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Research Article  |   June 2009
Dynamics of chromatic visual system processing differ in complexity between children and adults
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Journal of Vision June 2009, Vol.9, 22. doi:10.1167/9.6.22
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      Mei Ying Boon, Catherine M. Suttle, Bruce I. Henry, Stephen J. Dain; Dynamics of chromatic visual system processing differ in complexity between children and adults. Journal of Vision 2009;9(6):22. doi: 10.1167/9.6.22.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Measures of chromatic contrast sensitivity in children are lower than those of adults. This may be related to immaturities in signal processing at or near threshold. We have found that children's VEPs in response to low contrast supra-threshold chromatic stimuli are more intra-individually variable than those recorded from adults. Here, we report on linear and nonlinear analyses of chromatic VEPs recorded from children and adults. Two measures of signal-to-noise ratio are similar between the adults and children, suggesting that relatively high noise is unlikely to account for the poor clarity of negative and positive peak components in the children's VEPs. Nonlinear analysis indicates higher complexity of adults' than children's chromatic VEPs, at levels of chromatic contrast around and well above threshold.

Introduction
Psychophysical (Knoblauch, Vital-Durand, & Barbur, 2001; Ling, 2004; Ling & Dain, 2008) and VEP (Boon, Suttle, & Dain, 2007) measures of chromatic contrast sensitivity are lower in children than in adults. In children but not in adults, VEP estimates of chromatic contrast sensitivity (assessed on the basis of the smallest chromatic contrast, which elicits a repeatable VEP) are higher than psychophysical estimates (Boon et al., 2007). VEPs recorded from children, in response to stimuli of moderate to high chromatic contrast, are repeatable and clearly defined but differ from adults' responses in terms of morphology (Boon et al., 2007; Madrid & Crognale, 2000; Pompe, Kranjc, & Brecelj, 2006). However, children's VEPs in response to stimuli set at their individual psychophysically determined chromatic contrast threshold (T%) or at twice this level (2T%), unlike adults', do not contain recognizable VEP components, which are distinguishable from baseline activity in terms of morphology or are repeatable in latency (defined as having a difference in latency of no longer than 10% of the longest latency on successive averaged VEPs; Boon et al., 2007). Representative VEPs illustrating this trend are presented in Figure 1. In this case, the VEPs are in response to a 2-Hz chromatic onset–offset VEP, which should result in two distinctive VEP responses in the 1000-ms epoch shown here. The adult's VEPs show the characteristic N–P complex for stimuli set at psychophysical threshold (T%), 2T% and 42% for the two averaged sweeps (indicated in light gray) and over the 1000-ms epoch. However, the child's VEPs were not repeatable either between averaged sweeps or over the 1000-ms epoch. Although there is a level of examiner subjectivity in identifying peaks and troughs in VEP morphology, VEP findings indicate immaturity of the chromatic visual system in children, which is characterized by decreased VEP component repeatability at low to moderate chromatic contrasts. The child's VEPs at T% and 2T% also show a strong rhythmic alpha frequency component at baseline, T% and 2T% that also creates ambiguity in the clarity of any rhythmic VEP components, such as negative and positive peaks related to chromatic contrast. 
Figure 1
 
Representative VEPs from one adult (EA, 25.7 years old, left column) and one child (JY, 8.3 years old, right column) in response to chromatic contrasts ranging from 0% to 42%, as indicated by the central numbers (adult–child). The gray lines show two VEPs (average of 30 sweeps each). The dark bold lines show the average of two VEPs (i.e., average of 60 sweeps). The upward pointing arrows indicate the dominant N-peaks, downward pointing arrows indicate the dominant P-peaks, and the slanted arrows indicate the shoulders. Where there are no arrows plotted, this indicates that there were no recognizable VEP components that were repeatable (components with longest latency within 10% of each other between averaged sweeps or across the 1000-ms epoch). It can be seen that VEPs are repeatable for 42%, 2T%, and T% in the adult but only becomes repeatable at 14% chromatic contrast in the child. Psychophysical chromatic contrast thresholds were approximately 5% for both subjects EA and JY.
Figure 1
 
