Invited review
Brain–computer interfaces for communication and control
Jonathan R.Wolpaw a,b,*,Niels Birbaumer c,d ,Dennis J.McFarland a ,
Gert Pfurtscheller e ,Theresa M.Vaughan a
a
Laboratory of Nervous System Disorders,Wadsworth Center,New York State Department of Health,P.O.Box 509,Empire State Plaza,
Albany,NY 12201-0509,USA
b
State University of New York,Albany,NY,USA地动仪发明于哪个朝代
c
刘梓健
Institute of Medical Psychology and Behavioral Neurobiology,University of Tuebingen,Tuebingen,Germany
手工艺品制作
d
Department of Psychophysiology,University of Padova,Padova,Italy
e
Department of Medical Informatics,Institute of Biomedical Engineering,Technical University of Graz,Graz,Austria
Accepted 2March 2002
Abstract
For many years people have speculated that electroencephalographic activity or other electrophysiological measures of brain function might provide a new non-muscular channel for nding messages and commands to the external world –a brain–computer interface (BCI).Over the past 15years,productive BCI rearch programs have arin.Encouraged by new understanding of b午餐食谱大全家常菜
rain function,by the advent of powerful low-cost computer equipment,and by growing recognition of the needs and potentials of people with disabilities,the programs concentrate on developing new augmentative communication and control technology for tho with vere neuromuscular disorders,such as amyotrophic lateral sclerosis,brainstem stroke,and spinal cord injury.The immediate goal is to provide the urs,who may be completely paralyzed,or ‘locked in’,with basic communication capabilities so that they can express their wishes to caregivers or even operate word processing programs or neuroprosthes.Prent-day BCIs determine the intent of the ur from a variety of different electrophysiological signals.The signals include slow cortical potentials,P300potentials,and mu or beta rhythms recorded from the scalp,and cortical neuronal activity recorded by implanted electrodes.They are translated in real-time into commands that operate a computer display or other device.Successful operation requires that the ur encode commands in the signals and that the BCI derive the commands from the signals.Thus,the ur and the BCI system need to adapt to each other both initially and continually so as to ensure stable performance.Current BCIs have maximum information transfer rates up to 10–25bits/min.This limited capacity can be valuable for people who vere disabilities prevent them from using conventional augmentative communication methods.At the same time,many possible applications of BCI technology,such as neuroprosthesis control,may require higher information transfer rates.Future pro
gress will depend on:recognition that BCI rearch and development is an interdisciplinary problem,involving neurobiology,psychology,engineering,mathematics,and computer science;identi-fication of tho signals,whether evoked potentials,spontaneous rhythms,or neuronal firing rates,that urs are best able to control independent of activity in conventional motor output pathways;development of training methods for helping urs to gain and maintain that control;delineation of the best algorithms for translating the signals into device commands;attention to the identification and elimination of artifacts such as electromyographic and electro-oculographic activity;adoption of preci and objective procedures for evaluating BCI performance;recognition of the need for long-term as well as short-term asssment of BCI performance;identification of appropriate BCI applications and appropriate matching of applications and urs;and attention to factors that affect ur acceptance of augmentative technology,including ea of u,cosmesis,and provision of tho communication and control capacities that are most important to the ur.Development of BCI technology will also benefit from greater emphasis on peer-reviewed rearch publications and avoidance of the hyperbolic and often misleading media attention that tends to generate unrealistic expectations in the public and skepticism in other rearchers.With adequate recognition and effective engagement of all the issues,BCI systems could eventually provide an important new communication and control option for tho with motor dis
abilities and might also give tho without disabilities a supple-mentary control channel or a control channel uful in special circumstances.q 2002Elvier Science Ireland Ltd.All rights rerved.
Keywords :Brain–computer interface;Electroencephalography;Augmentative communication;Rehabilitation;Neuroprosthesis;Brain–machine interface
Clinical Neurophysiology 113(2002)
767–791
CLINPH 2001764
*Corresponding author.Tel.:11-518-473-3631;fax:11-518-486-4910.E-mail address:wolpaw@wadsworth (J.R.Wolpaw).
