Aging and the Spectral Properties of Brain Hemodynamics

Abstract

Cerebral glucose metabolism (CMRGlc) systematically decreases with advancing age. We sought to identify correlates of decreased CMRGlc in the spectral properties of fMRI signals imaged in the task‐free state. Lifespan resting‐state fMRI data acquired in 455 healthy adults (ages 18–87 years) and cerebral metabolic data acquired in a separate cohort of 94 healthy adults (ages 25–45 years, 65–85 years) were analyzed. The spectral properties of the fMRI data were characterized in terms of the relative predominance of slow versus fast activity using the spectral slope (SS) measure. We found that the relative proportion of fast activity increases with advancing age (SS flattening) across most cortical regions. The regional distribution of spectral slope was topographically correlated with CMRGlc in young adults. Notably, whereas most older adults maintain a youthful pattern of SS topography, a distinct subset of older adults significantly diverged from the youthful pattern. This subset of older adults also diverged from the youthful pattern of CMRGlc metabolism. This divergent pattern was associated with T2‐weighted signal changes in frontal lobe white matter, an independent marker of small vessel disease. These findings suggest that BOLD signal spectral slope flattening may represent a biomarker of age‐associated neurometabolic pathology.

As the brain ages, its metabolic demands decline—but not uniformly. Here, spectral slope flattening of resting‐state fMRI signals is proposed as a potential biomarker of pathologic brain aging. A subset of older adults diverges from youthful spectral and metabolic patterns, with changes linked to frontal white matter pathology and regional loss of aerobic glycolysis.

1. Introduction

Brain metabolism and physiologic integrity decline with age in a manner parallel to numerous other measures.^{[ 1} , ^{2 ]} This principle has been demonstrated with positron emission tomography (PET)^{[ 3} , ⁴ , ^{5 ]} as well as resting‐state functional magnetic resonance imaging (rs‐fMRI).^{[ 6 ]} In particular, cerebral blood flow and oxidative metabolism of glucose globally decline with advancing age.^{[ 3 ]} In contrast, glycolytic metabolism of glucose declines most in regions with high values in youth.^{[ 7} , ^{8 ]} Thus, the regional pattern of cerebral metabolism in older adults often diverges from the normative youthful pattern.^{[ 7 ]} Intriguingly, some older adults retain youthful metabolic patterns while others do not.^{[ 7 ]}

Previous rs‐fMRI studies of aging have largely focused on functional connectivity (FC).^{[ 6 ]} FC refers to pairwise correlations of blood‐oxygen‐level‐dependent (BOLD) signals in functionally related regions known as resting state networks (RSNs).^{[ 9} , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ^{16 ]} Age‐related FC changes—particularly within the default mode network—and reductions in network segregation have been widely reported.^{[ 17} , ¹⁸ , ^{19 ]} However, studies that rigorously controlled for preclinical Alzheimer's disease using CSF and imaging biomarkers found that age‐FC associations are modest.^{[ 20} , ^{21 ]} On the other hand, it has been shown that advanced age leads to reductions in the amplitude of spontaneous BOLD signal fluctuations.^{[ 22} , ^{23 ]}

Comparatively fewer studies have evaluated age‐related changes in the statistics of regional spontaneous BOLD signals. These studies have employed a variety of metrics including amplitude of low‐frequency fluctuations (ALFF) and BOLD signal variability, both of which relate to the temporal variance of BOLD fMRI signals. The developmental trajectory of ALFF up to the age of 20 years follows a topographic gradient along the sensorimotor‐association cortex axis.^{[ 24 ]} In aging, both signal amplitude and between‐region variability are reduced in older compared to younger adults.^{[ 22} , ^{25 ]} However, whereas these measures quantify amplitude‐based features of BOLD, they do not address changes in the spectral characteristics of BOLD fMRI signals.

BOLD fluctuations are 1/f‐like, that is, characterized by an approximately linear decrease in log spectral power with increasing frequency.^{[ 26} , ²⁷ , ^{28 ]} Importantly, the spectral properties of resting‐state BOLD signals vary across brain networks,^{[ 29 ]} depend on the task state,^{[ 27 ]} and change in patients with glioblastomas and clinical comorbidities.^{[ 30 ]} These effects may be related to changes in brain glucose metabolism. It has been repeatedly shown that the spectral properties of BOLD signals vary regionally in relation to brain glucose metabolism.^{[ 31} , ³² , ^{33 ]}

The preceding considerations suggest that the spectral characteristics of resting‐state BOLD signal fluctuations may correspond with changes in cerebral blood flow and metabolism across the lifespan. To address this question, we evaluated the spectral properties of BOLD signal fluctuations and their correlations with cerebral blood flow and metabolism using two independent datasets: the Cambridge Centre for Ageing and Neuroscience (Cam‐CAN) rs‐fMRI dataset of 455 subjects aged 20–87 years^{[ 34} , ^{35 ]} and the adult metabolism and brain resilience (AMBR) metabolic dataset including 94 subjects aged 25–85 years.^{[ 7 ]}

2. Results

We evaluated changes in the spectral slope (SS) of BOLD fluctuations across the cortex using a cross‐sectional group of 455 individuals aged 20 to 87 years. SS was computed using linear regression of log power against frequency within the 0.015–0.145 Hz band. In general terms, this metric indexes the relative prevalence of slow versus fast BOLD activity. Prior works have demonstrated a correlation between steeper spectral slopes, that is, greater coherence at lower frequencies within the infraslow frequency range, and higher glucose metabolism.^{[ 31} , ^{32 ]} To characterize age‐related SS changes for each cortical parcel, we fit parcel‐specific, generalized additive models (GAMs), parametric in age, with sex and head motion as linear covariates, as previously described in ref. [24] Each GAM estimates the parcel‐wise trajectory of changes in SS with age.

