A novel method for PET connectomics guided by fibre‐tracking MRI: Application to Alzheimer's disease

Abstract

This study introduces a novel brain connectome matrix, track‐weighted PET connectivity (twPC) matrix, which combines positron emission tomography (PET) and diffusion magnetic resonance imaging data to compute a PET‐weighted connectome at the individual subject level. The new method is applied to characterise connectivity changes in the Alzheimer's disease (AD) continuum. The proposed twPC samples PET tracer uptake guided by the underlying white matter fibre‐tracking streamline point‐to‐point connectivity calculated from diffusion MRI (dMRI). Using tau‐PET, dMRI and T1‐weighted MRI from the Alzheimer's Disease Neuroimaging Initiative database, structural connectivity (SC) and twPC matrices were computed and analysed using the network‐based statistic (NBS) technique to examine topological alterations in early mild cognitive impairment (MCI), late MCI and AD participants. Correlation analysis was also performed to explore the coupling between SC and twPC. The NBS analysis revealed progressive topological alterations in both SC and twPC as cognitive decline progressed along the continuum. Compared to healthy controls, networks with decreased SC were identified in late MCI and AD, and networks with increased twPC were identified in early MCI, late MCI and AD. The altered network topologies were mostly different between twPC and SC, although with several common edges largely involving the bilateral hippocampus, fusiform gyrus and entorhinal cortex. Negative correlations were observed between twPC and SC across all subject groups, although displaying an overall reduction in the strength of anti‐correlation with disease progression. twPC provides a new means for analysing subject‐specific PET and MRI‐derived information within a hybrid connectome using established network analysis methods, providing valuable insights into the relationship between structural connections and molecular distributions.

Practitioner Points

• New method is proposed to compute patient‐specific PET connectome guided by MRI fibre‐tracking.

• Track‐weighted PET connectivity (twPC) matrix allows to leverage PET and structural connectivity information.

• twPC was applied to dementia, to characterise the PET nework abnormalities in Alzheimer's disease and mild cognitive impairment.

We have developed a novel track‐weighted PET connectivity (twPC) that combines information from PET and diffusion MRI. The hybrid twPC enables analysis of subject‐specific PET and MRI‐derived information using network‐based analysis, providing valuable insights into the relationship between structural connectivity and molecular tracer distributions in the Alzheimer's spectrum.

1. INTRODUCTION

Neurological and psychiatric disorders often propagate through axonal pathways, leading to pathological perturbations in multiple connected regions (Fornito et al., 2015). A useful technique to characterise these structural changes, as well as the efficiency of information transfer across brain regions is brain connectivity (Sporns, 2013). Structural connectivity (SC) disturbances can be detected with magnetic resonance imaging (MRI) as the disease progresses due to neuronal and synaptic losses. SC, derived from diffusion MRI (dMRI), maps the white matter fibre pathways connecting different brain regions. It can be used to compute the structural connectome (a matrix describing the inter‐regional connectivity patterns), which has been used to characterise disease processes (Jones, 2010). In addition to MRI connectivity studies, methods to analyse network‐based information have been also adapted to positron emission tomography (PET). For example, PET‐derived regional covariances, or metabolic connectivity maps, have been used to characterise network topology in FDG‐PET (Di et al., 2012) and more recently in amyloid (Gonzalez‐Escamilla et al., 2021; Ossenkoppele et al., 2019; Pereira et al., 2018) and tau PET (Ossenkoppele et al., 2019). In these recent studies, two nodes are considered ‘connected’ in PET networks if these regions have standardised uptake value ratios (SUVR) correlated with each other within a subject group (i.e. along the ‘subject’ dimension) (Aiello et al., 2016). Connectivity analysis is often then done at the group level, although a few recent studies computed metabolic connectivity at the subject level (Huang et al., 2020; Li et al., 2020; Sun et al., 2022). In the case of dynamic PET data, individual‐level metabolic connectivity can also be computed using methods such as independent component analysis based (Li et al., 2020) and Euclidean distance‐based approaches (Volpi et al., 2023). This contrasts with widely used MRI approaches, where connectivity matrices can be computed at the individual subject level. In this study, we introduce a new method, which we will refer to as track‐weighted PET connectivity (twPC) matrix, that combines PET and dMRI data to compute a PET‐weighted connectome at the individual subject level.

Alzheimer's disease (AD) represents a compelling candidate for connectivity‐based investigations, given that it is characterised by a pronounced pattern of neuronal network dysfunction and degeneration across multiple connected brain regions. The staging and diagnoses of AD can be determined by a combination of clinical, molecular biomarkers, and epidemiological and neuropsychological evidence (Sperling et al., 2011). Multimodal diagnostic techniques have been increasingly used to map pathophysiological alterations since these changes often occur prior to the clinical signs of dementia (DeTure & Dickson, 2019). The early stage of the disease is often characterised by memory impairment caused by the loss of neurons and synapses as well as by a decline in neuronal connectivity (Jahn, 2013). Furthermore, biological evidence of abnormal accumulation of amyloid‐$\beta$ (A$\beta$) and phosphorylated tau proteins are hallmarks of AD, which are used for disease staging. Several frameworks (Jack et al., 2018) have been proposed to provide guidelines for the research and clinical staging of AD. For instance, the ATN biomarker‐based classification framework (Jack et al., 2016) highlights three major biomarker categories, namely ‘A’ for amyloid‐$\beta$, ‘T’ for tau and ‘N’ for neurodegeneration. A$\beta$ and tau proteins can be visualised and quantified using PET imaging (Mathis et al., 2017) or cerebrospinal fluid assays. Various techniques can be used to measure biomarkers of neurodegeneration, such as FDG‐PET, functional MRI and electroencephalography/magnetoencephalography (Young et al., 2020).

