Human saccadic eye movements

• John Findlay, University of Durham, UK

• Robin Walker, Department of Psychology, Royal Holloway, University of London. UK

Figure 1: This figure shows a 'scan path' - the patterns of saccades and fixations made when viewing a picture of a face for 3 minutes. (From Yarbus 1967, Fig 115).

Saccade refers to a rapid jerk-like movement of the eyeball which subserves vision by redirecting the visual axis to a new location.

Saccadic Eye Movements

The ability to look at things is a familiar part of the process of seeing. Looking is achieved by orienting the eyes, that is to say directing their visual axes to point to a new location. Large orienting movements involve co-ordinated action of the eyes, head and body, but smaller movements, such as those made when looking at a picture (See Figure 1) are made with the eyes alone (Yarbus, 1967). The brain commands sent to the eye muscles result in the eyes making a rapid step-like rotation following which the eyes remain stationary at their new position. These step movements are known as saccades or saccadic eye movements. Saccades direct the fovea onto an object or region of interest which enables subsequent high-acuity detailed visual analysis at that location. In normal viewing, several saccades are made each second and their destinations are selected by cognitive brain process without any awareness being involved. Vision is dependent upon the information taken in during fixation pauses between saccades: no useful visual information is taken in while the eyes are making a saccadic movement.

A considerable amount has been learned about the control of saccades by studying in detail the simple situation in which an observer is asked to move their eyes to orient to a newly appearing target. It is possible to measure the time elapsing between the appearance of the target and the initiation of the orienting saccade. The term saccadic latency is used to refer to this time delay (units milliseconds). It is also possible to measure accurately the saccadic metrics, that is the size and direction of the orienting step, using an angular measure to describe the rotation of the eyeball (units degrees visual angle). Finally, it is possible to measure the detailed progression of the movement itself, the trajectory made between these points.

Saccades are stereotyped and ballistic

To a surprisingly good approximation, every saccade made shows a similar pattern. Saccadic duration increases in a non-linear manner as the amplitude (size) of the saccade increases, from about 20ms for the smallest movements to over 100ms for the largest possible ones. The velocity with which the eyes move shows a corresponding increase in a similarly stereotyped way, with the maximum velocity increasing from around 10 deg/sec for small microsaccades to over 300 deg/sec for large saccadic movements. The term 'main sequence' has been appropriated from astrophysics to describe these regularities (Bahill, Clark, & Stark, 1975). The trajectory taken by the eye rotation is similarly stereotyped although subject to interesting sources of variability.

Figure 2: This figure shows the relationship between saccade peak velocity (deg/sec) and magnitude (or amplitude) in degrees of visual angle. From Bahill, Clark, Stark, (1975).

This stereotypy applies not just to saccades made in orienting situations but applies under all circumstances in which saccades are made. Systematic small deviations have been found, for example saccades made in the dark are slightly slower than those made in the light (and see section 'Trajectory modulation').

A ballistic movement is one whose destination is pre-determined at the outset. Saccadic eye movements are found to have this nature. New visual information can only influence a saccade if it occurs 70ms or more before its initiation (see section 'The double-step paradigm'). However, the trajectories of saccades show slight curvature homing in on the target location. This shows that an internal reference signal is used to make small on-line corrections during the generation process (Quaia, Lefévre, & Optican, 1999).

It is frequently found that a saccade is followed by a second smaller corrective saccade that brings the eye closer to the target. Corrective saccades typically occur after a very short delay (inter-saccadic interval - ISI). These short ISI’s between saccades have been taken as evidence for the parallel programming of the secondary response (Walker & McSorley, 2006). Corrective saccades can occur even if the target is made to disappear before the eye reaches it. However, they are more likely when the target remains visible. Similar small saccades, presumed to be corrective, are found during reading and other visual tasks (See Eye movements). Corrective saccades are frequent because saccadic accuracy is only moderate – 5%-10% of the saccade amplitude (Kowler & Blaser, 1995). However adaptive mechanisms operate over multiple movements to maintain long-term calibration in the saccadic system (Deubel, 1999).

