Dissociation of tau pathology and neuronal hypometabolism within the ATN framework of Alzheimer’s disease

Alzheimer’s disease (AD) is defined by amyloid (A) and tau (T) pathologies, with T better correlated to neurodegeneration (N). However, T and N have complex regional relationships in part related to non-AD factors that influence N. With machine learning, we assessed heterogeneity in 18F-flortaucipir vs. 18F-fluorodeoxyglucose positron emission tomography as markers of T and neuronal hypometabolism (NM) in 289 symptomatic patients from the Alzheimer’s Disease Neuroimaging Initiative. We identified six T/NM clusters with differing limbic and cortical patterns. The canonical group was defined as the T/NM pattern with lowest regression residuals. Groups resilient to T had less hypometabolism than expected relative to T and displayed better cognition than the canonical group. Groups susceptible to T had more hypometabolism than expected given T and exhibited worse cognitive decline, with imaging and clinical measures concordant with non-AD copathologies. Together, T/NM mismatch reveals distinct imaging signatures with pathobiological and prognostic implications for AD.

A lzheimer's disease (AD) causes cognitive impairment with substantial between-patient variability in clinical presentation as well as the burden and distribution of pathology [1][2][3] . This clinicopathologic heterogeneity is both a challenge and opportunity for systematic, biomarker-based studies to refine our understanding of AD biology, diagnosis and management. AD hallmark pathologies begin with accumulation of amyloid (A) plaques, followed by deposition of tau (T) tangles and subsequent neuronal injury/neurodegeneration (N) 3 . A and T aggregates are bound by specialized radiotracers for in vivo positron emission tomography (PET) imaging (such as 18 F-Flortaucipir for T tangles). N may be assessed via neuronal hypometabolism (N M ) with 18 F-fluorodeoxyglucose ( 18 F-FDG) PET or structural atrophy (N S ) with magnetic resonance imaging (MRI). Additional polypathologies contribute to clinical progression in AD, including vascular and inflammatory etiologies, α-synucleinopathy and TAR DNA-binding protein-43 (TDP-43) diseases, many of which do not currently have specific in vivo measures 3,4 .
To address this complexity and provide a biological, rather than clinical, definition of AD, the National Institute on Aging and Alzheimer's Association proposed the ATN research framework 3 . These criteria designate the global presence (+) or absence (−) of three AD dimensions: A, T and N. Patients with A+ status are included in the Alzheimer's continuum while a research diagnosis of AD necessitates both A+ and T+, consistent with the definition of AD neuropathologic change on autopsy. This model consolidates various pathological interactions in the Alzheimer's continuum to classify heterogeneous groups by a panel of dichotomized biomarkers. Such categorical approach has already shed light on differential rates of memory decline 5,6 and clinical risks/outcomes 7,8 in patients with certain ATN combinations.
Neurodegeneration in AD is largely thought to be driven by T neurofibrillary tangles 9,10 and much work has supported a strong spatial, quantitative link between measures of T and N M 11-13 . However, both T and N show variability in patterns across the brain and between individuals, and this T/N relationship is not a complete one-to-one mapping 14,15 . Compared to a typical relationship between deposition of neurofibrillary tangles and neuronal hypometabolism (N M~T ), a relative decoupling of T and N M may arise when patients have less N than expected given their T level (N M < T as metabolic resilience to T), or greater N than expected given their T (N M > T as susceptibility). Quantification of relative T/N M mismatch may capture resilience and vulnerability in neuronal metabolic responses to T, perhaps linked to non-AD pathophysiology not currently operationalized within ATN criteria.
Here, we developed a machine learning-based clustering method to identify mismatch between T and N M using symptomatic patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort. We posited that mismatch analyses from PET markers of T and N M would reveal imaging signatures of patient groups including a typical or canonical T/N M relationship as well as unique patterns of resilience and susceptibility to T. We hypothesized for a given level of T, susceptible patients with greater than expected N M have worse cognitive decline compared to participants with canonical T/N M relationships, potentially due to more concomitant non-AD pathologies than the canonical group (Fig. 1a). Given that AD autopsy studies reveal widespread prevalence of non-AD copathology 16 , we predicted that some of the dissociation between T and N M is attributable to a spectrum of mixed disease burden. The N M > T scenario may encompass patients with metabolic vulnerability to T along with the presence of non-AD copathologies such as αsynuclein and TDP-43 that contribute to N M independently of T and at levels greater than the canonical group. Moreover, we expected that the canonical group likely has some intermediate amount of mixed disease, while resilient groups may have less copathology and slower cognitive decline To this end, we evaluated T/N M mismatch and its relation to clinical features, cognitive progression and supportive evidence for copathologies. Since non-AD pathologies and risk factors are expected to be present in both A+ or A− individuals, we performed post hoc analyses in the whole cohort and A+ or A− groups. Our findings were replicated with a cohort of cognitively normal older adults in the Harvard Aging Brain Study (HABS). Overall, we demonstrate the utility of T/N M mismatch in modeling AD heterogeneity, predicting progression and providing pathophysiological insight for cognitive impairment.