Representative VEPs from one adult (EA, 25.7 years old, left column) and one child (JY, 8.3 years old, right column) in response to chromatic contrasts ranging from 0% to 42%, as indicated by the central numbers (adult–child). The gray lines show two VEPs (average of 30 sweeps each). The dark bold lines show the average of two VEPs (i.e., average of 60 sweeps). The upward pointing arrows indicate the dominant N-peaks, downward pointing arrows indicate the dominant P-peaks, and the slanted arrows indicate the shoulders. Where there are no arrows plotted, this indicates that there were no recognizable VEP components that were repeatable (components with longest latency within 10% of each other between averaged sweeps or across the 1000-ms epoch). It can be seen that VEPs are repeatable for 42%, 2T%, and T% in the adult but only becomes repeatable at 14% chromatic contrast in the child. Psychophysical chromatic contrast thresholds were approximately 5% for both subjects EA and JY.
Recently, we have found that transient chromatic VEPs recorded from adults may be modeled as arising from a nonlinear deterministic (future states arising from initial states) dynamical (evolving over time) system (Boon, Henry, Suttle, & Dain, 2008) according to coupled differential equations, which contain nonlinear terms (Sprott, 2003). Such systems may be sensitive to initial states so that similar inputs may generate very different outputs (Sprott, 2003). Furthermore, the outputs may be random and variable when analyzed as time series in the time and frequency domains. However, the deterministic structure is apparent when the time series is embedded in an abstract mathematical space called phase space (Grassberger & Procaccia, 1983a, 1983b). One way to measure the presence or absence of deterministic structure is to estimate the correlation dimensions of the time series as it is embedded in several dimensions of phase space and compare these estimates with time series known to be stochastic (Grassberger & Procaccia, 1983a, 1983b). The smallest dimension of space that is able to contain the phase space embeddings provides an estimate of the minimum number of dynamical variables (variables that evolve in time) required to model the dynamical system (Grassberger & Procaccia, 1983a, 1983b). When applied to electrophysiological signals derived from the brain, these dynamical variables must logically derive from the source generators of the electroencephalogram (EEG). Each of the dynamical variables might model the collective behavior of an independent population of active neuronal assemblies (Müller, Lutzenberger, Preissl, Pulvermüller, & Birbaumer, 2003; Sprott, 2003). The dynamical variables have also been conceptualized as active functional systems (Anokhin, Birbaumer, Lutzenberger, Nikolaev, & Vogel, 1996). It is likely that children's chromatic VEPs may also be modeled as arising from a nonlinear dynamical system such that the relative complexity of the visual systems of children and adults may be compared (Boon et al., 2008). 
VEP morphology is characterized in the time domain. However, if structure is not evident within the time domain (e.g., recognizable VEP components), structure may be more evident in the frequency and phase space domains, which are accessible through Fourier and nonlinear dynamical analyses, respectively. Therefore, the aim of this study was to gain insights into the dynamics of chromatic contrast processing in children using Fourier and nonlinear dynamical analyses. 
Methods
Design
This study examined and compared transient chromatic VEPs in response to four levels of chromatic contrast (42%, 2T%, T%, and 0%; where T = psychophysical threshold) in children (4.8–12.6 years) and adults (26–33 years) using linear (Fourier analysis) and nonlinear dynamical (correlation dimension) analyses. The VEPs were compared in terms of Fourier power spectra, signal-to-noise ratio (SNR), evidence for nonlinearity, and level of complexity, hence the minimum number of dynamical variables making a significant contribution to the VEPs. VEP data were drawn from a previous study (Boon et al., 2007). 
Participants
All methods were approved by the University of New South Wales (UNSW) human research ethics committee and followed the tenets of the Declaration of Helsinki. Children and adults were recruited by advertisement in a UNSW newsletter and a local newspaper. Participants were divided into four age groups as follows: Adults (n = 11, mean age: 28 years, range 26–33, 5 males, 6 females), 10 to 13 years ( n = 9, mean age: 11.3 years, 4 M, 5 F), 7 to <10 years ( n = 14, mean age: 8.7 years, 6 M, 8 F), and 4.8 to <7 years ( n = 8, mean age: 5.9 years, 6 M, 2 F). The children were divided into these three age ranges (approximately early, middle, and late childhood) so that maturational changes could be investigated. All participants had normal visual acuity, color vision (on screening with Ishihara pseudoisochromatic plate test), no ocular abnormality (as assessed by direct undilated ophthalmoscopy), no amblyopia, or uncorrected astigmatism. 
Stimuli
The stimuli for both psychophysical and electrophysiological testing were identical in order to maximize comparability of the two methods. In both cases, the stimuli were heterochromatic (magenta–cyan), nominally isoluminant, obliquely oriented (45° or 135°) sinusoidal gratings of spatial frequency 1 cycle per degree (cpd) presented in square-wave pattern onset–offset mode at a temporal frequency of 2 Hz and a duty cycle of 1:4 (stimulus on for 100 ms then off for 400 ms) on a background and surround of the same mean chromaticity (x = 0.305, y = 0.310) and luminance (20 cd m −2). Because of known raster and oblique effects (Rabin, Switkes, Crognale, Schneck, & Adams, 1994), the stimuli were oriented obliquely (45° or 135°) rather than horizontally and vertically. The grating stimuli were centrally located, to avoid isoluminance variations with retinal location (Bilodeau & Faubert, 1999; Kulikowski, Robson, & McKeefry, 1996), presented as a square patch with sides subtending an angle of 5°. At maximum contrast, the colors were of CIE chromaticity coordinates x = 0.38, y = 0.27 (magenta) and x = 0.23, y = 0.35 (cyan), resulting in cone excitations of L magenta = 12.1, L cyan = 14.4, M magenta = 5.6, M cyan = 7.9, S magenta = 0.21, Scyan = 0.20. If cyan is regarded as the stimulus color and magenta as the background color, the L-, M- and S-cone contrasts elicited were −0.16, 0.40, and −0.07 (Cole & Hine, 1992). In the present study, chromatic contrast threshold was expressed as a percentage of maximum available chromatic contrast. The spatial, temporal, and chromatic parameters of the stimuli were chosen to stimulate the L–M chromatic contrast system preferentially (Kulikowski, McKeefry, & Robson, 1997; McKeefry, Russell, Murray, & Kulikowski, 1996; Mullen, 1985; Murray, Parry, Carden, & Kulikowski, 1987; Rabin et al., 1994; Suttle & Harding, 1999) while minimizing the effects of chromatic aberration (Flitcroft, 1989). 
Isoluminance was determined using heterochromatic flicker photometry (mean of 11 determinations of minimal flicker of centrally presented heterochromatic magenta–cyan stimuli with a spatial frequency of 1.0 cpd, field size of 2.5° and square-wave phase reversed at a 15-Hz temporal frequency). The color ratio (L color1 / (L color1 + L color2)) was varied by the participant (method of adjustment). For nine of the adults and three of the children, stimuli were at their individual isoluminance color ratios. The remaining participants were tested at the average isoluminance color ratio of a larger group of adult participants. Two of the adults were tested using an average value as their VEPs because no individual isoluminance measure was made. Most of the children were tested using an average adult value as the concept of minimal flicker in the heterochromatic flicker photometry task was difficult to grasp in preliminary work on children. Previous researchers have used mean adult values for isoluminance as an approximation of the color ratio of children's isoluminance (Crognale, 2002; Till, Westall, Koren, Nulman, & Rovet, 2005) and this has been assessed as a valid procedure under certain conditions (Pereverzeva, Hui-Lin Chien, Palmer, & Teller, 2002) so an average adult value was used with the understanding that luminance cues may be introduced if the participant's individual isoluminance color ratio is different from the average isoluminance color ratio employed. 
All stimuli were generated using a VSG 2/5 card (Cambridge Research Systems, England) and were presented on a Sony CPD-G500 21-inch Trintron color monitor that was both gamma corrected and calibrated for correct color and luminance rendering using a luminance meter (Minolta LS-110) and a CRT tricolorimeter (Minolta TV CA 2150). 
VEP recording
VEPs were drawn from an earlier experiment, which compared VEP and psychophysical thresholds (Boon et al., 2007). In that study (Boon et al., 2007), VEP thresholds were assessed using an adaptive staircase method where VEP threshold was defined as the minimum contrast resulting in repeatable waveforms (defined as successive averaged recordings containing identifiable peaks/troughs with latency that differ by no more than 10% of the longest latency; Boon et al., 2007; McCulloch & Skarf, 1991, 1994). In the adaptive staircase, 42% and 0% chromatic contrast VEPs were first recorded in order to gain an understanding of the typical morphologies of chromatic and baseline electrophysiological activities for that individual participant. The next VEP was recorded in response to the participant's individual psychophysical chromatic thresholds (T%). If the VEP was not repeatable in morphology, chromatic contrast was doubled for the next VEP recording. If the VEP was repeatable in morphology, the next VEP was decreased by half the difference in chromatic contrast between the highest chromatic contrast that did not result in a repeatable VEP and the lowest chromatic contrast that resulted in a repeatable VEP. If this step size was less than or equal to 2%, recording was stopped and VEP threshold was defined as the lowest chromatic contrast that resulted in a VEP of repeatable morphology. According to this method, the only chromatic contrasts that were common across all participants were 0%, T%, 2T%, and 42%. For this reason, the VEPs in response to these chromatic contrasts were selected for comparison and analysis in the present study. 
VEPs were recorded from Oz (active), Fz (earth), and Cz (reference) locations using the 10–20 system (Odom et al., 2004). Two VEPs were recorded for each stimulus condition using a Medelec Synergy averager (Radiometer, Sydney, Australia) at a 1000-Hz sampling frequency, 1-s epochs (sweep durations), an amplifier range of 2.5 mV, and low- and high-pass filters of 1 to 50 Hz. Each VEP was the average of 30 single sweeps and the single sweeps that made up the averaged VEPs were not accessible in the hardware/software configuration. This number of sweeps was selected to ensure that the children did not lose attention during each recording. 
Psychophysical threshold was determined using a two-alternative forced choice (orientation) technique using a 3-down 1-up staircase method. In this study, we aimed to discover whether Fourier or nonlinear analysis may provide further insights into the differences in VEP morphology between children and adults in response to chromatic contrast. Fourier analysis included an exploration of Fourier power spectra and signal-to-noise ratio. Nonlinear analysis included assessment of one complexity measure (the correlation dimension) and whether the signal contained chaotic characteristics such as nonlinearity. 
VEP analysis
We focused on linear (Fourier power spectra and signal-to-noise ratio) and nonlinear (correlation dimension) VEP analyses, based on previously described methods (Boon et al., 2008, 2007; Boon, Suttle, & Henry, 2005). 
Calculation of signal-to-noise ratio (SNR)
Several methods of calculating SNR using Fourier analysis have been described (Norcia, Clarke, & Tyler, 1985; Norcia & Tyler, 1985; Victor & Mast, 1991; Weiss & Kelly, 2003). They may be based on the variability of single-sweep recordings (e.g., Victor & Mast, 1991) or involve a direct comparison between the power of signal-related and noise-related frequencies (Norcia & Tyler, 1985). Signal-related frequencies have been found to be associated with the stimulus temporal frequency (McKeefry et al., 1996), but for transient VEPs Fourier power may be distributed at frequencies that are not necessarily harmonics of the stimulus temporal frequency (Boon et al., 2005; Spekreijse, 1966). This latter characteristic has been described as nonlinearity in terms of input and output frequencies (Spekreijse, 1966). In addition, Fourier analysis assumes that an epoch is typical of a recurring cycle so if there is a large discontinuity in amplitude between the start and the end of the epoch, artifacts may result. This issue is of great importance when analyzing steady-state VEPs of sinusoidal waveform (Bach & Meigen, 1999). However, because the VEP data analyzed in the present study commenced from baseline activity and returned to baseline by the end of the epoch, discontinuities of this kind were minimized. Methods of calculating SNR using single sweeps could not be applied to our data as our electrophysiological recording setup did not allow recording of single sweeps without lengthy delays between each sweep recording. Therefore, for comparison at least with steady-state SNR calculations, two measures of SNR were made by defining signal as the average power at 2, 4, 6, and 8 Hz and noise as the average power at 1, 3, 5, 7, and 9 Hz (SNR1) or as the average power of four randomly selected frequencies between 1 and 10 Hz (SNR2). These signal and noise frequencies were based on observations of the peaks in the Fourier power spectra shown in Figure 2 for responses to 42% chromatic contrast stimuli. The spectra show relatively high peaks at fundamental and harmonic frequencies of 2, 4, 6, and 8 Hz, consistent with previous reports that signal-related frequencies are related to stimulus temporal frequency (McKeefry et al., 1996; Suttle, Banks, & Graf, 2002). The use of nonharmonic frequencies that are one-way frequencies unrelated to the stimulus temporal frequency can be targeted as an approximation of noise (Norcia & Tyler, 1985). The use of random frequencies in the calculation of SNR2 is an attempt to acknowledge that noise frequencies can occur at frequencies that are harmonic, nonharmonic, and subharmonic to the stimulus temporal frequency (Boon et al., 2005; Spekreijse, 1966), particularly in nonlinear oscillator systems. It must be kept in mind that alternative algorithms for SNR calculation may yield different outcomes. 
Figure 2
 
