Proximity and path efficiency: measuring a search well

Opening

Picture a probe trial. The platform has been taken away, and a trained rat is searching for it. It heads straight for the right area, and spends the next half minute circling tightly around the spot where the platform used to be. Close, closer, just to one side, just to the other. But by chance, it never swims directly over the exact spot.

Now picture a second rat. It swims in a broad loop across the whole pool and, purely by luck, passes straight over the platform's old position twice.

Count platform crossings, and the second rat wins, two to nothing. But which one actually remembers where the platform was?

Measuring well

This episode is about measuring well. Once a rodent has swum in the water maze, a computer has a record of where it was, many times every second. What should we do with all those numbers? Over the past few decades, researchers have argued that some of the most obvious measures can mislead, and that measures based on distance and direction tell us much more. Let's find out why.

The classic measures

Start with the classic measures. In training trials, the oldest is latency, the time taken to reach the platform. It's easy to measure, even with a stopwatch, and it falls as animals learn.

But latency depends on how fast the animal swims. A slow swimmer takes longer to cover the same route. So many researchers prefer path length, the distance swum to reach the platform. As a widely used protocol from 2006 puts it, path length has the advantage of being immune to swimming speed.

In probe trials, the classics are the time spent in the target quadrant, and the number of times the animal crosses the exact spot where the platform was. Both are useful. But both have weak points, as our opening example showed. A quadrant is a big slice of the pool, a quarter of it, and an animal can spend a lot of time in it without being anywhere near the right spot. A crossing, on the other hand, is all or nothing. Miss by a whisker, and it doesn't count.

Proximity

The answer to both problems is to measure distance continuously. That idea is closely associated with Michela Gallagher and her colleagues Rebecca Burwell and Margaret Burchinal, at the University of North Carolina at Chapel Hill.

In 1993, they published a paper in Behavioral Neuroscience about the severity of spatial learning impairment in ageing. They noted that the water maze was designed to test a rat's ability to navigate to a specific location in a relatively large space. Why not measure, directly, how close the rat stays to that location?

Their basic new measure used computer tracking to identify the rat's position relative to the target, throughout the trial. In other words, at each moment, how far is the animal from the goal? Average those distances, and you get proximity. A low average means the animal searched close to the goal. A high average means it was far away.

Go back to our two rats. In a pool around two metres across, imagine the first rat averaging about thirty centimetres from the old platform position over the trial. The second, looping around the whole pool, might average eighty centimetres or more. Proximity ranks them correctly, even though the crossings count got it backwards.

This proximity measure turned out to be highly sensitive to age-related impairment, when comparing young and aged male Long-Evans rats. It captured differences that other measures missed.

The team went a step further. They developed a learning index, a single continuous number describing how impaired an individual animal was. The point of that was to study individual differences. Not every old rat declines in the same way. Some old rats perform almost as well as young ones, while others are badly impaired. A graded score for each animal makes it possible to correlate memory with other measures, for example changes in the brain.

That's why ageing research pushed this kind of measurement forward. If you want to know why some older animals keep their memory and others lose it, you need more than a pass or fail. You need a scale fine enough to rank every animal, so that differences in the brain can be lined up against differences in behaviour. A stopwatch, or a simple count of crossings, can't do that well.

Does proximity perform better?

So, does proximity really perform better? A large analysis from 2009, which we covered in our episode on the probe trial, put it to the test. Hamid Maei, Paul Frankland and colleagues in Toronto compared four probe measures using more than sixteen hundred mouse probe tests. Mean proximity to the former platform location consistently outperformed time in a zone, time in a quadrant, and platform crossings in its ability to detect real differences between groups.

The 2006 protocol points the same way. Its authors wrote that average distance to the target site, time or distance in the target quadrant, and first bearing provide more robust measures of memory than exact site crossings. They also described cumulative distance from the platform, which many tracking programs calculate by measuring distance every second or so, as one of the better measures of spatial learning ability.

Direction and path efficiency

Distance is one dimension. Direction is another. First bearing measures the animal's swim angle at the start of a trial, compared with a straight line from the start to the goal. A well-trained animal sets off pointing towards the platform. A lost one sets off in any direction.

The 2006 authors noticed something interesting about this. In their data, latency, path length and cumulative distance were all highly correlated with each other. That makes sense, since they all reflect performance across the whole trial. First bearing was much less correlated with the others. It's a snapshot of a single moment, the start. So it adds information the other measures don't.

There's also path efficiency, which compares the path the animal actually took with the most direct route. Expressed as direct distance divided by actual distance, a perfect, straight swim scores one, and a long, wandering path scores close to zero. Some software gives the ratio the other way up, so a higher number means a longer detour. Path efficiency doesn't depend on swim speed, and because it's a ratio, it allows fair comparison between trials with different start points.

Heading error is a related idea, the angle between the direction the animal is swimming and the ideal direction to the goal. Specialist analysis software also uses corridor and cone tests, checking whether the path stays within a narrow band or a widening cone aimed at the goal, adjusted for different distances.

Why the measures matter

Why does all this matter? Because the measures shape the conclusions. A study using only latency might report that a treatment has no effect, when a proximity measure would reveal a clear difference. And sample sizes matter. The Toronto analysis showed that a more sensitive measure lets a study detect real differences with fewer animals, which is both good science and good for animal welfare.

Proximity measures also help in a subtle way. The platform isn't always in the middle of a quadrant. If it's near a quadrant boundary, the quadrant measure can give an odd picture. Distance to the platform doesn't care about boundaries.

Time also matters within a trial. Behaviour in the first fifteen seconds of a probe is often different from behaviour in the last fifteen, once the animal has checked the spot and found nothing. Splitting the trial into segments, and calculating proximity for each, keeps that early signal from being diluted.

The limits

Of course, these measures have limits too. Proximity tells you how close an animal searched on average, but not how it got there. An animal swimming in a tight circle around the pool's centre might score a moderate proximity for every platform position, without knowing where any of them are. That's why distance measures work best alongside strategy analysis.

Different tracking systems also calculate these measures in slightly different ways, sampling at different rates or excluding the start of the trial. Results are most meaningful when methods are clearly reported. A proximity score from one lab isn't automatically comparable with a score from another, unless both describe how it was calculated, over what part of the trial, and in what size of pool.

And no measure fixes a poorly designed experiment. If the room lacks clear cues, if animals are anxious, or if swim speed differs between groups, then even the best measure needs careful interpretation.

Back to the two rats

Back to those two rats in the probe trial. One circled tightly round the right spot without ever touching it. The other wandered and got lucky. Count crossings, and you'd get the wrong answer. Measure distance, and the first rat's memory is obvious. The water maze hasn't changed much in four decades, but the way we read it has, and that makes all the difference.

You'll find the papers we mentioned, and a transcript, at water-maze.com.