Results
T/N M mismatch defines groups by regional residual patterns. We measured the relationship between T and N M (Fig. 1a) by regressions of 18 F-FDG vs. tau standardized uptake value ratios (SUVRs) for each region-of-interest (ROI) and individual. Within our ADNI cohort (n = 289, Supplementary Table 1), clustering on T/N M regression residuals resulted in six groups with sizes ranging from 16 to 89 members. These groups were labeled based on the relative spatial pattern of metabolic resilience or vulnerability to T, which we describe below. As an example, group identity (the cluster to which a participant belongs) was mapped onto graphs for regions such as inferior temporal gyrus (Fig. 1b). This ROI is involved in early symptomatic stages of AD progression and is a representative of between-group differences in T/N M relations 5,17 . Similar T/N M relations were seen in residual heatmaps across all ROIs and patients ( Supplementary Fig. 1). Next, we assessed the consistency of our clustering across different visualization methods. A principal component analysis (PCA) (Fig. 1c) and t-distributed stochastic neighbor embedding (t-SNE) method ( Supplementary Fig. 1) map the 104 ROI dimensions onto two axes and both corroborated the betweengroup separation of clusters. A dendrogram visualized the withingroup similarity across clustered patients (Fig. 1d). Therefore, the consistency of these groups across several dimensionality reduction methods substantiates this clustering approach.
There was no significant between-group difference in A status. Despite this lack of statistically significant difference, some groups appeared more enriched in A+ individuals, so we covaried by A status, as well as for sex, age, education level and T burden in the inferior temporal gyrus in subsequent omnibus and betweengroup analyses. There were between-group differences, including significant differences in sex and education, across all participants (Table 1) and specifically among A+ (Table 2) or A− patients (Supplementary Table 2). There were no significant differences in age. The groups had similar average tau SUVRs across all regions; the distribution of individuals with regional T patterns that correspond to AD Braak stages were also similar across groups for all participants (Fig. 2). Hence, these groups likely do not depict distinct stages of AD progression but instead appear to represent unique spatial patterns of the relationship between T pathology and its functional consequences.
Herein, we characterize our six T/N M mismatch groups. The largest group of individuals (89/289) were found close to the regression line across most regions, with the smallest residuals. This canonical group defines the condition where relative N M was statistically commensurate to the level of T (N M~T ). The other five groups were compared to the canonical group by T/N M residuals in three-and two-dimensional regional maps across all participants (Fig. 2a), visualizing regions where N M is greater or less than what is observed in the canonical group given the T level. Groups derived from clustering all participants showed distinct neuroanatomical patterns; these patterns were similar across subcohorts of A+ patients (Fig. 2b) and A− patients ( Supplementary Fig. 3).
There were 3 groups with less N relative to their T level compared to the canonical group (positive residuals), thus classified as resilient to T (Fig. 2). The resilient groups had relative differences in spatial patterns of T/N M mismatch corresponding to prominent regions either throughout the cerebral cortex, termed the cortical resilient groups, or limbic areas, termed the limbic resilient group. Cortical resilient patterns stratified into two groups based on either high or low magnitude residuals. The high cortical resilient group (50/289) had higher T/ N M residuals across most cortical and limbic ROIs compared to the canonical group and was the first group to split in clustering (Fig. 1d). The low cortical resilient group (62/289) had positive residuals throughout the cortex compared to the canonical or limbic resilient groups. While both cortical resilient groups had similar T levels ( Supplementary Fig. 2), the high cortical resilient group had greater T/N M residuals (Fig. 2). Both high and low cortical resilient groups had similar distributions of positive residuals but the low cortical resilient group had lower magnitude residuals, especially in limbic structures. The limbic resilient group (16/289) had high positive T/N M residuals localized to the medial temporal lobe (MTL), anterior temporal and orbitofrontal regions compared to the canonical or other resilient groups, while other cortical regions had lower residuals here relative to the canonical group. Two groups had worse N than typical for their level of T (negative residuals) and were considered susceptible to T (Fig. 2). These groups also had a relative predilection forspatial patterns involving predominantly cortical or limbic regions, though these regional distributions were less distinct compared to those in the resilient groups. The cortical susceptible group (47/289) had lower residuals generally in cortical regions, with lesser extent in limbic regions than other groups. The limbic susceptible group (25/289) had a pattern of low residuals in primarily limbic and anterior frontotemporal areas.