Fourier power spectra of VEPs in response to 42% chromatic contrast in order of age (years) along the z-axis. It can be seen that children have higher amplitude Fourier power spectra than adults.
Figure 2
 
Fourier power spectra of VEPs in response to 42% chromatic contrast in order of age (years) along the z-axis. It can be seen that children have higher amplitude Fourier power spectra than adults.
The VEPs were not exponentially windowed for the SNR calculations. Instead, the default rectangular window was used. This was because preliminary analysis revealed that exponential windowing of the raw VEP data changed the start and end values of the sweep by very little as the start and end of the sweep were baseline electrophysiological responses. 
Nonlinear analysis
VEPs were analyzed for evidence of nonlinearity using the correlation dimension (the method by Grassberger & Procaccia, 1983a, 1983b), a nonlinear fractal measure that is used to characterize the complexity of time series. The method has been applied to visual evoked potential time series (Arle & Simon, 1990; Schmeisser, 1993) and EEGs (Fell, Röschke, Mann, & Schäffner, 1996; Müller, Lutzenberger, Pulvermüller, Mohr, & Birbaumer, 2001; Stam et al., 1995). Its main advantages are that it is an objective measure of physiological signals, which can differentiate between signals that are not distinguishable on the basis of spectral analysis (Boon et al., 2008; Fell et al., 1996), and that it can be used to quantify the number of components contributing to a signal (Grassberger & Procaccia, 1983a, 1983b). 
The methods used to calculate the correlation dimension and to test for nonlinearity of the children's VEPs are described elsewhere (Boon et al., 2008). A brief outline of the method is given below. 
Firstly, the time series data were transformed from the time domain into phase space. Specifically, the time series (represented as y( t 1), y( t 2),…) were converted into evolving sets of coordinates in different dimensions of phase space using the following formula: X i = ( y( t i), y( t i + τ), y( t i + 2 τ),…, y( t i + ( m − 1) τ), where X i is the reconstructed phase space trajectory, m is the embedding dimension, τ is a constant known as the delay time, and the index i denotes ordering in time. In the present study, two delay times ( τ = 4 ms and 6 ms) were used and the correlation dimension, D 2, was estimated for five embedding dimensions in phase space, m = 1, 2, 3, 4, and 5. 
In Grassberger and Procaccia's (1983a, 1983b) method, the correlation dimension is determined for different reconstructions of the phase space trajectory in different dimensions of phase space. The maximum correlation dimension that can be estimated is limited by the number of dimensions in which the phase space trajectory is embedded (i.e., a 3-dimensional fractal object will be estimated as a maximum of 2 dimensions in 2-dimensional phase space but as 3 dimensions in phase spaces of 3 dimensions and above). A characteristic of stochastic noise is that it tends to fill in all the available phase space subject to limitations imposed by the number of points such that linearly filtered noise results in a lower estimated correlation dimension compared to unfiltered noise (Lo and Principe, 1989). Thus, one common test for nonlinearity is to compare the signal data to surrogate data (a stochastic signal of the same mean variance and power spectrum as the signal, equivalent to colored noise; Theiler, Eubank, Longtin, Galdrikian, & Doyne Farmer, 1992). If the correlation dimension is plotted as a function of embedding phase space dimension for both the signal and the surrogate data and their behaviors are found to be significantly different from each other (i.e., a significantly different value at which the correlation dimension plateaus), then the signal can be regarded as significantly different from stochastic noise. 
For each reconstructed phase space trajectory, the distances between all points in the trajectory were calculated and the logarithm of the smallest distance (represented by r min) and the logarithm of the largest distance (represented by r max) were computed. A series of “bins” was then created to record the Correlation Sum, C(r), which is the normalized number of pairs of points with a separation distance of less than a specified distance r. In this study, 64 bins (an arbitrary number) were used and the width of each bin was set to ( r maxr min) / 64. Thus, from first to last, the separation distances used in the analysis were defined by the series r 1, r 2,… r n, where the radius r n = r min + n( r maxr min) / 64, where n = 1 to 64. D 2 is then approximated by D 2 ∼ log( C( r)) / log( r) (Grassberger and Procaccia, 1983a, 1983b). “∼” indicates that this is a scaling relationship, so D2 was calculated as the slope, dlog(C(r)) / dlog(r), of the linear scaling portion of the plot of log(C(r)) versus log(r). In this study, the slope of the scaling portion of the plot was calculated by determining the slopes of i consecutive local portions of the plots, with each portion consisting of k consecutive points (k = 6, 12), and finding a local maximum slope in a region where the slopes were relatively constant. The slope for each ith portion was determined to be the slope of the line of best fit (least squares method) drawn through the points that were part of the ith portion of the plot. 
The VEPs were tested for nonlinearity by creating two surrogate time series (being identical to the original VEP data in terms of Fourier amplitudes but with randomized phase) and examining plots of D 2 as a function of m for these data (Theiler et al., 1992). The plateau index (PI; Boon et al., 2008) was calculated to determine whether the function plateaued. PI < 0.3, where PI = (D2 at m = 5) − (D2 at m = 4) was taken to indicate that the function did plateau. PI was compared between VEP and surrogate data to determine whether the VEPs were nonlinear. 
Statistical analysis
Repeated measures analysis of variance was used to test for interactions between age group and the VEP in response to differing levels of stimulus chromatic contrast, and for significant differences within and between groups. Pearson's correlation was used to test the relationship between correlation dimension, stimulus chromatic contrast, and Fourier power. To assess the level of concordance or agreement of the rankings of VEP fractal dimension (as a function of power and chromatic contrast) across subjects within each group, the nonparametric test Kendall's W was used. 
Results
Linear analysis
The normalized (to the highest power overall) Fourier powers of harmonic and nonharmonic frequencies from 1 to 12 Hz derived from VEPs in response to 42% contrast stimuli are presented in Figure 2. It may be seen that VEPs recorded from children have much higher power than those recorded from adults ( Figure 2), and this finding is consistent with previous work showing relatively high amplitude VEPs in children (Allison, Hume, Wood, & Goff, 1984; Balachandran, Klistorner, & Billson, 2004; Brecelj, 2003; Madrid & Crognale, 2000; Snyder, Dustman, & Shearer, 1981). The signal in response to the 42% chromatic stimulus at all tested age groups (4.5 to <7 years old, 7 to <10 years old, 10 to 13 years old, adults) is characterized by a Fourier profile with power concentrated at 2, 4, and 6 Hz (equivalent to the fundamental and harmonics of the stimulus temporal frequency), in agreement with previous findings (McKeefry et al., 1996). 
Low signal-to-noise ratio (SNR) may result in poorer VEP repeatability of components in the time domain. SNR1 and SNR2 for each age group and each stimulus condition are presented in Figure 3. A repeated measures ANOVA was run with stimulus contrast as a within-subjects factor (4 levels), type of SNR as a within-subjects factor (2 levels), and age group as a between-groups factor. Overall, there was no significant difference in SNR between the age groups ( p = 0.39), no significant interaction between type of SNR and age group ( p = 0.63), and no significant interaction between stimulus contrast and age group ( p = 0.61). Pairwise comparisons indicated that the SNR of 42% was significantly different from all other chromatic contrasts ( p < 0.0001, Bonferroni corrected) but that SNR of 2T%, T%, and 0% were not significantly different from each other ( p ranged from 0.08 to 1.00, Bonferroni corrected). Pairwise comparisons also indicated that SNR2 was lower than SNR1 estimates ( p < 0.0001, Bonferroni corrected) by approximately 0.38. 
Figure 3
 
