Phase-versus-time analysis of the steady-state evoked potential latency* A. Leonard Diamond Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 (Received 16 December 1976) Steady-state EP (evoked potential) latency can be derived either from a phase or time difference between stimulus and EP. Phase derivation employs a sinusoidal stimulus and assumes a linear stimulus-EP system. Time derivation employs any stimulus waveform and does not require linearity. The two methods are complementary in application.
The steady-state visual E P (evoked potential) is a measure of the brain response to a light flickering usually faster than 8 Hz. 1 - 4 Such a flicker measure has been accomplished with sinusoidally modulated light stimuli 5 " 7 and nonsinusoidal, pulsed, strobe stim uli. 2 - 4 , 8 E P latency is the time it takes for the E P to occur following a stimulation. This time period, or delay, is estimated in steady-state sinusoidal stimulation from an analysis of the phase difference between the stimulus and a synchronous component in the E P . In the nonsinusoidal method, EP latency is estimated from an analysis of the time differences between stimulus and E P peak points. At first glance, a comparison of phase versus time latency analysis would seem to r e quire only a simple mathematical statement relating the two. Except for certain linear stimulus-EP s y s tems, however, a simple reciprocity is not valid. 1 Although the phase-difference analysis has already been described from a number of points of view, 1 , 5 - 7 , 9 a brief summary is necessary for comparison. Phase analysis calculates E P latency t from the phase angle difference φ resulting from the amount by which an o s cillating EP lags a sinusoidal stimulus. A basic un derlying assumption is that the EP also is sinusoidal and that the stimulus-EP system is linear. 1 , 6 Specif ically, if the system is a linear, minimum phase-shift system plus a fixed delay, and if E P amplitude changes little with frequency, 1 then t-1/360dφ/dƒ, where t is in seconds, φ is in degrees, and ƒ, the stimulus frequen cy, in hertz. Latency is directly determined then by the slope of the phase-difference change with frequency.
terest, e . g . , positive E P peak points. The time-difference analysis can be graphically un derstood from Fig. 1. The E P curves on the right side of Fig. 1(a) are artificial but representative of electron ically averaged steady-state nonsinusoidal d a t a . 2 - 4 ' 8 These EP curves are what would be seen in an averaged time sample (as delimited by the total sweep duration of the electronic averager) of the EP-following-re sponse to a flickering light stimulus. F o r each s t i m ulus flash [on the left side of Fig. 1(a)], repeated at dif ferent interstimulus intervals, ISI, there is an a s s o c i ated E P cycle. A calculation of stimulus-EP latency, t, would identify which E P cycle is associated with which particular stimulus flash. In order to calculate t, a plot of the stimulus and EP peak (reference) points, Ps and Pe, is necessary. This is done in Fig. 1(b) with ISI on the ordinate and sweep duration on the abscissa. It can be seen that when ISI mathematically becomes zero, the regression lines
The phase-difference approach has been repeatedly employed in basic and clinical r e s e a r c h . 1 , 9 - 1 3 it lends itself to a particularly precise on-line latency calcula tion which utilizes the narrow bandwidth of a Fourier analyzer. 14 The time-difference analysis8 calculates E P latency from the time differences between stimulus and E P peaks. Since these differences a r e measured only b e tween peak reference points in the stimulus and E P cycles, other portions of the waveforms a r e unimpor tant, at least for latency calculation, and the assump tion of a linear stimulus-EP system is unnecessary. The measure requires only that, for a constant set of experimental conditions, E P latency is constant, and the reference points chosen in the stimulus and E P cycles a r e consistently identifiable at the same approx imate time points within each cycle. The choice of the reference points depends upon the experimenter's in 841
J. Opt. Soc. Am., Vol. 67, No. 6, June 1977
FIG. 1. Graphic description of time-difference latency cal culation. EP curves are artificial but representative of electronically averaged steady-state EP traces plotted over a total sweep duration of 150 ms. (a) EP (on right) to pulsed stimulus (on left) repeated at three interstimulus intervals, ISI. T indicates stimuli which trigger electronic averager at the zero value of its sweep duration. Ps and Pe are the stim ulus and EP reference points chosen for the analysis. The sweep duration axis is broken and spread so stimulus and EP can be viewed apart. (b) Plot of stimulus and EP peaks, ps and Pe. Regression lines through points converge to two in tercepts, Ds and De at ISI = 0. EP latency =De- D s . Copyright © 1977 by the Optical Society of America