Classification of saccadic eye movements

Reflexive and Voluntary saccades

Orienting to a newly appearing target by means of a saccadic eye movement is a very natural response. A saccade made to a target that appears eccentric to the point of fixation is sometimes called a ‘reflexive’ (or ‘stimulus-elicited’) saccade in contrast with those made in situations that depend more heavily on voluntary (or ‘endogenous’) cognitive control processes (for example when directed by a simple instruction “look to the left”). The broad classification into stimulus-elicited and voluntary saccades is supported by the differences in the basic behavioural characteristics of these two types of movement (Walker, Walker, Husain, & Kennard, 2000). In a strict sense, however, all saccades are essentially voluntary in nature as an observer can always decide not to move the eyes. Also if the time and place of a target’s appearance can be predicted, an anticipatory saccade often occurs before the target itself appears, or too briefly subsequently for visual guidance to have occurred.

In everyday vision, the eyes are frequently very active, making several scanning saccades each second. In the laboratory, several paradigms have developed to allow the study of voluntary saccades while retaining the advantages of using a well-defined target which appears in the periphery. These include delayed saccades, memory-guided saccades and anti-saccades. Finally, even when the eye is held in a fixed position for a long period, for example by instructions to maintain fixation, it is found that some very small movements occur, including small step movements known as microsaccades.

Delayed saccades and memory-guided saccades

In this situation participants are instructed to make a saccade to a peripherally presented stimulus, but following a delay period (typically lasting some seconds), often signalled by the offset of a central fixation point. The delayed saccade paradigm therefore involves the ability to suppress making a response and has been used to investigate the underlying deficits in conditions that involve a deficit of inhibitory processes involved in the flexible control of behaviour such as Parkinson’s disease and schizophrenia (Hutton, Joyce, Barnes, & Kennard, 2002; Lueck, Tanyeri, Crawford, Henderson, & Kennard, 1992)

The memory-guided saccade is similar but in this case the target is only flashed briefly so that saccades are directed to a remembered location. Such saccades tend to show a decrease in accuracy in normal individuals and especially in patients with damage to the basal ganglia and regions of the frontal lobe involved in processes of working memory.

Anti-saccades

The anti-saccade task was introduced by Hallett (Hallett, 1978; Hallett & Adams, 1980) and has since become one of the most widely used endogenous saccade paradigms (Munoz & Everling, 2004). An anti-saccade is a response directed away from a peripheral target - to the opposite (mirror image) location. Anti-saccades require the suppression of a response to the target and the voluntary control over saccade direction to make the response in the opposite direction. Anti-saccades have longer latency (around 250-350ms) than saccades made towards a target (mean around 150-250ms) and on a proportion of trials errors (termed ‘pro-saccade errors’) are observed in which the observer fails to suppress making a response towards the target. In normal human participants pro-saccade errors are quite frequent (typically 10-20% of trials), although there can be large individual differences in error rates and they decrease with practice (Evdokimidis et al., 2002). Damage to regions of the frontal cortex dramatically increases error rates (Guitton, Buchtel, & Douglas, 1985; Walker, Husain, Hodgson, Harrison, & Kennard, 1998).

Microsaccades

Although we may assume that our eyes are not moving when we fixate an object, in fact they are in continual small-scale motion, showing irregular drift and tremor, interspersed by miniature saccadic movements (less than 0.5 deg). These fixational eye movements are essential to prevent our visual percept from fading (Martinez-Conde, Macknik, & Hubel, 2004). Microsaccades occur at a rate (mean frequency) of typically around 1 per second. although their rate can be varied with instructions and they are suppressed for short periods in a variety of situations (Rolfs, 2009).

Saccade Latency

The average latency with which a saccade is made in the orienting situation varies considerably from individual to individual and from trial to trial for any particular observer. However a typical latency is around 200ms (Carpenter, 1988). This figure is surprisingly long for a reflex-like response, contrasting with under 20ms for the time taken to initiate an eye-blink response to an air-puff.

There is of course variability in individual latencies and some saccadic latencies can be extremely short (80-100 ms). Saccades with such short latencies were first noted in monkeys by Fischer and Boch (1983), who revealed a bimodal distribution of latency with a first population of short latency (80-120ms) that they termed 'express' saccades and a second, later, population (120-200ms) termed 'fast regular' saccades (Figure 3). Such early saccades are also found in humans although individuals vary in the extent to which they will show separate populations of express saccades and regular saccades (Kingstone & Klein, 1993; Wenban-Smith & Findlay, 1991). Express saccades occur more often in the gap situation (see below), with predictable targets and after extensive training. The production of express saccades can be linked to the detailed properties of neurons in the superior colliculus (Dorris & Munoz, 1995), an important brain centre for saccade generation (Neural substrates of eye movements).