2.1. Spectral Slope Flattens Across the Lifespan

SS flattens with increasing age. In Figure 1 , panel A shows BOLD fluctuations sampled from the same ROIs in two subjects in both time and frequency domains. Panel B illustrates the average power spectra, computed by averaging across all cortical voxels and participants within each age group. Panel C shows the topography of SS change from youth to old age. Warmer hues indicate a steeper SS, reflecting a greater prevalence of slow over fast activity within the infra‐slow frequency range. The steepest spectral slopes were observed in medial and lateral parietal, prefrontal, and visual cortices. This topography remained consistent across all age groups, suggesting that, despite a general flattening observed in the brain, major features of SS topography are generally preserved in most older individuals.

Figure 1.

Spectral slope (SS) flattens with advancing age. A) Two distinct BOLD fluctuations, sampled from the same ROIs, in two exemplar subjects, shown in both time and frequency domains. B) (left) Averaged power spectra across participants in three age groups. (right) Averaged power spectra plotted as log power versus frequency. SS is defined as the negative of the first derivative of the slope fitted to the log power. C) Parcellated surface SS maps (footnote: the volumetric data was projected onto the Conte‐69 average inflated surface for surface‐based visualization), averaged across participants within three age groups, illustrate the topography of age‐related SS flattening across the lifespan. Cortical regions with steep spectral slopes include medial and lateral parietal, prefrontal, posterior cingulate, and visual cortices (warmer hues). The age cohorts are 20–40 years (n = 113), 41–65 years (n = 179), and 66–87 years (n = 163). Although age‐related SS flattening differs across cortical regions, the characteristic features of SS topography persist across all age groups.

2.2. Spectral Slope Flattening Exhibits Regional Specificity

Visualization of regional fits with significant age‐related effects suggested that there were two distinct trajectories of spectral slope behavior across the lifespan: 1) consistent flattening of spectral slope throughout life, or 2) no decline until mid‐adulthood, followed by marked and continuous flattening. Fuzzy c‐means clustering confirmed the presence of these varying trajectories across cortical parcels. Silhouette score analysis^{[ 38 ]} indicated that two clusters were optimal (see Supporting Information). Whereas most cortical regions exhibited continuous SS flattening (Figure 2A), certain regions, particularly those coinciding with auditory (AUD), cingulo‐opercular (CON), and salience networks (SAL), exhibited flattening starting in mid‐adulthood (Figure 2B). Regions within Cluster 2 include dorsal anterior cingulate cortex (dACC), frontal operculum, supplementary motor area (SMA), supramarginal gyrus (SMG), inferior frontal gyrus (IFG), pars marginalis of the cingulate gyrus, and the mesial surface of the visual cortex.

Figure 2.

Trajectories of age‐related SS flattening across cortical parcels (Schaefer 300 parcellation scheme), identified by fuzzy c‐means clustering. A) Cluster 1, comprising the majority of cortical parcels, exhibits a consistent flattening of the spectral slope with age. The right‐most panel displays the “RSN‐Cluster1 Correspondence Index,” computed as the normalized sum of dot products between RSN probability maps^{[ 36 ]} and membership values for Cluster 1. B) Cluster 2, comprising cortical parcels primarily within the auditory, cingulo‐opercular, and salience networks, exhibits delayed flattening that begins in mid‐adulthood (≈50 years). The “RSN‐Cluster2 Correspondence Index” is shown on the rightmost panel. Clustering analysis was done using the Schaefer 300 parcellation scheme in a volumetric space; results are subsequently projected onto a surface for visualization. Parcels heavily affected by susceptibility‐related signal loss^{[ 37 ]}) or insignificant age‐related effects were excluded in this analysis.

2.3. Spectral Flattening is Most Prominent in Cortical Regions with High Glycolytic Metabolism

Significant SS changes were observed in 82% of cortical parcels (p _FDR < 0.05). The regional magnitude of age effects was assessed using the age‐specific R ² difference, which measures the differences in explained variance between the full model (with age) and the reduced model (without age) (Figure 3A). Age‐specific R ² difference varied from 0 to 0.12, where 0 indicates that the SS change is attributable to covariates other than age. High age‐specific R ² difference values denote regions where age heavily contributed to SS change. Significant age effects were found in lateral and medial prefrontal regions, superior parietal lobule, intraparietal sulcus, the posterior cingulate cortex, and the medial surface of the visual cortex. Interestingly, age‐specific R ² difference topography markedly resembled the distribution of CMRGlc across the cortical regions (Figure 3B,C; Spearman correlation ρ = 0.66, spin test p‐value (p _spin) = 3e‐04). Brain regions with higher levels of glucose metabolism in youth showed greater effects of age on SS (Figure 3C).

Figure 3.

A) Effect of age on SS (age‐specific R ² difference) across the cortical surface. B) Parcellated cerebral metabolic rate of glucose use (CMRGlc) map averaged across 30 healthy young adults aged 25–45 years (AMBR dataset from ref. [7]). C) Spearman correlation between age‐specific R ² difference and the average CMRGlc map (rho = 0.66, p = 3e‐04). Each symbol represents one parcel. Both metrics were evaluated using the Schaefer 200 parcellation scheme in a volumetric space and subsequently projected onto the surface for visualization.