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drawn through the plotted peak points converge to two intercept values, Ds and Des on the sweep duration axis. Since E P latency is defined as the time difference by which the EP lags the stimulus, then t = De - Ds. And since DS=0 [because the averager sweep is always t r i g gered at zero-sweep-duration by a trigger stimulus T, in Fig. 1(a)], then t = De and is calculated, by least squares, as the average intercept of the E P regression lines in Fig. 1(b). Such a straight-line regression solu tion assumes a constant EP latency over the ISI range studied and for the reference points chosen. Such a constancy can be tested empirically by the calculation of E P latencies for smaller ISI ranges within the range studied. The general usefulness of the time-difference calcula tion of latency is in its application to stimuli or E P ' s of any repetitive waveform (including sinusoidal). Be cause of this, it is complementary to the phase-differ ence approach, since it can be employed for latency cal culation in experiments, such as studies of light-dark ratio in flicker, which necessarily employ nonsinusoidal stimulation. 1 5 That is, the phase-difference approach requires a linear stimulus-EP system for the logic of its latency calculation, 1 and nαnsinusoidal stimulation does not produce such linearity. The time-difference method is also complementary where it makes possible the analysis of specific p o r tions, or time components, of the steady-state E P . A study, for example, of latency and amplitude differ ences between the positive and negative deflections in the steady-state EP might provide additional clues to an understanding of E P polarity shifts already studied in the transient E P . 1 6 The relationship between phase and time analysis is described by De -Ds= φ/360ƒ but is valid only for certain linear stimulus-EP systems. 1 It should be noted that although the phase difference φ has usually been plotted as a negatively sloping func tion, 5 - 7 the polarity of the slope may be either negative or positive [see Fig. 1(b)]. Both phase and time analysis yield latency values in dependent of peaks in the E P record. In fact, the steady-state latency, as measured by De in Fig. 1(b), is often not coincident in time with an E P peak. 1 7 If this is also true for transient EP latencies, then transient studies, which usually measure latency at an E P peak, may not accurately reflect the time of occurrence or the form of the underlying " a r r i v a l " process in the brain.
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*Supported in part by NRC Grant A9940. 1 D. Regan, Evoked potentials in psychology, sensory physiolo gy and clinical medicine (Chapman and Hall. London, 1972), p. 328. See p. 75 for a discussion of transient versus steady-state stimulation. Also see p. 77 for latency calcula tion and p. 236 for linearity. 2 N. W. Perry and D. G. Childers, The human visual evoked response (Thomas, Springfield, Ill., 1969), p. 187. 3 J. A. S. Kinney, C. L. McKay, A. J. Mensch, and S. M. Luria "Visual evoked responses elicited by rapid stimulation," Electroenceph. Clin. Neurophysiol. 34, 7-13 (1973). 4 K. Sato, H. KLtajima, K. Mimura, N. Hirota, Y. Tagawa, and N. Ochi, "Cerebral visual evoked potentials in relation to EEG," Electroenceph. Clin. Neurophysiol. 30, 123-138 (1971). 5 L. H. Van der Tweel and H. F. E. Verduyn Lunel, "Human visual responses to sinusoidally modulated light," Electro enceph. Clin. Neurophysiol. 18, 287-298 (1965). 6 H. Spekreijse, "Analysis of EEG responses in man evoked by sine wave modulated light," Thesis, University of Amsterdam, p. 161 (1966). 7 D. Regan, "Some characteristics of average steady-state and transient responses evoked by modulated light," Electroen ceph. Clin. Neurophysiol. 20, 238-248 (1966). 8 A. L. Diamond, "Latency of the steady-state visual evoked potential," Electroenceph. Clin. Neurophysiol. 42, 125-127 (1977). 9 D. Regan, B. A. Milner, and J. R. Heron, "Delayed visual perception and delayed visual evoked potentials in the spinal form of multiple sclerosis and retrobulbar neuritis," Brain 99, 43-66 (1976). 10 D. Regan, "Rapid objective refraction using evoked brain potentials," Invest. Ophthal. 12, 669-679(1973). 11 D. Regan and R. F. Cartwright, "A method of measuring the potentials evoked by simultaneous stimulation of different retinal regions," Electroenceph. Clin. Neurophysiol. 28, 314-319 (1970). l2 D. Regan and J. R. Heron, "Clinical investigation of lesions of the visual pathway, a new objective technique," J. Neurol, Neurosurg. Psychiat. 32, 479-483 (1969). 13 B. A. Milner, D. Regan, and J. R. Heron, "Differential diagnosis of multiple sclerosis by visual evoked potential recording," Brain 97, 755-772 (1974). l4 D. Regan, "Latencies of evoked potentials to flicker and to pattern speedily estimated by simultaneous stimulation meth od," Electroenceph. Clin. Neurophysiol. 40, 654-660 (1976). 15 C. H. Graham, editor, Vision and Visual Perception (Wiley, New York, 1965), p. 637. 16 D. A. Jeffreys, "CorticaL source locations of pattern related visual evoked potentials recorded from the human scalp," Nature 229, 502-504 (1971). Thus far, the present author has found no significant differences in steady-state latencies of positive versus negative EP peaks. The parameters stud ied in Jeffreys' transient experiment, however, have yet to be explored. 17 Unpublished finding by the present author.