Figure 3: Populations of 'express' and 'fast regular' saccades. Adapted from Fischer and Ramsperger, 1984

The Gap Effect

Saslow (Saslow, 1967) first reported an important result showing that latency could be substantially affected by visual events at the start location for the eye movement. He recorded latencies in the standard situation of orienting from an initial fixation point to a newly appearing target. However, he arranged that the fixation point would disappear around the time that the target appeared but varied the exact time relationship so that it was not always synchronous. If the fixation point disappeared shortly before the target appeared, leaving a gap, latencies were shorter than when these events occurred at the same time. If the fixation point remained on, known as overlap, latencies were still longer. This latency change has become known as the gap effect. It occurs whether or not the target position is known in advance

Subsequent detailed investigation of the gap effect has shown that there are two effects of the fixation point disappearance. First the offset of a foveal visual signal directly reduces the fixation-maintaining process (and a neurophysiological correlate has been demonstrated). Second, the disappearance acts like a warning signal to allow the exact time of the target onset to be predicted (Reuter-Lorenz, Oonk, Barnes, & Hughes, 1995)

The Remote Distractor Effect

The remote distractor effect is a related automatic effect on saccadic latencies found when a visual onset occurs elsewhere in the visual field simultaneously with the appearance of a saccade target (Walker, Deubel, Schneider, & Findlay, 1997 Figure 4). Such an occurrence results in a prolongation of saccadic latency whether or not the location of the target is completely predictable. The timing of the distractor onset has been shown to modulate the magnitude of the RDE with distractors presented within ±50ms of the target producing the greatest effect. Although first noted with onsets in the opposite hemifield to the target, the effect is also found with distractors in the same hemifield, provided they are outside a sector-shaped region about 20 degrees each side of the target axis. Distractors inside this sector do not result in the saccadic latency increase found with more remote distractors, but instead affect the saccadic landing position in a similar manner to the global effect. The remote distractor effect has greatest magnitude for distractors at the fovea, with the size of the latency increase decreasing in a very systematic manner at more eccentric locations. Importantly, the magnitude is dependent on the distance of the distractor from the fovea, not from the target. This relationship suggests that the effect operates through the fixation-maintaining process.

Figure 4: This figure shows mean saccade latency (n=5) for saccades made to single targets at 4 and 8 deg (dashed lines) and those made when a distractor appeared at fixation (D0), or 2, 4, 8 and 16 deg in the opposite visual field. The smaller plot shows the mean increase in latency observed on distractor trials the remote distractor effect After: Walker et al. (1997)

Saccadic Inhibition

Studies of eye movements in continuous tasks, such as reading (Reingold & Stampe, 2002) have shown that a task-irrelevant visual transient (for example a flash of a portion of the computer display) can interfere with the production of scanning saccades. There is an absence or near-absence of saccades initiated around 80-120ms following the transient. This inhibitory effect (termed saccadic inhibition, or SI) is also observed in simple saccade experiments using small visual targets and it has been suggested that SI may be similar to, or underlie, the remote distractor effect (Buonocore & McIntosh, 2008; Reingold & Stampe, 2002).

Saccadic Metrics

The double-step paradigm

In the double-step paradigm, an observer is asked to follow with their eyes a target which jumps to a new location and a short time later makes a second jump to a further different location. Usually trials with such a sequence are intermingled with control, single-jump, trials. If the inter-jump interval is long, then two successive saccades are made to the first and second target locations respectively. If, on the other hand, the inter-jump interval is very short, a single saccade occurs to the second location, ignoring the first jump entirely. With intermediate durations of the interval, a third outcome is found under some conditions and is particularly evident when the two target locations are both on the same axis away from the initial fixation point. Two saccades are made but the first one is not directed accurately to the first target, but rather falls at an intermediate location between the two target locations. Becker and Jürgens (Becker & Jürgens, 1979) showed that the outcome was determined in a lawful manner by the interval between the occurrence of the second step and that of the initiation of the first saccade. If this interval is shorter than about 70 ms, the first saccade is directed accurately at the first target location. For longer intervals, the first saccade is directed at an intermediate location between the targets. As the interval increases, an amplitude transition function is found, with the first saccade landing progressively closer to the second target location. When the interval is longer than about 250 ms, a single saccade lands at the second target location.