2.4. Outliers from the Normative Aging Group Identified by the SS Youthful Index

With increasing age, cerebral glucose metabolism not only decreases quantitatively^{[ 5} , ⁸ , ^{39 ]} but also loses its youthful regional patterns in some – but not all – older adults.^{[ 7 ]} Considering the established association between the spectral properties of BOLD signals and CMRGlc,^{[ 31} , ³² , ^{33 ]} and based on our present finding that SS flattens with aging, we asked whether SS topography – its inherent youthful regional variations in spectral slope – also loses its youthful pattern with increasing age. We assessed this by evaluating the SS youthful index (SSYI), evaluated as the Spearman correlation between individual SS maps and the averaged SS_young map (see Experimental Section; Figure 4A).

Figure 4.

(Top) Topography of average spectral slope (SS) maps, CMRGlc, CMRO₂, and CBF of the younger cohort (25–45 years). The SS_young map was computed by averaging SS maps of younger participants (<45 years) in the CamCAN dataset. CMRGlc, CBF, and CMRO₂ maps are from the AMBR dataset (see Experimental Section). (Bottom) Each symbol (grey or red) represents an individual's Spearman correlation between their SS map and CamCAN‐average SS_young map (panel A defined as SS Youthful Index). Spearman correlations between SS maps and AMBR‐average CMRGlc_young, CMRO2_young, and CBF_young maps are shown in panels (B–D). Red symbols identify outlier individuals whose correlation values are greater than 3 scaled median absolute deviations from the median. These individuals also show negative and weaker correlations with CMRGlc_young and CMRO2_young maps. Correlations between SS maps and CBF_young and CMRO2_young are weaker as compared to those with CMRGlc_young. SS Youthful Indices (panel A) and correlations between CMRGlc_young and SS maps (panel B) are generally positive in younger CamCAN participants. However, an increasing fraction of individuals diverge from the youthful pattern starting at age ≈45.

Notably, the youthful pattern of SS topography generally persisted across the lifespan. However, SSYI inter‐subject variability increased cross‐sectionally with advancing age. Importantly, a distinct subset of older individuals displayed significantly weaker or even negative values of SSYI (less than three scaled median absolute deviations from the median). We labeled these individuals as outliers (red symbols in Figure 4A) for further analysis. Interestingly, these outliers also exhibited weaker correlations with CMRGlc_young and CMRO2_young (Figure 4B,C). This trend appeared much less distinguishable when correlated with CBF (Figure 4D).

2.5. SS Youthful Index Divergence is Associated with Frontal White Matter Changes

Considering that older subjects typically exhibit greater grey matter atrophy and increased head motion, we hypothesized that the identified outliers (red symbols in Figure 4A) would demonstrate smaller cortical volume and/or more head motion. Moreover, as previous findings demonstrated that the adult female brain is metabolically more “youthful”,^{[ 41 ]} we assessed the effect of sex on the SS Youthful index in outliers and non‐outliers aged over 45 years. No significant differences were observed in grey matter volume, head motion, or sex between these groups. InFigure  5A,B, the overlays of black symbols on red symbols indicate comparable distributions of grey matter volume and head motion in both groups. The histogram in Figure 5C shows no clear dominance of either sex in either group.

Figure 5.

SS Youthful Index is significantly negatively associated with frontal lobe white matter (FLWM) T2w image intensities. SS Youthful Index is not associated with grey matter volume, head motion, and sex. A group of older subjects (age > 45 years) was selected to determine if the outliers identified in Figure 4 exhibited significant differences in their grey matter volume, head motion, sex, or WM T2w image intensities (see Experimental Section). Outliers (red symbols in Figure 4) are shown as red symbols. Non‐outliers (grey symbols in Figure 4) are shown in black. A) Grey matter volume versus SS Youthful Index. B) Head motion (mm) versus SS Youthful Index. C) Differences in sex distributions between the two groups: non‐outliers (top, black symbols in Figure 5A,B) and outliers (bottom, red symbols in Figure 5A,B). D) Voxelwise correlations across participants between normalized T2w signal intensity and SSYI (as in voxel‐based lesion‐symptom mapping (VLSM)^{[ 40 ]}). Significant Pearson correlations (p < 0.05) are shown in blue. E) Averaged T2w signal intensity within the blue‐shaded regions in panel D versus SSYI. Statistical significance was evaluated in terms of linear regression model fit of age, gray matter volume, head motion, sex, and frontal lobe WM T2w image intensity as predictors of SS Youthful Index outlier status. The p‐values shown in panels A–C and E are from the fit linear regression model result (see Table S1, Supporting Information).

Intriguingly, however, SS Youthful Index was associated with higher T2‐weighted image intensities, predominantly in the frontal lobe white matter (FLWM; left panel in Figure 5D). This focal topography was identified by correlating participants normalized T2w image intensities with SS Youthful Indices in each voxel (see Experimental Section). The right panel of Figure 5D illustrates the relation between SSYI and FLWM T2w intensity values in the blue‐shaded regions of FLWM.

To quantify these observations, we fit a linear regression model using age, grey matter volume, head motion, FLWM T2w image intensities, and sex as predictors, and the binarized SS Youthful Index as the response variable. The only statistically significant predictor was FLWM T2w image intensity (estimate = −7.40, p‐value = 1.99e‐06). This result suggests that, among the middle‐aged to elderly subjects, deviations in the SS Youthful Index are more associated with frontal lobe white matter abnormalities than grey matter atrophy, head motion, sex, or age (Table S1, Supporting Information). FLWM T2w image intensities were also significantly positively correlated with body mass index (BMI) (Figure S3, Supporting Information).

3. Discussion

As the global population ages, there is a pressing need for accessible whole‐brain imaging biomarkers of functional integrity of the brain. Here, we propose that the spectral properties of rs‐fMRI BOLD signals may provide a functional biomarker of pathologic brain aging. fMRI has historically been primarily used for mapping task‐based regional changes or identifying functional topographies using resting‐state functional connectivity.^{[ 42 ]} The current work focuses on a complementary approach that evaluates age‐related changes in BOLD signal spectra, with a particular focus on their relations with cerebral metabolism.

