Journal of Neuroscience Methods 174 (2008) 292–300

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Journal of Neuroscience Methods

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Endogenous multifractal brain dynamics are modulated by age, cholinergicblockade and cognitive performance

John Sucklinga,∗, Alle Meije Winkb, Frederic A. Bernardc, Anna Barnesa, Edward Bullmorea

a Brain Mapping Unit, University of Cambridge, Department of Psychiatry, Addenbrooke’s Hospital, Cambridge CB2 0QQ, UKb Imaging Sciences Division, Imperial College, Hammersmith Hospital, London, UKc Département d’Etudes Cognitives, Ecole Normale Supérieure, Paris, France

a r t i c l e i n f o

Article history:Received 5 March 2008Received in revised form 5 June 2008Accepted 25 June 2008

Keywords:FractalMultifractalAgeingScopolamineRecognition

a b s t r a c t

The intuitive notion that a healthy organism is characterised by regular, homeostatic function has beenchallenged by observations that a loss of complexity is, in fact, indicative of ill-health. Monofractals suc-cinctly describe complex processes and are controlled by a single time-invariant scaling exponent, H,simply related to the fractal dimension. Previous analyses of resting fMRI time-series demonstrated thatageing and scopolamine administration were both associated with increases in H and that faster responsein a prior encoding task was also associated with increased H. We revisit this experiment with a novel, mul-tifractal approach in which fractal dynamics are assumed to be non-stationary and defined by a spectrumof local singularity exponents. Parameterisation of this spectrum was capable of refracting the effects ofage, scopolamine and task performance as well as a refining a description of the associated signal changes.Using the same imaging data, we also explored turbulence as a possible mechanism underlying multi-

Self-organisedCritical phase

fractal dynamics. Evidence is provided that Carstaing’s model of turbulent information flow from high tolow scales has only limited validity, and that scale invariance of energy dissipation is better explained bycritical-phase phenomena, supporting the proposition that the brain maintains a state of self-organised

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. Introduction

Fractals – signals that display scale-invariant or self-similarehaviour – are ubiquitous in nature and result from a wide varietyf physical processes, including diffusion, erosion, turbulence andriticality. The traditional view that the healthy state of an organ-sm is represented by homeostatic, regular, steady-state behaviouras been challenged by the observation that many physiologicalignals are, in fact, non-linear, inhomogeneous and fractal (Ivanovt al., 1999; Goldberger et al., 2002). From this viewpoint, healthyunction is regarded as the capacity to adapt to a wide varietyf exogenous or endogenous stimuli, which is compatible withhaotic physiological dynamics. In contrast, the emergence of sim-ler dynamics, such as white noise or a purely periodic oscillation,an be seen as a degradation of fractal complexity and an indication

f ill-health or maladaptivity (Ivanov et al., 2001).

Fractals are quantified by decomposing a signal into a hierarchyf temporal or spatial scales: from a coarse-scale representationf long-term variations through to high-frequency fluctuations at

∗ Corresponding author. Tel.: +44 1223 336063; fax: +44 1223 336581.E-mail address: js369@cam.ac.uk (J. Suckling).

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165-0270/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.jneumeth.2008.06.037

© 2008 Elsevier B.V. All rights reserved.

ne scales. The high and low frequency limits of the scale range areetermined ultimately by the resolution of the measuring devicend the total length of the time-series, respectively. If the propertyf interest shows a simple relationship to change of scale, e.g. thepectral density is related to frequency by a power law, then therocess is said to be a monofractal. The appearance of monofractalignals may well be irregular and include a number of singularitiespoints at which it is non-differentiable). However, the propertiesf these singularities are constant in time and the entire processan be adequately characterised by a single scaling exponent, theurst exponent, H, which is simply related to the fractal dimensionr the spectral exponent of the process (Schroeder, 1991).

Although monofractal analysis of physiological signals hasielded a number of interesting observations in health and diseaseBullmore et al., 2004; Beckers et al., 2006), it has become clear thatfuller description of physiological dynamics is required to better

apture their inhomogeneity and non-stationarity (Goldberger etl., 2002). We can allow that the scaling behaviour of the process

ill not be governed by a single, stationary parameter but instead

y a number of local scaling exponents. Such a multifractal signals characterised by the histogram of Hölder exponents, h, knowns the singularity spectrum (Muzy et al., 1991, 1993; Turiel et al.,006), that generally spans 0 < h < 1.5. Values of the spectrum h < 0.5

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orrespond to anti-persistent or negatively correlated behaviournd h > 0.5 to persistent or positively correlated behaviour. Sin-ularity spectra with non-zero widths, indicative of multifractalynamics, have been measured in electrocardiographic (ECG) sig-als (Ivanov et al., 1999, 2001; Chiu et al., 2007; Wang et al., 2007;avlov et al., 2005), human gait recordings (West and Latka, 2005),lectroencephalographic (EEG) signals (Song et al., 2005), and func-ional magnetic resonance imaging (fMRI) time-series (Shimizu etl., 2004). Studies of multifractal properties of ECG signals espe-ially have shown that the maximum (peak) value and width of theingularity spectrum are affected by disease (cardiac failure) andgeing, confirming that these parameters are sensitive to dynamicepartures from health.