T/N M groups have differences in N but not T markers. We evaluated whether clustering in T/N M residuals was generally driven by either tau or 18 F-FDG SUVR. Notably, our groups did not significantly vary by T burden ( Supplementary Fig. 2), indicating that residual-based clustering was more influenced by between-group 18 F-FDG SUVR differences, even after covarying for sex, age, education, A status and T level. Among resilient groups, T/N M residual patterns (Fig. 2) were not linked to regional differences in tau SUVR (Fig. 3a), but rather 18 F-FDG SUVR (Fig. 3b). The high cortical resilient group had significantly higher covariate-adjusted 18 F-FDG SUVR across several representative regions compared to the canonical and other resilient groups (p's < 0.005). Significant differences between covariateadjusted 18 F-FDG SUVR in the limbic and low cortical resilient groups matched the group differences in T/N M residuals. Compared to the canonical group, the limbic resilient group had significantly higher 18 F-FDG SUVR in MTL structures while the low cortical resilient group had elevated 18 F-FDG SUVR throughout the cortex (p's < 0.005). Likewise, across susceptible groups, there were no regional differences in tau SUVR (Fig. 3c), but instead 18 F-FDG SUVR (Fig. 3d). Compared to the canonical group, the limbic susceptible group had lower 18 F-FDG SUVR in limbic areas while the cortical susceptible group had worse 18 F-FDG SUVR in other cortical regions (p's < 0.005). Regional resilience and susceptibility patterns across the cohort (Fig. 3a-d) were replicated in subgroups of A+ patients (Fig. 3e-h) and A− patients ( Supplementary Fig. 4). Additionally, mean cortical thickness differed among groups (Tables 1 and 2). In the whole cohort, thickness was greater in the low cortical resilient (2.10 mm, p = 0.01, unadjusted) and high cortical resilient group (2.09 mm, p = 0.04, unadjusted) compared to the canonical group (1.87 mm).
T/N M clustering shows consistency across internal and external validation. We aimed to internally validate our clustering approach within those participants demonstrating AD pathologic change. We performed clustering on A+ participants only, who overall also demonstrate higher T burden (since 87% of A+ participants were T+). Indeed, groups generated from A+ participants alone resembled groups formed from clustering all participants, in overall patterns and group identity ( Supplementary  Fig. 5). Then, we compared the robustness of clustering on subsets of 150 randomly selected participants over ten folds. Clustering was stable across folds ( Supplementary Fig. 6). About 90% of participants had a match between their original group identity and the group identity endorsed by a majority of folds, while 9% of participants had group identity shift in the same residual direction (such as between high and low cortical resilience). These experiments demonstrate the robustness of our clustering.
Because clustering was similar across A+ and A− cognitively impaired ADNI participants, next we corroborated clustering in the external HABS cohort of cognitively normal older adults with lower levels of A and T pathology (Supplementary Tables 3 and  4). Six T/N M groups were generated from the whole HABS cohort, demonstrating similar regional patterns to those found in symptomatic ADNI participants: canonical, high and low cortical resilience, limbic resilience, cortical susceptibility and limbicpredominant susceptibility ( Supplementary Fig. 7). Thus, patterns of T/N M dissociation similar to those in symptomatic AD may be shared across settings of preclinical AD and cognitive aging, where resilience factors or non-AD pathologies may influence 18 F-FDG metabolism at low or intermediate levels of T.
T/N M groups exhibit different cognitive trajectories. We hypothesized that relative hypometabolism for a given level of T may be associated with differences in cross-sectional and longitudinal cognitive measures. Although T and N markers both strongly associate with cognitive impairment, we predicted that susceptible participants may have additional copathologies contributing to N and leading to greater cognitive decline than predicted by T. We found significant cross-sectional group differences across the cohort for various cognitive tests at the time of 18 F-FDG scan even after controlling for covariates such as sex, age, education, baseline cognition, A status and T level (Table 1). In absolute terms, the canonical group had mid-range impaired ADAS-Cog (22.9), while resilient groups had lower, better scores (19.6, 20.0, 18.8) and susceptible groups had higher, worse scores (25.6, 26.0). These results were replicated with additional global cognitive measures (Mini-Mental Status Exam (MMSE) and Clinical Dementia Rating sum of boxes (CDR-SOB)). For cross-sectional covariate-adjusted pairwise comparisons, significant differences were noted between the canonical and low cortical resilient groups on the ADAS-Cog (p = 0.0003) and MMSE (p = 0.002). Such differences were also seen in the A+ cohort (Table 2).
Then, we compared longitudinal cognitive trajectories by linear mixed effects models with covariates ( Fig. 4 and Supplementary Table 5). Across groups, the canonical group had mid-range decline on ADAS-Cog (+0.8 points/year) (Fig. 4a). The resilient groups (high cortical, limbic, low cortical) had the slowest progression on ADAS-Cog (-0.07, +0.6, +0.6 points/year, respectively). Though ADAS-Cog slopes in resilient groups did not significantly differ from the canonical group, the high cortical   resilient group showed less decline on CDR-SOB than the canonical group (p = 0.04, uncorrected). In contrast, there was significantly steeper decline on ADAS-Cog in the cortical susceptible (+2.4 points/year, p = 0.002) and limbic susceptible groups (+3.9 points/year, p < 0.0005) than the canonical group (Fig. 4a). Significant differences between canonical and susceptible trajectories were also found for CDR-SOB and MMSE (Fig. 4b,c). Among A+ participants (Fig. 4d-f) and A− patients only ( Supplementary Fig. 8), between-group differences in cognitive progression rates were comparable to the whole cohort.