Cerebral metabolism declines with age.^{[ 8 ]} The author found that resting‐state BOLD fMRI signal fluctuations typically exhibit progressive spectral slope (SS) flattening with age. Similar findings, obtained using a different computational strategy, have recently been reported by Wu and Gollo.^{[ 88 ]} Spectral slope changes likely reflect multiple factors, including accumulated clinical comorbidities,^{[ 30 ]} normal effects of aging (e.g., less sleep), and lifestyle changes (e.g., increased use of caffeine). In our data, spectral flattening was most prominent in cortical regions with high levels of glycolytic metabolism in younger individuals. These same regions also exhibit age‐associated loss of aerobic glycolysis.^{[ 7 ]} Thus, spectral flattening appears to be associated with loss of aerobic glycolysis. Consistent with prior work, we demonstrate a topographical correlation between the spectral characteristics of BOLD fluctuations and CMRGlc,^{[ 31} , ³² , ^{33 ]} which is most apparent in younger adults. Additionally, the present results suggest that while most older individuals maintain a youthful SS topography (as evaluated using SSYI), a subset of older individuals deviates significantly from the youthful pattern. Notably, lower SSYI is associated with higher T2‐weighted image intensities in frontal lobe white matter. Increased T2‐weighted signal intensity is a marker of white matter disease,^{[ 43 ]} previously shown to be particularly prominent in older individuals in the same regions highlighted in Figure 5D.^{[ 44} , ^{45 ]} These observations suggest that SSYI correlates with other biomarkers of pathological neurometabolic aging.

3.1. Analyzing BOLD Fluctuations in the Temporal Frequency Domain

The physiological significance of spectral slope flattening follows from the notion that infraslow frequencies (nominally, <0.1 Hz) primarily reflect signals of neural origin,^{[ 46} , ^{47 ]} whereas faster frequencies represent artifact, primarily thermal noise, and head motion.^{[ 48 ]} As head motion manifests as intermittent burst noise, its spectrum is theoretically white, as is that of thermal noise. In contrast, direct measurements show that BOLD fMRI signals are very attenuated at frequencies greater than 0.2 Hz.^{[ 49 ]} Thus, BOLD power spectra generally assume the characteristic of a 1/f‐like spectrum superimposed on a flat noise floor. Hence, the spectral slope (SS) indexes the extent to which BOLD fMRI fluctuations are of neural‐ as opposed to non‐neural origin. Empirically, in glioblastoma patients, an increased proportion of high versus low‐frequency rs‐fMRI BOLD activity is associated with compromised brain integrity.^{[ 30 ]} Here, we extend this principle to aging.

3.2. Spectral Slope Flattening in Aging

The underlying physiology defining the spectral slope of the BOLD signal, as well as its changes, is as yet uncertain. Despite this limited understanding, prior work has shown that the spectral properties of rs‐fMRI signals depend on task state^{[ 27 ]} correlate with cerebral glucose metabolism^{[ 31} , ³² , ^{33 ]} and are functionally organized.^{[ 29 ]} Critically, regions with steeper spectral slopes exhibit stronger functional connectivity across extensive regions^{[ 29 ]} and spatially correspond with higher baseline CMRGlc (Figure 4B). This circumstantial evidence suggests a potential relation between the required metabolic supply and the maintenance of cellular or synaptic dynamics^{[ 50 ]} engaging in large‐scale circuits over multiple timescales. Aging affects this process, perhaps owing to the simplification of neuronal architecture (e.g., reduced arborizations and dendritic length, decreased spine numbers,^{[ 51 ]} accumulation of DNA damage and mutations,^{[ 52 ]} or inefficiencies in DNA repair processes.^{[ 53 ]} Accordingly, it is plausible that age‐related neuropathology manifests as spectral slope flattening of BOLD signals.

Importantly, age‐associated spectral slope flattening is more pronounced in regions with higher CMRGlc in young adults (Figure 3). The pathophysiological mechanisms underlying this relation are incompletely understood. It is known that Aβ deposition is a correlate of neural activity in the APP mouse model of Alzheimer disease.^{[ 54 ]} Moreover, Aβ deposition is more prevalent in parts of the brain that are more strongly functionally connected with other parts of the brain (i.e., increased global FC magnitude), both in the APP mouse^{[ 55 ]} and healthy humans.^{[ 56 ]} These observations suggest a potential “burn‐out” mechanism for neural integrity over the lifespan. The relevant stressor may not be a single unit discharge, as action potentials are energetically inexpensive.^{[ 57 ]} Speculatively, the relevant stressor may be limits on the extent to which synaptic reweighting is able to preserve previously learned memories while simultaneously encoding new information.^{[ 58} , ^{59 ]} This would be consistent with the observation that sustained neural plasticity over a lifetime is associated with loss of synaptic spines and dendritic simplification.^{[ 51 ]} The preceding considerations suggest that these histological findings should be especially prevalent in individuals here identified as SS outliers. Testing this hypothesis would require a study combining ante‐mortem rs‐fMRI with post‐mortem histology.

3.3. Delayed Onset of SS Flattening Exhibits Regional Specificity

While the majority of cortical regions showed continuous flattening of SS with increasing age, a subset of regions exhibited a delayed onset of SS flattening starting in mid‐adulthood (Figure 2). Despite their unique and varied functions, many of these regions share a common role in initiating and controlling goal‐directed behaviors. Specifically, dACC, frontal operculum, and SMG are key components of the cingulo‐opercular network, associated with initiating, maintaining, and controlling task sets.^{[ 17} , ⁶⁰ , ^{61 ]} SMA and IFG (includes Broca's area) are involved in initiating and controlling movements and expressive language.^{[ 62} , ^{63 ]} The dorsal PCC is functionally distinct from the DMN and has been proposed to be involved in both detecting and responding to changes in the environment.^{[ 64 ]} The delayed onset of changes in these brain regions may indicate a decline in the control of complex motor behaviors in older age, as individuals become more sedentary.

