On the time course of short-term forgetting: a human experimental model for the sense of balance

The present findings clearly show that for a simple spatial orientation task (adjusting a luminous line in darkness so that it coincides with the perceived horizontal plane) the forgetting of a roll angular displacement is better represented by an exponential function than by a power function; the RMS was smaller for the exponential function in the vast majority of cases.

A simple exponential decay is usually defined by the formula y = Ae^−bt, where A is the initial value of y (at t = 0); the time constant T is defined as 1/b. As regards the SVH, there is often a small deviation from the true horizontal. In vestibularly healthy subjects, sitting upright in the static 1-g environment, this deviation is rarely greater than 2.5° but it appears to be a comparatively persistent individual characteristic (Tribukait 2006). At an increased G level in a centrifuge this static component (i.e. after decay of semicircular canal effects) of the SVH can be greater (Tribukait and Eiken 2006b), possibly because of asymmetries in the graviceptive systems. This must be taken into account when establishing the time course for the decline in the SVH tilt. Thus, when establishing the exponential time course for the decay of the SVH tilt, we use the function SVH = Ae^−bt + C, where C represents the asymptote. In several other memory tasks, where an amount of information is to be recalled, C < 0 is impossible and C > 0 would imply that a proportion of the initially presented information will remain in memory forever. On the present measurement scale, however, 0° (the horizontal plane of the gondola) does not represent an absolute limit. Rather, the individual asymptote C corresponds to zero in a task where an amount of information is to be recalled. Nevertheless, although the individual asymptote often differed notably from zero, the group mean did not. In addition, in no case did the initial value for the exponential function (A + C) exceed the magnitude of the roll tilt of the gondola (66° at 2.5G).

For the sake of comparability with respect to goodness of fit we have used an asymptote, C, also when fitting the power function. This asymptote tended to assume a negative value, often far beyond the physiological range (i.e. it would suggest a sensation of being rotated several revolutions in roll, which is clearly unreasonable in the present experimental situation). Since the power function goes to infinity as t approaches 0 from the right, we have restricted our attention to an interval ranging from 4 s to 360 s (i.e. the interval during which empirical data were obtained). Within this interval the power function gave reasonable values for all individuals. Nevertheless, even if its parameters were not constrained to what might be considered a physiological range, only in a few single cases did the power function provide a better fit (in terms of RMS error) to data than the exponential function.

In 1682, the physicist and inventor Robert Hooke presented a model of memory that implies a power function for decay (see Hintzman 2003, for an analysis). The systematic experimental study of human forgetting seems to have started 200 years later, namely with the investigations by Ebbinghaus (1885) on his own ability to remember lists of nonsense syllables. He measured the time necessary for re-learning lists at different time intervals—retention intervals—after first having learnt them. Naturally, re-learning a given list required less time than learning it at the first occasion. The time saved because of the first learning occasion decreased in a characteristic way with increasing retention intervals (ranging from 21 min to 31 days). Many attempts to mathematically characterize this “savings function” have been made (see Rubin and Wenzel 1996 or White 2001, for references).

Conceivably, the mathematical characteristics of forgetting might differ between memory systems. On the one hand, it seems reasonable that a very simple task, as that employed in the present study, will yield forgetting curves reflecting basic neural mechanisms. On the other hand, the forgetting of complex impressions might be optimized with respect to the odds that a given event will occur again in the natural environment (Anderson and Schooler 1991); an individual’s forgetting of a particular situation would, thus, not be merely a passive process—or a failure phenomenon—but adapted to the declining probability of encountering a similar situation again.

A common distinction is that between short-term and long-term memory. In 1973 Wickelgren suggested that this distinction could be made on the basis of the form of the retention function; he had observed that while the exponential function provided a good fit to certain data for retention intervals smaller than 20 s, for intervals ranging between 20 s and 2 years the power function was more adequate. However, in a later publication Wickelgren (1974) refuted the distinction in favour of his “single-trace fragility theory”, stating that the decay of a memory trace is determined by the passage of time as well as by interference according to the function m = λ(1 + βt)^−ψe^−πt. According to this view, the retention curve could be predominated either by the power-function characteristic of time decay or by the exponential-function characteristic of interference, the latter, according to Wickelgren, being the case in many short-term memory tasks.