Turbulent energy transfer is a well-known physical process thatesults in multifractal dynamics (Arneodo et al., 1996; Chevillard etl., 2006). In fully developed turbulent flow, kinetic energy injectednto a liquid via a stirrer generates vortices at scales similar to thatf the stirrer. The generation of smaller vortices from the cascadef energy occurs with increasing rapidity as scale decreases, untilnergy is ultimately dissipated at the molecular level through vis-ous interactions. The local velocity differences measured duringurbulent flow have magnitude and directional changes that haveeen observed to be non-differentiable (i.e., singular) over a rangef spatial (Castaing et al., 1990) and temporal (Budaev, 2004) scales.

Criticality, or the state of a system close to a phase transition, isnother physical phenomenon that has been associated with mul-ifractal dynamics. For example, multifractal signals are observedn the flow of information through a computational network as theolume of traffic approaches the critical point of transition to a con-ested state (Li and Shang, 2005; Takayasu et al., 2000). Empiricalvidence to suggest the preferential adoption of either mechanisms an explanatory model for neuroimaging data would be beneficialor interpretation of multifractality at a brain systems level.

In this article we revisit functional MRI datasets that we havereviously analysed using a wavelet-based algorithm that assumedhe endogenous brain dynamics were monofractal and could beppropriately summarised by the Hurst exponent (Wink et al.,006, 2008). On this basis, we reported that healthy ageing andholinergic receptor blockade by scopolamine were both associ-ted with significant increase in H, implying that increased H mighte a marker of suboptimal neurophysiological dynamics (Winkt al., 2006). However, we also reported that faster processingpeed in a fame decision/facial encoding task was associated withncreased H, implying that increased H might be associated withaster cognitive performance (Wink et al., 2008). To investigate thispparent discrepancy we here apply multifractal analysis to time-eries extracted from brain regions demonstrating these variousffects on the Hurst exponent to address the question: are thereubtle differences in the dynamics associated with ageing, scopo-amine and faster cognitive processing that are better differentiatedy a multifractal analysis than by a monofractal analysis? Havingstablished the utility of multifractal properties in fMRI time-seriese investigate the plausibility of different generative mechanisms,sing the algorithm of Castaing et al. (1990), and ask the question:

s there evidence for either turbulence or criticality in endogenousrain dynamics measured using fMRI?

. Methods

.1. Study sample

Twenty-three, right-handed, healthy participants took part inhe study. Data from one participant were omitted due to a scan-er malfunction leaving 22 participants for analysis: 11 young (6

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ce Methods 174 (2008) 292–300 293

emale, 5 male; mean age = 22.4 years, range = 20–25 years), 11lder (6 female, 5 male; mean age = 65.3 years, range = 60–70 years).he groups were matched for education (t = 1.48, d.f. = 20, p = 0.15).ll participants had a normal clinical examination to exclude anyedical, neurological, or psychiatric disorder, or any contraindica-

ion to MRI.In order to exclude possible non-clinical dementia cases in

he older group, older participants were screened using theini-mental state examination (MMSE; maximum score = 30):ean = 29.6, range 29–30. Additionally all participants were

creened radiologically for brain structural lesions. Within the olderroup, one participant was currently medicated with thyroxine andne participant was undergoing hormone replacement therapy.

All participants gave informed consent in writing. The proto-ol was approved by the Addenbrooke’s NHS Trust Local Researchthics Committee.

.2. Study design

We used a randomized, double blind, placebo-controlled design.articipants were scanned using functional MRI in two separateessions scheduled at least 1 week apart. Sixty minutes beforeach fMRI session, participants received one of two treatments: (1)copolamine hydrochloride 0.3 mg (0.75 ml) subcutaneously or (2)aline placebo (0.75 ml) subcutaneously. The order of treatmentsas counterbalanced across participants. A more detailed descrip-

ion is given in Wink et al. (2006).

.3. Session design

During each session there were four sets of fMRI data acquisi-ion: (1) during a fame decision/facial encoding task (8 min 15 s); (2)uring a serial reaction time task (9 min 44 s); (3) during two recog-ition tasks (one with famous faces, the other with non-famous

aces; total of 16 min and 30 s); (4) whilst participants lay qui-tly at rest (9 min and 36 s). The order of the four acquisitions wasaintained across participants, although the order of famous and

on-famous face presentations during the recognition task wasounterbalanced. Tasks were separated by a few minutes so thatreparations could be made for the next acquisition.

