1.1.

Within- and Between-Person Analyses

Given that the majority of the extant neural variability literature is based on average between-person effects (e.g., does the older age group exhibit less variability than the younger age group?), it is of particular interest to investigate whether associations between behavior and neural function are also observed within persons (i.e., for any given individual, on occasions when neural variability is higher, is behavioral performance also better?). It has long been known that analyses executed at separate levels of nested-data hierarchies (i.e., the between- and within-person levels) do not necessarily yield equivalent results. Referred to as the ecological fallacy,¹⁷ results at the individual level may be of particular magnitude and direction, but when aggregated at the group level, can not only differ in pattern but may also be influenced by between-person confounds (e.g., age and cognitive status) that may obscure the effect of interest. For example, it is both conceptually and statistically possible for predictors to account for large proportions of variance within-persons, but to exhibit relatively little or no effect (or even opposite effects) when pooled across individuals.¹⁸ Similarly, research on ergodicity¹⁹ underscores the importance of examining within-person associations and suggests that (a) process-oriented phenomena (such as neural variability) are best examined within-persons over time and (b) a singular reliance on between-person averages to study such associations is incongruent with theoretical accounts. Therefore, despite being defined by the same outcome, the variation at between- and within-person levels of analysis may represent and be driven by completely different theoretical constructs (e.g., the reason person A performs better on a cognitive task relative to person B may be completely different from why both individuals each exhibit gains across the duration of a task).

1.2.

Present Study

In the present study, we examined mean and variability operationalizations of the cortical hemodynamic response, at both the within- and between-person levels, for older adults performing an executive functioning task. Several key research aims were explored. First, functional estimates for mean and variability during an executive function task were derived. Relative to fMRI, the faster fNIRS sampling frequency arguably yields a more precise and reliable estimate of neural variability. Although several operationalizations of neural variability have been employed including a block normalized SD approach (fMRI literature) as well as multivariate multiscale entropy (MSE: EEG literature), these various approaches and the signals they index may not be equivalent.³ The findings reported in this investigation are based upon the normalized SD computation.⁹

Time-varying covariation models were then employed to estimate the within-person (at the individual level) and between-person (at the sample average level) associations for these two oxyhemoglobin (HbO) indicators on behavioral cognitive performance [Multisource Interference Task (MSIT) response latency and accuracy] across all performance blocks within the experiment. For variables such as functional activation that are studied over any longitudinal interval, an estimate for any given cross-sectional sample (e.g., block 1) comprises both between- and within-person sources of variance.²⁰ Accordingly, failure to decompose variance into between- and within-person sources results in estimates that conflate the two—of particular concern to the extent that between-person variance for the phenomenon under study (e.g., the association between neural variability on cognitive performance) is distinct from patterns observed for within-person variance. Our investigation is particularly innovative as most investigations of neural variability are based upon between-person differences; here, we directly examine effects at both the between-person (i.e., effects that pertain to differences in level of neural variability between persons in relation to cognitive function) and within-person (i.e., effects that pertain to neural variability and how this couples with cognitive function within an individual) levels. As so few fMRI and fNIRS investigations have explored neural variability, with virtually all focusing exclusively on between-person differences, key foci of this objective were (a) to examine associations of HbO mean and variability with cognitive function at both the between- and within-person levels, (b) to document whether the patterns were similar in magnitude and direction of effect (an empirical question given the fact that between- and within-person findings need not be identical), and (c) to establish benchmark patterns for both the between- and within-person effects, representing patterns for unconfounded sources of variance, to be replicated in subsequent studies.

Finally, a related research objective pertains to understanding whether the complementary operationalizations (mean and standard deviation) of cortical hemoglobin concentrations were differentially modulated as a function of cognitive load (control versus interference conditions) on the MSIT task. Neural variability remains poorly understood for higher-order cognitive measures, such as executive function, and the modulation of neural variability has not been explored within persons. Consistent with some interpretations offered in the functional literature for the impact of load modulation on mean neural activations,^2,13,21 we hypothesized that the more demanding interference condition would result in greater recruitment of neural tissue,² but that the patterns would differ across operationalizations of the hemodynamic response as well by behavioral metric (accuracy versus latency) and cortical region.