Whereas the power function has since long possessed a certain status within psychology—in laws regarding the perception of stimulus intensity (Stevens 1970) as well as when it comes to the effects of training (several examples are given by Newell and Rosenbloom 1981)—Wickelgren is often quoted for having introduced it in the study of forgetting. In 1991 Wixted and Ebbesen presented three experiments which differed considerably not only with respect to the time scale but also as regards the nature of the task; in a delayed matching-to-sample task with pigeons the maximum retention interval was 6 s while in a face-recognition test with human test subjects the retention interval ranged between 1 h and 2 weeks. Strikingly, in all cases the power function provided a better fit to data than five alternatives, including the exponential function (see also Wixted and Ebbesen 1997). In the search for regularities and laws Rubin and Wenzel (1996) made adaptations of 105 different 2-parameter functions to 210 sets of forgetting data found in the literature. The power function and the exponential in the square root of time were among the four that could be satisfactorily fit to a wide range of data.

Several authors have pointed out that if there is a substantial inter-individual variability in the time constant for a truly exponential memory decay, then group data may nevertheless be best represented by a power function (Anderson 2001; Anderson and Tweney 1997; Murre and Chessa 2011). This observation has been made also in the study of learning. Heathcote et al. (2000) analyzed 40 data sets representing 475 subjects in 24 skill-acquisition experiments. In more than 80 % of individual cases the exponential function provided a better description of the time course for learning. However, averaging produced a bias in favour of the power function. In the present material, the individual RMS error was on average 31 % greater for the power function than for the exponential function; however, the difference in RMS was negligible if a single curve fit was made to all 921 data points. This confirms that averaging truly exponential forgetting curves may generate a power function.

According to Sikström (1999) forgetting in accordance with the power law would occur also within individuals if performance is dependent on multiple memory traces decaying exponentially with different time constants. Thus, on the perceptual or behavioural level exponential forgetting curves would most likely be encountered if the measured quantity corresponds to a basic percept, such as the subjective visual horizontal.

Rubin et al. (1999) have proposed six criteria that would define a data set useful for discriminating between mathematical functions. These are, briefly: (1) there should be nine or more retention intervals. (2) Time values should be precise. (3) The data set should have a large ratio of the most to least amount remembered and a large ratio of the longest to shortest retention intervals. (4) To make the time between presentation and testing unambiguous, each item should be presented only once. (5) The activity that fills the retention intervals should be constant. (6) To prevent generating a group function that is not applicable to individuals, retention functions should be fitted to data of individuals.

Although some of these criteria are perhaps not directly applicable to the stimulus and task of the present study, it might be noted that (1) all individuals made 15 or more settings of the luminous line during the 360-s recording interval, (2) for each setting there is a precise time value, (3) in all cases the ratio between the change in SVH during the recording interval and the RMS was large; the same holds true regarding the ratio between the time values for the last and first settings, (4) the nature of the task used in the present study is such that multiple measurements can be made after one single stimulus, (5) it might be assumed that any mental activity would not considerably influence a basic vestibular percept like the SVH, (6) curve fitting could be performed in every individual case.

Thus, also on the basis of such task-independent criteria it appears that the present methodology, i.e. using a simple visual indicator to quantify the perceptual effects of a vestibular stimulus, could serve as a tool in the study of short-term forgetting. If the decline of the SVH represents a more general mechanism for short-term memory, as could possibly be established by considering inter-individual variability and the degree of correlation across tasks, then the simplicity of the present test paradigm would be useful, for instance, when investigating how pharmacological substances influence short-term memory.