.3.1. Fame decision/facial encoding taskThe stimuli for the episodic memory task consisted of viewing

0 famous faces, 40 unfamiliar faces and 40 fixation crosses in aandomised order with each presented for 4 s. Participants werenstructed to press one of two response buttons to indicate whetherface was famous or not, as well as at the presentation of a fixa-

ion cross (either button). Participants were also instructed to try toncode the faces so that they would recognize them in a subsequentecognition task. Due to technical failure, data from two partici-ants (one from the young group and one from the older group)ere unavailable, leaving 20 participants used in the subsequent

nalysis involving this paradigm.

.3.2. Resting acquisitionDuring resting state data acquisition, participants were

nstructed to lie quietly with their eyes closed.

.4. FMRI data acquisition

Data depicting BOLD contrast were acquired using a Brukeredspec scanner (Ettlingen, Germany) operating at 3 T in the Wolf-

on Brain Imaging Centre, Cambridge, UK. For each gradient-echo,cho-planar imaging (EPI) acquisition 21 slices of data parallelo the intercommissural (AC-PC) line were specified with the

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ollowing parameters: TE = 30 ms, TR = 1100 ms, flip angle = 65◦,lice thickness = 4 mm plus 1 mm interslice gap, in-plane resolu-ion = 3.75 mm.

During the fame decision/facial encoding task 450 EPI data vol-mes were acquired, the first 6 of which were discarded leaving44 volumes for analysis. During the resting state acquisition, 524olumes were acquired of which the first 12 were discarded.

.5. FMRI data analysis

.5.1. Analysis of the fame decision/facial encoding taskFollowing temporal and spatial motion correction of the imag-

ng data, regression analysis modelled the contrast of famous andon-famous decision trials against cross-hair fixation trials, whilstarticipants were under the explicit instruction to encode the facesor later recall. Group median responses were statistically tested inhe standard anatomical space of the Montreal Neurological Insti-ute (MNI) against the two-tailed null-hypothesis of no stimuluselated activation based on permutation of the original time-serieshat preserved their spectral properties (Bullmore et al., 2001).robabilistic thresholding was performed at a three-dimensionalluster level at a threshold such that the expected number of falseositive tests was less than one per map. Full details of the method-logy are given elsewhere (Bullmore et al., 1999; Suckling et al.,006).

.5.2. Estimation of H from resting state acquisitionFractal signals typically demonstrate a positive autocorrelation

unction over a large number of lags and a corresponding spectralensity function with a 1/f form: S(f) ∼ f� . The slope of a straight

ine fitted to the log-log plot is defined as the spectral exponent,.e., log S(f) ∼ � log f. The spectral exponent � is related to the Hurstxponent, H = 2� + 1, of the process (see Bullmore et al., 2004 for aeview).

Following temporal and spatial motion correction, maps of Hn acquisition space for each individual were estimated by maxi-

um likelihood in the wavelet domain (Maxim et al., 2005) andegistered into MNI standard space with an affine spatial transfor-ation.

.5.3. Relationship between H and fame decision/facial encodingask reaction time

To identify regions that showed a significant relationshipetween H and the mean reaction time of all correct decision tasks,between-subjects linear model was regressed by least-squares atach intracerebral voxel in standard space using subject data underhe placebo condition only. The observed regression coefficient,ormalized by its standard error, was tested for significance againsttwo-tailed null-distribution generated following permutation of

he reaction times across participants to simulate conditions underhe null-hypothesis of no linear relationship. In the same way as thenalysis of group median activation during the fame decision/facialncoding task, significant effects were identified at the cluster-levelBullmore et al., 1999). Again, the cluster-wise threshold for signif-cance was such that the expected number of false positive testsas less than one across the entire map.

.5.4. Two-way ANOVA of HA mixed effects analysis of variance (ANOVA) model, with age

s the between-subject factor and drug as the within-subject fac-

or was estimated with the 22 estimates of H at each voxel as theependent variable. Statistical significance of the main effects and

nteraction was tested by a permutation test on local voxel clustersf large F statistics (Wink et al., 2006; Suckling and Bullmore, 2004).he threshold for cluster-level significance was set such that under

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he null-hypothesis we expect less than one false positive test perap.