JOSA Letters
842
The steady-state visual E P (evoked potential) is a measure of the brain response to a light flickering usually faster than 8 Hz. 1 - 4 Such a flicker measure has been accomplished with sinusoidally modulated light stimuli 5 " 7 and nonsinusoidal, pulsed, strobe stim uli. 2 - 4 , 8 E P latency is the time it takes for the E P to occur following a stimulation. This time period, or delay, is estimated in steady-state sinusoidal stimulation from an analysis of the phase difference between the stimulus and a synchronous component in the E P . In the nonsinusoidal method, EP latency is estimated from an analysis of the time differences between stimulus and E P peak points. At first glance, a comparison of phase versus time latency analysis would seem to r e quire only a simple mathematical statement relating the two. Except for certain linear stimulus-EP s y s tems, however, a simple reciprocity is not valid. 1 Although the phase-difference analysis has already been described from a number of points of view, 1 , 5 - 7 , 9 a brief summary is necessary for comparison. Phase analysis calculates E P latency t from the phase angle difference φ resulting from the amount by which an o s cillating EP lags a sinusoidal stimulus. A basic un derlying assumption is that the EP also is sinusoidal and that the stimulus-EP system is linear. 1 , 6 Specif ically, if the system is a linear, minimum phase-shift system plus a fixed delay, and if E P amplitude changes little with frequency, 1 then t-1/360dφ/dƒ, where t is in seconds, φ is in degrees, and ƒ, the stimulus frequen cy, in hertz. Latency is directly determined then by the slope of the phase-difference change with frequency.
terest, e . g . , positive E P peak points. The time-difference analysis can be graphically un derstood from Fig. 1. The E P curves on the right side of Fig. 1(a) are artificial but representative of electron ically averaged steady-state nonsinusoidal d a t a . 2 - 4 ' 8 These EP curves are what would be seen in an averaged time sample (as delimited by the total sweep duration of the electronic averager) of the EP-following-re sponse to a flickering light stimulus. F o r each s t i m ulus flash [on the left side of Fig. 1(a)], repeated at dif ferent interstimulus intervals, ISI, there is an a s s o c i ated E P cycle. A calculation of stimulus-EP latency, t, would identify which E P cycle is associated with which particular stimulus flash. In order to calculate t, a plot of the stimulus and EP peak (reference) points, Ps and Pe, is necessary. This is done in Fig. 1(b) with ISI on the ordinate and sweep duration on the abscissa. It can be seen that when ISI mathematically becomes zero, the regression lines
The phase-difference approach has been repeatedly employed in basic and clinical r e s e a r c h . 1 , 9 - 1 3 it lends itself to a particularly precise on-line latency calcula tion which utilizes the narrow bandwidth of a Fourier analyzer. 14 The time-difference analysis8 calculates E P latency from the time differences between stimulus and E P peaks. Since these differences a r e measured only b e tween peak reference points in the stimulus and E P cycles, other portions of the waveforms a r e unimpor tant, at least for latency calculation, and the assump tion of a linear stimulus-EP system is unnecessary. The measure requires only that, for a constant set of experimental conditions, E P latency is constant, and the reference points chosen in the stimulus and E P cycles a r e consistently identifiable at the same approx imate time points within each cycle. The choice of the reference points depends upon the experimenter's in 841
J. Opt. Soc. Am., Vol. 67, No. 6, June 1977
FIG. 1. Graphic description of time-difference latency cal culation. EP curves are artificial but representative of electronically averaged steady-state EP traces plotted over a total sweep duration of 150 ms. (a) EP (on right) to pulsed stimulus (on left) repeated at three interstimulus intervals, ISI. T indicates stimuli which trigger electronic averager at the zero value of its sweep duration. Ps and Pe are the stim ulus and EP reference points chosen for the analysis. The sweep duration axis is broken and spread so stimulus and EP can be viewed apart. (b) Plot of stimulus and EP peaks, ps and Pe. Regression lines through points converge to two in tercepts, Ds and De at ISI = 0. EP latency =De- D s . Copyright © 1977 by the Optical Society of America
841