Global effect: The double-target paradigm

Saccades landing at an intermediate locations are also commonly found when an orienting response is made to target consisting of two or more separated elements (Deubel, Wolf, & Hauske, 1984; Findlay, 1982). The saccade landing point is influenced by low-level stimulus manipulations – such as the size, luminance, or spatial frequency of the elements, which suggests it arises from within the visual pathway. The term 'centre-of-gravity effect,' or 'global effect,' describes this tendency. The effect is also found with saccades in free-scanning situations (Findlay & Brown, 2006; Vitu, 1991), although it is possible, when required, to make an accurate scanning saccade and ignore a neighbouring distractor (Findlay & Blythe, 2009). The global effect appears to represent a default option for the saccadic system although it can be modulated by higher-level cognitive strategies.

Trajectory modulation

Saccadic trajectories are also influenced by the appearance of a task-irrelevant distractor which occurs at the same time as the target. In a series of studies designed to test their premotor theory Sheliga and Rizzolatti examined the effects of orienting attention covertly (away from central fixation) on the path of vertical saccades (Sheliga, Riggio, & Rizzolatti, 1994). They found that saccades deviated away from the attended location which was taken as adding further support to the view that shifts of covert attention involve the preparation to make a saccade to that location. Subsequent work has shown that saccades deviate also away from a task-irrelevant distractor, without the requirement to shift attention covertly (Doyle & Walker, 2001 Figure 5) and that similar deviations can be observed with distractors from other modalities (Doyle & Walker, 2002). The direction of trajectory deviation, towards or away from a distractor, has been found to depend on saccade latency - short latency saccades tend to deviate towards a distractor, while longer latency saccades deviate away from the distractor (McSorley, Haggard, & Walker, 2006). Explanations of saccade trajectory effects focus on competitive interactions between separate populations of activity representing the target the distractor in the visuomotor map involved in encoding the saccade vector (For a review see: Walker & McSorley, 2008) [1]).

Figure 5: The trajectories of vertical saccades showing deviation away from a distractor onset in the upper left box. Modified from Doyle and Walker, (2001)

Binocular saccades

The two eyes are yoked and a saccadic movement in one eye is invariably accompanied by a saccade in the same direction in the other eye. Such same-directed movements are termed conjugate, in contrast to disjunctive, or vergence movements when the two eyes move in opposite directions. Vergence movements are much slower than saccades, typically under 20 deg/sec. When the eyes move between locations in different depth planes, the saccades may have different magnitudes in each eye (Collewijn, Erkelens, & Steinman, 1997; Enright, 1984). Such saccadic disconjugacy enables efficient scanning of everyday scenes where objects are located at different distances from the observer.

Parallel processes are involved in saccade generation

As noted in the section on the gap effect, part of the processes involved in the programming of a saccadic eye movement can take place without knowledge of the movement’s goal. This has led to the view that separable parallel WHEN and WHERE mechanisms can be considered to control the saccade timing and saccade spatial processes respectively, for example in the model of (Findlay & Walker, 1999), which was partly inspired by known brain processes (Munoz & Wurtz, 1992, 1993a, 1993b, 1995). Another finding supported by physiological studies is that two competing processes are involved in the triggering of saccades (the WHEN signal). One process promotes movement, resulting from the appearance of the target, and acts in competition with a second process acting to maintain the eyes in their existing position. Neural correlates of these processes have been identified. The convergence between behavioural and physiological findings in understanding the generation of saccades is an outstanding accomplishment of neuroscience.