Akin to cognitively impaired ADNI participants, cognitively normal HABS participants had a significant group difference in     Table 4). On MMSE, groups corresponding to T/N M susceptibility had significantly lower baseline scores. Together, our data suggests that the decoupling of T and N M may relate to factors affecting cognitive outcomes in both symptomatic and asymptomatic individuals across the distribution of T level.
Exploratory analysis of copathology factors driving T/N M mismatch. Since susceptible groups had greater N than expected given their T and faster cognitive progression, we considered potential roles of copathology in driving advanced N (Fig. 5a). The cortical and limbic susceptible groups had significantly greater number of vascular clinical risk factors than the canonical group (p = 0.0003, p = 0.04, respectively) (Fig. 5b). The limbic susceptible group had significantly higher average subcortical infarct burden than the canonical group (p = 0.04) (Fig. 5c). White matter hyperintensity (WMH) volumes were higher in susceptible groups compared to the canonical group though such trends were not significant (Supplementary Fig. 9A). We also explored APOE, a gene harboring a common variant linked to dementia. APOE4 risk allele frequency was higher in the susceptible groups than other groups but not significantly different than the canonical group ( Supplementary Fig. 9B). Next, we studied how mixed proteinopathies may contribute to susceptible groups. While there are no definitive imaging or cognitive markers for the presence of α-synuclein or TDP-43, we assessed the consilience of several suggestive imaging and a b c  cognitive tests to provide some indication for what additional copathologies may be present in the setting of T/N M mismatch. We tested imaging and clinical markers of α-synuclein (Lewy body) pathology in the cortical susceptible group. A well-studied, potential indicator of Lewy Body Disease (LBD) is the cingulate island sign [18][19][20] , the relative sparing of 18 F-FDG SUVR in the posterior cingulate cortex relative to precuneus and cuneus (Fig. 5a). There was significantly higher cingulate island ratio in the cortical susceptible group compared to the limbic susceptible and canonical groups (p's < 0.005, Fig. 5d). Differences were also significant in A+ and A− cohorts. We also assessed cognitive features linked to LBD, such as visuospatial impairment 17 . Compared to the canonical group, the cortical susceptible group had significantly worse covariate-adjusted Clock Drawing scores (p = 0.03) and other visuospatial markers ( Fig. 5e and Supplementary Fig. 9C) and trended toward higher proportion of patients with hallucinations on the Neuropsychiatric Inventory (NPI) and worse visuospatial z-scores (Fig. 5f, g). Thus, these imaging and cognitive results suggest potential α-synuclein pathology in the cortical susceptible group.
We analyzed the possibility of Limbic-predominant Age-related TDP-43 Encephalopathy (LATE) copathology in the limbic susceptible group given a pattern of severe anterior temporal/ MTL hypometabolism relative to T (Figs. 2 and 5a). We utilized the I/MTL/FSO ratio, defined as worse MTL and frontal supraorbital (FSO) hypometabolism relative to inferior temporal gyrus (I). Higher I/MTL/FSO ratio signifies worse MTL hypometabolism and correlates to LATE in clinicopathologic studies 21,22 . The limbic susceptible group had significantly higher I/MTL/FSO 18 F-FDG ratio relative to the canonical group (p = 0.01) (Fig. 5h). LATE commonly presents with asymmetric hippocampal sclerosis 23 , so we evaluated MTL asymmetry indices 24 for 18 F-FDG hypometabolism and atrophy. The limbic susceptible group had significantly higher MTL asymmetry in 18 F-FDG SUVR and thickness (Fig. 5i, j) than canonical and cortical susceptible groups (p's < 0.005). We further evaluated memory phenotypes linked to LATE 23 . Compared to the canonical group, the limbic susceptible group had worse semantic memory with significant covariate-adjusted differences in category fluency (p = 0.02) (Fig. 5k), Multilingual Naming Test (p = 0.008) (Supplementary Fig. 9D) and ADNI domain z-scores for language and memory (p's < 0.05) (Fig. 5l, m). These imaging and cognitive profiles imply possible TDP-43 pathology in the limbic susceptible group.
Overall, these findings suggest that symptomatic susceptible groups had more copathology-related factors than the canonical group. Cognitively normal groups resembling T/N M susceptibility patterns in the HABS cohort also demonstrate covariate-adjusted biomarker elevations consistent with greater non-AD pathology ( Supplementary Fig. 10). When we evaluate the same biomarkers of copathology in the resilient groups, we generally observed less evidence of mixed pathology burden than the canonical group, particularly the cingulate island ratio as well as I/MTL/FSO ratio and MTL thickness asymmetry ( Supplementary Fig. 11). Overall, non-AD pathology biomarkers convey higher burden in susceptible groups and lower burden in resilient groups compared to the canonical group, indicating that relative levels of mixed pathologies contribute to T/N M mismatch and that canonical patients have some degree of copathology concordant with their commonality in autopsy series 16 .