Recent advancements in imaging techniques, such as the development of new PET tracers (Barthel et al., 2022) and MRI analysis methods (Yousaf et al., 2018), have prompted the need for updating AD clinical and research frameworks. PET imaging‐based molecular biomarkers provide valuable information for examining disease subtypes and create personalised treatment plans. Recent connectomics studies have now linked the patterns of amyloid/tau accumulation and spread in AD with the structural/functional network organisation, providing insights into the disease mechanisms (Yu et al., 2021). The most common approach is to apply statistical analyses to establish correlations or differences between brain SC measures and PET tracer distribution (Mito et al., 2018). Computational models have also been proposed to predict the pathological spreading patterns based on connectivity information (Wen et al., 2021). Studies also tried to compare the differences and similarities between patterns of PET covariance networks and MRI‐based functional networks (Ossenkoppele et al., 2019). While a number of studies exploited the relationship between connectivity information and PET biomarkers, methods to exploit the synergies between SC and the distribution of molecular biomarkers in the brain remain surprisingly limited.

This study presents a novel type of subject‐level connectome, twPC, whereby the ‘connections’ correspond to PET tracer uptake values weighted by dMRI‐based SC. A matrix element (edge) in the twPC matrix can be interpreted as the joint value (a summary statistic value, such as the mean, median and sum) of the PET tracer uptake in the corresponding pair of structurally connected nodes in individual participants. Built upon the previously proposed track‐weighted imaging (TWI) framework (Calamante et al., 2012), twPC combines the quantitative measurements of PET imaging and the end‐to‐end spatial connections through fibre‐tracking streamlines generated from dMRI. TwPC provides a novel and convenient tool for enabling subject‐specific PET and MRI‐derived information to be analysed within one hybrid connectome using network analysis methods, such as graph theory analysis (Rubinov & Sporns, 2010) and network‐based statistical analysis (NBS) (Zalesky et al., 2010). We apply this method to the AD continuum and demonstrate that can be used to investigate the clinical significance of concordant versus discordant information found within structural connections and molecular distributions.

2. METHODS

The overall flow chart of the analysis carried out in this study is shown in Figure 1. After data preprocessing and fibre‐tracking analysis of the dMRI data, SC and twPC matrices were generated. NBS analysis was performed to evaluate the patterns of abnormal connectivity, followed by coupling analysis to explore the correlations between SC and twPC.

FIGURE 1.

Overview of the study pipeline. (A) Diffusion‐weighted images (DWIs) were first processed and fibre tracking was performed. Using the Desikan‐Killiany Atlas in Freesurfer, structural connectivity (SC) was derived by summing SIFT2 streamline weights and a structural connectome matrix was constructed. Track‐weighted PET connectivity (twPC) was derived by sampling positron emission tomography (PET) image intensities at the end‐points of connected fibre tracks, to compute a track‐weighted PET connectome matrix. (B) Top: Network‐based statistics were performed on SC and twPC matrices separately to examine differences between healthy controls, participants with early mild cognitive impairment (MCI), late MCI and Alzheimer's disease. Bottom: For each node, SC‐twPC coupling was measured as the Spearman rank correlation between the row of the SC matrix corresponding to the node and its corresponding row in the twPC matrix; this analysis was done at the subject level, and SC‐twPC couplings were then compared between groups.

2.1. Participants and imaging data

In this study, we included data from participants classified as ‘clinical’ EMCI, LMCI, AD and healthy controls (HCs) based on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (www.adni.loni.usc.edu). This database was established with the aim of testing whether serial MRI, PET, other biological markers and clinical and neuropsychological assessment can be combined to characterise the progression of MCI and early AD. Due to the availability of tau‐PET images, all data used in this study were selected from the ADNI3 phase. Demographic and clinical characteristics of participants in this study are summarised in Table 1.

TABLE 1.

Demographic and clinical characteristics of participants in this study.

	HC	EMCI	LMCI	AD
	n = 24	n = 12	n = 11	n = 12
Age ± SD (years)	72.1 ± 8.0	76.1 ± 5.4	74.4 ± 9.3	73.6 ± 10.3
Sex, male (%)	42%	58%	55%	50%
MMSE	29.6	26.4	26.6	22.3
ADAS_13	7.2	16.8	16.8	28.2
CDGLOBAL	0.0	0.5	0.5	1.0
LDELTOTAL
EDU ≥ 16	14.7	8.3	4.5	0.2
EDU 8–15	11.5 (4)	6.4 (5)	8.25 (4)	0.2 (5)
EDU 0–7	/	/	/	/

Note: All clinical scores are matched to the approximate dates of magnetic resonance imaging and positron emission tomography imaging session.