References

• Bahill, A. T., Clark, M. R., & Stark, L. (1975). The main sequence a tool for studying human eye movements. Mathematical Biosciences, 24(3-4), 191-204. doi: 10.1016/0025-5564(75)90075-9
• Becker, W., & Jürgens, R. (1979). An analysis of the saccadic system by means of double-step stimuli. Vision Research, 19, 967-983.
• Buonocore, A., & McIntosh, R. D. (2008). Saccadic inhibition underlies the remote distractor effect. Experimental Brain Research, 191(1), 117-122. doi: 10.1007/s00221-008-1558-7
• Carpenter, R. H. S. (1988). Movements of the eyes (2nd edition). London: Pion.
• Collewijn, H., Erkelens, C. J., & Steinman, R. M. (1997). Trajectories of the human binocular fixation point during conjugate and non-conjugate gaze-shifts. Vision Research, 37(8), 1049-1069. doi: 10.1016/s0042-6989(96)00245-3
• Deubel, H. (1999). Separate mechanisms for the adaptive control of reactive, volitional, and memory-guided saccadic eye movements. In D. K. A. Gopher (Ed.), Attention and Performance Xvii: Cognitive Regulation of Performance: Interaction of Theory and Application (Vol. 17, pp. 697-721).
• Deubel, H., Wolf, W., & Hauske, G. (1984). The evaluation of oculomotor error signals. In A. G. Gale & F. Johnson (Eds.), Theoretical and applied aspects of oculomotor research. (pp. 55-62). Amsterdam: Elsevier.
• Dorris, M. C., & Munoz, D. P. (1995). A neural correlate for the gap effect on saccadic reaction times in monkeys. Journal of Neurophysiology, 73(6), 2558-2562.
• Doyle, M., & Walker, R. (2001). Curved saccade trajectories: Voluntary and reflexive saccades curve away from irrelevant distractors. Experimental Brain Research, 139(3), 333-344.
• Doyle, M., & Walker, R. (2002). Multisensory interactions in saccade target selection: curved saccade trajectories. Experimental Brain Research, 142, 116-130.
• Enright, J. T. (1984). Changes in vergenec mediated by saccades. Journal of Physiology-London, 350(MAY), 9-31.
• Evdokimidis, I., Smyrnis, N., Constantinidis, T. S., Stefanis, N. C., Avramopoulos, D., Paximadis, C., . . . Stefanis, C. N. (2002). The antisaccade task in a sample of 2,006 young men - I. Normal population characteristics. Experimental Brain Research, 147(1), 45-52. doi: 10.1007/s00221-002-1208-4
• Findlay, J. M. (1982). Global processing for saccadic eye movements. Vision Research, 22, 1033-1045.
• Findlay, J. M., & Blythe, H. I. (2009). Saccade target selection: Do distractors affect saccade accuracy? Vision Research, 49(10), 1267-1274. doi: 10.1016/j.visres.2008.07.005
• Findlay, J. M., & Brown, V. (2006). Eye scanning of multi-element displays: II. Saccade planning. Vision Research, 46(1-2), 216-227. doi: 10.1016/j.visres.2005.07.035
• Findlay, J. M., & Walker, R. (1999). A model of saccade generation based on parallel processing and competitive inhibition. Behavioral and Brain Sciences., 22(4), 661-721.
• Fischer, B., & Boch, R. (1983). Saccadic eye movements after extremely short reaction times in the monkey. Brain Research, 260, 21-26.
• Fischer, B., & Ramsperger, E. (1984). Human express saccades: Extremely short reaction times of goal directed eye movements. Experimental Brain Research, 57, 191-195.
• Guitton, D., Buchtel, H. A., & Douglas, R. M. (1985). Frontal lobe lesions in man cause difficulties in suppressing reflexive glances and in generation of goal directed saccades. Experimental Brain Research, 58, 455-472.
• Hallett, P. E. (1978). Primary and secondary saccades to goals defined by instructions. Vision Research, 18, 1279-1296.
• Hallett, P. E., & Adams, W. D. (1980). The predictability of saccadic latency in a novel oculomotor task. Vision Research, 20, 329-339.
• Hutton, S. B., Joyce, E. M., Barnes, T. R. E., & Kennard, C. (2002). Saccadic distractibility in first-episode schizophrenia. Neurpsychologia, 40(10), 1729-1736.
• Kingstone, A., & Klein, R. M. (1993). What are human express saccades? Perception and Psychophysics, 54(2), 260-273.
• Kowler, E., & Blaser, E. (1995). The accuracy and precisiomn of saccades to small and large targets. . Vision Research, 35(12), 1741-1754. doi: 10.1016/0042-6989(94)00255-k
