Using the Spatial Learning Index to Evaluate Performance on the Water Maze

Abstract

The Morris Water Maze was developed in 1981, and quickly became the standard task for assessing spatial memory and spatial navigation. Twenty years ago, (Gallagher, Burwell, & Burchinal, 1993) reported new variables and measures, including a spatial learning index, that greatly enhanced the utility of the Morris Water Maze for assessing subtle differences in performance on the task. The learning index provided a single number that could be used to elucidate neurobiological measures of hippocampal dysfunction, for example correlation of learning performance with a biomarker of aging. In this review, as part of the commemoration of the 30th anniversary of Behavioral Neuroscience, we describe how the spatial learning index has contributed to the field of learning and memory, how it has advanced our understanding of normal and pathological cognitive aging, and how it has contributed to translation of findings into other species. Finally, we provide instruction into how the learning index can be extended to other tasks and datasets.

The Morris water maze task was described over three decades ago (R. G. Morris, Garrud, Rawlins, & O’Keefe, 1982; R. G. M. Morris, 1981) and revolutionized the way neuroscientists study navigation and hippocampal-dependent memory. The article under review (Gallagher et al., 1993) introduced a new measure, proximity to platform location, and a method for condensing a complex behavioral task into a single index of performance. This spatial learning index greatly facilitates within-group comparisons and correlations with neurobiological markers or other behavioral measures. Additionally, the 1993 study demonstrated that, similar to research in humans, the Long-Evans rat model displays wide variability in age-related cognitive decline. The proximity measure proved to be sensitive to subtle changes in behavior among aged individuals. In many studies, this sensitivity of the proximity measure allowed the separation of an aged subgroup characterized by cognitive decline from an aged subgroup that exhibited substantial sparing of cognitive function. The development of the spatial learning index was crucial for associating variability in cognitive function with mechanisms underlying the normal aging. Studies using this rodent model and the measures developed in the target article have contributed to a better understanding of age-related cognitive decline and continue to yield insights about the mechanisms that contribute to the maintainance of cognitive function in older age.

Originally, the Morris water maze was developed to take advantage of the innate spatial navigation and swimming abilities of rats. The task is conducted in a large tank filled with opaque water that has an escape platform concealed under water. In the spatial reference memory version, animals are placed in the tank in a different starting point for each trial, and have to use the spatial layout of the room to navigate to the platform that is kept in a constant location. Typically, normal young animals learn to swim to the platform more quickly over time, and reach behavioral asymptote over several trials. These learning trials, sometimes called training trials, can be spaced out over days or condensed into one day. Additionally, probe trials may be used at different time points during learning to assess the pattern of spatial memory acquisition. For these probe trials, the platform is made temporarily unavailable, and the search pattern of the animals is analyzed with respect to the position of the platform in previous learning trials. In recent years, taking advantage of developments in virtual machine software, some studies have adapted this task for use in human studies (Daugherty et al., 2014; Goodrich-Hunsaker, Livingstone, Skelton, & Hopkins, 2010; Sandstrom, Kaufman, & Huettel, 1998), greatly increasing the translation potential of the findings in rodents.

Measures for Evaluating Water Maze Performance

One of the first measures used to quantify behavior in the Morris water maze task was the latency to reach the hidden platform. While informative, this measure can vary for reasons unrelated to the learning ability of the animal. For example, different swimming speeds can lead to different latencies, even if the path taken is the same. To control for this possibility, the path length, a measure of the total distance navigated to reach the goal, was used along with latency. This measure, however, is still limited because some navigation strategies can lead to shorter path lengths despite lack of knowledge of the platform location. For example, a rat can learn that the platform is a certain distance from the wall of the maze, swim a circular path around the edge (thygmotaxis), and find the platform relatively efficiently, even if the animal has no representation of its location (see Figure 1 in the original publication).

Figure 1.