Signal-to-noise ratio (mean ± standard error) across age groups for four stimulus contrast levels. The upper panel uses the algorithm of SNR1 and the lower panel uses the algorithm of SNR2 to calculate signal-to-noise ratio.
Figure 3
 
Signal-to-noise ratio (mean ± standard error) across age groups for four stimulus contrast levels. The upper panel uses the algorithm of SNR1 and the lower panel uses the algorithm of SNR2 to calculate signal-to-noise ratio.
Nonlinear analysis
The correlation dimension ( D 2) of all of the VEP data combined (responses to all contrast levels) and their surrogates for each age group are presented in Figure 4. The plateau index was also determined and compared across VEP and surrogate data, as shown in Figure 5. The surrogate and VEP measures were found to be significantly different ( p < 0.05) indicating that the D 2 of the VEPs recorded from children is the fractal dimension of a nonlinear dynamical system, which is not equivalent to stochastic noise. Therefore, the correlation dimension at m = 5 may be considered an estimate of the fractal dimension of the underlying system. 
Figure 4
 
VEP and surrogate data correlation dimensions by age group (mean and standard deviations, error bars). VEP and surrogate correlation dimensions were significantly different ( p < 0.05).
Figure 4
 
VEP and surrogate data correlation dimensions by age group (mean and standard deviations, error bars). VEP and surrogate correlation dimensions were significantly different ( p < 0.05).
Figure 5
 
VEP and surrogate data plateau indices by age group (mean and standard deviations, error bars). It can be seen that the VEP data plateau (indicated by a plateau index value that is close to 0.0, here arbitrarily defined as 0.3) but the surrogate data do not.
Figure 5
 
VEP and surrogate data plateau indices by age group (mean and standard deviations, error bars). It can be seen that the VEP data plateau (indicated by a plateau index value that is close to 0.0, here arbitrarily defined as 0.3) but the surrogate data do not.
A plot of the mean fractal dimensions by age group and stimulus contrast is presented in Figure 6. VEPs recorded from adults were of higher fractal dimension than those recorded from children. The correlation dimensions of VEPs from all four age groups were compared using repeated measures ANOVA. Stimulus contrast (42%, 2T%, T%, and 0%) was the within-subjects variable and age group was the between-groups variable. There was a significant overall effect of stimulus contrast ( F(3, 33) = 33.141, p < 0.0001). There was no interaction between stimulus contrast and age group ( F(9, 105) = 0.942, p = 0.492). There was a significant within-subjects effect of stimulus contrast ( F(3, 105) = 40.074, p < 0.0001) and a significant effect due to age group ( F(3, 35) = 14.374, p < 0.0001). Paired comparisons indicated that the fractal dimensions of the adult VEPs were significantly different from each of the child groups ( p < 0.0001), but that the children's groups were not significantly different from each other ( p = 0.68 to 0.94). The children's fractal dimension data were lower than the adult data by an average of 0.55 ( Figure 6). Paired comparisons also revealed that the fractal dimension for all chromatic contrasts were significantly different from each other ( p ≤ 0.002) except for 2T% and 0% ( p = 0.419). Thus, the order from lowest to highest fractal dimension VEP was 42%, 2T% = 0%, T%. This trend is similar in children and adults (see also Boon et al., 2008). 
Figure 6
 
Mean and standard errors of fractal dimension by stimulus contrast for the different age groups. The shaded box represents fractal dimensions of unevoked potentials (VEP in response to 0% contrast), where there was no time-locked visual stimulus.
Figure 6
 