1.Introduction
1.1.Options for restoring function to tho with motor disabilities
Many different disorders can disrupt the neuromuscular channels through which the brain communicates with and controls its external environment.Amyotrophic lateral sclerosis(ALS),brainstem stroke,brain or spinal cord injury,cerebral palsy,muscular dystrophies,multiple sclerosis,and numerous other dias impair the neural pathways that control muscles or impair the muscles them-lves.They affect nearly two million people in the United States alone,and far more around the world(Ficke,1991; NABMRR,1992;Murray and Lopez,1996;Carter,1997). Tho most verely affected may lo all voluntary muscle control,including eye movements and respiration,and may be completely locked in to their bodies,unable to commu-nicate in any way.Modern life-support technology can allow most individuals,even tho who are locked-in,to live long lives,so that the personal,social,and economic b
urdens of their disabilities are prolonged and vere.
In the abnce of methods for repairing the damage done by the disorders,there are3options for restoring function. Thefirst is to increa the capabilities of remaining pathways. Muscles that remain under voluntary control can substitute for paralyzed muscles.People largely paralyzed by massive brainstem lesions can often u eye movements to answer questions,give simple commands,or even operate a word processing program;and verely dysarthric patients can u hand movements to produce synthetic Damper et al.,1987;LaCour and Hladik,1990;Chen et al.,1999; Kubota et al.,2000).The cond option is to restore function by detouring around breaks in the neural pathways that control muscles.In patients with spinal cord injury,electro-myographic(EMG)activity from muscles above the level of the lesion can control direct electrical stimulation of paral-yzed muscles,and thereby restore uful movement(Hoffer et al.,1996;Kilgore et al.,1997;Ferguson et al.,1999). Thefinal option for restoring function to tho with motor impairments is to provide the brain with a new,non-muscular communication and control channel,a direct brain–computer interface(BCI)for conveying messages and commands to the external world.A variety of methods for monitoring brain activity might rve as a BCI.The include,besides electro-encephalography(EEG)and more invasive electrophysiolo-gical methods,magnetoencephalography(
隐形眼睛MEG),positron emission tomography(PET),functional magnetic resonance imaging(fMRI),and optical imaging.However,MEG,PET, fMRI,and optical imaging are still technically demanding and expensive.Furthermore,PET,fMRI,and optical imaging,which depend on bloodflow,have long time constants and thus are less amenable to rapid communica-tion.At prent,only EEG and related methods,which have relatively short time constants,can function in most environ-ments,and require relatively simple and inexpensive equip-ment,offer the possibility of a new non-muscular communication and control channel,a practical BCI.
1.2.The fourth application of the EEG
In the7decades since Hans Berger’s original paper (Berger,1929),the EEG has been ud mainly to evaluate neurological disorders in the clinic and to investigate brain function in the laboratory;and a few studies have explored its therapeutic Travis et al.,1975;Kuhl-man,1978;Elbert et al.,1980;Rockstroh et al.,1989;Rice et al.,1993;Sterman,2000).Over this time,people have also speculated that the EEG could have a fourth applica-tion,that it could be ud to decipher thoughts,or intent,so that a person could communicate with others or control devices directly by means of brain activity,without using the normal channels of peripheral nerves and muscles.This idea has appeared often in popularfiction and fantasy(such as the movie‘Firefox’in which an airplane
is controlled in part by the pilot’s EEG(Thomas,1977)).However,EEG-bad communication attracted little rious scientific atten-tion until recently,for at least3reasons.
First,while the EEG reflects brain activity,so that a person’s intent could in theory be detected in it,the resolu-tion and reliability of the information detectable in the spon-taneous EEG is limited by the vast number of electrically active neuronal elements,the complex electrical and spatial geometry of the brain and head,and the disconcerting trial-to-trial variability of brain function.The possibility of recognizing a single message or command amidst this complexity,distortion,and variability appeared to be extre-mely remote.Second,EEG-bad communication requires the capacity to analyze the EEG in real-time,and until recently the requisite technology either did not exist or was extremely expensive.Third,there was in the past little interest in the limited communication capacity that afirst-generation EEG-bad BCI was likely to offer.