Examples of training trials and probe trials used for calculating measures based on proximity to the target platform location. Solid lines represent the path to the platform location. Dotted lines represent one second averages of the proximity of the rat to the platform location. A. Representation of an animal’s path to the platform on example trials early (left) and late right) in training. On the left, path length was 745 cm and latency was 27 seconds. Thus, proximity averaged for each second was summed to a cumulative search error of 2388 cm. On the right, path length was 220 cm and latency was 9 seconds. Thus, proximity averaged for each of the nine seconds was summed to a cumulative search error of 605 cm. Cumulative search error is sensitive to both latency and path accuracy. B. These two examples of 30 second probe trials, for which the platform is removed, illustrate the issues with the path length and platform crossing measures. The path shown on the right clearly exhibits a better knowledge of platform location, yet the path lengths are similar. The path on the left is 733 cm and crosses the platform once. The path on the right is 736 cm and does not cross the platform location. Average proximity (the mean of 30 one second averages) does distinguish performance; average proximity is 72.6 cm for the example on the left and 38.6 cm for the example on the right.

Other frequently used measures are based on the probe trials for which the submerged platform is not present. These include the relative time spent in the target quadrant (or zone around the platform) and number of platform location crossings. These measures are more representative of a targeted location search, but they suffer from lack of reliability. For example, two rats might spend the same time in the target quadrant, but one may search more closely to the actual location of the platform. Likewise, a rat may search in a tight circle very close to the platform location while failing to cross the location. Additionally, for these measures, there is insufficient within-group variability to provide the parametric space necessary for reliable correlation analysis with other behavioral or neurobiological markers.

To better characterize the search strategy the animal employs in learning trials, (Gallagher et al., 1993) introduced the proximity measure, a measure that relies on the ongoing assessment of the distance between the platform location and the animal. In the original paper, proximity was calculated ten times per second and a mean was taken every second. The dotted lines in Figure 1 represent the one-second mean proximity between the rat and the target platform location. From this measure two additional variables can be derived. In learning or training trials, a cumulative search error is calculated by summing the one-second proximity means for each second the rat is searching for the platform. Figure 1A illustrates how cumulative search error is computed from proximity in example trials early (left) and late (right) in learning. In these examples, the path length and latency are both greater for the early trial. Cumulative search error, the accumulation of one-second mean proximities represented by the dotted lines, provides a more sensitive measure of spatial memory, yielding 2388 cm for the early trial and 220 cm for the late trial. The distance between the entry point into the maze to the location of the platform is sometimes subtracted from the cumulative search error to normalize over different start locations.

The proximity measure is even more powerful in probe trials, in which the platform is removed, especially as compared to the time in quadrant and platform crossings measures (Maei, Zaslavsky, Teixeira, & Frankland, 2009). Figure 1B shows two examples of 30 second probe trials in which swimming speed and path length were comparable. In the trial on the left, the rat has adopted a strategy of swimming at a relatively fixed distance from the wall. The subject spent 10.6 seconds in the target quadrant and crossed the platform location one time. In the trial on the right, the rat is making a targeted search, spending 18.9 seconds in the target quadrant, but not actually crossing the platform location. Average proximity is much more sensitive for distinguishing the performances on these two example probe trials than time in quadrant or platform location crossings. In Figure 1B, again, each dotted line represents a one-second mean proximity to the goal for each second of the 30-second probe trial. When these thirty numbers are averaged to obtain the mean proximity, the left trial has an average proximity of 72.6 cm whereas the trial on the right is 38.6 cm. The sensitivity of these measures allows for better quantification of even small differences in behavior.

In an effort to compare the methods used to quantify water maze behavior in mouse model studies, Mael et al. (2009) performed a large scale comparison of the effectiveness of different measures. The data were control and experimental groups drawn from datasets from multiple pharmacological, genetic, and anatomical lesion studies. The measures compared were platform crossings, time in target quadrant, time in target zone, and proximity. Using Monte Carlo simulation experiments based on 1600 individual probe trials performed in the same conditions, this study shows that the proximity measure is better able to identify group differences than the other measures in all conditions tested. The conditions included different sample sizes, different effect sizes, and the use of parametric or non-parametric statistical analyses. This study provided strong evidence for that the proximity measure is more sensitive for detecting group differences that the more commonly used time in quadrant/zone and platform crossings. Therefore, the use of proximity measures can reduce the numbers of animals needed in experiments. With regard to mouse model studies, the measure can increase throughput of behavioral characterization facilities.