Mean and standard errors of fractal dimension by stimulus contrast for the different age groups. The shaded box represents fractal dimensions of unevoked potentials (VEP in response to 0% contrast), where there was no time-locked visual stimulus.
Correlation analyses were run to determine whether there was a relationship between the chromatic contrast (42%, 2T%, and T% only; note that 0% was not included as this would represent a brain state in which the chromatic visual system is not stimulated), fractal dimension, and Fourier powers of VEPs recorded from children (see Figure 7). The data were first checked for normality and transformed (square root or logarithmic transformations) if necessary before running Pearson's correlation. Pearson's correlation showed that for each of the children's age groups, fractal dimension and stimulus contrasts above zero (42%, 2T%, T%) are negatively correlated (4.5 to <7 years old: R = −0.56, p = 0.005, n = 24; 7 to <10 years old, R = −0.38, p = 0.03, n = 32; 10 to 13 years old, R = −0.49, p = 0.006, n = 30), which was also true for the adults' data (see also Boon et al., 2008). Pearson's correlation also showed that fractal dimension and power are moderately negatively correlated for VEPs in response to stimulus contrasts above zero (42%, 2T%, T%; 4.5 to <7 years old: R = −0.62, p = 0.002; n = 24; 7 to <10 years old, R = −0.55, p = 0.002, n = 29; 10 to 13 years old, R = −0.67, p < 0.0001, n = 28). 
Figure 7
 
VEP correlation dimension, here equivalent to fractal dimension, as a function of chromatic contrast (column 1) and power (column 2) and power as a function of chromatic contrast (column 3) for the four age groups (4.5 to <7, 7 to <10, 10 to 13, 20 to <40) in order from youngest to oldest (a, b, c, and d). The data points of each individual subject have been joined by lines (separate lines for each subject). The lines join the data points representative of correlation dimension in order of the rank of the powers for (a) and in order of the ranks of chromatic contrast for (b).
Figure 7
 
VEP correlation dimension, here equivalent to fractal dimension, as a function of chromatic contrast (column 1) and power (column 2) and power as a function of chromatic contrast (column 3) for the four age groups (4.5 to <7, 7 to <10, 10 to 13, 20 to <40) in order from youngest to oldest (a, b, c, and d). The data points of each individual subject have been joined by lines (separate lines for each subject). The lines join the data points representative of correlation dimension in order of the rank of the powers for (a) and in order of the ranks of chromatic contrast for (b).
In order to determine whether there was agreement of the rankings of VEP fractal dimension (as a function of power and chromatic contrast) across subjects within each group, the nonparametric Kendall's W (coefficient of concordance) was calculated. For each age group, the highest fractal dimension was attributable to T% chromatic contrast, followed by 2T% and 42%. However, the degree of concordance of rankings within each group differed between age groups. It was strongest in the adults (Kendall's W = 0.83, p = 0.001; data from Boon et al., 2008), then the youngest children (Kendall's W = 0.67, p = 0.005), the second youngest group of children (Kendall's W = 0.49, p = 0.007) and lowest in the oldest group of children (Kendall's W = 0.48, p = 0.008). As shown by Figure 7 (center column), correlation dimension was more strongly correlated with power in children than in adults (Spearman's rho = 0.30, p = 0.09; data from Boon et al., 2008). The degree of concordance of rankings was moderate in the youngest age group (Kendall's W = 0.67, p = 0.004) and middle age group of children (Kendall's W = 0.49, p = 0.007) and low in the oldest group of children (Kendall's W = 0.37, p = 0.02). 
Group-averaged VEPs show subtle differences in morphology between the 42% VEPs recorded from children of different age groups. For example, the early N-peak is increasingly apparent with maturation (Boon et al., 2007). However, closer examination of individual VEP morphologies within each of the children's age groups reveals that morphology does not progress in an orderly fashion as group-averaged waveforms might appear to suggest. The children's VEPs were usually dominated by a large positive (P) peak followed by an equally large or slightly smaller negative (N) peak. On the other hand, adult VEPs were usually dominated by a large negative peak followed by a large positive peak. There were variations that included shoulders or additional late components, but these were secondary to the dominant morphology of the P–N complex in the children (left and middle panels, Figure 8) and N–P complex in the adults (right panel, Figure 8). 
Figure 8
 
VEPs in response to 42% chromatic contrast from two children and one adult (left to right). The children's VEPs show P–N complexes with one additional shoulder (left) and no shoulder (middle) and the adult panel shows an N–P complex with one shoulder.
Figure 8
 