3.4. SS Youthful Index Progressively Separates Outliers from the “Normal” Aging Group with Increasing Age; This Separation Correlates with Frontal Lobe White Matter Changes

The youthful pattern of spectral slope topography is generally maintained across the lifespan in most individuals. However, a subset of older individuals showed weaker and even negative SS Youthful Index values (Figure 4A). Although all participants included in this study are cognitively unimpaired (as defined by MMSE score greater than 24),^{[ 35 ]} cognitive normality does not exclude the possibility of asymptomatic neuropathology. In fact, the appearance of abnormal biomarker values often precedes the onset of clinical symptoms by several years.^{[ 65} , ^{66 ]} Furthermore, studies of normal aging have been shown to be confounded by failure to exclude participants positive for preclinical biomarkers (e.g., CSF biomarkers including Aβ42 and tau).^{[ 20 ]} Hence, it is plausible that the present outlier subset in our sample harbors covert neuropathology.

Notably, SS Youthful Index was independent from grey matter volume or head motion, and differences in sex (Figure 5A–C). However, we identified a significant negative correlation between SS Youthful Index and frontal lobe white matter (FLWM) T2w image intensities (Figure 5D). This finding echoes previous work that linked white matter hyperintensity burden to the loss of the youthful pattern of brain aerobic glycolysis.^{[ 7 ]} Additionally, aged white matter is more vulnerable to neurological disorders,^{[ 43 ]} and significant changes in FLWM have been observed as correlates of aging and AD.^{[ 44} , ^{45 ]} Hence, it is conceivable that macrostructural frontal lobe white matter damage could contribute to a greater decline in neural function related to both aging and metabolic health.

Moreover, we found a significant positive correlation between FLWM T2w image intensities and body mass index (BMI) (see Figure S4, Supporting Information). Whole brain spectral slope (averaged over parcels) and SSYI also were also independently associated with BMI after accounting for age, sex, and head motion as covariates (Figure S3, Tables S2, and S3, Supporting Information). White matter hyperintensities are known to be associated with hypertension^{[ 67} , ⁶⁸ , ^{69 ]} and BMI, a crude measure of body fat percentage, which is often regarded as a risk factor for cardiovascular disease.^{[ 70 ]} Thus, multiple lines of evidence suggest that systemic metabolic health impacts brain structure and function. Future studies with more heterogeneous cohorts may disambiguate the extent to which these effects are related to age versus cardiovascular disease or other pathologies.

3.5. rs‐fMRI Spectral Slope: A Potential Biomarker of Neuropathology

We propose a conceptual framework wherein biomarkers of neuropathology are characterized by change points at which the range of observed values progressively increases with age. In some cases, pathology leads to decreased values (e.g., hippocampal volume^{[ 71 ]} or cortical thickness.^{[ 72} , ^{73 ]} In other cases, pathology leads to increased values (e.g., white matter hyperintensities,^{[ 74 ]} Aβ deposition,^{[ 71 ]} and accumulation of p‐tau.^{[ 71 ]} In either case, the variance of biomarker values increases with age: some individuals maintain a normative or youthful state, whereas others deviate significantly from the youthful pattern. Within this framework, we hypothesize that the spectral slope of rs‐fMRI BOLD signals is a potential accessible biomarker of pathological neurometabolic aging. The underlying mechanisms that lead to changes in the spectral characteristics of BOLD signal fluctuations remain to be determined.

4. Limitations

We discuss several limitations of this work. BOLD signals are inherently sensitive to vascular and respiratory factors, as well as head motion, which is more prevalent in aging populations. Despite stringent quality control measures and accounting for head motion as a covariate, these factors may still affect the current findings. Additionally, partial volume correction (PVC) was applied in the AMBR dataset but not in the CamCAN dataset. PVC is particularly important in PET studies owing to the poor spatial resolution of older PET images (5–6 mm full‐width half maximum) and is likely to have a lesser impact on fMRI images. However, it is still conceivable that the increased inter‐subject variability observed in correlations between SS topographies and youthful metabolic maps may be attributed, at least in part, to a greater partial volume effect with aging. We also evaluated spatial correlations between rs‐fMRI and PET‐derived maps from two different cohorts. Despite efforts to account for methodological differences, for example, performing analyses at a coarse (200‐parcel) resolution and applying validated partial volume correction procedures for the PET data, dataset‐specific idiosyncrasies may still contribute to the current findings. Future studies incorporating both PET and rs‐fMRI from the same individuals would eliminate potential cohort‐dependent confounds. To evaluate white matter abnormalities, we used T2‐weighted images, implementing a technique previously described by ref.,^{[ 75 ]} which normalizes each participant's T2w image intensities to a reference intensity atlas. Future studies would benefit from using FLAIR to more accurately quantify abnormal white matter hyperintensities. Finally, the cross‐sectional nature of our study limits our ability to track within‐individual changes in BOLD fluctuations with aging. Longitudinal studies could provide more direct evidence of co‐occurring age‐related changes in metabolism and BOLD spectral slope.