Discussion
We leveraged paired tau and 18 F-FDG PET studies to assess the in vivo dissociation of T and N M relationships in cognitively impaired individuals in the ADNI dataset. Clustering identified six groups of patients, including a canonical group that defines the expected relationship between T and N M (N M~T ) and additional groups that were either more resilient (N M < T) or susceptible (N M > T) to T, defined by less or greater N M than expected for a given level of T, respectively. We also clustered residuals from the T/N M relationship across ten folds on random subsets of participants, and with A+ participants only, which did not impact overall clustering. Groups resembling our six T/N M groups in symptomatic ADNI participants appeared in the asymptomatic HABS cohort, further validating the spatial patterns presented here.
Our T/N M groups had significant differences in 18 F-FDG and not tau SUVR at a group level (Fig. 3). This fact does not necessarily signify that T/N M clustering was solely driven by 18 F-FDG, but rather that clustering depends on variation in 18 F-FDG relative to tau SUVR at an individual level. Certain participants can be identified with similar cortical 18 F-FDG SUVR, but vastly different tau SUVR. For instance, a patient with high tau SUVR may have lower N M (more metabolism) than expected given their level of T and may be placed in the low cortical resilient group, whereas a patient with low tau SUVR may have higher N M (less metabolism) than expected given their T and may fall in the cortical susceptible group. Compared to clustering on just N M , T/ N M clustering enables regional and relative comparisons of N M given a level of T and promotes the evaluation of factors beyond AD stage or pathology that may not be captured from N M alone.
Relative to the canonical group, the resilient groups had better baseline cognitive scores whereas susceptible groups had faster cognitive decline over time. Metabolic and cognitive phenotypes in the T/N M resilient and susceptible groups were shared across A+ and A− cohorts. The observations of impaired cognition and hypometabolism in A− susceptible groups strengthen the notion that factors influencing the T/N M relationship in AD (like copathology) are also present in non-AD symptomatic patients. In other words, the A+ group may reflect AD plus additional factors, including copathologies, whereas the A− group may have these non-AD factors alone affecting this clustering. Our results support the use of T/N M mismatch as a complement to direct measures of ATN biomarkers to study disorders of AD and non-AD pathology.
It is important to note that T/N M groups also differed with regard to cortical atrophy (Tables 1 and 2). Since N S and N M are linked, it is reasonable to predict that T/N S and T/N M relationships are also associated. Indeed, clustering with T/N S approaches yields groups with relative resilience or vulnerability to T 25 . The median regional correlation coefficient between T/N S and T/N M residuals was 0.29, suggesting that while T/N S and T/N M relationships are similar, they may provide some unique information. For example, metabolism may be more sensitive to Lewy body pathology than structure 18,19 . Likewise, metabolism may reflect aspects of functional reserve and synaptic activity not captured by structural markers while, alternatively, structure may be less affected by non-disease related functional variability than metabolism. Thus, it is likely the case that T/N S and T/N M mismatch each offer complementary, yet unique characterizations.
Intriguingly, both resilient and susceptible groups appeared to divide along patterns roughly involving either limbic or cortical regions. Several studies demonstrate similar spatial separation. For example, heterogeneity in either T or N alone has been examined by regional involvement and disease trajectories 15,[26][27][28] . Here, we investigate the variability in relationships between T and N M biomarkers with an integrative approach that evinces consistent patterns of neuroimaging and cognitive measures within the disentangling of N M relative to T. To some extent, this dividing line between limbic vs. cortical involvement perhaps parallels the dissociable MTL networks described by [29][30][31][32] . This previous work supports the existence of the anterior temporal network, most akin to the limbic regions described here, and a posterior-medial network that largely conforms to the default mode network. Prior research has also suggested differential changes within these networks across the AD continuum 29,33,34 . Non-AD pathologies, such as TDP-43, might also split along this anterior-posterior axis 35 . Though we observed two cortical resilient groups (high and low), it is unclear what factors beyond metabolism distinguish high and low cortical resilience. These T/ N M differences were enough for these groups to strongly cluster separately since the high cortical resilient group was the first group to separate in terms of dendrogram distance (Fig. 1d). That said, these two groups may reflect a continuum of cortical resilience. Together, our findings may indicate differentially connected networks harbor not only dissociable vulnerabilities to accumulation of different pathologies, but also relative resiliencies to these pathological states.
We probed several factors that may influence the link between T and N M , including association of surrogate markers for three copathologies (vascular disease, α-synuclein and TDP-43). While our groups did not differ in mean tau SUVR burden or inferred Braak stage distribution ( Fig. 3 and Supplementary Fig. 2), they did separate in terms of cognitive profiles, progression, and copathology-associated markers, suggesting that non-AD pathologies contribute to the dissociation of T and N M and, thus, to the cognitive trajectory beyond Braak stage. In fact, longitudinal group differences were found even when covarying for baseline tau SUVR, which further suppresses effects of AD severity. Other aspects of resilience or vulnerability outside copathology also may influence outcomes beyond Braak staging. To this point, there was evidence of greater burden of vascular disease, a common copathology in AD 3 , in the susceptible patients, suggesting that the elevated levels of cerebrovascular disease compared to the canonical group are a factor in their relative vulnerability.