VEPs in response to 42% chromatic contrast from two children and one adult (left to right). The children's VEPs show P–N complexes with one additional shoulder (left) and no shoulder (middle) and the adult panel shows an N–P complex with one shoulder.
There were exceptions. Two out of nine adults had VEPs in response to 42% chromatic contrast that displayed PN morphology and one child's VEP displayed NP morphology. We further divided VEP morphology into four categories for the children's and adults' data: (1) P-EN—indicated a large P-peak followed by an equally large N-peak, (2) P-SN—indicated a large P-peak followed by a smaller N-peak, (3) N-LP—indicated an N-peak followed by a larger P-peak, and (4) N-EP—indicated an N-peak followed by an equally large P-peak. When morphology category was examined for differences in age, the N-EP morphology group was found to be significantly older than each of the other morphology types ( F(3, 33) = 24.911, p < 0.0001, ANOVA; mean difference: 17.1–19.6 years older; p ≤ 0.03), but the other groups were not significantly different from each other. When morphology category was examined for differences in fractal dimension, again the N-EP morphology group was found to be significantly different from each of the other groups ( F(3,29) = 6.757, p = 0.001, ANOVA; mean difference: 0.10 to 0.15 higher in fractal dimension than other groups; p ≤ 0.047), but the other groups were not significantly different from each other. 
Discussion
Insights from linear Fourier analysis
Signal-to-noise ratio did not differ significantly between adults and children. This suggests that poor recognizability of VEP components (due to poor repeatability of VEP components) of the children's transient chromatic VEPs in the time domain is not due to lower SNR in this group. It should be noted, however, that different methods of noise estimation, and different methods of SNR calculation such as those based on the variability of single-sweep recordings (e.g., Victor & Mast, 1991), may produce different results. It has been suggested previously that low SNR may be due to poor signal recognition algorithms, which cannot distinguish rhythmic VEP power from rhythmic EEG power such as alpha rhythms (Klistorner & Graham, 2001). Unfortunately, the VEP recording hardware and software used in this study did not enable us to record single sweeps in a timely manner; therefore, the alternative methods of SNR calculation could not be used. Optimization of SNR algorithms for averaged transient VEPs would be beneficial. 
Insights from nonlinear dynamical analysis
Nonlinear time series analysis using Grassberger and Procaccia's (1983a, 1983b) algorithm indicates that transient chromatic VEPs recorded from children may, as is the case in adults (Boon et al., 2008), be regarded as components of nonlinear dynamical systems and are not equivalent to colored (linearly filtered) noise. In other words, VEPs without clear, repeatable components are not composed of high levels of stochastic noise. In all subject age groups tested here, VEPs recorded in response to stimuli at different chromatic contrasts (42%, 2T%, T%, and 0%) showed significantly different levels of VEP complexity as quantified by the correlation dimension at m = 5. Therefore, the correlation dimension at m = 5 may be regarded as an estimate of the fractal dimension of the dynamical system. Of the stimuli modulated in chromatic contrast (42%, 2T%, and T%), T% had the highest mean fractal dimension in all age groups. This finding could be taken to suggest that the fractal dimension may prove useful as a preliminary discriminant of chromatic contrast threshold in both adults (Boon et al., 2008) and children. In addition, the fractal dimension was significantly different between 42%, 2T% and T% and 0% in both children and adults (grouped data) despite the VEP morphology between 2T%, T% and 0% being indistinguishable in the children. As the Kendall W results showed, the fractal dimension was not a strong indicator of psychophysical threshold for individual child participants, indicating that it is not likely to be generally useful as an indicator of contrast threshold in children. Subtle differences in 42% VEP morphology between children in the three age groups were not reflected in the fractal dimension, which was similar across the three age groups. However, this may be because the group averaged VEP morphologies do not fully reflect the variability of the morphology of individuals within each of the children's age groups. In each age group, there were individuals with and without late components, with and without early N-peaks and shoulders ( Figure 8). Instead, the fractal dimension appeared to be associated with the most obvious difference between the adult and child VEPs, which was the order and magnitude of the largest repeatable VEP components (PN in the children and NP in the adults). 
Fractal dimensions were found to be significantly lower in all children's age groups than in the adult group. This trend of simpler dynamics in children occurs for both chromatic processing (of 42%, 2T%, and T% stimuli) and when there is no chromatic stimulus (0%). Variation of fractal dimension with stimulus contrast, as discussed above, follows a similar trend in the children and adults. One interpretation of this finding, based on nonlinear dynamics, is that fewer independent dynamical variables contribute to the transient chromatic VEP in children than in adults. It should be noted, however, that the mean difference in dimension between children and adults was less than 1, which may indicate relatively high complexity of VEPs recorded from adults, and not necessarily the presence of one additional component (Sauer, Yorke, & Casdagli, 1991). In the framework of nonlinear dynamics, it appears that at least three independent dynamical variables account for transient chromatic VEPs recorded from children and at least three to four independent variables are needed to account for the VEPs recorded from adults. Since the mean fractal dimension at T% in adults is above 3.0, in theory this could indicate that a minimum of four variables is implicated in processing. Relatively low complexity of responses from children may also be related to higher chromatic contrast thresholds of the children compared with adults (Knoblauch et al., 2001; Ling, 2004; Ling & Dain, 2008), with fewer and/or different populations of neurons being involved at T% in the children than in adults. This is consistent with previous findings in face and object recognition (Gathers, Bhatt, Corbly, Farley, & Joseph, 2004). 
Models of VEP generation usually include at least three components. For example, Kremlácek and Kuba (1999) and Kremlácek, Kuba, and Holcík (2002) modeled the magnocellular VEP with each visual area or neuronal population (e.g., LGN, V1, V2, higher processing areas) acting as a nonlinear oscillator with delays in activation times. Such a model suggests a higher number of dynamical variables than are indicated by the present research. Arroyo, Lesser, Poon, Webber, and Gordon (1997), however, notes that scalp recordings of VEPs are likely to be a “simplified representation” of neural activity that occurs at the cortex and that convergence of stimuli or existence of parallel streams of processing may not be easily differentiated. Furthermore, it is possible that magnocellular and parvocellular processing differs in complexity; however, this requires further research. Other models of scalp VEP generation have looked at cellular interactions and have also identified a minimum of three contributors to the VEP signal, namely communications between pyramidal cells and local excitatory and inhibitory interneurons (e.g., Jansen, Zouridakis, & Brandt, 1993). 
In a previous paper in which we focused on the adult data (Boon et al., 2008), we discussed why the fractal dimension in the absence of visual stimulation (0% contrast) may be lower than at psychophysical threshold (T%). Theoretically, the fractal dimension is closely related to the minimum number of dynamical variables (in this case, populations of neuronal assemblies involved in generation of the electrophysiological signal; Müller et al., 2003), which are activated. We suggested that the coherent activity of neurons in response to a high contrast stimulus or at baseline results in a lower fractal dimension than less coherent activity in response to a stimulus at threshold. Support for this interpretation may be found in physiological work by Grinvald, Arieli, Tsodyks, and Kenet ( 2003) who investigated the activity of cortical cell assemblies in response to optimal, nonoptimal, and no visual stimulation in the cat using voltage sensitive dyes. It was found that single neurons fire and behave as part of an assembly, even when firing spontaneously in the absence of stimulation. The statistical analysis of the children's data indicates that they follow the same trends as the adult data, with a maximum at T% and a significant difference between T% and 0% but with a lower absolute level of complexity. 
The lack of a difference between the fractal dimension in response to 2T% and 0% VEPs is not evidence of a lack of difference between the origins of these responses. Because the fractal dimension is closely related to either complexity or the number of dynamical variables (neuronal populations), which are active, it is possible that the number of dynamical variables for two different states (in this case response to 2T% and 0% stimuli) may be similar, but the neuronal populations that make up the dynamical variables are different. 
What are the possible reasons for the absolute difference in complexity between responses from adults and children and is the magnitude of this difference (0.55) of any significance? Since the maturation of the fractal dimension of the VEP has not been analyzed previously, the closest comparison with previous studies may be found in work investigating the maturation of the fractal dimension of the EEG. Comparison with EEGs must be made with care as the use of different electrode montages may result in differences in recorded responses (Tomberg, Desmedt, & Ozaki, 1991). Anokhin et al. (1996) and Anokhin, Lutzenberger, Nikolaev, and Birbaumer (2000) used the earlobe as the reference electrode location (Cz was used in the present study) and found that EEG dimensions of 60-year-old adults are approximately 1.0 higher than in 7-year-old children. As Anokhin et al. (2000) only examined one age group of children (7–8 years) and two groups of adolescents (13–14 years and 16–17 years), we do not know whether any change in EEG dimension of the 0% VEP is expected for the age range of 4.8–12.6 years examined in the present study. As stated earlier, the results of the present study did not show any age-related change across the three groups of children in VEP fractal dimension at 0% chromatic contrast, which could be regarded as an approximation of the background EEG dimension. Furthermore, Anokhin et al. (2000) examined the resting state EEG under closed-eye conditions, rather than the open-eye conditions used in the present study. The complexity of the closed-eye resting EEG is thought to be dependent on “internally generated activity…rather than on sensory stimulation or task requirements” (Anokhin et al., 2000). 