5. Experimental Section

Datasets‐Cam‐CAN Dataset

The study included 455 participants from the adult lifespan Cambridge Centre for Ageing and Neuroscience (CamCAN) dataset.^{[ 34} , ^{35 ]} As specified by Shafto et al., participants of this study were given written informed consent for the study. Exclusion criteria included suboptimal registration due to compromised structural scans or significant head motion (averaged changes in head displacement and rotation in quadrature > 0.5 mm). The demographics of this sample include an age range of 18 to 88 years (54.7 ± 18.5 years), comprising 276 males and 179 females. The recruitment and selection processes of the study participants are detailed in the ref. [34] Briefly, inclusion criteria included cognitively healthy subjects without communication or mobility issues, substance abuse problems, and those eligible for MRI scans. MRI datasets were collected at a single site using a 3T Siemens TIM Trio scanner with a 32‐channel head coil. T1w and T2w structural images and resting state scans were used in this analysis. The resting‐state fMRI data included an 8‐minute 40‐second run (261 frames) acquired while participants rested with their eyes closed. A T2*‐weighted echoplanar imaging) sequence was used to collect 261 volumes, each containing 32 axial slices with slice thickness of 3.7 mm, interslice gap of 0.74 mm for whole brain coverage (TR = 1970 ms; TE = 30 ms; flip angle = 78°; field of view (FOV) = 192 × 192 mm; voxel‐size = 3 × 3 × 4.44 mm).^{[ 35 ]}

Aging Metabolism and Brain Resilience (AMBR) Dataset

Cognitively unimpaired adults without evidence of brain Alzheimer's Disease (AD) pathology were recruited from the Washington University in St. Louis community and the Knight Alzheimer's Disease Research Center. A detailed explanation of the full dataset is in the ref. [7] All research participants provided informed consent. All study procedures were approved by the Washington University School of Medicine Institutional Review Board. Data from a total of 94 participants from this dataset were selected and divided into two groups: 30 young adults (ages 25–45 years; 16 males, 14 females); 64 older adults (ages 65–85 years; 32 males, 32 females). All participants had undergone positron emission tomography (PET) imaging using a Siemens ECAT HR+ scanner. The protocol included a single 18F‐FDG scan, following a slow intravenous injection of ≈5 mCi FDG, and two sets of ¹⁵O PET scans. The final 20 min (40–60 min post‐injection) of dynamic acquisition of the FDG images were summed and converted to SUVR measurements relative to the whole brain to assess the cerebral metabolic rate of glucose (CMRGlc). Each ¹⁵O PET session consisted of two sessions of three scans to measure cerebral blood volume, cerebral blood flow (CBF), and cerebral metabolic rate of O₂ (CMRO₂). Participants were instructed to remain awake with their eyes closed throughout the scans. Please see ref. [7] for full details regarding data acquisition and preprocessing methods.

Data Acquisition and Preprocessing—Cam‐CAN Dataset

Initial fMRI preprocessing followed the conventional practice.^{[ 76 ]} Briefly, this included compensation for slice‐dependent time shifts and rigid body correction of head movement within and across runs.^{[ 77 ]} The preprocessed data were then resampled to align the structural data in (3 mm)³ atlas space using a composition of an initial affine transform and a warping map (computed using the Advanced Normalization Tools (ANTs) registration) connecting the fMRI volumes with the T1w structural image. Details of the steps regarding ANTs registration are outlined in the ref. [30] Motion correction was included in the final resampling to generate volumetric timeseries in (3 mm)³ atlas space. Further preprocessing steps included the removal of voxel‐wise linear trends from each fMRI run, temporal low‐pass filtering to retain frequencies below 0.15 Hz, and regression of nuisance waveforms. These regressors included six head motion timeseries, average signals from CSF regions, and the signal evaluated over the whole brain (global signal regression). Finally, spatial smoothing was applied (6 mm full width at half maximum Gaussian blur in each direction).

Adult Metabolism and Brain Resilience (AMBR) Dataset

To accurately estimate metabolic activity specific to a tissue type, partial volume correction (PVC) was essential owing to the limited spatial resolution of PET scans. The necessity arised from both “tissue fraction” and “point spread function” effects.^{[ 78 ]} Here, a parcel‐based approach was employed for PVC, using Schaefer's 200 parcellation scheme (detailed in the Experimental Section), presuming that each parcel exhibited a distinct and uniform activity level. A region‐based, symmetric geometric transfer matrix (sGTM) framework for PVC was used, processing both PET images and parcel maps to compute a scalar activity estimate for each parcel. In brief, sGTM models signaled spill‐over between regions using regional spread functions, derived by convolving each parcel mask with the PET scanner's point spread function. This generated a symmetric transfer matrix, which was solved using least‐squares fitting to recover the true regional tracer uptake. Compared to conventional GTM, sGTM provided similar accuracy with improved noise robustness, computational efficiency, and better performance in the presence of misregistration or PSF estimation errors.^{[ 78 ]} The current results were derived from sGTM‐corrected PET measures of CMRglc, CBF, and CMRO₂.

Parcellations

Resting state networks (RSNs) were hierarchically organized at multiple levels of granularity.^{[ 79} , ^{80 ]} In this study, cortical parcellations were obtained from ref. [81] and resampled to the (3 mm)³ atlas space. For analyses involving GAMs, the 300‐parcellation scheme was used. From these 300 parcels, regions with a low signal‐to‐noise ratio, as defined previously on the basis of a mean BOLD signal map^{[ 37 ]} comprising the medial prefrontal cortex and anterior/ventral portions of the temporal lobe, were excluded. These regions were mainly associated with the limbic network as defined in Schaefer's 17 networks, reducing the number of parcels to 271 for analysis. For comparing spectral slope maps with metabolic measures from the AMBR dataset, which was processed for PVC using the 200‐parcellation scheme, the 200‐parcellation scheme was also used.