2.1.

Participants

This study was approved by the University of Victoria Human Research Ethics Board and was conducted in accordance with institutional guidelines. Data were collected from a narrow-age cohort 71- to 81-years of age ($m=75.88$ and $\mathrm{SD}=3.28$) of 25 older adults (13 females and 12 males), 92% of whom were right-handed. Exclusionary criteria included self-report of (a) a physician-diagnosed major medical illness with residual motor or sensory deficits (e.g., Parkinson’s disease, stroke, heart disease, dementia, cancer, and brain tumor), (b) severe sensory impairment (e.g., difficulty reading newspaper-sized print, difficulty hearing a normal spoken conversation, and difficulty writing or pressing buttons), (c) drug or alcohol abuse, (d) history of inpatient psychiatric treatment, (e) significant cognitive impairment (i.e., Mini Mental State Examination score below 24), or (f) English as a second language.

2.2.

Measures

Participants completed the MSIT, which is a computerized task of cognitive interference, and was designed to activate the cingulo-frontal-parietal cognitive attention network in subjects while undergoing functional neuroimaging.^22,23 The task shares similarities with the Stroop, Eriksen Flanker, and Simon tasks and is suitable for the purposes of this investigation for notable reasons. Previous investigations using the MSIT have elucidated a reliable network of neuroanatomical correlates that are engaged during task performance,^22,23 including several that are accessible by fNIRS methodology using a relatively basic array positioned over the forehead (see Fig. 1). The MSIT was designed with the assessment of neuropsychiatric populations in mind and is regularly employed in the studies of cognitive aging; however, it has yet to be used to examine variability in functional brain activity. The nature of the MSIT is such that behavioral performance can be readily yoked to neural activity, as the task demands remain relatively constant from trial to trial within a block of the experiment.

Fig. 1

The MSIT. Participants are presented with three numbers and indicate the value of the number that is different. The value and location are congruent during control and incongruent during the interference condition.

In the MSIT, participants are presented with an array of three numbers (ranging in value from 0 to 3), one of which is a different numerical value than the others. Using a serial response input device (Psychology Software Tools, Inc.) to ensure $+/-1\mathrm{ms}$ timing latency, participants respond to the value of the odd target as quickly as possible while remaining accurate, across a total of 15 trials within a 30-s block. Trial durations are fixed at 2000 ms, allowing behavioral responses to be time-locked to the corresponding samples within a neuroimaging recording. Participants begin with either the control (location and value of the target are congruent) or interference condition (location and value of the target are incongruent), and complete a total of four blocks for each of the conditions, which alternate (see Fig. 1). A rest block of 20 s separates each experimental block and a baseline of at least 90 s preceded the onset of the task. A measure of interference can be derived by comparing the easier (control) to the more demanding (interference) condition, across several outcome measures of interest, including accuracy (percent correct), response time (RT), and hemodynamic response.

2.3.

Functional Near-Infrared Spectroscopy Recording

fNIRS data were recorded using a continuous-wave TechEn CW6 system (TechEn Inc., Milford, Massachusetts), with a sampling frequency of 50 Hz (corresponding to $\mathrm{TR}=20\mathrm{ms}$) (For selected individuals ($n=6$), the frequency of fNIRS data acquisition was downsampled to 25 Hz. Despite this, sufficient individual samples were available to derive reliable estimates of HbO mean and variability, with analyses indicating no significant influences of these sampling differences on our estimates or pattern of results.), resulting in 100 images every 2 s. During computerized testing, the fNIRS system recorded cortical hemodynamic responses that were time-locked to events within the tasks. Participants wore custom-built fNIRS headgear consisting of an array positioned over prefrontal cortex (PFC) [Fig. 2(a)] containing 10 channels (8 at 3 cm separation, 2 at 1.5 cm separation) and were tested using wavelengths of 690 and 830 nm to index deoxyhemoglobin (HbR) and oxyhemoglobin (HbO), respectively. The array was designed to maximize the coverage of PFC, given the relevance of PFC areas during performance on the MSIT.