AD can present with multiple proteinopathies, including αsynuclein 18 and TDP-43 inclusions 23 . While there are not yet well-established biomarkers for these pathologies, 18 F-FDG PET studies have provided patterns probabilistically related to both entities [19][20][21][22] . We emphasize that this analysis was exploratory and requires further comprehensive validation. The cortical susceptible group harbored higher cingulate island ratio and worse visuospatial processing and trended toward greater frequency of hallucinations, all supportive of concomitant LBD 18,19 . In contrast, the limbic susceptible group had the greatest average age among groups (78.9 ± 6.1 years) and a pattern of MTLpredominant hypometabolism with asymmetry, all features that have been associated with LATE 21,22 . Parallel to semantic and episodic memory impairment associated with TDP-43 pathology [36][37][38] , the limbic susceptible group had the worst categorical and naming fluency. While these features are correlative and not comprehensive, the convergence of imaging, cognitive and clinical evidence support a potential contribution of copathology to susceptible groups with greater hypometabolism than expected given their level of T.
Resilience and susceptibility as defined here by N M < T and N M > T, respectively, may be thought of as a combination of separate yet related features, including relative levels of copathology and factors that directly influence the neuronal and glial responses to T pathology. Currently, it is more straightforward to assess the former, but the latter may reflect intrinsic resilience or vulnerability to T, perhaps related to genetic/epigenetic factors. Our copathology analyses suggest that susceptible groups have mixed cognitive impairment with more evidence of copathologies than the canonical group to contribute to hypometabolism not accounted for by T alone. Given the frequency of mixed disease on autopsy 16 , non-AD pathologies may represent an orthogonal axis along which canonical groups have intermediate levels of copathology, while resilient and susceptible groups have less or more mixed pathology, respectively ( Fig. 5 and Supplementary  Fig. 11). In the context of AD, these copathologies may be synergistic as non-AD proteinopathies can influence how neurons and glia respond to T [39][40][41] . Additional differences in nondisease related genetic, lifestyle and environmental factors also decouple the T/N M relationship, representing attributes that affect how neurons respond to injury perhaps related to or distinct from copathology. The metabolic and cognitive profiles in resilient and susceptible groups were shared across A+ and A− cohorts and in symptomatic and asymptomatic patients. The observations of similar patterns of T/N M mismatch and impaired cognition between A+ and A− susceptible groups are expected, as factors influencing the T/N M relationship in AD may also be present in non-AD symptomatic patients. Given current constraints of in vivo biomarkers, autopsy data must confirm these hypotheses regarding specific copathology.
The study had several limitations. First, neuropathological validation is important for this work, but currently no datasets with tau PET, 18 F-FDG PET and autopsy were available to us. Analyses in symptomatic individuals were performed on one cohort (ADNI) which includes multiple sites but with wellestablished data harmonization methods. Given the ADNI inclusion/exclusion criteria, this sample may not be representative of the broader population of cognitively impaired patients that harbor more mixed pathology, particularly vascular disease. A more heterogeneous sample might show more phenotypes/ groups. However, the HABS dataset offers corresponding evidence of T/N M dissociation patterns in cognitively normal older adults known to harbor significant regional relationships between tau and 18 F-FDG PET 42 . Notably, these similar T/N M groups arose with use of two distinct processing methods (ANTs for ADNI data and FreeSurfer for HABS data), indicating robustness of clustering to specific processing pipelines. Despite this, the separation of susceptible groups by imaging and cognitive factors associated with copathology highlight the non-trivial amount of copathology in ADNI participants. To this point, autopsy study of an ADNI subset demonstrated that α-synuclein and TDP-43 polypathology are frequently present in ADNI patients and correlate with antemortem imaging markers 16 . The canonical group is a statistical designation and does not quantify the absolute amount of AD vs. non-AD pathology. However, the canonical group does provide a relative benchmark for the population. While there was not much available data to study resiliencerelated factors, our initial analysis of resilient and susceptible groups supports the continued search for genetic, epigenetic and pathophysiological features that influence these relationships. Note that resilient groups had significantly higher APOE2 carrier frequency and the susceptible groups trended toward higher APOE4 frequency, though these differences were not seen after adjusting for A status (Supplementary Fig. 9B). Investigations into additional AD-associated features, such as glial and immune cell-mediated inflammation as well as blood brain barrier dysfunction, may also be warranted 4,43,44 .
Despite these limitations, the T/N M mismatch approach may hold utility for biomedical research, specifically allowing clinical trials to measure heterogeneity across the Alzheimer's continuum. For instance, the group of N M > T susceptible patients may have mixed pathologies, which could reduce study power and complicate the assessment of investigational treatments designed to target single pathways. Consequently, future trials for antiamyloid or anti-tau therapies might intentionally recruit patients or stratify findings based on T/N M groups.