• Lueck, C. J., Tanyeri, S., Crawford, T. J., Henderson, L., & Kennard, C. (1992). Saccadic eye movements in Parkinsons' disease: I. Delayed Saccades. The Quarterely Journal of Experimental Psychology: Human Experimental Psychology, 45A(2), 193-210.
• Martinez-Conde, S., Macknik, S. L., & Hubel, D. H. (2004). The role of fixational eye movements in visual perception. Nature Reviews Neuroscience, 5(3), 229-240.
• McSorley, E., Haggard, P., & Walker, R. (2006). Time-course of oculomotor inhibition revealed by saccade trajectory modulation. Journal of Neurophysiology., 96(3), 1420-1424.
• Munoz, D. P., & Everling, S. (2004). Look away: the anti-saccade task and the voluntary control of movement. Nature Neuroscience, 5, 217-228.
• Munoz, D. P., & Wurtz, R. H. (1992). Role of the rostral superior colliculus in active visual fixation and execution of express saccades. Journal of Neurophysiology, 67(4), 1000-1002.
• Munoz, D. P., & Wurtz, R. H. (1993a). Fixation cells in monkey superior colliculus I. Characteristics of cell discharge. Journal of Neurophysiology, 70(2), 559-575.
• Munoz, D. P., & Wurtz, R. H. (1993b). Fixation cells in monkey superior colliculus II. Reversible activation and deactivation. Journal of Neurophysiology, 70(2), 576-589.
• Munoz, D. P., & Wurtz, R. H. (1995). Saccade-related activity in monkey superior colliculus 1. Characteristics of burst and buildup cells. Journal of Neurophysiology, 73(6), 2313-2333.
• Quaia, C., Lefévre, P., & Optican, L. M. (1999). Model of the control of saccades by superior colliculus and cerebellum. Journal of Neurophysiology, 82, 999-1018.
• Reingold, E. M., & Stampe, D. M. (2002). Saccadic inhibition in voluntary and reflexive saccades. Journal of Cognitive Neuroscience, 14(3), 371-388.
• Reuter-Lorenz, P. A., Oonk, H. M., Barnes, L. L., & Hughes, H. C. (1995). Effects of warning signals and fixation point offsets on the latencies of pro versus anti-saccades: Implications for an interpretation of the gap effect. Experimental Brain Research, 103(2), 287-293.
• Rolfs, M. (2009). Microsaccades: Small steps on a long way. Vision Research, 49(20), 2415-2441. doi: 10.1016/j.visres.2009.08.010
• Saslow, M. G. (1967). Effects of components of displacement-step stimuli upon latency for saccadic eye movement. Journal of the Optical Society of America, 57(8), 1024-1029.
• Sheliga, B. M., Riggio, L., & Rizzolatti, G. (1994). Orienting of attention and eye movements. Experimental Brain Research, 98, 507-522.
• Vitu, F. (1991). The existence of a centre of gravity effect during reading. Vision Research, 31, 1289-1313.
• Walker, R., Deubel, H., Schneider, W. X., & Findlay, J. M. (1997). Effect of remote distractors on saccade programming: evidence for an extended fixation zone. Journal of Neurophysiology, 78(2), 1108-1119.
• Walker, R., Husain, M., Hodgson, T. L., Harrison, J., & Kennard, C. (1998). Saccadic eye movement and working memory deficits following damage to human prefrontal cortex. Neuropsychologia, 36(11), 1141-1159.
• Walker, R., & McSorley, E. (2006). The parallel programming of voluntary and reflexive saccades. Vision Research, 46, 2082-2093.
• Walker, R., & McSorley, E. (2008). The Influence of Distractors on Saccade-Target Selection: Saccade Trajectory Effects. Journal of Eye Movement Research, 2(3), 1-9.
• Walker, R., Walker, D. G., Husain, M., & Kennard, C. (2000). Control of voluntary and reflexive saccades. Experimental Brain Research, 130(4), 540-544.
• Wenban-Smith, M. G., & Findlay, J. M. (1991). Express saccades: Is there a separate population in humans? Experimental Brain Research, 87, 218-222.
• Yarbus, A. (1967). Eye movements and vision. New York: Plenium Press.

Sponsored by: Eugene M. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia

Reviewed by: Dr. Keith Rayner, Psychology Department, University of California, San Diego

Reviewed by: Eugene M. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia

Accepted on: 2011-11-15 10:04:16 GMT