Abbreviations: AD, Alzheimer's disease; ADAS_13, ADAS 13 items total scores; CDGLOBAL, Clinical Dementia Rating Scale global scores; EDU, participants' years of education; EMCI, early mild cognitive impairment; HC, healthy control; LDELTOTAL, neuropsychological test delayed memory recall total scores; LMCI, late mild cognitive impairment; MMSE, Mini‐Mental State Examination.

The clinical diagnosis of all participants was retrieved from the ADNI database. In brief, ADNI implemented the following diagnostic criteria (Petersen et al., 2010): (1) subjective memory concern; (2) memory function documented by scoring within the education adjusted ranges on the Logical Memory II subscale (Delayed Paragraph Recall, Paragraph A only) from the Wechsler Memory Scale—Revised. Cognitive normal participants scored ≥9 for 16+ years of education, ≥5 for 8–15 years of education and ≥3 for 0–7 years of education. EMCI participants scored 9–11 for 16+ years education, 5–9 for 8–15 years of education and 3–6 for 0–7 years of education; LMCI and AD participants scored ≤8 for 8+ years education, ≤4 for 8–15 years education and ≤2 for 0–7 years of education. (3) Mini‐Mental State Examination (MMSE) score; (4) clinical dementia rating; (5) cognition and functional performance and (6) stability of permitted medications for 4 weeks. For a complete list of inclusion/exclusion criteria, please refer to the study protocol on www.adni-info.org.

In order to improve data quality consistency, all MRI data selected from ADNI3 in this study were acquired on 3T Siemens systems (scanner models: Prisma/Prisma Fit/Skyra). The following acquisition parameters were used: T1‐ MPRAGE: TE = 3 ms; TI = 900 ms; TR = 2300 ms; matrix = $240\times 256\times 208$; voxel size = $1.0\mathrm{m}{\mathrm{m}}^3$. dMRI was acquired using ADNI3 basic single‐shell protocol for Siemens scanners: TE = 56.0 ms; TR = 9600.0 ms; matrix = $116\times 116\times 80$; voxel size = $2.0\mathrm{m}{\mathrm{m}}^3$. 7 b0 volumes and 48 b = $1000\mathrm{s}/\mathrm{m}{\mathrm{m}}^2$ volumes were included for each diffusion‐weighted imaging (DWI) dataset. T1‐weighted (T1w) and DWI were acquired during the same imaging session.

[¹⁸F]AV‐1451 tau PET scans were acquired according to the standard ADNI3 PET Technical Procedures Manual (http://adni.loni.usc.edu/). Tau‐PET scans were selected no more than 1 year apart from the same subject's dMRI sessions. The median time interval between PET and MRI was 30 days. Data used in the current study were acquired across multiple sites on the following PET/CT scanner models: Philips GEMINI TF TOF 16, GE Discovery STE/710/MI DR and Siemens Biograph 40/64 TruePoint. After intravenous injection of 370 MBq [¹⁸F]AV‐1451, participants underwent a 30‐min PET scan (six 5‐min frames) after the tracer injection.

In ADNI3, 16 LMCI and 26 AD participants were available in ADNI3 with both dMRI data (acquired by Siemens scanner and with 54 gradient directions) and AV1451‐PET data available. Detailed information about the acquisition parameters and scanner information is included in Table S9. We had to further filter down this number by having the imaging acquisition dates of PET and dMRI to be less than 1 year apart. Thus, we chose n = 12 to be the number of participants in each group for the current study. One participant had to be excluded due to failed dMRI pre‐processing. We also included n = 24 HCs for a larger, but comparable sample size.

2.2. MRI processing

DWI was pre‐processed using the single‐shell multi‐tissue pipeline using MRtrix3Tissue (https://3Tissue.github.io), a fork of MRtrix3 (Tournier et al., 2019). The step‐by‐step MRtrix3 commands for dMRI preprocessing are included in Supporting Information. DWI was first denoised, and Gibbs ringing removal was performed. Motion and distortion correction were performed using Synb0 (Schilling et al., 2019, 2020) in conjunction with FSL's top‐up (Smith et al., 2004) and eddy (Andersson & Sotiropoulos, 2016) tools. Synb0 allows distortion correction of DWI without reverse phase‐encoding scans by synthesising undistorted b0 volumes. Synb0 first applied a trained network to the MPRAGE dataset to generate a synthesised b0 image; for our study, we used the default parameter implementation of Synb0. The synthesised b0 was then aligned with the real b0 image through rigid registration and concatenation for input into FSL TOPUP. Within TOPUP, motion and susceptibility distortions were estimated using the merged b0 volume. DWI bias field correction was performed using dwibiascorrect (Zhang et al., 2001) in MRtrix3. Following preprocessing, 3‐tissue response function estimation was obtained with the Dhollander (Dhollander et al., 2019) algorithm, and 3‐tissue CSD modelling for single‐shell data was done using the single‐shell 3‐tissue CSD (SS3T‐CSD) method (Dhollander & Connelly, 2016).