.5.5. Calculation of the regional singularity spectrumThe formalism for multifractals has its origins in the work of

olmogorov (1941) on fluid turbulence, but has been successful inccounting for a wide range of phenomena with varying underlyinghysical processes (Mandelbrot, 1982). In fully developed three-imensional turbulence, the energy cascade from large to smallcales occurs in the inertial range. Over these spatial scales the q-rder moments of the mean velocity changes between two pointsdistance r apart, 〈|�v(r)|q〉 = 〈|v(x + r) − v(x)|q〉, and the energy

issipation averaged over a sphere of radius r, 〈ε(r)〉, both have aower law dependence on r: 〈|�v(r)|q〉| ∝ r�(q) and 〈ε(r)q〉 ∝ r�(q);here �(q) and �(q) are the velocity and the energy dissipa-

ion scaling exponents, respectively. This is a property known asself-similarity” and �(q) is linearly related to q for monofractals.owever, under the time-variant conditions of a multifractal sig-al, �(q) is a non-linear function of q. To model these circumstanceshe exponent of the power law is restricted to a temporal localityTuriel et al., 2006) such that the energy in region r at time t:

r(t) ∝ rh(t), as r → 0 (1)

here the exponent, h(t) ≡ h, is also known as the singularity orölder exponent.

The wavelet transform modulus maxima (WTMM) methodMuzy et al., 1993; Turiel et al., 2006) decomposes the total energyf the system into a hierarchy of scales using the wavelet trans-orm, Tg(r, f), of the original time-series f(t); i.e., the convolution of(t), with the continuous wavelet basis function g, in this case theaussian derivative dilated to scale r. For multifractal signals:

Tg(r, f (t))∣∣ ∼ rh(t), as r → 0 (2)

The partition function describes the energy (information) of aystem at each of its states (scales) and from which the macroscopicroperties of the system can be deduced. The partition function of aignal can be represented by the set of points where the modulus ofhe wavelet transform of the signal is locally maximal (Muzy et al.,991), connected across scale space in terms of their nearest neigh-ours with unconnected lines deleted (Turiel et al., 2006; Wink etl., 2008)—the skeleton. Formally, the partition function, Z(r,q), ofrder q is:

(r, q) ≡∑

i

∣∣Tg(r, f (ti(r))q∣∣ ∼ r�(q) (3)

here ti(r) is the set of points defining the skeleton. The partitionunction is related to the self-similarity exponents of order q by theelation:

og Z(r, q) ∼ �(q) log r + C(q) (4)

eaning the self-similarity exponents �(q) can be estimated by theradient of a straight line regressed by least-squares to a double loglot of the partition function Z(j,q) versus scale r, for each q.

Averaging the values of �(q) obtained from time-series acrossll voxels of a region-of-interest and repeating the regression for aange of values of q, yields the regional relationship between q and(q). Finally, the Legendre transform of this relationship gives theegional singularity spectrum, D(h):

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(h) = q

dq− �(q) (5)

Two parameters were derived from D(h): the value of h at whichhe distribution is a maximum, hmax, and the negative and positivealf-width at half-height, W− and W+, respectively (Wink et al.,

science Methods 174 (2008) 292–300 295

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008). Regional mean values: hmax, W− and W+, were subsequentlyalculated for each participant.

These values were entered as the dependent variables into mul-ivariate general linear models that paralleled the image-basednalysis described above; i.e., with task reaction time as the inde-endent variable, a two-way repeated-measures factorial designas used to assess the main effects of age and drug.

.5.6. Regional probability density functions for cascade modelsExperimentally, as r approaches the larger scales, where energy

s injected into a fully developed turbulent system, the proba-ility density function (PDF) of ��(r) is Gaussian. In the inertialange, intermittent large fluctuations lead to a non-Gaussian PDFith heavy-tails (Naert et al., 1994). Similar empirical observationsave demonstrated that this behaviour is generally a signature

or random multiplicative cascade processes (of which turbu-ence is an example) (Kiyono et al., 2004; 2006; Bacry et al.,001).

The ersatz model of the PDF of ��(r) (Castaing et al., 1990) makeshe distinction between two levels of fluctuations. First, for a fixedalue of ε(r) the PDF for ��(r) is a Gaussian, determined by itsariance �. Second, the fluctuations of ε(r) are postulated as havinglog-normal distribution determined by , the variance of ln �. Theistribution of ��(r) is then:

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Empirical PDFs of the differences in BOLD signal (analogous to�(r)) at temporal distances r = 2, 4, 8, 16, 32, 48 and 64 time-pointsere obtained from mean zero and unit variance voxelwise time-

eries contained within the regions identified as significant throughunivariate test of H, as described above. The theoretical PDF (Eq.

6)) was then regressed onto the data using Simpson’s rule for thentegration over � and a Golden Search to obtain the value of 2 cor-esponding to a least-squares minimum between data and modelFig. 1).

If the underlying process is turbulent information flow then theelationship between ln 2 and ln r will be linear (Castaing et al.,990). Alternatively, scale invariance of 2 is associated with criticalhase phenomena (Mehta et al., 2002).