drawn through the plotted peak points converge to two intercept values, Ds and Des on the sweep duration axis. Since E P latency is defined as the time difference by which the EP lags the stimulus, then t = De - Ds. And since DS=0 [because the averager sweep is always t r i g gered at zero-sweep-duration by a trigger stimulus T, in Fig. 1(a)], then t = De and is calculated, by least squares, as the average intercept of the E P regression lines in Fig. 1(b). Such a straight-line regression solu tion assumes a constant EP latency over the ISI range studied and for the reference points chosen. Such a constancy can be tested empirically by the calculation of E P latencies for smaller ISI ranges within the range studied. The general usefulness of the time-difference calcula tion of latency is in its application to stimuli or E P ' s of any repetitive waveform (including sinusoidal). Be cause of this, it is complementary to the phase-differ ence approach, since it can be employed for latency cal culation in experiments, such as studies of light-dark ratio in flicker, which necessarily employ nonsinusoidal stimulation. 1 5 That is, the phase-difference approach requires a linear stimulus-EP system for the logic of its latency calculation, 1 and nαnsinusoidal stimulation does not produce such linearity. The time-difference method is also complementary where it makes possible the analysis of specific p o r tions, or time components, of the steady-state E P . A study, for example, of latency and amplitude differ ences between the positive and negative deflections in the steady-state EP might provide additional clues to an understanding of E P polarity shifts already studied in the transient E P . 1 6 The relationship between phase and time analysis is described by De -Ds= φ/360ƒ but is valid only for certain linear stimulus-EP systems. 1 It should be noted that although the phase difference φ has usually been plotted as a negatively sloping func tion, 5 - 7 the polarity of the slope may be either negative or positive [see Fig. 1(b)]. Both phase and time analysis yield latency values in dependent of peaks in the E P record. In fact, the steady-state latency, as measured by De in Fig. 1(b), is often not coincident in time with an E P peak. 1 7 If this is also true for transient EP latencies, then transient studies, which usually measure latency at an E P peak, may not accurately reflect the time of occurrence or the form of the underlying " a r r i v a l " process in the brain.
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J. Opt. Soc. Am., Vol. 67, No. 6, June 1977
*Supported in part by NRC Grant A9940. 1 D. Regan, Evoked potentials in psychology, sensory physiolo gy and clinical medicine (Chapman and Hall. London, 1972), p. 328. See p. 75 for a discussion of transient versus steady-state stimulation. Also see p. 77 for latency calcula tion and p. 236 for linearity. 2 N. W. Perry and D. G. Childers, The human visual evoked response (Thomas, Springfield, Ill., 1969), p. 187. 3 J. A. S. Kinney, C. L. McKay, A. J. Mensch, and S. M. Luria "Visual evoked responses elicited by rapid stimulation," Electroenceph. Clin. Neurophysiol. 34, 7-13 (1973). 4 K. Sato, H. KLtajima, K. Mimura, N. Hirota, Y. Tagawa, and N. Ochi, "Cerebral visual evoked potentials in relation to EEG," Electroenceph. Clin. Neurophysiol. 30, 123-138 (1971). 5 L. H. Van der Tweel and H. F. E. Verduyn Lunel, "Human visual responses to sinusoidally modulated light," Electro enceph. Clin. Neurophysiol. 18, 287-298 (1965). 6 H. Spekreijse, "Analysis of EEG responses in man evoked by sine wave modulated light," Thesis, University of Amsterdam, p. 161 (1966). 7 D. Regan, "Some characteristics of average steady-state and transient responses evoked by modulated light," Electroen ceph. Clin. Neurophysiol. 20, 238-248 (1966). 8 A. L. Diamond, "Latency of the steady-state visual evoked potential," Electroenceph. Clin. Neurophysiol. 42, 125-127 (1977). 9 D. Regan, B. A. Milner, and J. R. Heron, "Delayed visual perception and delayed visual evoked potentials in the spinal form of multiple sclerosis and retrobulbar neuritis," Brain 99, 43-66 (1976). 10 D. Regan, "Rapid objective refraction using evoked brain potentials," Invest. Ophthal. 12, 669-679(1973). 11 D. Regan and R. F. Cartwright, "A method of measuring the potentials evoked by simultaneous stimulation of different retinal regions," Electroenceph. Clin. Neurophysiol. 28, 314-319 (1970). l2 D. Regan and J. R. Heron, "Clinical investigation of lesions of the visual pathway, a new objective technique," J. Neurol, Neurosurg. Psychiat. 32, 479-483 (1969). 13 B. A. Milner, D. Regan, and J. R. Heron, "Differential diagnosis of multiple sclerosis by visual evoked potential recording," Brain 97, 755-772 (1974). l4 D. Regan, "Latencies of evoked potentials to flicker and to pattern speedily estimated by simultaneous stimulation meth od," Electroenceph. Clin. Neurophysiol. 40, 654-660 (1976). 15 C. H. Graham, editor, Vision and Visual Perception (Wiley, New York, 1965), p. 637. 16 D. A. Jeffreys, "CorticaL source locations of pattern related visual evoked potentials recorded from the human scalp," Nature 229, 502-504 (1971). Thus far, the present author has found no significant differences in steady-state latencies of positive versus negative EP peaks. The parameters stud ied in Jeffreys' transient experiment, however, have yet to be explored. 17 Unpublished finding by the present author.
JOSA Letters
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