In the present study we have used a psychophysical method to record how a short-term memory for semicircular canal information is reflected in a simple visual percept. It is a point of the method that the SVH is not likely to be influenced by cognitive reasoning; the orientation of a line is among the basic properties of visual stimuli that are analysed in the primary visual cortex, V1 (Hubel and Wiesel 1977, Spillmann 2014). A large number of studies have elucidated the nature of a non-conscious system devoted to elementary attributes of visual objects or sceneries. This so-called perceptual representation system (Tulving and Schacter 1990) is located early in the cortical processing stream but beyond V1 (see Magnussen and Greenlee 1999, for a review). It is constituted by a number of independent mechanisms, each comprising a separate memory function, which process, in parallel, the different dimensions of visual impressions. A pioneering study on this system was performed by Hegelmaier (1852), who tested his own memory for the length of lines, i.e. a visual attribute, the retention of which is not likely to be influenced by verbal coding strategies. More recent works have investigated the short-term memory for spatial frequency (Magnussen et al. 1990), motion (Magnussen and Greenlee 1992), and—notably—orientation (Magnussen et al. 1998).

The perceived stability of the visual world during changes in roll head position is another phenomenon that seems likely to be attained via such unconscious processing. In humans, ocular counter-torsion—“external compensation” for head tilt—is only vestigial (i.e. it amounts to approximately 10 % of the head-tilt angle); our perception of the visual surroundings as upright also during head tilt with respect to gravity must therefore be dependent on a purely neural mechanism, sometimes denoted “internal compensation” (Bischof 1974; Petrov and Zenkin 1973). As to the localisation in the brain of such vestibular influence on visual perception one possibility is the parietal cortex (Andersen 1997; Bremmer et al. 2002), a region which has important functional connections with the hippocampus (Save et al. 2005).

When considering spatial memory phenomena and the sense of balance a brain region of particular interest is the hippocampal formation. It plays a key role both in spatial orientation (O’Keefe 1990) and in the formation and retrieval of memories, including the linkage of episodes to a spatial context (Burgess et al. 2002; Hayakawa et al. 2015; Kumaran and Maguire 2007; Ventriglia 2008; Wagatsuma and Yamaguchi 2007). The hippocampus receives input from many areas of the cerebral association cortex, e.g. the parietal cortex, whose integrity is significant for several spatial functions (for a review of experimental evidence, see Rolls 1996). The rodent hippocampus is well known for the so-called place cells, a set of neurons, each having its maximum firing rate when the animal is at a certain position in space (O’Keefe 1979). Also in monkeys, single cell recordings have revealed a variety of hippocampal neurons activated in conjunction with spatial stimuli or tasks (for a review, see Rolls 1996). A cell type common in primates is the “view cell”, i.e. pyramidal neurons whose activity is dependent on what part of the surroundings the monkey is looking at irrespectively of its own position (Rolls and O’Mara 1995; Killian et al. 2012; Rolls et al. 1997). It also appears that the firing of view cells is independent of the position of the eye with respect to the head (Georges-Francois et al. 1999). It has been convincingly argued that while the rodent hippocampus contains a map-like representation with neurons representing places where the rat can be, the corresponding system in the primate hippocampus would be devoted to visual exploration of the surroundings (Rolls 2006). Nevertheless, a functioning view-cell system must be dependent also on mechanisms for tracking the animal’s position and orientation with respect to the surroundings, i.e. on place cells and head direction cells (see below). Even if these cell types have been studied mainly for the horizontal plane it is tempting to postulate that similar neural mechanisms exist also for the roll (frontal) plane, e.g. when it comes to the ability to perceive the orientation of a line with respect to gravity.