Power Spectral Density (PSD) Calculation from Autocorrelation Function

The PSD was computed from the lagged autocovariance function by employing a cosine‐based Fourier transform (“Wiener‐Khinchin theorem”) to allow for the exclusion of high‐motion frames. First, a scaled temporal lag q associated with each lag m (q = (m − 1)*TR/30) was computed, where TR represents the sampling interval, and 30 serves as a normalization factor for this analysis. The autocovariance values were adjusted by an exponential decay factor (exp(−0.5q ²)/n) to account for the decrease in signal similarity with increasing time lags. This exponential decay factor was based on the temporal weighting factor q as well as the number of valid frame pairs n, thereby ensuring the analysis considers only those frames that were relatively motion‐free (the term “motion‐free” was used loosely, as these frames were still subject to head motion, albeit less so than the censored frames). Finally, a cosine transform was applied to the adjusted lagged autocovariance function for each voxel, yielding the PSD for each voxel.

Spectral Slope Calculation

BOLD fluctuations exhibited a scale‐free activity.^{[ 27 ]} He and colleagues previously established that a power–law function, particularly within the <0.1 Hz frequency range, more accurately fits the fMRI power spectrum than exponential and log‐normal functions.^{[ 27 ]} Following this work, the prior work used the power–law exponent.^{[ 30 ]} In the current study, the “fitness” of the spectral slope between fitting the slope in log–log versus log‐normal function was compared by evaluating R ²‐values. Log‐normal functions consistently yield higher R ²‐values compared to those derived from the log–log functions (see Supporting Information). Accordingly, in the present study, spectral slope was defined as the negative of the first derivative of the slope fitted to the logged power versus raw frequency values.

Characterizing Age Effects—Generalized Additive Models (GAMs)

Statistics for GAMs were performed using RStudio 2023.12.1 + 402 “Ocean Storm” and R 4.3.3. Drawing from prior work that utilized GAMs to analyze developmental effects,^{[ 24} , ^{82 ]} the current study expanded on GAMs to characterize the impacts of aging, seen as part of continuing development/lifespan changes. GAMs were advantageous for the flexibility in modeling both linear and non‐linear relations between independent and dependent variables. The methodology for GAMs used in this work followed the framework detailed in ref. [24] Briefly, GAMs were fit with parcel‐specific spectral slope as the dependent variable, including age as a smooth term and sex and in‐scanner head motion as linear covariates. Models for each parcel were evaluated using thin plate regression splines as the smooth term basis set, applying the restricted maximal likelihood approach for smoothing parameters and limiting the maximum basis complexity (k) to 4. The significance of the association between spectral slope and age for each parcel was assessed using an analysis of variance (ANOVA), contrasting the full model (including both age and covariates) with a reduced model (only including covariates). The difference in the explained variance between the full model and the reduced model was denoted as the age‐specific R ² difference. A significant result indicated a substantial reduction in residual deviation when age was included, as determined using the χ ²‐test statistic. The p‐values from the ANOVA across all parcel‐specific GAMs were adjusted using the FDR correction. The threshold for statistical significance was set at P _FDR < 0.05.

Associations with Cerebral Metabolic Rate of Glucose (CMRGlc)

The authors evaluated whether the extent to which spectral slope changed with age correlated spatially with “normative” CMRGlc topography. The “normative” CMRGlc topography was defined by the average baseline CMRGlc of young adults, corrected for PVC across Schaefer's 200 parcels in the AMBR dataset. The correlation coefficient was computed between the age‐specific R ² values (comparing the full GAM model against the reduced GAM model) and the “normative” CMRglc map. The association between these two spatial maps was quantified with Spearman correlation, a non‐parametric, rank‐based method that did not depend on the assumption of normality.

To test the significance of Spearman correlation, spin permutation tests similar to those described by^{[ 83} , ^{84 ]} were adapted. Since age‐specific R ² difference and CMRGlc values were both computed in volumetric space using the Schaefer 200 parcellation scheme, the centroid coordinates of these parcellations were first resampled in surface space for random rotations. Each random rotation, repeated 10 000 times using the quaternion approach^{[ 85 ]} generated distributions of randomly rotated age‐specific R ² difference values. The detailed approach is included in the Supporting Information. In each rotation, parcels rotated into the medial wall were excluded when computing Spearman correlation between the rotated values and parcel‐specific CMRGlc values. The p‐value from the spin permutation tests, p _spin, was defined as the number of permuted correlations that were greater than the original Spearman correlations.

Fuzzy c‐Means Clustering

The fuzzy‐c‐means clustering analysis was conducted in MATLAB 2023b. The predict function in R used for the full GAM model outputs the smooth function for age, which function represented the lifespan trajectory of each parcel's spectral slope. Observing distinct patterns in each parcel's lifespan trajectory showing varying levels of linearity, fuzzy c‐means clustering was applied to assign a weighted membership between zero and one to each parcel's trajectory. First, to determine the optimal cluster number, fcm was evaluated by incrementally increasing the cluster count (N = 2–15). Options used for fcm were as follows: the exponent of the fuzzy partition matrix was set to 5 to allow a greater degree of overlap; the maximum iteration count was set to 10 000; the default value for the minimum objective function improvement between two consecutive iterations was used (1e‐5); Euclidean distance was used as a distance metric. Subsequently, for each cluster number, a silhouette score was computed by first converting the weighted membership into a binary format using a winner‐take‐all analysis. Two clusters resulted in the highest silhouette score (see Supporting Information). Thus, N = 2 was used to cluster the trajectories and their corresponding cortical regions. Subsequently, the authors evaluated whether clustering based on aging trajectories aligned with well‐known resting state networks (RSNs).^{[ 86} , ^{87 ]} Specifically, voxelwise RSN membership probability maps^{[ 36 ]} were leveraged and computed the normalized sum of dot products between RSN probability maps and clustering membership values assigned for all parcels in each cluster.