. Results

.1. Fame decision/facial encoding task analysis

Under the placebo condition, the overall accuracy for cor-ect recognition of famous faces was 0.79 ± 0.16 with meaneaction time 1.091 ± 0.220 s, and for correctly rejecting non-amous faces accuracy was 0.94 ± 0.07 with mean reaction timef 1.228 ± 0.211 s. Participants were significantly more accuraten making non-famous than famous decisions (t(d.f. = 19) = 2.586,= 0.018), and reaction times were significantly faster for famous

han non-famous decisions (t(d.f. = 19) = 3.500, p = 0.002). Reactionime and accuracy were negatively correlated for both famousR = −0.689, p = 0.001) and non-famous (R = −0.439, p = 0.050) deci-ions. A regression of age on reaction time was not significantF(1,19) = 1.434, p = 0.247).

Activated regions from a comparison of face trials > cross-hairxation are shown in Fig. 2b as yellow regions. The regions

dentified included bilateral cerebellum, bilateral visual cortex,ippocampus, fusiform and lingual gyri, as well as right inferiornd middle frontal gyrus located at MNI standard space coordi-ates: x = −40 mm, y = +22 mm, z = +2 mm. This pattern of activationlosely resembles that previously reported from a similar paradigm

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easurements, �v(r), separated in time by r. Data points represent values of (topo bottom) r = 2, 4, 8, 16, 32 and 64 time-points (vertically offset for clarity) and theolid line is the regressed fit of the turbulence model.

Bernard et al., 2004). These occipito-temporal regions, includinghe fusiform face area, are primarily involved in the processing ofaces (familiar or unfamiliar). The bilateral activations of the medialemporal regions suggest a contribution of these structures in thettempt to match perceived faces with pre-existing semantic rep-esentations stored in long-term memory.

Regions of deactivation (face trials < cross-hair fixation) are dis-layed in blue in Fig. 2b and describe a pattern consistent with theefault mode network (Greicius et al., 2003; Gusnard and Raichle,001) including anterior and posterior cingulate cortex and largereas of parietal lobe. There is notable overlap of the detected deac-ivation with white matter tracts within the parietal lobe. A majorontribution to the BOLD effect is from macrovascular structures,hich can extend some tens of millimetres from the activation

ite (Menon, 2002). Regions activated by a working memory task,ncluding the superior parietal cortex, medial frontal, middle, andnferior frontal gyri, are particularly sensitive to this effect pre-umably due to the influence of the middle cerebral vein, whichriginates near the prefrontal cortex and extends along the lateralerebral fissure (Tomasi and Caparelli, 2007). This effect is furthernhanced by the relative low intrinsic spatial resolution of EPI andubsequent degradation by data pre-processing as well as the supe-ior sensitivity of cluster-based, non-parametric statistical testingSuckling et al., 2006; Thirion et al., 2007).

A focal region in the right middle and inferior frontalyrus (located at MNI standard space coordinates: x = −42 mm,= +22 mm, z = −10 mm and including the right inferior frontal (tri-ngular part); Fig. 2a) demonstrated a significant linear relationshipetween H, calculated from resting state time-series, and the meaneaction time across all famous and non-famous decisions in the

ame decision/facial encoding task. This region and the regions ofask activation (Fig. 2b) are very similar to those reported previ-usly using half this sample; that is, young subjects only (Wink etl., 2008).

296 J. Suckling et al. / Journal of Neuroscience Methods 174 (2008) 292–300

Fig. 2. Coronal (y = +22 mm), saggital (x = −42 mm) and axial (z = −10 mm) views of the MNI template with (a) top row: significant negative correlation between mean reactiond fromo . Yelloc in. (Ft

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uring the fame decision/facial encoding task and estimates of the Hurst exponentf all faces against cross-hair fixation during the fame decision/facial encoding taskorresponds to the right-hand of the brain. R = right and L = left hand-sides of the brahe reader is referred to the web version of the article.)

The results from the two-way analysis of variance of H areescribed in detail in Wink et al. (2006) and reproduced in Fig. 3.

n summary, there was a significant main effect of age in bilateraledial temporal lobe structures, including hippocampus, amyg-

ala and parahippocampal gyrus. In all these regions, H wasncreased in older participants. There was a significant main effectf drug on H in right medial temporal lobe structures including hip-ocampus, amygdala and parahippocampal gyrus. In these regions,was increased by scopolamine compared to placebo.

.2. Can multifractal analysis further differentiate effects ofgeing, scopolamine and faster cognitive performance on fMRIynamics?

Within the single region of significant linear relationshipetween H calculated from the resting acquisition and fameecision reaction time, univariate regression analysis was non-ignificant for each parameter derived from the regional singularitypectrum (Table 1), and non-significant for the multivariate testF(1,18) = 1.738, p = 0.204).