Indexing Spatial Memory in the Morris Water Maze

The proximity measures, in general, allowed for better quantification of the navigation ability of animals in the Morris water maze task. Relating performance on this task with other behaviors or with brain biomarkers was still difficult to do because the learning rate was described by repeated measures, and the asymptotic performance was often insensitive to individual or group differences. In the original article, (Gallagher et al., 1993) developed the learning index, an additional measure that can be used for the purpose of relating spatial learning ability with other behavioral or neurobiological measures. Rats were given three trials per day. Every other day, the third trial was a probe trial in which the platform was either removed or lowered to the bottom of the pool for the initial 30 seconds. In more recent protocols, the platform is raised to its original location after the initial 30 sec, thus preventing extinction learning and reinforcing earlier learning trials. By the fourth probe trial, the control group had reached asymptotic performance. The average proximity for the four probe trials were combined into the learning index. Importantly, each probe trial was weighted differently. The weightings were designed to enhance the contribution of early learning, so that better performance on earlier probe trials is reflected in a better learning index. Therefore, differences in scores on early probe trials have greater impact on the learning index than differences in the later probe trials, when it is more likely that all animals have learned the task. Generally, the procedure for calculating the weighting factors is based on performance of a cohort of control animals or on archival data. A detailed description of the methodology used to calculate the learning index for the water maze and other tasks is given in the section “Using a Learning Index for Other Learning Tasks” below.

Use of the New Measures in the Field

Since the publication of the target article, the measures developed by Gallagher and colleagues have been used in many studies to characterize water maze performance of both rats and mice. Particularly, in mutant and transgenic mouse models, cumulative search error and average proximity are now frequently used to assess hippocampal dependent memory, similar to how LTP and LTD are used to measure synaptic plasticity. For example, studies using the proximity measure established important roles for calcineurin (Malleret et al., 2001), EphB2(Grunwald et al., 2001), CREB (Pittenger et al., 2002), CamKIIalpha (Miller et al., 2002), and NF1 and Ras (Costa et al., 2002) in spatial memory. The proximity measure has also been used in water maze procedures in which only one probe trial is used. These studies have, for example, characterized changes in synaptic plasticity and place field properties in aged animals (Barnes, Suster, Shen, & McNaughton, 1997; Rosenzweig, Rao, McNaughton, & Barnes, 1997).

The learning index has also been used to assess hippocampal integrity, particularly in studies in which impairment is more subtle, for example, studies of cognitive aging. In an early study, the learning index was used to show that hippocampal neuron number does not predict age-related spatial memory impairment (Rapp & Gallagher, 1996). The index was also important in identifying features that positively contribute to the maintenance of cognitive abilities with aging, as is the case with the levels of hippocampal synaptophysin (Smith, Adams, Gallagher, Morrison, & Rapp, 2000). In addition, different types of hippocampal LTP and LTD are differently correlated with learning index in young and aged rat cohorts (Lee, Min, Gallagher, & Kirkwood, 2005; Yang et al., 2013). The distribution of N-methyl-D-aspartate (NMDA) receptor subunits is also altered in the hippocampus and prefrontal cortex of mice in a way that relates to spatial memory performance as assessed by the learning index (Magnusson, Scruggs, Zhao, & Hammersmark, 2007). The changes in glutamate receptor composition in aged animals may contribute to the physiological changes demonstrated by altered place cell properties (Barnes et al., 1997) that correlate with the learning index (Wilson et al., 2003). Additionally, subregional hippocampal decreases in the number of somatostatin and GAD-67 expressing interneurons are related to the impairment described by the learning index (Spiegel, Koh, Vogt, Rapp, & Gallagher, 2013). Finally, changes in epigenetic mechanisms are proposed to contribute to age-related memory impairments in mice (Peleg et al., 2010), but when related to a more precise cognitive measure like the learning index in rats, the results suggest a more nuanced contribution of epigenetic factors to age-related cognitive impairments (Castellano et al., 2012; Tomas Pereira et al., 2013).