Useful comparisons may be made between our findings and those of other studies in which complexity has been shown to change. For example, a change in fractal dimension of 0.5–1.0 is associated with a change in the number and complexity of mental tasks (Lutzenberger, Birbaumer, Flor, Rockstroh, & Elbert, 1992; Mölle et al., 1996; Xu & Xu, 1988) and for the same mental task but with a change in the complexity of a stimulus (Liu, Yang, Yao, Brown, & Yue, 2005; Müller et al., 2003). As the difference in complexity between adults and children in the present study (approximately 0.55) falls within that range, the statistically significant difference may also represent a functionally significant increase in the number and complexity of mental calculations used in the processing of chromatic contrast in adults compared with children. 
In addition, complexity of brain signals is also known to change with disease states such as Alzheimer's disease (e.g., Besthorn, Sattel, Geiger-Kabisch, Zerfass, & Förstl, 1995; Jelles et al., 2008) and brain injury (0.5 increase; Spasic, Kalauzi, Grbic, Martac, & Culic, 2005), which suggests that structural changes in the brain that accompany the disease are associated with changes in fractal dimension of electrophysiological signals. The direction of change, increased or decreased complexity, should in theory reflect the relative number of active functional systems acting coherently such that greater coherence (similarity of phase between multiple channels) is associated with lower complexity and vice versa (Anokhin et al., 1996). Experimental evidence supports this view. For example, mania (Bahrami, Seyedsadjadi, Babadi, & Noroozian, 2005) is associated with decreased levels of coherence and increased fractal dimension. Alzheimer's disease, which results in decreased coherence in the beta, upper alpha, and gamma frequency bands, is associated with increased fractal dimension in these bands (Jelles et al., 2008). Jelles et al. (2008) interpreted this as indicating decreased functional connectivity in these bands. Theta band activity, however, has shown conflicting results and could influence the direction of the global EEG complexity (Jelles et al., 2008). Certain phases of an epileptic seizure result in strengthened long-range interactions and a decrease in fractal dimension (Liu et al., 2005). Thus disease or injury may result in either increases or decreases in fractal dimension depending on how the pattern of communication between neuronal assemblies is affected. Goldberger et al. (2002) described breakdowns of “fractal physiological complexity” as being associated with “excessive order (pathologic periodicity)” or “uncorrelated randomness.” Variability of direction of change in complexity within the same brain depending on which aspects of brain activity are examined is not unique to epilepsy. In fact, in healthy controls, EEGs recorded from different cortical sites can show different and even opposite movements in fractal dimension in response to the same stimulus or task (Mölle et al., 1996; Tomberg, 1999; Xu & Xu, 1988) suggesting that the fractal dimension may reflect localized activity of the areas underlying the active electrode (Tomberg, 1999). 
It has been suggested that for each physiological system, “there is a range of connectedness that is optimal” (Buchman, 2002). The difference in complexity of VEPs recorded from adults and children in the present study may reflect structural maturation of the connectivity of neurons within the visual system. Decreased coherence, and greater complexity, may arise if a higher number of neuronal assemblies are active and their activity is not identical in phase or function reflecting greater differentiation of activity. Greater complexity of processing may also occur if additional neuronal assemblies are recruited for a task. For example, improvement in juggling ability is associated with increases in gray matter in the visuo-motor processing areas of the brain (mid-temporal area (hMT/V5) and the left posterior intraparietal sulcus) independently of other areas (Draganski et al., 2004). Therefore, the recruitment of additional neurons can be beneficial perhaps providing an increase in processing power toward optimal levels of connectedness as postulated by Buchman ( 2002) and may result in improved function. 
In the present study, the higher complexity in adults than in children is likely to reflect maturation of the visual system's neuronal network (Parker, 2006). Evidence for development of the visual system specifically has been revealed by several studies, which show that the main immaturities in the visual cortices of children are smaller V2, V3, VP, and V4v visual areas (Conner, Sharma, Lemieux, & Mendola, 2004), lower complexity of cortical morphology (Blanton et al., 2001), less cortical folding and curvature (Chung et al., 2003), and less variable size of brain structure in children than in adults (Lange, Giedd, Xavier Castellanos, Vaituzis, & Rapoport, 1997). Cortical immaturities also include the growth and pruning of synapses and neurons up to the age of 22 years (Giedd, 2004; Huttenlocher, de Courten, Garey, & Van der Loos, 1982), the process of myelination that may proceed up to the age of 30 years (Courchesne et al., 2000; Dubois et al., 2008; Matsuzawa et al., 2001), the increase in occipital lobe gray matter between 4 and 22 years of age (Giedd et al., 1999), and higher energy consumption profiles in children (Chugani, 1998). Thus, it is likely that many of these changes are reflected in the difference in complexity of the adult and child electrophysiological responses. It must also be kept in mind that the VEP reflects the function of subcortical as well as cortical components of the visual system. Therefore, in the chromatic visual systems specifically of the age groups examined in the present study, we may expect maturation in retinal function for the participants below 5 to 10 years of age (Brecelj, Strucl, Zidar, & Tekavcic-Pompe, 2002) and cortical changes for all of the children. Moreover, although the stimulus used in the present study preferentially modulates the L- and M-cones, the S-cones were also modulated to a lesser extent; therefore, differences in the level of maturation of the S–(L + M) and L–M chromatic systems at the level of the retinal photoreceptors may also have an impact on the chromatic VEPs measured here. 
However, most of the developmental changes noted above are not specific to the visual system, highlighting another important point. Because the difference in fractal dimension of the VEPs between adults and children was similar (approximately 0.55) during chromatic stimulation (42%, 2T%, and T%) and in the absence of chromatic stimulation (0%), this change in complexity could reflect not only visual function but also nonvisual function. Fractal dimension of the eyes-closed EEG is about 0.9 higher in adults than in children (Anokhin et al., 1996), a greater difference than our finding for the eyes-open 0% response. In the present study, the activity while viewing the 0% stimulus was recorded from Oz, overlying the visual cortex, and may or may not reflect activity that is specific to the visual system. Further research examining nonchromatic VEPs and the EEG derived from locations other than Oz would assist in understanding how much of the decrease in complexity is specific to the visual system. 
Despite evidence that shows that the fractal dimension reflects activity specific to the sources of a scalp electrode (as fractal dimensions derived from recordings from differently sited electrodes can respond differently in magnitude and direction to the same stimulus; Mölle et al., 1996; Xu & Xu, 1988), it is also known that general brain dynamics can have an impact on the transient chromatic VEP (Lehmann, Michel, Pal, & Pascual-Marqui, 1994; Makeig et al., 2002) and multifocal VEP (Balachandran et al., 2004; Klistorner & Graham, 2001). These factors may include genetic factors (Anokhin, Müller, Lindenberger, Heath, & Myers, 2006), brain area organization (Hoffman, Straube, & Bach, 2003), and the effects of learning and experience (Draganski et al., 2004). In addition, modeling has suggested that the neural populations that generate the spontaneous EEG are also involved in the generation of VEPs (Jansen et al., 1993) such that any maturation of the EEG will contribute toward maturation of the VEP. It has been suggested that complexity of neurophysiological structure may be related to complexity of the response (West, 1988), such that the more complex the structure, the more complex the response. If this is correct, as the structural complexity of the brain has been shown to increase during childhood (Blanton et al., 2001), then children's VEPs and EEGs should be relatively less complex in dynamics than those of adults, which is consistent with the results of the present experiment and Anokhin et al.'s (1996, 2000) findings. 
Because the main changes in fractal dimension with age were less than 1.0 in this study, based on current understanding of the relationship between the fractal dimensions of electrophysiological signals and underlying function, it is not possible to determine with certainty whether this change is due to a change in the pattern of electrical activity or an increase in the number of activated neuronal populations, or perhaps a combination of both. Interestingly, although the analysis of fMRI data is problematic (Chu et al., 2004; Scannell & Young, 1999), there are indications that while increases in neural electrical activity are associated with increases in fMRI BOLD signal amplitude, increases in activated neuronal population size are associated with decreases in BOLD signal amplitude (Marcar, Straessle, Girard, Loenneker, & Martin, 2004). For example, in adults, Marcar et al.'s ( 2004) results suggest that the neural change that occurs with pattern onset stimuli at the level of the cortex is an increase in the firing of electrical activity rather than an increase in the population of neurons. This characteristic may be exploited to better understand whether the increase in fractal dimension between childhood and adulthood represents an increased complexity in processing or the involvement of additional neuronal assemblies. 
Conclusion
Chromatic contrast processing in children can be described as part of a nonlinear dynamical system. The results of this study suggest that the absence of repeatable VEP components at low to moderate contrasts in children is not due to differences in signal-to-noise ratio between the age groups but is due to nonlinearities in the visual system. The transient chromatic VEP and the unevoked potential are both less dynamically complex in children than in adults by an average of 0.55 in fractal dimension. This may reflect immaturities in the pattern of electrical activity and/or the number of activated neuronal populations contributing to these potentials. Information derived from fractal analysis may be a useful objective parameter in models of visual system function, including changes to function during maturation and in disease states. 
Acknowledgments
We thank the participants and their families for their generosity and time. 
Commercial relationships: none. 
Corresponding author: Mei Ying Boon. 
Email: m.boon@unsw.edu.au. 
Address: School of Optometry and Vision Science, University of New South Wales (UNSW), Sydney, NSW 2052, Australia. 
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Figure 1
 