After registering T1w to DWI using affine transformation (Jenkinson & Smith, 2001) in FSL, the so‐called segmented five‐tissue‐type (5TT) image (Smith et al., 2012) was obtained based the Hybrid Surface and Volume Segmentation (HSVS) algorithm (Smith et al., 2020). Anatomically constrained tractography (Smith et al., 2012) was then performed to obtain whole‐brain tractography of 10 million fibre tracks using the default (‘iFOD2’) probabilistic tractography algorithm (Tounier et al., 2010). The brain mask of DWI was chosen as the seeding image, and an FOD amplitude threshold of 0.07 for terminating tracks was chosen following the recommended SS3T‐CSD single subject pipeline (https://3tissue.github.io/doc/single-subject.html). SIFT2 (Smith et al., 2015) was then performed to optimise connectivity quantification. SIFT2 generated a weighting factor for each streamline and a global proportionality coefficient $\mu$ for each tractogram, which will be factored into the structural connectome during the network construction step. The use of advanced analysis methods, including multi‐tissue CSD, ACT and SIFT2, leads to more reliable SC estimates (Calamante, 2019).

2.3. PET data processing

Six 5‐min PET frames were first summed to produce a single 30‐min PET uptake image for further processing. The PET images in the ADNI3 databased had been reconstructed and pre‐smoothed according to different preprocessing protocols to produce images of uniform isotropic resolution of 8 mm FWHM. Each subject's PET images were first co‐registered to the subject's own T1‐weighted MRI (which had been pre‐aligned to the DWI, and masked out the spinal cord) using affine transformation in FSL (Jenkinson & Smith, 2001). Because the PET images had relatively poor resolution, preserving the skull during registration yielded the best registration outcomes. Figure S1 shows an example of the T1w and PET co‐registered images. Visual inspection was performed to ensure satisfactory quality of image registration.

2.4. Network construction

2.4.1. Structural connectome

T1w images were processed using Freesurfer to generate 84 nodes based on the Desikan‐Killiany atlas (Desikan et al., 2006). Table S2 lists all the node names and the corresponding abbreviations (each node is present in the left and right hemispheres). SC matrices for individual participants were generated based on the 10 million tractogram applied with SIFT2 streamline weighting. This default SC metric computes the sum of SIFT2 weights of the streamlines connecting each pair of nodes. As the final step, the global proportionality coefficient $\mu$ for each tractogram, which was previously generated during SIFT2, was multiplied by the resulting connectivity matrix to normalise across participants. $\mu$ normalisation allows for calculating streamline volume estimates as an accurate representation of the underlying biological fibre densities of normal brains or brains with structural deficits.

2.4.2. Track‐weighted PET connectome

The proposed twPC is built upon the TWI (Calamante, 2017; Calamante et al., 2012) framework, which computes a weighted combination of PET image values (in our case, the co‐registered tau PET image) measured at the coordinates of the streamlines. Figure 2 provides a schematic illustration of the steps to generate twPC matrices for individual participants. The pre‐processed PET images were first smoothed with a 3D median filter of 5 mm in all directions. This smoothing step reduces the effect of noise on sampling accuracy, given that only PET values at the streamline end‐points (which are located at the grey/white matter interface due to the use of ACT for fibre‐tracking) were sampled for twPC—see also Section 4. PET intensity values at the endpoints of each fibre track were sampled, where these fibre tracks were generated from the corresponding DWI of the same subject. The chosen sampling statistic was the geometric mean in the present study, but the same procedure can be applied to compute other statistics (e.g. median, max). The result of this step is that each fibre track is assigned with a value (twPET) that corresponds to the geometric mean of the underlying PET intensities at the two endpoints of this fibre track (i.e. streamlines that connect two PET high uptake areas will be assigned a higher value than one that connects a high uptake area to a low uptake area, which in turn will be higher than one that connects two low uptake areas). The geometric mean was calculated by taking the square root of the product of the two end‐point intensity values.

FIGURE 2.

A schematic illustration of the proposed track‐weighted PET connectivity (tw‐PC) method on an example where 4 streamlines connect 3 nodes. The values in the 3 node regions shown in A represent median filtered positron emission tomography (PET) image intensity values in each voxel. (a) Each streamline is assigned a PET sampled value (indicated by the grey squared value) by computing the geometric mean of the PET intensity values at its streamline endpoints. The SIFT2 weighting for each streamline is indicated by the blue star values. (b) The PET sampled values of all streamlines in an edge are averaged into one edge value and normalized by the structural connectivity (SC) edge strength to form the tw‐PC matrix value for that edge.

Finally, to generate the twPC matrix, the sampled twPET values of all streamlines connecting each pair of nodes $I$ and $J$ of the same Desikan‐Killiany atlas were averaged into one edge value according to the following:

$${\text{twPC}}_{I,J}=\frac{{\sum }_s\left(\text{SIFT}{2}_s\times {\text{twPET}}_s\right)}{{\sum }_s\text{SIFT}{2}_s},$$ (1)

where $s$ denotes any streamline traversing through node $I$ and $J$, $\mathrm{SIF}{\mathrm{T}}_s$ denotes the corresponding SIFT2 weight for streamline $s$ and $\text{twPE}{\mathrm{T}}_s$ is the sampled PET values for streamline $s$ obtained from the previous step. This creates a subject‐level twPC matrix that has the same dimensions as the SC, and each edge in a twPC matrix corresponds to the (SIFT2 weighted) geometric mean value of the PET tracer distribution across each pair of structurally connected nodes.