The learning index can also be used to relate age-related changes in performance on the water maze task to performance in other behavioral assessments, whether hippocampal dependent or not. Predictably, tasks that depend on hippocampal integrity, like recognition memory tasks, show impairments that are correlated with spatial learning and the learning index (Robitsek, Fortin, Koh, Gallagher, & Eichenbaum, 2008). This study further demonstrates that the significant correlation is restricted to the hippocampal based recollection process, but not the familiarity component of recognition memory. Additionally, the learning index has been useful in comparisons between hippocampal impairment and declines in other cognitive domains. Whereas performance in an odor discrimination task is correlated with water maze performance (LaSarge et al., 2007), executive functions dependent on prefrontal cortical function, like reversal and set-shifting, seem to show deficits that are unrelated to the learning index (Beas, Setlow, & Bizon, 2013; Schoenbaum, Nugent, Saddoris, & Gallagher, 2002). Likewise, age-related changes in reaction time are not related to spatial learning in the water maze assessed by the learning index (Burwell & Gallagher, 1993). In summary, the learning index has been used in many studies characterizing the variability of the aging process and the mechanisms that may underlie successful cognitive aging, thus suggesting avenues of intervention that may reverse those deficits.

A great majority of the studies employing the learning index to characterize performance on the water maze task (only a few of which have been reviewed here) have focused on the study of aging populations. The learning index can, however, be used to compare discrete changes in behavior in other settings. For example, the learning index was used to demonstrate that rats with selective cholinergic basal forebrain lesions show similar spatial learning and navigation properties than their control counterparts (Baxter, Bucci, Gorman, Wiley, & Gallagher, 1995). Another study used the learning index to relate water maze performance of animals with perirhinal, postrhinal and entorhinal cortex lesions to other behavioral dimensions, such as contextual fear discrimination and passive avoidance (Burwell, Saddoris, Bucci, & Wiig, 2004).

Using a Learning Index for Other Learning Tasks

The ability to describe performance on a task with a single number is useful in behavioral neuroscience for reasons already described. Most learning variables, however, are collected over multiple time points. Mean performance or asymptotic performance can be used, but learning curves sometimes show that subjects often differ only in initial performance and rate of acquisition, such that mean or asymptotic performance obscures group differences. A learning index that incorporates rate of acquisition can be derived empirically from any repeated variable. In the case of Gallagher et al. (1993), the weights used in the learning index were derived from normative data collected over a large number of young rats. Many laboratories that consistently use a paradigm for multiple studies will have such normative control data. When normative data are not available, however, it is also possible to use the mean data from the control group in the study itself. Examples shown in Figure 2 are test data generated for two model experiments to illustrate how an index can be derived in a single study.

Figure 2.

Test datasets illustrating how a learning index can be derived for any repeated measure that changes with learning. A. A dataset of trials to criterion (TTC) on six discrimination problems was generated for a control group (CNTL, n=8) and two treatment groups (TMT1 and TMT2, n=8). In this test dataset, all groups show decreased TTC with each problem. TTC decreases more rapidly and is lower on the last problem for the control group. B. Learning indices were calculated for each subject using the multipliers shown in Table 1. Indices are lower for better learners. C. A dataset of percent accuracy (chance is 20%) on a learning task was generated for six blocks of four training trials, also for three groups (n=8 per group). D. Learning indices for the subjects in C, calculated using the multipliers shown in Table 2. Because the primary variable (accuracy) increases with learning, the indices are higher for better learners.

