two key performance indicators (KPIs):

  1. Turnaround time (TAT)
    This is the time taken from ‘decision to discharge’ to ‘completion of discharge’. We believe that speeding up the discharge process will ensure that things will get better. Not necessarily. You can only bring forward the median hour of discharge to median hour of decision + average TAT. You can only shift the median hour of discharge by, perhaps, half your TAT. By sweating blood, you can get from 4 hours to 2 hours? By contrast, the median hour of decision can have a direct effect.

  2. Length of stay (LOS)
    We care about length of stay. A lot. Because it’s important to safety and outcomes and, we assume, to flow. But let’s break it down. LOS, measured in hours, is in three parts:
  • hours between admission and midnight on the first day
  • full days in a bed (x 24)
  • hours between midnight and discharge on the last day (MHD)

But … the first and last of these components will move in sync. Despite its outsized effect on bed availability, changes to the MHD will not change LOS because getting patients out the door quicker will mean they are admitted to beds earlier in the day.

Worse – it means that the corollary may also be true: reducing LOS will probably not improve bed availability. Shock.

I accept that if you reduce the overnight stays by one, then for every patient who stays one less night, you will increase the number of discharges available by 1. In our example, we go from 100 to 101 available beds. By any analysis, this is a second order effect without a large effect on bed availability, especially when compared to shifting the MHD to the left.

The true measure of flow performance, the true KEY performance indicator is median hour of discharge – MHD.

How do we shift that, then?

So, the question is: what will shift the MHD to the left?

The answer, which we mentioned earlier, is to shift the median hour of decision while either reducing the TAT or keeping it steady.

Here are some questions to think about:

  • How do we inform staff and patients about a planned discharge?
  • Who takes the decision?
  • Crucially: when is that decision made?
  • Could it be done earlier? The previous evening? During the night?
  • How do we communicate and coordinate this decision with people involved in the other parts of the discharge process: pharmacy, physio, social care, OT, transport, relatives?
  • How do we keep track of the tasks or actions that stand in the way of the actual discharge?

I should make mention of one way in which some hospitals approach this. They funnel patients into a ‘waiting room’ for discharges – often known as the ‘discharge lounge’. This seems like a good idea, but it can balloon into a waste of resources: you need space, people and then …. guess what? The lounge rapidly fills up and the queue jams up again. A discharge lounge of, say 10 chairs, will free up 10 beds (briefly). But it won’t make the dramatic high-order shift, freeing up 50% of your beds by midday, that an earlier actual discharge will make. It may sound obvious, but what counts is getting patients out the door, not storing them in another location.

The other way in which this problem is tackled is by ‘nurse-led’ or ‘criteria-led’ discharges. The main reason for this is to remove where possible the most senior doctor from the discharge process. The consultant is often seen as a ‘key decision maker’ but may also just be a ‘bottleneck’. Agreeing that patients can be discharged under certain criteria, without the specific agreement of the managing doctor, will allow more patients to be discharged in circumstances where that doctor is not available.

My own personal experience of interminable ward-rounds lasting from 8am until 3pm would support the thesis that leaving discharges in the hands of busy doctors can waste resources. But using criteria-led discharge does not solve the problem on its own. Those criteria need to be applied early enough in the day (or late enough in the previous day) and with a TAT can then deliver an MHD that works for the hospital.

My point here is not to negate the need for discharge lounges or criteria-led discharge, or indeed any of the other valuable and brilliant initiatives that are implemented throughout our health system.

It’s that this should all be done in service of moving the MHD.

But what about the crisis in social care?

One of the strong objections to this analysis is that hospitals are constrained by the problem of placing patients in downstream facilities.

If we can’t find a place for a patient in a specialised nursing facility, care home, step-down, community hospital … or discharge them home with a sufficiently robust ‘package of care’, then they will stay in the hospital.

I agree. The proportion of total beds that are taken up in this way can be as high as 1 in 3. Every day this happens, each patient will increase their LOS by 1 and reduce the number of potential discharges by 1.

But at a hospital level, this problem may be largely unsolvable.

The point about concentrating on the MHD is that this is a metric that is largely in the hands of the hospital and it has a non-linear effect.

Again, this argument does not negate the need to work on improving the availability of downstream facilities. It just means that, again, this should be done in service of the MHD.

In this analysis, it is better to work on the time that the patient leaves the hospital than whether they will be going home today or tomorrow.

This sounds counterintuitive, but it is at the heart of this argument about measuring and chasing the right measure – the MHD.

Give ‘em the tools …

The final piece of this puzzle, of course, concerns the problem of information. We all know that the larger electronic medical systems (EMRs) struggle to support staff with agility when processes change. It can take months to implement any modifications.

Staff need digital tools that actually help them by connecting teams and individuals together and which can, ideally, reach out into the community. The coordination necessary for rapid discharge is complex, which is why it’s so hard to solve. And most IT systems don’t actually support the process.

Because of this, most doctors and hospital managers use instant messaging systems to coordinate care. However, ‘off the shelf’ systems don’t really solve the problem because they are not designed to provide comms, task management and the presentation of important clinical information at the same time – all of which are necessary to make rapid, high-quality decisions.

The key here is to find and implement a system that is capable of doing this, providing the necessary functionality to make real-time clinical coordination possible.


So, as promised, that is my contribution to the discussion about how to solve the crisis in our emergency departments and in our hospitals and to save lives through better patient flow.

My suggested steps are:

  1. Concentrate on the median hour of discharge (MHD) as your key metric.
  2. Measure the median hour of decision and the turnaround time (TAT) to understand the two key components of this.
  3. Use discharge lounges, criteria-led discharges and social-care initiatives primarily in service of the MHD – not simply as means to increase the number of discharges on a particular day.
  4. Once you have a MHD that is early enough and can be maintained, only then shift focus to the initiatives that will increase the number of discharges per day. I’ll emphasise this again. Don’t concentrate initially on the number of discharges. Go for timing first, volume later.
  5. Support staff with the tools and IT systems that allow you to measure and implement changes to the MHD.