The twPC matrices were further normalised by the mean PET values of the cerebellum, similar to the normalisation step in computing SUVRs in PET. Grey‐matter cerebellum, defined by processing the T1w image using FreeSurfer (Fischl, 2012), was chosen as the normalisation region, and each twPC matrix was then weighted by this normalisation factor to enable comparisons between participants. Alternatively, this normalisation step can be carried out on individual unnormalised PET images (rather than on the twPC matrices) to achieve identical results.

2.5. Network analysis

NBS (Zalesky et al., 2010) analysis was performed to examine alterations in structural and track‐weighted PET connectivity in patients using the Network Based Statistic Toolbox (https://sites.google.com/site/bctnet). NBS analysis controls the family‐wise error (FWE) rate through permutation testing, to identify a set of connected edges or networks associated with an effect (e.g. a difference between two groups). A cluster‐defining suprathreshold is first applied to extract a subset of connected components, or clusters. Then permutation testing is performed to compute p‐values (which are controlled for FWE) for these connected components. During this permutation test, participants get randomly assigned to both groups to regenerate a set of test‐statistics for the null hypothesis, and the maximum component size is obtained. Then a normalised p‐value of the maximum component size is computed based on the outcomes of the permutation test. This provides an estimate of the null distribution, which is then used to detect significant effects. Compared to conventional comparison methods corrected for FWE, NBS improves the statistical power, thus making it a useful tool to identify significantly altered networks, especially in data with limited sample sizes (Zalesky et al., 2010).

In the present study, the chosen p‐value suprathreshold was $p<.001$. To further explore twPC and to compare with SC, a relatively more relaxed suprathreshold of $p<.005$ was also tested and included in Supporting Information. Finally, the corrected p‐value was determined through 10,000 permutations, which calculated the probability of the null distribution of maximal connected component size. Connectome visualisation was done using the NME toolbox (Gramfort et al., 2013) in Python (https://mne.tools/).

2.6. Node‐level SC‐twPC coupling

The coupling between SC and twPC (SC‐twPC coupling) at the node level was assessed similar to approaches used for MRI‐derived structural‐functional connectivity coupling (Honey et al., 2009) (Figure S3). A group average connection matrix mask was first generated based on the raw streamline counts, where edges with a group average of fewer than 10 streamlines were excluded from the analysis. This was done to reduce the effect of outliers, which could be due to false positive fibre tracks, on affecting the correlation analysis. Then vectors of SC and twPC from one node to all the other nodes (i.e. the matrix rows corresponding to that node) were extracted for individual participants; each vector can be seen as the fingerprint of the connectivity between that node and every other node of the parcellation. SC‐twPC coupling for each node was then computed as the Spearman rank correlation between all the non‐zero elements of the SC and twPC, to account for the fact that the distributions of SC and twPC differed considerably: while twPC follows an exponential distribution, SC follows an approximately normal distribution. For each node, t‐test was performed to assess whether SC‐twPC couplings showed significant group differences ($p<.05$, FDR corrected) between participants with EMCI, LMCI, AD and HC. Results were plotted using the ENIGMA toolbox (Larivière et al., 2021) toolbox (https://enigma-toolbox.readthedocs.io/).

3. RESULTS

3.1. Structural connectivity

Figure 3 (top row) shows the group average SC matrices. The histograms of group‐average SC are included in Figure S4. Overall, NBS analysis identified structural networks that significantly decreased ($p<.05$) their connectivity as the disease stages progressed (HC → EMCI → LMCI → AD). Using a suprathreshold of $p<.001$, networks with decreased SC were identified in participants with LMCI and AD compared to HC. No SC network with altered connectivity was identified in participants with EMCI when compared with the other three groups. Figure 4a displays the altered SC networks in three views, and Figure 4b displays the corresponding nodes of the altered connections in the format of connectograms. In LMCI participants, 1 network with 6 edges connecting 7 different regions (corrected $p=.015$) showed decreased structural connections when compared to HCs. These connections linked the bilateral hippocampus and the isthmus cingulate gyrus, fusiform gyrus, entorhinal cortex, lingual gyrus and medial orbitofrontal gyrus with predominately intra‐hemispheric connections (top row of Figure 4a,b). In AD participants, 1 altered network with 24 edges connecting 24 nodes (corrected $p=.032$) showed decreased SC when compared to HC (middle row). These intra‐ and inter‐hemispheric connections spread out cross multiple subcortical and cortical regions.

FIGURE 3.

Group average structural connectivity (SC) and track‐weighted PET connectivity (twPC) matrices for the healthy control (HC), early mild cognitive impairment (EMCI), later MCI, and Alzheimer's (AD) groups.

FIGURE 4.

The Network‐based statistics (NBS) results at a cluster‐defining threshold of $p<.001$ showed decreased structural connectivity (SC) in participants with late mild cognitive impairment (LMCI, red) and Alzheimer's disease (AD) participants compared with healthy controls (HC) and decreased SC in AD compared to LMCI. No significant changes were found between HC and EMCI. (a) Structural networks with decreased connections ($p<.05$, NBS corrected). (b) The corresponding connectogram. Top row: HC > LMCI; Middle row: HC > AD; Bottom row: LMCI > AD. L: left; R: right. (c) Common edges between groups (rows) with decreased SC.