Fig. 2

(a) The array design showing the location of the sources (star), detectors (circle), channels (dashed line), and Brodmann’s areas (squares). (b) Sensitivity profile based on the Monte Carlo forward model (${10}^6$ photons) for the fNIRS array.

The optical array was positioned relative to several 10 to 20 landmarks (Fpz, Fz, F7, and F8). 3-D coordinates of scalp reference and optode locations were obtained using a Polhemus Fastrak digitizer system (Polhemus, Colchester, Vermont), to perform probabilistic spatial registration.^24,25 Following this procedure, Montreal Neurological Institute (MNI) coordinates were generated for the midpoint of each source–detector pair (i.e., channel) for each participant, as well as the average and composite standard deviation values across the group (Table 1). Lastly, we converted the MNI coordinates to Brodmann’s areas (BA) to ascertain macroanatomical labels using Talairach Client software.²⁶ The lateral-most channels in both hemispheres recorded over BA 46, with all the remaining channels recording over BA 10 [Fig. 2(b)]. The 1.5 cm short-separation channels (B4 and C8) were not of interest for the present investigation, given the inability of these channels to capture information at the cortical surface or to facilitate regression of the cardiac signal. Therefore, they were dropped from subsequent analyses. Left hemisphere channels covered inferior frontal gyrus (A1) and middle frontal gyrus (A2, B2, and B3) and right hemisphere channels covered superior frontal gyrus (C5 and C6) and middle frontal gyrus (D6 and D7). To further ascertain whether the array facilitated adequate coverage from PFC regions of interest, the probabilistic path of the light photons using the Monte Carlo forward model (${10}^6$ photons) was simulated, to derive a sensitivity matrix²⁷ [Fig. 2(b)]. This model was based on the Colin27 atlas, which specifies the absorption properties of scalp, skull, cerebral spinal fluid, gray matter, and white matter. As is evident, the array captured information that is uniformly distributed across PFC.

Table 1

Group average MNI coordinates for the eight-channel array.

The methods undertaken as part of this study were well situated to investigate the within- and between-person associations between HbO variability and behavioral performance, as well as the modulation of neural variability by cognitive load. Although fNIRS is limited in its spatial resolution to cortical regions, the greatest age-related group differences in BOLD variability (between young and old) have emerged in relation to cortical regions.⁹ Further, the PFC in particular is linked with greater inconsistency in behavioral performance²⁸ and is heavily implicated in executive functions (e.g., cognitive interference).²⁹ Thus, the array used in this study is limited to the coverage of PFC, which is the area relevant to the phenomenon of interest.

2.4.

Preprocessing

Preprocessing of the fNIRS data was performed using Homer 2 software.³⁰ After converting the raw wavelengths to optical density values, we corrected for motion using a wavelet transformation algorithm³¹ using an interquartile range of 0.1.^32,33 Next, we applied bandpass filtering to correct for physiological noise using a high-pass filter value of 0.01 Hz and a low-pass filter value of 0.1 Hz. We then converted from optical density to hemoglobin concentrations by applying the modified Beer–Lambert law, and then exported for subsequent operationalizations. Figure 3 displays the group-averaged time-course data, sampled at 50 Hz.

Fig. 3

Group-averaged time-course data for the MSIT task, sampled at 50 Hz. The presence of each hemodynamic response function corresponds to a 30-s experimental block, separated by 20-s of rest.

2.5.

Mean and Standard Deviation Operationalizations

Mean- and SD-based operationalizations of HbO were derived for the purpose of this study. Outliers were identified as values $>3$ SD from the sample mean across block estimates and were deleted pairwise, with subsequent modeling based on restricted maximum likelihood.

Mean estimates of HbO were estimated by aggregating across all samples contained within a given experimental condition. We employed a block design to index HbO within each condition. Specifically, we derived single estimates of HbO within a given block. This equated to eight segments for the MSIT (four control and four interference). Signal variance was estimated with block independent estimates, based on in-house software following the approach used by Garrett and colleagues.^3,9,10 Percentage change from the onset value of a given block was computed for each sample, with the corresponding values subsequently averaged within a given block. Given our interest in examining the within-person time-varying covariation between HbO estimates (mean and SD) and behavioral performance (described further below), we did not normalize concatenated blocks to examine single SD estimates, condition wise. In similar fashion, the corresponding estimates for SD HbO were computed per block to facilitate estimation of the time-varying covariation models examining within-person associations between neural activity and cognitive performance.