Several lines of research indicate a certain relationship between the hippocampus and the sense of balance. It has even been proposed that the development of the hippocampus during evolution was to a high extent dependent on vestibular information about head movements and about the orientation of the head in the gravitational force field (Smith et al. 2009). More specifically, place cells in the rodent hippocampus can be modulated by vestibular stimulation (Gavrilov et al. 1995; Wiener et al. 1995). In monkeys, there are hippocampal neurons responding to passive whole-body angular displacements even in the absence of visual cues (O’Mara et al. 1994). In humans, stimulation of the semicircular canals by caloric irrigation causes an activation of the hippocampus, as revealed by means of fMRI (Vitte et al. 1996; Suzuki et al. 2001). Bilateral loss of vestibular function disrupts the activity of hippocampal place cells in rodents (Russell et al. 2003, Stackman et al. 2002); in humans it may result in a substantial reduction in the volume of the hippocampus (Brandt et al. 2005). Thus, although neural mechanisms of spatial orientation are difficult to study directly in human subjects, there are indirect evidences as to the significance of the hippocampus for vestibular phenomena also in humans.

A navigational system must also be capable of keeping track of the animal’s direction. Neurons whose firing rate is a function of the animal’s head direction in the plane of locomotion have been found in several regions of the mammalian brain. These so-called “head direction (HD) cells” are hierarchically organized in a circuit originating in the dorsal tegmental nucleus (Sharp et al. 2001b) and projecting serially via the lateral mammillary nucleus (Blair et al. 1998; Stackman and Taube 1998), anterodorsal thalamus (Taube 1995; Blair and Sharp 1995) and postsubiculum (Ranck 1984; Taube et al. 1990a) to the entorhinal cortex (Sargolini et al. 2006) the latter being a major link between the hippocampus and other regions of the brain (Hayakawa et al. 2015; Zhang et al. 2013). For detailed accounts on the head direction system, the reader should consult reviews by Hartley et al. (2013), Knierim and Hamilton (2011) or Taube (2007).

Head direction cells integrate multimodal information regarding the animal’s movements with respect to the surroundings. The functional integrity of the semicircular canals is critical for the HD system—for the mere generation of a stable HD signal as well as for its continuous updating during head movements. Thus, whereas the properties of HD cells are maintained in darkness, permanent inactivation of the semicircular canals leads to an irreversible disruption of the HD signal (Muir et al. 2004; Stackman and Taube 1997; Stackman et al. 2002). Nevertheless, visual input about external landmarks seems likely to be necessary to avoid the accumulation of errors in the HD system; rotation of a salient visual landmark can induce a corresponding shift in the head direction signal (Taube 1995; Taube et al. 1990b). Thus, the way of functioning of the head direction system reflects an intimate interaction between vision and the sense of balance.

The HD system is believed to constitute a continuous attractor network which can perform angular path integration, i.e. integrate the angular-velocity signal from the semicircular canals over time to obtain a measure of angular displacement (Barry and Burgess 2014; Clark and Taube 2012; Sharp et al. 2001a). A representation of angular head velocity is conveyed from the medial vestibular nucleus via the supragenual nucleus (Biazoli et al. 2006) and the nucleus prepositus hypoglossi (Lannou et al. 1984) to the dorsal tegmental nucleus (Brown et al. 2005) (For a review, see Yoder and Taube 2014). In models of this neural integrator, HD cells are interconnected in a circular arrangement, each cell firing maximally for a particular head direction. Neurons with similar preferred head directions have excitatory connections whereas cells which differ greatly in preferred direction inhibit each other. This principle for interconnections gives rise to a self-maintaining activation hill (the attractor state) which corresponds to the HD signal. At a given point in time, the firing pattern can only represent one single head direction, but, in case of a head turn, the system integrates the canal angular-velocity signal over time whereby the activity hill is smoothly moved to a new stable state (Barry and Burgess 2014; Clark and Taube 2012).