Overall, we define PET-based T/N M mismatch measurements to evaluate the varying relationships of neuronal metabolism to T pathology in participants with cognitive decline. Dissociation in the T/N M relationship demonstrates distinct groups with some showing resilience and others depicting susceptibility to T in terms of regional distributions of hypometabolism, cognition and pathological factors. T/N M mismatch provides a quantitative spatial approach to assess neuroanatomical patterns of metabolic states affected by T pathology. This may improve our understanding of the biology and prognostication of subgroups in the Alzheimer's and non-AD continuums. Additional studies may elucidate the heterogeneity of cellular metabolic responses to AD features as a step toward the successful implementation of precision medicine in AD.  Table 3. For the ADNI data, human subjects approval was obtained by the ADNI investigators to comply with the Institutional Review Board at each participating ADNI site. All participating ADNI sites received approval from their site's Institutional Review Board; a complete listing of ADNI sites is provided at the end of the article file. All ADNI participants provided written informed consent. ADNI data was accessed according to the policies of the ADNI data sharing and publications committee. For the HABS data, HABS protocols were approved by the Partners Human Research Committee, the Institutional Review Board for the Massachusetts General Hospital and Brigham and Women's Hospital, and all participants gave informed consent. HABS data was accessed according to the policies of the HABS data committee.

Methods
Imaging data. Post-processed PET images from the ADNI data archive (http:// adni.loni.usc.edu/data-samples/access-data/) were obtained 46 . Tau PET imaging was originally performed using the ADNI protocol with 30-min brain scans (six 5-min frames) starting 75 min after intravenous administration of~10.0 mCi 18 F-Flortaucipir. 18 F-FDG PET imaging consisted of a 30-min scan (six 5-min frames) at 30 min after 5.0 mCi 18 F-FDG injection. For amyloid PET, a 20-min brain scan (four 5-min frames) was performed 50 min after~10.0 mCi 18 F-Florbetapir or 90 min following~8.1 mCi 18 F-Florbetaben injection. Processed PET images with uniform isotropic resolution (8 mm full-width-at-half-maximum) were obtained with the ADNI archive description "Coreg, Avg, Std Img and Vox Size, Uniform Resolution." ADNI MRI included a T1-weighted structural scan (resolution 1.0 × 1.0 × 1.2 mm 3 ) and fluid attenuated inversion recovery (FLAIR) sequence MRI scan were acquired in the same session. For the HABS cohort 42,45 , we accessed spreadsheets of tau SUVR, 18 F-FDG SUVR and 11 C-Pittsburgh compound B distribution volume ratio.
Image processing and PET regional analysis. MRI studies were processed using the ANTs (v2) pipeline 47 for inhomogeneity correction, brain extraction, template registration and cortical thickness measurement 48,49 . MRI scans were divided into 104 cortical and subcortical ROIs with multi-atlas segmentation 50,51 (http:// neuromorphometrics.com/ParcellationProtocol_2010-04-05.PDF). PET images were co-registered to T1-weighted MRI with ANTs using rigid-body transformation 47 . SUVR maps were generated by convert3D (v1.1.0) with reference regions specific for each tracer: inferior cerebellar cortex for 18 F-Flortaucipir 52 , cerebellar cortex for 18 F-FDG 53 and cerebellum for 18 F-Florbetapir or 18 F-Florbetaben 54,55 . Mean regional T and N M measures were extracted from tau and 18 F-FDG SUVR maps. Amyloid status (A+/A−) was determined with 18 F-Florbetapir SUVR ≥ 1.11 or 18 F-Florbetaben SUVR ≥ 1.08 computed from a composite ROI from middle frontal, anterior cingulate, posterior cingulate, inferior parietal, precuneus, supramarginal, middle temporal and superior temporal cortex 54,55 . Comparison between our amyloid SUVRs with available amyloid SUVRs from ADNI SUMMARYSUVR_WHOLECEREBNORM (UCBERKE-LEYAV45_01_14_21 and UCBERKELEYFBB_01_14_21, accessed 8/2021) revealed a strong correlation between amyloid measurements with R 2 = 0.973 and slope β = 0.987 with no change in results. Two cases without amyloid PET had CSF amyloid-β 42 < 980 pg/ml, meeting the threshold for A+ classification 56 . Braak staging was from separate processed ADNI data (UCBERKE-LEYAV1451_11_16_21, UCBERKELEYAV1451_PVC_11_16_21, accessed 11/ 2021) and thresholds (for Braak stages 1/2, 3/4, 5/6) derived from decision trees of tau SUVRs 57 . The HABS data consisted of amyloid status, tau and 18 F-FDG SUVR spreadsheets in 84 cortical regions with FreeSurfer (v6) as generated in 42,45 (data release 2.0; accessed 11/2021). Definition of regional T/N M mismatch by clustering. Spatial patterns of T/N M mismatch were investigated by clustering of the residuals on a regression model of 18 F-FDG vs. tau SUVR. Robust linear regressions of individual 18 F-FDG SUVR vs. a log transform of tau SUVR (to ameliorate effects of a skewed distribution of T) across all patients were performed in each of the 104 gray matter ROIs (Fig. 1) to yield T/N M mismatch residuals (in units of 18 F-FDG SUVR). A bi-square weighting function minimized the influence of outliers in robust regression. To attenuate the effect of outliers on clustering, regression residuals for each ROI and individual were discretized into a vector based on whether the residual was greater than 0.6 SD from the regression line (a cutpoint that identifies the farthest~25% of points above or~25% of points below the regression line) and if the residual was negative or positive, generating an array of 104 ROIs across 289 participants where each entry was −1, 0, or 1. Discretized residuals were inputs for Ward's agglomerative hierarchical clustering 58 with the hclust and cluster packages on R (v4.0.5) to create T/N M mismatch groups. The number of clusters was selected by elbow and silhouette analysis 59 , which both suggested that k = 6 clusters optimizes within-cluster similarity. These methods did not agree on lower values, which would not capture as much between-group variation in specific regional patterns. Dimensionality reduction on discretized residuals was performed by PCA ( Fig. 1) and t-SNE ( Supplementary Fig. 1A). Regional mean residuals were visualized in cohort-based heatmaps, brain maps and three-dimensional renderings by ITK-SNAP 60 and MRIcroGL 61 . Clustering validation was performed across 10-folds of 150 randomly selected ADNI participants, which showed stable group patterns and identities.