Two regions of significant main effect of age on resting acqui-ition H were identified in the left and right hemispheres of the

eocortex. Within the left-hemispheric region the multivariateLM was significant: F(19,2) = 3.785, p = 0.041. The univariate testas significant for hmax and W− but not for W+ (Table 1). For the

ight-hemispheric region, the multivariate GLM was significant:(19,2) = 4.144, p = 0.032. The univariate tests were significant for

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subsequent resting time-series; (b) bottom row: activation elicited by the contrastw corresponds to activated regions, blue to deactivated regions. Left of the image

or interpretation of the references R = right and L = left to color in this figure legend,

max (larger for older participants), at trend for W− (larger for olderarticipants), but non-significant for W+ (Table 1). To illustrateraphically these differences, singularity spectra for participantsith the highest and lowest values of H are shown in Fig. 4a and

oxplots of the regional means for each of the parameters in Fig. 5a.Within the single region of significant main effect of drug

n resting acquisition H, the multivariate GLM was significant:(19,2) = 5.384, p = 0.014. Univariate tests were also significant formax, W− and W+ (Table 1), with scopolamine generating largeralues of these parameters in comparison to placebo. Singularitypectra for participants with the highest and lowest values of Hre shown in Fig. 4b (right) and Fig. 4c (left) with boxplots for theegional mean parameters extracted from right (Fig. 5b) and leftFig. 5c) regions of effect.

.3. Are fMRI dynamics turbulent?

The behaviour of 2 estimated as a function of separation inime, r, of the difference in BOLD measurements is shown inig. 6 for each of the regions identified by the univariate analy-es of H (Fig. 3). Decreasing values of 2 correspond to increasinglyaussian-like distribution of the PDF. Relatively low values of 2

ere observed for small r, likely reflecting the white noise com-onent of the signal. For r > 8, values of 2 were constant and of aimilar magnitude across all regions, suggesting that the underly-ng process is not turbulent. However, 2 was not correlated with

and was unable to distinguish the effects of ageing (Fig. 6a and

J. Suckling et al. / Journal of Neuroscience Methods 174 (2008) 292–300 297

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ig. 3. Regions of significant main effects of (a) age and (b) drug on the Hurst expoy the right side of the image; the origin of the x and y dimensions of Talairach spntercommissural plane, is indicated by numbers adjacent to each section. Reprodu

), scopolamine administration (Fig. 6c) or correlation with taskerformance (Fig. 6d).

. Discussion

.1. Can multifractal analysis further differentiate effects ofgeing, scopolamine and faster cognitive performance on fMRIynamics?

We have previously reported (Wink et al., 2006) that the Hurstxponent is a measure sensitive to both age and scopolaminedministration. From that initial study the conclusion was drawnhat the BOLD signal contains information on the dynamics of therain that can be influenced by long-term trends (age) and short-erm perturbations (psychoactive drug). However, the monofractalssumptions implicit in the calculation of H yield a measure-ent that is limited in its ability to fully characterize the dynamic

esponses to such physiological challenges.The Hölder exponent, h, at a given point in time represents con-

ributions from the temporal hierarchy of singularities. High valuesf h correspond to those points at which the dominant contributions from (slowly decaying) singularities at lower frequencies and viceersa. The parameterisation of the singularity spectra derived from

MRI time-series has been capable of refracting the effects of agend scopolamine that have previously demonstrated both a similarirectional and magnitudinal change in H (Wink et al., 2006). Rel-tive to placebo, scolopamine significantly increased both upper,+, and lower, W−, ranges of the spectrum as well as positively

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able 1esults from statistical testing of multifractal parameters (hmax, W− and W+) extracted froependent variable the Hurst exponent

hmax

orrelation with encode decision reaction time F(18,1) = 1.738 (p = 0.204)ain effect of drug F(20,1) = 10.459 (p = 0.004)*

ain effect of ageLeft region F(20,1) = 6.156 (p = 0.022)*

Right region F(20,1) = 6.671 (p = 0.018)*

* Denotes significant at p < 0.05.

of resting fMRI time-series. For all maps, the right side of the brain is representedindicated by the cross-hair; the z coordinate of each section, i.e., mm below the

part (with permission) from Wink et al. (2006).

hifting the location of the spectral maxima, hmax (Table 1 and Figs.c and 5c). However, ageing did not significantly change W+, but

ncreased both W− (although the right medial temporal region onlyt trend levels) and hmax (Table 1 and Figs. 4a and b and 5a and b).