Recent scientific,technological,and societal events have changed this situation.First,basic and clinical rearch has yielded detailed knowledge of the signals that compri the EEG.For the major EEG rhythms and for a variety of evoked potentials,their sites and mechanisms of origin and their relationships with specific aspects of brain func-tion,are no longer wholly obscure.Numerous studies have demonstrated correlations between EEG signals and actual or imagined movements and betw
een EEG signals and mental Keirn and Aunon,1990;Lang et al., 1996;Pfurtscheller et al.,1997;Anderson et al.,1998; Altenmu¨ller and Gerloff,1999;McFarland et al.,2000a). Thus,rearchers are in a much better position to consider which EEG signals might be ud for communication and control,and how they might best be ud.Second,the extre-mely rapid and continuing development of inexpensive computer hardware and software supports sophisticated online analys of multichannel EEG.This digital revolu-tion has also led to appreciation of the fact that simple
J.R.Wolpaw et al./Clinical Neurophysiology113(2002)767–791 768
communication ‘Yes’or‘No’,‘On’or‘Off’) can be configured to rve complex word processing,prosthesis control).Third,greatly incread societal recognition of the needs and potential of people with vere neuromuscular disorders like spinal cord injury or cerebral palsy has generated clinical,scientific,and commercial interest in better augmentative communication and control technology.Development of such technology is both the impetus and the justification for current BCI rearch.BCI technology might rve people who cannot u conventional augmentative technologies;and the people couldfind even the limited capacities offirst-genera-tion BCI systems valuable.
In addition,advances in the development and u of elec-trophysiological recording methods employing epidural, subdural,or intracortical electrodes offer further options. Epidural and subdural electrodes can provide EEG with high topographical resolution,and intracortical electrodes can follow the activity of individual neurons(Schmidt, 1980;Ikeda and Shibbasaki,1992;Heetderks and Schmidt, 1995;Levine et al.,1999,2000;Wolpaw et al.,2000a). Furthermore,recent studies show that thefiring rates of an appropriate lection of cortical neurons can give a detailed picture of concurrent voluntary Georgopou-los et al.,1986;Schwartz,1993;Chapin et al.,1999;Wess-berg et al.,2000).Becau the methods are invasive,the threshold for their clinical u would presumably be higher than for methods bad on scalp-recorded EEG activity,and they would probably be ud mainly by tho with extremely vere disabilities.At the same time,they might support more rapid and preci communication and control than the scalp-recorded EEG.
1.3.The prent review
This review summarizes the current state of BCI rearch with emphasis on its application to the needs of tho with vere neuromuscular disabilities.In order to address all current BCI rearch,it includes approaches that u stan-dard scalp-recorded EEG as well as tho that u epidural, subdural,or intracortical recording.While all the prent-day BCIs u electrophysiological method
s,the basic prin-ciples of BCI design and operation discusd here should apply also to BCIs that u other methods to monitor brain MEG,fMRI).The next ctions describe the esntial elements of any BCI and the veral categories of electrophysiological BCIs,review current rearch,consider prospects for the future,and discuss the issues most impor-tant for further BCI development and application.
2.Definition and features of a BCI
2.1.Dependent and independent BCIs
A BCI is a communication system in which messages or commands that an individual nds to the external world do not pass through the brain’s normal output pathways of peripheral nerves and muscles.For example,in an EEG-bad BCI the messages are encoded in EEG activity.A BCI provides its ur with an alternative method for acting on the world.BCIs fall into two class:dependent and independent.
A dependent BCI does not u the brain’s normal output pathways to carry the message,but activity in the path-ways is needed to generate the brain EEG)that does carry it.For example,one dependent BCI prents the ur with a matrix of letters thatflash one at a time,and the
ur lects a specific letter by looking directly at it so that the visual evoked potential(VEP)recorded from the scalp over visual cortex when that letterflashes is much larger that the VEPs produced when other lettersflash(Sutter,1992). In this ca,the brain’s output channel is EEG,but the generation of the EEG signal depends on gaze direction, and therefore on extraocular muscles and the cranial nerves that activate them.A dependent BCI is esntially an alter-native method for detecting messages carried in the brain’s normal output pathways:in the prent example,gaze direc-tion is detected by monitoring EEG rather than by monitor-ing eye position directly.While a dependent BCI does not give the brain a new communication channel that is inde-pendent of conventional channels,it can still be Sutter and Tran,1992).