3.1.

Behavioral Data

MSIT scores were first screened for blocks with accuracy performance $<50\%$. Given the nature of the task and potential executive functioning difficulties experienced by the participants, there were several blocks of interference results in which participants appeared to have reversed the criteria, responding to the location of the target instead of its value. These blocks were removed from both behavioral and fNIRS analyses (36 interference blocks removed from a total of 100 across all participants). Table 2 displays the demographic and behavioral data.

Table 2

Descriptive statistics for the demographic and behavioral data. Data for MSIT control and interference conditions are based on blocks with at least 50% accuracy and RT data are based on correct trials only.

3.2.

Examining Within- and Between-Person Associations of Cognitive Function with HbO Mean and Variability

Hierarchical linear and nonlinear modeling (HLM) 6.08 software was used to fit linear mixed models to examine the time-varying covariation (or “coupling”) between each operationalization of hemoglobin (i.e., mean and SD) and behavioral performance (i.e., MSIT accuracy and response time), with separate models for each fNIRS channel (i.e., A1, A2, B2, B3, C5, C6, D6, and D7). In order to avoid a type II error and incorrectly rejecting a true finding, we did not correct for multiple comparisons.³⁴ Rather, given that the MSIT and variability operationalizations have not been used with fNIRS in older adults, our preference was to provide a full account of the results. Given our a priori hypotheses regarding expected directional effects, we employed one-tailed ($p<0.05$) tests for specific planned comparisons. To derive distinct between- and within-person estimates of cortical hemoglobin on behavioral performance, each person-mean operationalization of hemoglobin was centered, before entering it into the model.²⁰ In person-mean centering, the person mean of the time-varying predictor is subtracted from the original time-varying predictor, such that the new time-varying predictor represents variation about one’s own mean level, and thus facilitates the partitioning of HbO-cognition associations into discrete and orthogonal between- and within-person estimates. The following equations outline the analyses conducted to examine the block-to-block covariation between hemoglobin and behavioral performance (i.e., accuracy and response latency):

HbO mean: The within- and between-person associations of HbO mean on variation in behavioral performance were tested separately for each behavioral metric and fNIRS channel. Table 3 summarizes the effects. At the between-person level, greater HbO concentration in the control condition was associated with less accurate performance in two adjacent left hemisphere channels ($A_1$: ${\gamma }_{01}=-0.022$, $p=0.029$; $A_2$: ${\gamma }_{01}=-0.018$, $p=0.012$). At the within-person level, greater HbO concentration in the control condition was associated with faster performance in one right hemisphere channel ($D_6$: ${\gamma }_{20}=-23.14$, $p=0.019$, $\text{pseudo}{R}^2=0.137$), such that on blocks when participants recruited more HbO relative to their own mean, they tended to perform faster (23.14 ms faster for every $\mu \mathrm{Mol}$ increase in mean HbO, relative to a given person’s average). Of the total within-person variation in response time, 13.7% was accounted for by changes in HbO concentration, with the pseudo-$R^2$ estimate based upon the Snijders and Bosker computation.^35,36 Greater HbO concentration in the interference condition was associated with less accurate performance in both left and right hemisphere channels ($A_1$: ${\gamma }_{01}=-0.104$, $p=0.015$; $D_6$: ${\gamma }_{01}=-0.060$, $p=0.074$) and with slower performance in two left hemisphere channels ($A_1$: ${\gamma }_{01}=68.46$, $p=0.063$; $B_3$: ${\gamma }_{01}=59.55$, $p=0.085$) at the between-person level. At the within-person level, greater HbO concentration was associated with less accurate performance in one right hemisphere channel ($D_7$: ${\gamma }_{20}=-0.060$, $p=0.063$, $\text{pseudo-}{R}^2=0.049$), such that on occasions when participants recruited more HbO relative to their own mean, they tended to perform less accurately (0.06% less accurate for every $\mu \mathrm{Mol}$ increase in mean HbO, relative to a given person’s average). Of the total within-person variation in accuracy, 4.9% was accounted for by changes in HbO concentration.