Distinct from both these effects is the correlation seen betweenhe mean reaction time during the fame decision/facial encod-ng task and H calculated from resting state data acquired some0 min later (Fig. 2). For signals that are multifractal, the Hurstxponent measures the overall, ‘average’ behaviour of the sin-ularities and is generally correlated with hmax: main effect ofrug, R = 0.748, p < 10−6; main effect of age, R = 0.700, p < 10−6

right) and R = 0.738, p < 10−6 (left); correlation with reaction time,= 0.851, p < 10−6. Nevertheless, the parameterisation of the singu-

arity spectra adopted did not yield variables that demonstratedny significant univariate relationship with reaction time.

The analysis introduced in this article has been able to resolvehe apparently paradoxical situation in which increases in H wereositively correlated with increased age and administration of anntimusarinic agent known to reduce performance on memoryasks (Everitt and Robbins, 1997) in medial temporal regions, as wells faster reaction times for recognition of faces in inferior frontalegions. In fact, each of these experimental factors exerts distinctnfluences on the neural networks that are active during uncon-

trained (resting) wakefulness, which are apparent in the spectralroperties of the corresponding fMRI time-series. The descriptionf scopolamine as a mimic of ageing effects (Wink et al., 2006)an now be refined; low frequency singularities are promoted byoth factors and the distribution is generally shifted to positive val-

m within regions of the brain identified by prior whole brain analysis using as the

W− W+

F(18,1) = 0.025 (p = 0.877) F(18,1) = 0.012 (p = 0.913)F(20,1) = 8.632 (p = 0.008)* F(20,1) = 7.588 (p = 0.012)*

F(20,1) = 4.756 (p = 0.041)* F(20,1) = 1.453 (p = 0.242)F(20,1) = 3.894 (p = 0.062) F(20,1) = 1.273 (p = 0.272)

298 J. Suckling et al. / Journal of Neuroscien

Fig. 4. Singularity spectra extracted from regions demonstrating: (a) main effect ofadsl

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ge in right hemisphere; (b) main effect of age in left hemisphere; (c) main effect ofrug, based on a univariate voxelwise test of H. In each plot the hashed line is thepectrum extracted from the participant with the lowest value of H, and the solidine for the highest value of H in the labelled groups (drug or age).

es of h, in agreement with the increase in persistence observedy increases in H. However, rapidly decaying singularities appearnchanged by age, but are significantly increased by scopolamine.

Analysis of singularity spectra has been applied to a wide varietyf biological signals, although the overall literature is not extensive.orroborative evidence for the effects observed in this fMRI studyan be found in the multifractal analysis of ECG, which was able toistinguish between abnormal rhythms (Wang et al., 2007), diseasend ageing (Goldberger et al., 2002; Ivanov et al., 1999, 2001). In

articular, patients with severe heart failure demonstrated a loss ofultifractality and a tendency for signals to be purely monofractal,

et ageing effects were in the opposite direction when comparedith healthy young participants. In contrast to the report of car-iological disease states, singularity spectra calculated from EEG

qpicW

ce Methods 174 (2008) 292–300

ecordings were increased in width during epileptic seizures (Songt al., 2005). Drug effects also have had a measurable effect on ECGata where the administration of beta-blockers to patients withongestive heart failure restored the multifractal properties of theignal (Chiu et al., 2007) whereas administration to normal controlsesulted in a loss of multifractality (Amaral et al., 2001).

.2. Relationship of the resting state dynamics to taskerformance

We have previously reported on half this sample (younger par-icipants only) that the Hurst exponent calculated from the restingtate time-series was significantly correlated with reaction timef a fame decision/facial encoding task conducted during a sep-rate acquisition some 30 min previously (Wink et al., 2008). Weave confirmed this result with a larger sample, including the olderarticipants (Fig. 2a). As previously, this relationship between taskerformance and endogenous dynamics is located in a region ofhe right inferior frontal gyrus, associated with successful retrievalf information stored in long-term memory (Bernard et al., 2004)hat is close in location and size to a region that is active duringhe task (Fig. 2b). The design of the experimental sessions does notermit us to draw any conclusions on causality; that is, whether H

s modified by the task or if it is a signature of pre-existing endoge-ous dynamics that might predict performance. For this a specificxperimental design would be required.

As far as we know there are no prior examples in fMRI of usingultifractal resting state dynamics to refract the differential effects

f experimental factors. However, an increase in the width of theingularity spectrum calculated from frontal brain regions depictedn T2-weighted MRI images was associated with older comparedo younger healthy volunteers. Within the older group, the widthf the spectrum from the same region was positively correlatedith a reduction in executive performance. These results wereot repeated in a parieto-occiptial region (Takahashi et al., 2004).hilst there are a number of differences between this experiment

nd that reported in this article, both in terms of cognitive task andhe cohort involved, it illustrates the broad applicability of mul-ifractals to characterise both temporal and spatial patterns, andpecifically that parameters of the singularity spectrum are relatedo task performance and ageing.