NBS analysis was also performed between each pair of patient groups, namely EMCI versus LMCI, EMCI versus AD, and LMCI versus AD. Significant alterations in structural connections were only identified in patients with AD compared to LMCI (bottom row of Figure 4c). These altered connections, which consisted of 1 network with 13 edges connecting 13 nodes (corrected $p=.0322$), were mostly intra‐hemispheric and concentrated in the left hemisphere.

Altered structural networks between groups exhibited differential patterns, with a few common edges consistently present in the altered networks (Figure 4c). Structural connections between the left hippocampus and fusiform gyrus, left hippocampus and entorhinal cortex, right hippocampus and lingual gyrus, right hippocampus and medial orbitofrontal gyrus, and right entorhinal cortex and fusiform gyrus were present in both networks with reduced structural connections in participants with LMCI and AD compared to HC. Reduced connections between the left supra marginal gyrus and the left middle temporal gyrus were observed in both AD versus HC and LMCI versus AD.

3.2. Track‐weighted PET connectivity

Figure 3 (bottom row) shows the group average twPC matrices. The histograms of group‐average twPC are included in Figure S4. Overall, NBS analysis identified significantly increased ($p<.05$) twPC as the disease stages progressed (HC → EMCI → LMCI → AD), and the affected network sizes also increased as the disease stages progressed. Using a cluster defining suprathreshold of $p<.001$, networks with greater twPC in participants with EMCI, LMCI and AD than in HC (Figure 5a) were identified. In EMCI participants, 1 network with 8 edges connecting 8 different regions (corrected $p=.029$) showed increased twPC when compared to HC. In LMCI participants, 1 network with 21 edges connecting 21 different regions (corrected $p=.015$) showed increased twPC when compared to HC. In AD participants, 1 network with 63 edges connecting 50 different regions (corrected $p<.001$) showed increased twPC when compared to HC.

FIGURE 5.

Network‐based statistics (NBS) results at a cluster‐defining threshold of $p<.001$ showed increased track‐weighted PET connectivity (twPC) in participants with early mild cognitive impairment (EMCI, green), late mild cognitive impairment (LMCI, red) and Alzheimer's disease (AD, blue) compared with healthy controls (HC). (a) twPC networks with increased connections ($p<.05$, NBS corrected). (b) The corresponding connectogram. Top row: HC < EMCI; Middle row: HC < LMCI; Bottom row: HC < AD. L: left; R: right. (c) Common edges between group comparisons (rows) with increased structural connectivity.

At a suprathreshold of $p<.001$, no network alteration was detected between participants with EMCI and LMCI, EMCI and AD, or LMCI and AD in twPC. However, a small network consisting of 5 edges connecting 6 nodes was found with increased twPC in LMCI compared to AD at a lower suprathreshold of $p<.005$ (Figure S7).

Figure 5c shows common edges that are present in the altered twPC networks across groups. Six common edges were present in both networks with increased twPC in participants with LMCI and AD compared to HC, including between the left hippocampus and the left fusiform gyrus, the left isthmus‐cingulate gyrus and the left posterior cingulate, the left precentral gyrus and the right rostral anterior cingulate gyrus, the left superior parietal gyrus and the right isthmus‐cingulate gyrus, the right entorhinal cortex and the fusiform gyrus, the right hippocampus and the right medial orbitofrontal gyrus.

3.3. Similar and differential network patterns (SC vs. twPC results)

Results of structural and twPC network alterations revealed by NBS are summarised in Table 2. Structural networks with lower connectivity were found in participants with LMCI and AD when compared with HC. twPC networks with higher tau‐PET connectivity‐weighted uptake values were found in participants with EMCI, LMCI and AD when compared with HC. Participants with AD also revealed networks with decreased SC when compared with LMCI. No altered twPC network was detected when comparing EMCI, LMCI and AD.

TABLE 2.

Summary results of network‐based statistics.

Between‐groups	Structural connectome	tw‐PET connectome
HC versus EMCI	n.s.	HC < EMCI
HC versus LMCI	HC > LMCI	HC < LMCI
HC versus AD	HC > AD	HC < AD
EMCI versus LMCI	n.s.	n.s.
EMCI versus AD	n.s.	n.s.
LMCI versus AD	LMCI > AD	n.s.

Note: n.s. denotes that no significantly different network was detected.

Abbreviations: AD, Alzheimer's disease; EMCI, early mild cognitive impairment; HC, healthy control; LMCI, late mild cognitive impairment; tw‐PET, track‐weighted positron emission tomography.

Figure 6 summarises the topologies of altered SC and twPC networks revealed by NBS analysis. In EMCI participants compared to HC (Figure 6, top‐left), only an increased twPC network was identified. In LMCI participants compared to AD (Figure 6, bottom‐right), only a decreased SC network was identified. A significant number of common edges were found in decreased SC and increased twPC networks in LMCI and AD groups when compared to HC. In LMCI versus HC (Figure 6, top‐right), altered SC and twPC networks shared four common edges, including the left hippocampus to left fusiform gyrus, the right hippocampus to left isthmus cingulate gyrus, the right hippocampus to right medial orbitofrontal gyrus, and the right entorhinal to right fusiform gyrus. In AD compared to HC (Figure 6, bottom‐left), a total of 15 common edges were identified with the bilateral hippocampus appearing to be the common hubs (8 edges connecting to the hippocampus including the left hippocampus and the left entorhinal/fusiform gyrus/pericalcarine/right superior parietal gyrus, and between the right hippocampus and the right lingual gyrus, medial orbitofrontal, parahippocampal and the left superior parietal gyrus). Other common edges included the left inferior parietal gyrus to the left superior parietal/ medial temporal gyrus, the left medial temporal to the left supra marginal gyrus, the left parahippocampus to the left superior frontal gyrus, the left entorhinal to the left fusiform gyrus and the right entorhinal to the right fusiform/ inferior temporal gyrus.