Representative VEPs from one adult (EA, 25.7 years old, left column) and one child (JY, 8.3 years old, right column) in response to chromatic contrasts ranging from 0% to 42%, as indicated by the central numbers (adult–child). The gray lines show two VEPs (average of 30 sweeps each). The dark bold lines show the average of two VEPs (i.e., average of 60 sweeps). The upward pointing arrows indicate the dominant N-peaks, downward pointing arrows indicate the dominant P-peaks, and the slanted arrows indicate the shoulders. Where there are no arrows plotted, this indicates that there were no recognizable VEP components that were repeatable (components with longest latency within 10% of each other between averaged sweeps or across the 1000-ms epoch). It can be seen that VEPs are repeatable for 42%, 2T%, and T% in the adult but only becomes repeatable at 14% chromatic contrast in the child. Psychophysical chromatic contrast thresholds were approximately 5% for both subjects EA and JY.
Figure 1
 
Representative VEPs from one adult (EA, 25.7 years old, left column) and one child (JY, 8.3 years old, right column) in response to chromatic contrasts ranging from 0% to 42%, as indicated by the central numbers (adult–child). The gray lines show two VEPs (average of 30 sweeps each). The dark bold lines show the average of two VEPs (i.e., average of 60 sweeps). The upward pointing arrows indicate the dominant N-peaks, downward pointing arrows indicate the dominant P-peaks, and the slanted arrows indicate the shoulders. Where there are no arrows plotted, this indicates that there were no recognizable VEP components that were repeatable (components with longest latency within 10% of each other between averaged sweeps or across the 1000-ms epoch). It can be seen that VEPs are repeatable for 42%, 2T%, and T% in the adult but only becomes repeatable at 14% chromatic contrast in the child. Psychophysical chromatic contrast thresholds were approximately 5% for both subjects EA and JY.
Figure 2
 
Fourier power spectra of VEPs in response to 42% chromatic contrast in order of age (years) along the z-axis. It can be seen that children have higher amplitude Fourier power spectra than adults.
Figure 2
 
Fourier power spectra of VEPs in response to 42% chromatic contrast in order of age (years) along the z-axis. It can be seen that children have higher amplitude Fourier power spectra than adults.
Figure 3
 
Signal-to-noise ratio (mean ± standard error) across age groups for four stimulus contrast levels. The upper panel uses the algorithm of SNR1 and the lower panel uses the algorithm of SNR2 to calculate signal-to-noise ratio.
Figure 3
 
Signal-to-noise ratio (mean ± standard error) across age groups for four stimulus contrast levels. The upper panel uses the algorithm of SNR1 and the lower panel uses the algorithm of SNR2 to calculate signal-to-noise ratio.
Figure 4
 
VEP and surrogate data correlation dimensions by age group (mean and standard deviations, error bars). VEP and surrogate correlation dimensions were significantly different ( p < 0.05).
Figure 4
 
VEP and surrogate data correlation dimensions by age group (mean and standard deviations, error bars). VEP and surrogate correlation dimensions were significantly different ( p < 0.05).
Figure 5
 
VEP and surrogate data plateau indices by age group (mean and standard deviations, error bars). It can be seen that the VEP data plateau (indicated by a plateau index value that is close to 0.0, here arbitrarily defined as 0.3) but the surrogate data do not.
Figure 5
 
VEP and surrogate data plateau indices by age group (mean and standard deviations, error bars). It can be seen that the VEP data plateau (indicated by a plateau index value that is close to 0.0, here arbitrarily defined as 0.3) but the surrogate data do not.
Figure 6
 
Mean and standard errors of fractal dimension by stimulus contrast for the different age groups. The shaded box represents fractal dimensions of unevoked potentials (VEP in response to 0% contrast), where there was no time-locked visual stimulus.
Figure 6
 
Mean and standard errors of fractal dimension by stimulus contrast for the different age groups. The shaded box represents fractal dimensions of unevoked potentials (VEP in response to 0% contrast), where there was no time-locked visual stimulus.
Figure 7
 
VEP correlation dimension, here equivalent to fractal dimension, as a function of chromatic contrast (column 1) and power (column 2) and power as a function of chromatic contrast (column 3) for the four age groups (4.5 to <7, 7 to <10, 10 to 13, 20 to <40) in order from youngest to oldest (a, b, c, and d). The data points of each individual subject have been joined by lines (separate lines for each subject). The lines join the data points representative of correlation dimension in order of the rank of the powers for (a) and in order of the ranks of chromatic contrast for (b).
Figure 7
 
VEP correlation dimension, here equivalent to fractal dimension, as a function of chromatic contrast (column 1) and power (column 2) and power as a function of chromatic contrast (column 3) for the four age groups (4.5 to <7, 7 to <10, 10 to 13, 20 to <40) in order from youngest to oldest (a, b, c, and d). The data points of each individual subject have been joined by lines (separate lines for each subject). The lines join the data points representative of correlation dimension in order of the rank of the powers for (a) and in order of the ranks of chromatic contrast for (b).
Figure 8
 
VEPs in response to 42% chromatic contrast from two children and one adult (left to right). The children's VEPs show P–N complexes with one additional shoulder (left) and no shoulder (middle) and the adult panel shows an N–P complex with one shoulder.
Figure 8
 
VEPs in response to 42% chromatic contrast from two children and one adult (left to right). The children's VEPs show P–N complexes with one additional shoulder (left) and no shoulder (middle) and the adult panel shows an N–P complex with one shoulder.
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