In contrast,an independent BCI does not depend in any way on the brain’s normal output pathways.The message is not carried by peripheral nerves and muscles,and,further-more,activity in the pathways is not needed to generate the brain EEG)that does carry the message. For example,one independent BCI prents the ur with a matrix of letters thatflash one at a time,and the ur lects a specific letter by producing a P300evoked potential when that letterflashes(Farwell and Donchin,1988;Donchin et al.,2000).In this ca,the brain’s output channel is EEG, and the generation of the EEG signal depends mainly on the ur’s intent,not on the preci
orientation of the eyes (Sutton et al.,1965;Donchin,1981;Fabiani et al.,1987; Polich,1999).The normal output pathways of peripheral nerves and muscles do not have an esntial role in the operation of an independent BCI.Becau independent BCIs provide the brain with wholly new output pathways, they are of greater theoretical interest than dependent BCIs. Furthermore,for people with the most vere neuromuscu-lar disabilities,who may lack all normal output channels (including extraocular muscle control),independent BCIs are likely to be more uful.
2.2.BCI u is a skill
Most popular and many scientific speculations about BCIs start from the‘mind-reading’or‘wire-tapping’analogy,the assumption that the goal is simply to listen in on brain activity as reflected in electrophysiological signals and thereby determine a person’s wishes.This analogy
J.R.Wolpaw et al./Clinical Neurophysiology113(2002)767–791769
ignores the esntial and central fact of BCI development and operation.A BCI changes electrophysiological signals from mere reflections of central nervous system(CNS) activity into the intended products of that activity:messages and commands that act on the world.It changes a signal such as an EEG rhythm or a neuronalfiring rate from a reflection of brain function into the end produ
化工管道ct of that function:an output that,like output in conventional neuro-muscular channels,accomplishes the person’s intent.A BCI replaces nerves and muscles and the movements they produce with electrophysiological signals and the hardware and software that translate tho signals into actions.
The brain’s normal neuromuscular output channels depend for their successful operation on feedback.Both standard outputs such as speaking or walking and more specialized outputs such as singing or dancing require for their initial acquisition and subquent maintenance contin-ual adjustments bad on oversight of intermediate andfinal outcomes(Salmoni,1984;Ghez and Krakauer,2000). When feedback is abnt from the start,motor skills do not develop properly;and when feedback is lost later on, skills deteriorate.
As a replacement for the brain’s normal neuromuscular output channels,a BCI also depends on feedback and on adaptation of brain activity bad on that feedback.Thus,a BCI system must provide feedback and must interact in a productive fashion with the adaptations the brain makes in respon to that feedback.This means that BCI operation depends on the interaction of two adaptive controllers:the ur’s brain,which produces the signals measured by the BCI;and the BCI itlf,which translates the signals into specific commands.
Successful BCI operation requires that the ur develop and maintain a new skill,a skill that consists not of proper muscle control but rather of proper control of specific elec-trophysiological signals;and it also requires that the BCI translate that control into output that accomplishes the ur’s intent.This requirement can be expected to remain even when the skill does not require initial training.In the independent BCI described above,the P300generated in respon to the desired letter occurs without training.Never-theless,once this P300is engaged as a communication chan-nel,it is likely to undergo adaptive modification(Ronfeld, 1990;Coles and Rugg,1995),and the recognition and productive engagement of this adaptation will be important for continued successful BCI operation.
That the brain’s adaptive capacities extend to control of various electrophysiological signal features was initially suggested by studies exploring therapeutic applications of the EEG.They reported conditioning of the visual alpha rhythm,slow potentials,the mu rhythm,and other EEG features(Wyricka and Sterman,1968;Dalton,1969; Black et al.,1970;Nowles and Kamiya,1970;Black, 1971,1973;Travis et al.,1975;Kuhlman,1978;Rockstroh et al.,1989)(reviewed in Neidermeyer(1999)).The studies usually sought to produce an increa in the ampli-tude of a specific EEG feature.Becau they had therapeutic goals,such as reduction in izure frequency,they did not try to demonstrate rapid bidirectional control,that is,the ability to increa and
decrea a specific feature quickly and accurately,which is important for communication. Nevertheless,they suggested that bidirectional control is possible,and thus justified and encouraged efforts to develop EEG-bad communication.In addition,studies in monkeys showed that thefiring rates of individual corti-cal neurons could be operantly conditioned,and thus suggested that cortical neuronal activity provides another option for non-muscular communication and control(Fetz and Finocchio,1975;Wyler and Burchiel,1978;Wyler et al.,1979;Schmidt,1980).