Cognitive evaluation. ADNI and HABS performed cognitive testing using unified methodologies (accessed 8/2021 and 11/2021, respectively). We selected cognitive testing sessions closest to the 18 F-FDG scan along with longitudinal follow-up testing. Global measures included AD Assessment Scale-Cognition 13 item (ADAS, higher score is worse) 62 , Clinical Dementia Rating sum of boxes (CDR-SOB, higher is worse) 63 and Mini-Mental Status Exam (MMSE, lower is worse) 64 . Exploratory analysis was pursued with additional measures based on mismatch group findings and included the use of Clock Drawing Test 65 , NPI 66 item B for proportion of patients with hallucinations after scan, ADNI z-scores for visuospatial, language and memory domains 67,68 , categorical fluency of animals 69 , Everyday Cognition test 70 and Multilingual Naming Test 71 .
In follow-up analyses, we calculated 18 F-FDG PET measures which are thought to map to different non-AD pathologies. The cingulate island sign represents metabolic sparing of posterior cingulate cortex relative to precuneus and cuneus and has been associated with a-synuclein pathology. It was quantified as the ratio of posterior cingulate/precuneus/cuneus 18 F-FDG SUVR; higher cingulate island ratio is linked to α-synucleinopathy 19,20 . The presence of TDP-43 pathology has been associated with MTL and FSO hypometabolism relative to inferior temporal gyrus (I). The I/MTL/FSO ratio was calculated as the ratio of inferior temporal gyrus/ MTL/FSO gyrus 18 F-FDG SUVR. Higher I/MTL/FSO ratio is associated with TDP-43-related disease 21,22 . An MTL asymmetry index was computed as |left−right|/ (left+right) for 18 F-FDG SUVR and cortical thickness 24 as an additional potential marker of TDP-43 pathology 23 .
Statistical analysis. Statistical analysis was performed in R (v4.0.5). All statistical tests were two-sided. Comparisons for variables such as cognition or tau and 18 F-FDG SUVRs were performed with likelihood ratio tests by linear regression. Covariates included sex, age, education, amyloid status (A+/A−) and tau SUVR in the inferior temporal gyrus, a region where T correlates with disease severity 5,17 . Multiple test adjustment by Benjamini-Hochberg correction with false discovery rate = 0.05 was conducted for pairwise comparisons with the canonical group. Box plots show the data points as dots, mean as an X symbol, median as the middle box line, first quartile (Q1) and third quartiles (Q3) as box edges (denoting the NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-28941-1 ARTICLE NATURE COMMUNICATIONS | (2022) 13:1495 | https://doi.org/10.1038/s41467-022-28941-1 | www.nature.com/naturecommunications interquartile range, IQR), whiskers as the minimum/maximum points and outliers based on thresholds <Q1 − 1.5(IQR) or >Q3 + 1.5(IQR). Exploratory analyses (such as for copathology biomarkers) were also performed without multiple test adjustment. Genotype frequency comparisons were performed with χ 2 tests. Longitudinal cognitive trajectories were assessed with linear mixed effects models to account for participant-specific random intercepts with baseline cognitive score at scan, time from scan, cluster and cluster*time interaction as independent variables and sex, age, education and A status as covariates. Slopes of annual cognitive change for each cluster were defined as the sum of the time from scan slope and cluster*time interaction slope. Differences in decline rates were assessed by significance of the slope of the cluster*time interaction.
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
The raw and processed data including the participant scans and spreadsheets described above are available on the data archives of the Alzheimer's Disease Neuroimaging Initiative (ADNI) (http://adni.loni.usc.edu) and the Harvard Aging Brain Study (https:// habs.mgh.harvard.edu/) 45 . Supplementary Material is available online. Additional information can be provided by the authors upon reasonable request. Source data are provided with this paper.