In the first example (Figure 2A), the test data are trials to criterion (TTC) for six discrimination problems. Like probe trial average proximity in the Morris water maze, TTC decreases with each problem. Such decreases in TTC might reflect the acquisition of a learning set that can be used for learning each discrimination more quickly. In this test dataset, there are three groups of subjects: the group with the best acquisition is the control group, and the other two groups might be two different treatment groups. The computation of the learning index was empirically derived from the control group and the mean control data was used to derive a set of weights, or multipliers, that favor rapid acquisition of the learning set. The multiplier for each problem was the quotient of the mean TTC in the control group for the first problem, and the mean TTC for that problem, yielding a set of six multipliers shown in Table 1. TTC of the control group on the first problem is used as the numerator because this number reflects performance prior to formation of a learning set. The learning index is calculated as:

$$\text{Learning}\text{Index}=\sum _{\mathrm{i}=1}^n(\text{Mi}\ast \text{Si})$$

in which M is the multiplier, S is the score, and n is the number of scores. Since there was no difference in performance among the groups on the first problem, and presumably no learning set had been formed, TTC on the first problem does not contribute to the learning index. Here, we substituted the first multiplier with zero. Figure 2B shows the indices for subjects in each group. The distribution of individual values is still reflective of overall group differences but, additionally, each value represents, in a single number, the learning dynamics over the course of several days of training for an individual animal. For the purposes of relating learning ability to other relevant parameters (behavioral or neurobiological), the learning index provides major advantages, including better characterization of within group differences.

Table 1.

Multipliers for learning indices in Figure 2A and 2B

Problem	TTC	Multiplier Formula	Multiplier Value
1	40.0	M1 = C1/C1	1.0*
2	21.1	M2 = C1/C2	1.9
3	15.1	M3 = C1/C3	2.6
4	11.0	M4 = C1/C4	3.6
5	10.4	M5 = C1/C5	3.8
6	9.6	M6 = C1/C6	4.2

Abbreviations: C, mean TTC; M, multiplier; 1–6, number of C or M. The muliplier is the mean TTC for the first problem for the control group (in which there is presumably no learning) divided by the mean TTC for that problem. The learning index is the sum of the products of TTC and the appropriate multipliers for all problems. These multipliers are used both for the control group and the treatment groups.

^*Note that the first score can be dropped because there were no group differences at this point. This can be accomplished by substituting zero for the multiplier.

The second example (Figure 2C) is based on a variable that increases with learning, in this case, percent accuracy on six blocks of four trials, in a task in which chance performance is 20%. Again, there are three groups of subjects – a control group and two treatment groups – and the computation of the learning index was empirically derived from the control group. In this case, since the number in the numerator should reflect a time point prior to any learning, accuracy for the control group on the first trial (instead of first block) was used. The multiplier for each block was the quotient of the mean accuracy of that block and the mean control accuracy on the first trial, yielding a set of six multipliers shown in Table 2. Contrary to the example shown in Figures 2A and 2B, there was learning in the first block, so the multiplier for the first block is included in the index. Again, individual and group differences are readily apparent (Figure 2D) and are readily available for comparison with other relevant individual measures.

Table 2.

Multipliers for learning indices in Figure 2C and 2D

Block	Accuracy	Multiplier Formula	Multiplier Value
1	28.8	M1 = T1/B1	0.62
2	58.0	M2 = T1/B2	0.31
3	69.8	M3 = T1/B3	0.25
4	78.8	M4 = T1/B4	0.23
5	79.9	M5 = T1/B5	0.22
6	81.5	M6 = T1/B6	0.21

Abbreviations: B, block; M, multiplier; T, trial; 1–6, number of B, M or T. For accuracy or any variable that is averaged across a block of trials or sessions, the numerator for the multiplier is the first trial (or first session), as presumably little learning has occurred. The denominator is the average accuracy for that block. Again, the learning index is the sum of the products of TTC and the appropriate multipliers for all problems and the multipliers are used both for the control group and the treatment groups.

Summary and Conclusion

The measures developed in the original article (Gallagher et al., 1993) to better quantify performance in the Morris water maze task included the cumulative search error during learning trials, the average proximity during probe trials, and the spatial learning index to quantify overall learning of the task across days. These measures have had a significant impact in the field, and have been instrumental in relating performance on this task with other behavioral measures and neurobiological markers. We propose that a learning index can be used in a variety of other tasks and provide a detailed account of how to construct an index with different task types and different patterns of acquisitions.