At the same time,the studies did not indicate to what extent the control that people or animals develop over the electrophysiological phenomena depends on activity in conventional neuromuscular output Dewan, 1967).While studies indicated that conditioning of hippo-campal activity did not require mediation by motor respons(Dalton,1969;Black,1971),the issue was not resolved for other EEG features or for cortical neuronal activity.This question of independent control of the various electrophysiological signal features ud in current and contemplated BCIs is important both theoretically and prac-tically,and aris at multiple points in this review.
2.3.The parts of a BCI
Like any communication or control system,a BCI has lectrophysiological activity from the
ur), device commands),components that translate input into output,and a protocol that determines the ont, offt,and timing of operation.Fig.1shows the elements and their principal interactions.
2.3.1.Signal acquisition
In the BCIs discusd here,the input is EEG recorded from the scalp or the surface of the brain or neuronal activity recorded within the brain.Thus,in addition to the funda-mental distinction between dependent and independent BCIs(Section2.1above),electrophysiological BCIs can be categorized by whether they u EEG)or intracortical)methodology.They can also be categorized by whether they u evoked or spontaneous inputs.Evoked EEG produced by flashing letters)result from stereotyped nsory stimulation provided by the BCI.Spontaneous EEG rhythms over nsorimotor cortex)do not depend for their generation on such stimulation.There is,presumably,no reason why a BCI could not combine non-invasive and invasive methods or evoked and spontaneous inputs.In the signal-acquisition part of BCI operation,the chon input is acquired by the recording electrodes,amplified,and digitized.
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2.3.2.Signal processing:feature extraction
The digitized signals are then subjected to one or more of a variety of feature extraction procedures,such as spatial filter-ing,voltage amplitude measurements,spectral analys,or single-neuron paration.This analysis extracts the signal features that (hopefully)encode the ur ’s messages or commands.BCIs can u signal features that are in the time domain (e.g.evoked potential amplitudes or neuronal firing rates)or the frequency domain (e.g.mu or beta-rhythm amplitudes)(Farwell and Donchin,1988;Lopes da Silva and Mars,1987;Parday et al.,1996;Lopes da Silva,1999;Donchin et al.,2000;Kennedy et al.,2000;Wolpaw et al.,2000b;Pfurtscheller et al.,2000a;Penny et al.,2000;Kostov and Polak,2000).A BCI could conceivably u both time-domain and frequency-domain signal features,and might thereby improve performance (e.g.Schalk et al.,2000).In general,the signal features ud in prent-day BCIs re flect identi fiable brain events like the firing of a speci fic cortical neuron or the synchronized and rhythmic synaptic activation in nsorimotor cortex that produces a mu rhythm.Knowledge of the events can help guide BCI development.The location,size,and function of the cortical area generating a rhythm or an evoked potential can indicate how it should be recorded,how urs might best learn to control its amplitude,and how to recognize and eliminate the effects of non-CNS artifacts.It is also possible for
a BCI to u signal features,like ts of autoregressive parameters,that correlate with the ur ’s intent but do not necessarily re flect speci fic brain events.In such cas,it is particularly important (and may be more dif ficult)to ensure that the chon features are not contaminated by EMG,electro-oculography (EOG),or other non-CNS artifacts.
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Fig.1.Basic design and operation of any BCI system.Signals from the brain are acquired by electrodes on the scalp or in the head and procesd to extract speci fic signal features (e.g.amplitudes of evoked potentials or nsorimotor cortex rhythms,firing rates of cortical neurons)that re flect the ur ’s intent.The features are translated into commands that operate a device (e.g.a simple word processing program,a wheelchair,or a neuroprosthesis).Success depends on the interaction of two adaptive controllers,ur and system.The ur must develop and maintain good correlation between his or her intent and the signal features employed by the BCI;and the BCI must lect and extract features that the ur can control and must translate tho features into device commands correctly and ef ficiently.
2.3.3.Signal processing:the translation algorithm什么是绩效工资
Thefirst part of signal processing simply extracts specific signal features.The next stage,the translation algorithm, translates the signal features into device commands-orders that carry out the ur’s intent.This algorithm might u linear lassical statistical analys (Jain et al.,2000)or nonlinear ural networks).Whatever its nature,each algorithm changes independent signal features)into dependent device control commands).