Table 3

Two-level multilevel models examining between- and within-person associations for mean HbO with cognitive performance. Coefficients are reported for the between- (γ01) and within-subject (γ20) slope estimates. MSIT, multisource interference task; BS, between-subject; WS, within-subject; BA, Brodmann’s areas.

HbO SD: The within- and between-person associations of HbO SD on variation in behavioral performance were tested separately for each behavioral metric and fNIRS channel.

Table 4 summarizes the effects. At the between-person level, greater HbO variability in the control condition was associated with slower performance in two adjacent left hemisphere channels ($A_1$: ${\gamma }_{01}=0.66$, $p=0.041$; $A_2$: ${\gamma }_{01}=0.39$, $p=0.095$). At the within-person level, greater HbO variability in the control condition was associated with faster performance in one left hemisphere channel ($A_2$: ${\gamma }_{20}=-0.09$, $p=0.089$, $\text{pseudo-}{R}^2=0.063$), such that on blocks when participants were more variable in HbO relative to their own average variability, they tended to perform faster (0.09 ms faster for every $\mu \mathrm{Mol}$ increase in SD HbO, relative to a given person’s average). Of the total within-person variation in response time, 6.3% was accounted for by changes in HbO variability. We also found that greater HbO variability in the interference condition was associated with more accurate performance in one right hemisphere channel ($D_6$: ${\gamma }_{20}={29.0}^{-4}$, $p=0.087$, $\text{pseudo-}{R}^2=0.243$), such that on blocks when participants were more variable in HbO relative to their own mean, they tended to perform more accurately (0.003% more accurate for every $\mu \mathrm{Mol}$ increase in SD HbO, relative to a given person’s average). Of the total within-person variation in accuracy, 24.3% was accounted for by changes in HbO variability.

Table 4

Two-level multilevel models examining between- and within-person associations for SD HbO with cognitive performance. Coefficients are reported for the between- (γ01) and within-subject (γ20) slope estimates. MSIT, multisource interference task; BS, between-subject; WS, within-subject; BA, Brodmann’s areas.

4.1.

Limitations and Future Directions

The observed effects that have been reported in this study are limited due to sample size constraints and duration of task (i.e., number of blocks), resulting in decreased power. To ascertain fully the extent to which each operationalization of HbO is driven by within- or between-person effects, a greater sample size is required; ideally, one in which the incidence of a potential cognitive impairment is apparent (e.g., mild cognitive impairment). Similarly, additional experimental blocks would allow for greater exploration of the within-person associations between HbO and behavior. Event-related designs will also allow for more precise yoking of neural variability with behavioral performance, with an increased number of blocks increasing statistical power for the coupling analyses. The use of short-separation channels would have allowed for a more precise estimate of high-frequency physiological artifacts (e.g., Mayer waves),⁴² and future studies would benefit from this approach. In using bandpass filtering with relatively conservative thresholds, the reported variability operationalization may result in underestimating the true relationship of neural variability with behavioral performance; future research might replicate these findings employing less conservative screening criteria. As previous results have shown patterns of mean- and SD-based computations of neural activity that are spatially and inferentially distinct,⁹ the discrepancies reported here between associations of each operationalization of HbO with behavioral performance are likely to become clearer with greater statistical power. The block normalized SD computation was conducted for each channel yielding a total of eight estimates; a distinct approach from that employed in fMRI studies to date. In these studies, a whole-brain estimate across all voxels and regions is derived, which is used subsequently during inferential statistical comparisons (e.g., between young and old adults). Future investigations may seek to examine regional differences in neural variability (e.g., between frontal and parietal cortices) using expanded head coverage, as well as whole-brain SD, to facilitate comparison with fMRI reports. Given the originality of neural variability operationalizations in the fNIRS literature, replication and extension of the reported findings will be essential. Multimodal fNIRS–fMRI recording in particular would allow for an investigation of the comparability of the neural variability signal derived from the same collection.