.3. Evidence for a critical-phase model for brain function

From the time-series contained within the regions of significanthange of H (Fig. 3), the PDF of differences of BOLD measurementre invariant to the temporal distance, r. This is evidence that aurbulent model of information flow from high to low scales hasnly limited validity, and the invariance of the energy dissipationver temporal distances, r > 8 time-points (that is, constant 2 above9 s of separation) is better explained by critical-phase phenom-na in which competing or opposing ‘forces’ maintain the systemn a dynamic equilibrium. Strong scale invariance is encountered iniverse circumstances, including the changing polarisation of mag-etic domains in materials experiencing a continuously increasingxternal magnetic field (Mehta et al., 2002) and time-series of inter-eat intervals of the heart (Kiyono et al., 2004, 2006), which exhibitultifractal behaviour (Amaral et al., 2001).Systems operating at a phase transition are metastable with

espect to a set of control parameters, and capable of rapid

ualitative change in response to external stimuli. Behaviouralhase changes from syncopated to synchronised finger tapping

n response to a tone of increasing frequency are matched byorresponding neurophysiological fluctuations (Kelso et al., 1992;allenstein et al., 1995). Moreover, these transitions occur over

J. Suckling et al. / Journal of Neuroscience Methods 174 (2008) 292–300 299

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ig. 5. Boxplots of regional mean parameters hmax, W+ and W− extracted from regiof age in left hemisphere; (c) main effect of drug, based on a univariate, voxelwise t

hort and long spatial and temporal scales (Freeman, 2003) lend-ng credence to the proposition that the brain is maintained in atate of self-organised criticality (Bak et al., 1987). Under theseircumstances, the critical point of the system is not approachedy the systematic tuning of a parameter, rather it is a minimallytable state reached irrespective of the initial conditions and tohich it returns following a perturbation. Emergent properties of

his type are also observed in neurocomputational models wherehe number of long-range connections (axons) within a randometwork of cellular automata controls the robustness of the criti-ality to internal noise (Kozma et al., 2005). Whilst these models arencomplete in their description of the cortex, they draw interesting

arallels with the scale-invariant, small-world topologies observedrom resting state fMRI and MEG data (Achard et al., 2006, 2008).rom these observations and the results presented in this study,elf-organised criticality appears to offer a tractable model for theomplex spatial and temporal behaviours of the brain.

tatwo

ig. 6. Regional relationship between ln 2 and r for each of the regions identified in the uf drug; (c) correlation with mean reaction time of fame decision/facial encoding task.

monstrating significant: (a) main effect of age in right hemisphere; (b) main effectH.

.4. Methodological issues

Calculating the singularity spectrum can be undertaken via aumber of distinct algorithms. The wavelet transform maximumodulus method (Muzy et al., 1993) was chosen as it has been used

n a number of previous studies that provide a precedent for theesults reported in this article (Goldberger et al., 2002; Ivanov etl., 1999; Song et al., 2005; Chiu et al., 2007; Shimizu et al., 2004).owever, recent comparative testing with synthetic signals (Turielt al., 2006) has demonstrated that the WTMM method has a ten-ency towards linearization of the tail of the singularity spectrumowards higher values of h. Whilst this may have consequences for

he accuracy of the measurement of W+, it seems reasonable tossume that under the consistent spectral conditions of the BOLDime-series any bias will be equally present in all participants andill not unduly influence subsequent statistical inferences. More-

ver, the methods compared by Turiel et al. (2006) each had their

nivariate analyses of H. (a) Main effect of age (left and right regions); (b) main effect

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wn limitations and performance characteristics and further works indicated in the comparative testing of algorithms for obtain-ng the singularity spectrum with synthetic signals that adequatelyimulate time-series from resting state fMRI.

.5. Conclusions

BOLD signal dynamics acquired during resting wakefulnessemonstrate properties consistent with critical-phase systems.hese systems are known to produce multifractal behaviour, thenalysis of which is capable of distinguishing between the effectsn endogenous fMRI dynamics of ageing, drug administration andask performance more specifically than a univariate, monofrac-al approach. Nevertheless, the Hurst exponent is sensitive tohanges in multifractality and is adequate for exploratory statisti-al testing, defining the spatial regions for subsequent multivariateesting via parameterisation of the singularity spectrum. We sug-est this combined approach delivers a richer interpretation of thebserved changes in endogenous dynamics engendered by diverseactors.

cknowledgements

This neuroinformatics research was supported by a Humanrain Project grant from the National Institute of Mental Health andhe National Institute of Biomedical Imaging and Bioengineering.B is employed 50% by GlaxoSmithKline and 50% by the Universityf Cambridge. The work was conducted in the MRC/Wellcome Trustehavioural & Clinical Neurosciences Institute, Cambridge, UK.

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