Effective algorithms adapt to each ur on3levels.First, when a new urfirst access the BCI the algorithm adapts to that ur’s signal features.If the signal feature is mu-rhythm amplitude,the algorithm adjusts to the ur’s range of mu-rhythm amplitudes;if the feature is P300 amplitude,it adjusts to the ur’s characteristic P300ampli-tude;and if the feature is thefiring rate of a single cortical neuron,it adjusts to the neuron’s characteristic range of firing rates.A BCI that posss only thisfirst level of hat adjusts to the ur initially and never again,will continue to be effective only if the ur’s perfor-mance is very stable.However,EEG and other electrophy-siological signals typically display short-and long-term variations linked to time of day,hormonal levels,immediate environment,recent events,fatigue,illness,and other factors.Thus,effective BCIs need a cond level of adapta-tion:periodic online adjustments to reduce the impact of such spontaneous variations.A good translation algorithm will adjust to the variations so as to match as cloly as possible the ur’s current range of signal feature values to the available range of device command values.
绥化学院是几本While they are clearly important,neither of thefirst two levels of adaptation address the central fact of effective BCI operation:its dependence on the effective interaction of two adaptive controllers,the BCI and the ur’s brain.The third level of adaptation accommodates and engages th
e adaptive capacities of the brain.As discusd in Section 2.2,when an electrophysiological signal feature that is normally merely a reflection of brain function becomes the end product of that function,that is,when it becomes an output that carries the ur’s intent to the outside world,it engages the adaptive capacities of the brain.Like activity in the brain’s conventional neuromuscular communication and control channels,BCI signal features will be affected by the device commands they are translated into:the results of BCI operation will affect future BCI input.In the most desirable (and hopefully typical)ca,the brain will modify signal features so as to improve BCI operation.If,for example,the feature is mu-rhythm amplitude,the correlation between that amplitude and the ur’s intent will hopefully increa over time.An algorithm that incorporates the third level of adaptation could respond to this increa by rewarding the ur with faster communication.It would thereby recognize and encourage the ur’s development of greater skill in this new form of communication.On the other hand,excessive or inappropriate adaptation could impair performance or discourage further skill development.Proper design of this third level of adaptation is likely to prove crucial for BCI development.Becau this level involves the interaction of two adaptive controllers,the ur’s brain and the BCI system,its design is among the most difficult problems confronting BCI rearch.
2.3.4.The output device
For most current BCIs,the output device is a computer screen and the output is the lection of targets,letters,or icons prented on Farwell and Donchin,1988; Wolpaw et al.,1991;Perelmouter et al.,1999;Pfurtscheller et al.,2000a).Selection is indicated in various he letterflashes).Some BCIs also provide additional,interim output,such as cursor movement toward the item prior to its Wolpaw et al.,1991;Pfurtscheller et al., 2000a).In addition to being the intended product of BCI operation,this output is the feedback that the brain us to maintain and improve the accuracy and speed of commu-nication.Initial studies are also exploring BCI control of a neuroprosthesis or orthesis that provides hand closure to people with cervical spinal cord injuries(Lauer et al., 2000;Pfurtscheller et al.,2000b).In this prospective BCI application,the output device is the ur’s own hand.
2.3.5.The operating protocol
Each BCI has a protocol that guides its operation.This protocol defines how the system is turned on and off, whether communication is continuous or discontinuous, whether message transmission is triggered by the system (e.g.by the stimulus that evokes a P300)or by the ur, the quence and speed of interactions between ur and system,and what feedback is provided to the ur.
Most protocols ud in BCI rearch are not completely suitable for BCI applications that rve the needs of people with disabilities.Most laboratory BCIs do not give the ur on/off control:the investigator turns the system on and off. Becau they need to measure communication speed and accuracy,laboratory BCIs usually tell their urs what messages or commands to nd.In real life the ur picks the message.Such differences in protocol can complicate the transition from rearch to application.
3.Prent-day BCIs
While many studies have described electrophysiological or other measures of brain function that correlate with concurrent neuromuscular outputs or with intent and might therefore function in a BCI system,relatively few peer-reviewed articles have described human u of systems that satisfy the BCI definition given in Section2.1and illu-strated in Fig.1,systems that give the ur control over a device and concurrent feedback from the device.The studies are reviewed here.Studies from the vast group describing phenomena that might rve as the basis for a
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