FIGURE 6.

Summary connectograms of main network based statistics findings of altered structural connectivity (SC) and track‐weighted PET connectivity (twPC) networks at a clustering threshold of $p<.001$. In healthy controls (HC) versus late mild cognitive impairment (LMCI) and HC versus Alzheimer's disease (AD), both altered SC and twPC networks were identified ($p<.05$) and highlighted in red. Purple: reduced SC, yellow: elevated twPC, red: common edges present in both altered SC and twPC networks. EMCI, early mild cognitive impairment.

3.4. Altered node level SC‐twPC coupling

The relationship between structural and twPET connectivity was further explored by measuring group average SC‐twPC coupling (Figure 7), as indicated by Spearman rank correlation. All the couplings with $p<.05$ are negative (i.e. anti‐correlations) and are stable across all subject groups, although displaying an overall reduction in the strength of anti‐correlation as disease progresses (i.e. lighter shades of blue as disease progresses). The strongest negative couplings were found in the bilateral putamen, thalamus, precuneus, superior frontal gyrus, superior parietal gyrus, isthmus cingulate gyrus and the insula across all groups. The only node showing significantly altered (t‐test, FDR corrected $p<.05$) SC‐twPC coupling was the left hippocampus, with decreased coupling in participants with AD compared to the HC group (Figure 7d).

FIGURE 7.

Spatial pattern of couplings between structural and track weighted PET connectivity (SC‐twPC) (showing correlations with $p<.05$ only) in (a) healthy controls (HCs) and participants with (b) early mild cognitive impairment (EMCI), (c) late mild cognitive impairment (LMCI), (d) Alzheimer's disease (AD). Nodes with significantly altered SC‐twPC coupling (FDR corrected $p<.05$) are indicated by blue arrow. HI, hippocampus; L, left; R, right.

4. DISCUSSION

In this study, we exploited synergistic information from PET and dMRI‐based tractography to introduce a new type of connectome, the twPC, which samples PET tracer uptake according to the underlying white matter fibre streamline point‐to‐point connectivity. With the proposed twPC, robust network analysis methods widely used in MRI connectome studies (e.g. NBS, graph metrics) can be applied to analyse PET molecular connectivity information computed at the individual subject level. Thus, twPC provides a convenient framework for analysing the complex networks of functional and structural systems in the brain based on multimodal imaging biomarkers and the wealth of available graph theoretical network analysis tools. NBS analysis of twPC revealed distinct patterns of altered twPC networks when comparing HCs to participants with early and late mild cognitive impairment (MCI), as well as AD.

4.1. Structural networks

Network alterations of structural connections in participants with EMCI, LMCI and AD, compared with the HC group, were explored using NBS analysis. The results are consistent with previous findings that structural network disturbances begin in the limbic regions (Lama & Lee, 2020; Mallio et al., 2015). Furthermore, the present study provides additional insight into the time course of structural degradation. No altered network was observed in EMCI participants, aligned with previous ADNI findings suggesting heterogeneity within MCI (Nettiksimmons et al., 2014). Previous NBS analysis also suggested that only MCI A+N+ participants showed changes in hippocampus SC similar to patterns of AD, but not in other MCI subgroups (Jacquemont et al., 2017).

In the later LMCI stage, the limbic system was predominantly affected, including the cingulate, hippocampus, parahippocampus, palladium and the amygdala. The bilateral hippocampus appeared to be a major hub of connections to other nodes with the greatest number of connections. In addition to the limbic system, the bilateral entorhinal and fusiform gyrus were key nodes. The findings are consistent with the neuropathological staging of AD, which indicates that the first two stages involve alteration of transentorhinal/entorhinal regions, followed by limbic stages (Braak & Braak, 1991). A number of MRI structural and functional studies have also confirmed these findings, emphasising the role of the hippocampal and entorhinal regions in AD progression (Pennanen et al., 2004; Supekar et al., 2008).

In the more advanced stage of AD, NBS analysis showed a widespread distribution of nodes throughout the frontal, temporal, occipital, parietal, limbic and subcortical regions involved in the altered networks. A previous NBS analysis also demonstrated widespread SC alterations among AD patients, as measured by decreased fractional anisotropy (FA) and increased mean diffusivity (MD) in the entire brain (Filippi et al., 2018). Compared to LMCI, AD participants had a greater number of nodes in the frontal lobe of the abnormally reduced SC network, indicating that structural deficits in the frontal areas are likely to occur later in the disease process. The reduced structural network in AD compared to LMCI showed topological asymmetry with the majority of nodes and edges in the left hemisphere. The left hemisphere was previously reported to have earlier and faster neurodegeneration revealed by a faster rate of atrophy (Thompson et al., 2007) and brain network measures (Kim et al., 2012). Future specifically targeted studies to further characterise these asymmetries are warranted.