The HD system has several characteristics in common with the oculomotor neural integrator (Robinson 1989; see Taube and Bassett 2003, for an analysis). However, in oculomotor integrator neurons, whose firing rate is proportional to the deviation of the eye from its neutral position, there is a tendency to “leak”. In other words, when an animal is gazing in an eccentric direction in darkness, the eyes gradually return to their neutral position, and, in parallel, there is a decreasing firing in oculomotor integrator neurons. Considering the HD system as a ring attractor network, there seems to be no reason to assume that there would be such decay phenomena or any particular neutral direction. Nevertheless, it has been observed that upon removing external visual landmarks or extinguishing the light, the preferred direction of HD cells may drift during several minutes (Goodridge et al. 1998; Taube et al. 1990b). Further, during sensory conflicts, where vision and the sense of balance do not provide unanimous information, the preferred direction of a HD cell was often found to partially shift, its response being a compromise between the information from the two senses (Goodridge et al. 1998; Taube et al. 1990b).

The properties and organization of the HD system have been elucidated mainly via electrophysiological experiments on rats, but HD cells have been identified in several other species, including monkeys (Robertson et al. 1999; Rolls 2006). Studies using fMRI suggest that HD cells exist in the human medial parietal (Baumann and Mattingley 2010) and medial temporal (Vass and Epstein 2013) lobes.

Although the HD system has been investigated almost exclusively for the plane of navigation, it is reasonable to assume that memory processes for the roll (frontal) plane have a related neurophysiologic basis. In both cases it is a matter of semicircular canal information that must be integrated over time to yield an estimate of angular head displacement. Further, the shifts in a HD cell’s preferred direction observed during visuo-vestibular conflicts are reminiscent of the decay in the SVH tilt found during the otolith-semicircular canal conflict in the centrifuge. Finally, the changes in preferred direction of HD cells often occurred during several minutes (Goodridge et al. 1998; Taube et al. 1990b), which is compatible with the slow time course for the SVH observed in the present study.

Short-term memory phenomena are generally believed to depend on neuronal activation, or a change in action potential discharge, persisting after the presentation of a stimulus. Such so-called persistent neural activation has been observed in many areas of the cortex as well as in subcortical regions of the brain (see Curtis and Lee 2010 or Major and Tank 2004, for references). The mechanisms by which activity is maintained can, in principle, be intrinsic to individual neurons—as for instance when repeated brief stimuli result in a step-like depolarization via calcium influx at dendrites—as well as related to synaptic plasticity or neural network dynamics (for references, see Curtis and Lee 2010).

The above-mentioned hippocampal mechanisms for spatial orientation, as well as the role of the hippocampus in memory processes, makes it particularly relevant to consider this brain region when discussing the time constant for decay of the SVH tilt during gondola centrifugation. One mechanism that has been much studied in the hippocampus is the temporary increase in synaptic strength denoted short-term potentiation (STP). Anwyl et al. (1988) used in vitro slice preparations for studying STP in area CA1 pyramidal cells of the rodent hippocampus. In certain conditions the time constant for decay of STP was 60–80 s. More recently, it has been reported that interneurons in mice hippocampal slices are capable of performing a slow integration that causes action potential initiation in the distal axon (Sheffield et al. 2011). In these neurons repeated somatic current injections eventually triggered persistent firing, decaying with a time constant of 50–150 s. Thus, these cells were functioning like a leaky integrator. The phenomenon has been observed also in hippocampal slices from rats and it could be elicited with stimulus patterns recorded in vivo in an awake rat, suggesting that it was not an artefact of excessive spiking stimulation (Sheffield et al. 2011). Although these hippocampal decay phenomena have so far not been analyzed with respect to mathematical form (e.g. whether they proceed according to an exponential or a power function), they are both compatible with the time constant found in the present study (T = 85 s).

If the semicircular canal memory phenomenon concerned in the present paper were related to any of these mechanisms, then it would be of a somewhat more general interest regarding human hippocampal functioning, which is difficult to study directly in normal subjects. Possibly, the present test paradigm could be useful in the study of how the hippocampus is influenced by pharmacological substances. In a clinical perspective it should be noted that the roll inclination (swing out) of the gondola constitutes a tangible canal stimulus also for G levels considerably lower than 2.5G, making it feasible to test not only healthy subjects.