Spectral Slope Youthful Index Analysis—Spectral Slope Youthful Index

Goyal et al. introduced the “youthful pattern” analysis, where individual brain metabolism (fludeoxyglucose and oxygen metabolism) and cerebral blood flow (CBF) maps were compared to the corresponding group maps from a young adult cohort using Spearman rank correlation.^{[ 7 ]} Extending this approach, the spectral slope (SS) Youthful Index was defined by evaluating the Spearman correlation between individual SS maps and the averaged SS maps from younger individuals (<45 years) in the CamCAN dataset (dataset described in Experimental Section). For outlier analysis, subjects whose SS youthful indices were greater than 3 scaled median absolute deviations from the median across all individuals in the CamCAN dataset were identified. These outliers, represented as red symbols and outlined with a red dashed box in Figure 4A, are also highlighted in Figure 4B–D.

Spectral Slope Topography versus Metabolic and Hemodynamic Maps

SS maps were additionally compared with averaged metabolic (CMRGlc/CMRO₂) and hemodynamic (CBF) maps from individuals under 45 years in the AMBR dataset (dataset described in Experimental Section). The objective of this analysis was twofold: 1) to evaluate changes in SS topography with aging and 2) to assess its similarity and changes in its similarity to “youthful” CMRGlc/CMRO₂/CBF maps with aging.

Evaluation of Potential Confounders in Outliers Identified by the Spectral Slope Youthful Index

The authors tested whether outliers identified by the SS Youthful Index were driven by potential confounding factors including grey matter volume, head motion, sex differences, or white matter abnormalities. Considering the greater variability observed among older subjects, individuals aged over 45 years were specifically included. Grey matter volume for each individual was quantified using FSL FAST segmentation, which segmented the atlas‐registered individual's T1w image into three tissue types: grey matter, white matter, and CSF. Total individual‐specific grey matter volume was defined by summing the number of segmented grey matter voxels in (3 mm)³ atlas space. Head motion was assessed using the previously described realignment procedure.^{[ 30 ]} Briefly, this measure averaged the changes in head displacement and rotation in quadrature.

White matter abnormalities were assessed using normalized T2‐weighted (T2w) image intensities based on an intensity atlas, adopting a technique described in ref. [75] Brier and colleagues used T1‐weighted and FLAIR images. However, as the authors did not have an FLAIR image available, T1w and T2w images were used for image intensity normalization. The reference intensity atlas was computed based on CamCAN participants under 40 years. Each participant's T2w image was normalized to the reference intensity atlas. To analyze the association between white matter and SSYI on a voxel‐by‐voxel basis, an approach similar to voxel‐based lesion‐symptom mapping (VLSM) was implemented.^{[ 40 ]} For each voxel, instead of employing conventional group comparisons, SSYI and T2w image intensities were treated as continuous variables for computing Pearson correlations. Considering the exploratory nature of this analysis, the significance threshold was set at α = 0.05. Voxels showing significant correlations with SSYI were subsequently used as an ROI. The averaged T2w image intensity value within this ROI was used as a representative measure of white matter abnormalities.

To quantitatively determine if any of these variables explain the difference between individuals in the outlier versus non‐outlier groups, a linear regression model was fitted with the binarized SS Youthful Index as the response variable. Age, grey matter volume (GMV), head motion (HM), and frontal lobe white matter T2w image intensities (FLWM T2w) were used as continuous predictor variables, and sex as a categorical predictor variable:

$$\begin{array}{ccc}\hfill SSYouthfulIndex\approx {\beta }_o& +& {\beta }_{1}age+{\beta }_{2}GMV+{\beta }_{3}HM+{\beta }_{4}sex+\hfill \\ & & {\beta }_{5}FLWMT2w\hfill \end{array}$$ (1)

Statistical Analysis

Preprocessing steps for fMRI data—including PSD computation, spectral slope estimation, and fuzzy‐c‐means clustering—were performed in MATLAB 2023b and are described in detail in the Experimental Section. The fMRI preprocessing pipeline, including dataset‐specific details, is outlined in the Experimental Section, and the primary atlas registration tool used is publicly available at https://github.com/robbisg/4dfp_tools. Statistical analyses involving GAMs were conducted using RStudio 2023.12.1 with R version 4.3.3, as detailed in Section 6.1.

Conflict of Interest

K.Y.P., T.O.L., J.J.L., J.S.S., A.Z.S., and E.C.L.: Licensing of Intellectual Property: Sora Neuroscience E.C.L.: Stock ownership: Sora Neuroscience

Supporting information

Supporting Information

Park K. Y., Snyder A. Z., Goyal M. S., et al. “Aging and the Spectral Properties of Brain Hemodynamics.” Adv. Sci. 12, no. 37 (2025): 12, e17644. 10.1002/advs.202417644

Data Availability Statement

The Cam‐CAN dataset is publicly available at https://cam‐can.mrc‐cbu.cam.ac.uk/dataset/. AMBR dataset: Data availability is based on prior subject consents and the 2018 Common Rule. Coded and processed regional data, suitable for additional data and statistical analyses, can be obtained from the study authors upon reasonable request by a qualified researcher under a data use agreement. For access to raw imaging data, requests should be directed to the VG Lab (https://www.mir.wustl.edu/research/research‐centers/neuroimaging‐labs‐research‐center‐nil‐rc/labs/vlassenko‐goyal‐lab/), where these data were originally collected. The primary atlas registration pipeline used in this work is available at https://github.com/robbisg/4dfp_tools. ANTs registration can be found at http://stnava.github.io/ANTs/. Any other codes used in this study will be available upon request to KYP.