4.2. Tau‐PET networks

twPC provides a means to combine PET information and SC in a physiologically meaningful way. twPC is computed from the mean twPET values for the streamlines between two grey matter node regions, with the twPET value for each streamline reflecting the endpoint‐to‐endpoint PET connectivity, informed by the underlying structural white matter streamlines connecting the two regions. For instance, two structurally connected high tau‐PET uptake areas will have higher twPET connectivity than a connected pair comprising medium and low tau‐PET uptake areas, which in turn have higher twPET connectivity than two connected low tau‐PET uptake areas—thus creating a meaningful range of twPET connectivity values based on the structurally connected PET information. Note that the geometric mean was selected to help increase the dynamic range of these different connected scenarios. Importantly, without the streamline information, computing the tau statistics of two regions with unknown structural relationship would yield limited physiologically meaningful interpretation. When twPC is compared between different clinical groups, particularly in neurogenerative diseases, altered twPC networks suggest the likely pathways of propagation by identifying major disease hubs (highly connected regions) and vulnerable regions (regions with altered connections between the disease hubs).

In the current study, the NBS results revealed altered twPC networks characterised by a progressive increase in network size in EMCI, LMCI and AD participants when compared to HCs. The increased size of these networks may reflect the spreading of tau pathological processes and the involvement of additional brain regions as cognitive impairment advances.

Similar to SC, common edges, or shared connectivity disruptions, of the twPC networks were found in both LMCI and AD groups when compared to HCs. This implies that there are similar alterations in twPC patterns that are present in both LMCI and AD, suggesting a continuum of pathological changes across different stages. However, no common edges were found in the EMCI versus HC and LMCI versus HC group comparisons. It is important to note that this absence of common edges is likely due to the small size of the altered twPC network in EMCI versus HC. When the analysis was performed with a lower clustering threshold ($p<.005$), four common edges were identified between the EMCI versus HC and LMCI versus HC groups, suggesting some shared twPC disruptions at the early stages of MCI do occur.

In the altered twPC network for the EMCI versus HC comparison, specific nodes were identified as particularly relevant. These nodes included the left postcentral gyrus, left precentral gyrus, left middle temporal gyrus and right superior parietal gyrus. Importantly, these nodes were also found to be present in pathways associated with tau‐dMRI associations (Wen et al., 2021). Additionally, the left medial temporal gyrus has been identified as a significant disease hub in tau pathology.

In the altered twPC network of LMCI versus HC, similar to EMCI versus HC, several nodes were identified that are highly relevant in tau pathology. These nodes include the fusiform gyrus, medial orbital frontal gyrus, amygdala, entorhinal cortex, inferior parietal gyrus, lateral occipital fusiform gyrus and posterior orbital frontal gyrus (Cho et al., 2016; Insel et al., 2020). Additionally, many other nodes in this abnormal PET network were found to be highly relevant in pathways with tau‐dMRI associations in the literature, such as the inferior cingulate gyrus, lingual gyrus, postcentral gyrus, precentral gyrus, superior parietal gyrus, supramarginal gyrus and paracingulate gyrus (Wen et al., 2021).

The regions associated with altered tau‐PET networks in those with AD are highly consistent with areas that are crucial to tau pathology. Several parts of the temporal lobe were involved, including the bilateral entorhinal, inferior/middle temporal, temporal pole and fusiform. Tau in the medial temporal lobe has been found to be associated with memory decline and aging (Maass et al., 2017). The altered networks also included areas in the limbic system (parahippocampus, amygdala) and the inferior parietal lobe. In accordance with longitudinal modelling, the steepest increases in tau were found in the inferior temporal lobe, entorhinal cortex, fusiform, middle temporal lobe and amygdala (Márquez & Yassa, 2019). Moreover, the altered networks mostly comprised intra‐hemispheric edges, and were consistent with earlier observations that the right hemisphere seems to be less affected by tau than the left hemisphere (Schäfer et al., 2020) (Figure 5), a trend we also observed in our SC results (Figure 4, middle row).

4.3. Relationships between SC and twPC

The present research implemented two methods to explore the relationship between structural and track‐weighted PET connectivity alterations. First, the altered networks revealed by NBS analysis between SC and twPC were examined qualitatively (Figure 6; Figure S8 for the lower suprathreshold case). Overall, both SC and twPC showed progressive changes as the disease stages progressed from HC to AD while decreased SC and increased twPC networks were identified. Altered twPC networks were cross‐hemispheric while SC networks were predominantly intra‐hemispheric. This difference is likely due to the fact that twPC were mostly computed based on sampled PET SUVRs, so nodes with elevated PET SUVRs were more likely to yield high twPC regardless of whether there was strong structural connections between them.

twPC, however, was more sensitive to changes in EMCI participants when compared to the HC group. By contrast, no altered SC network was found in the EMCI versus HC comparison, even at a lower supra‐threshold, suggesting structural degradation at the network level might not occur at observable levels until later stages of disease progression. There were a number of common edges in altered SC and twPC networks in LMCIs and AD when compared to HC. The three edges that were present in altered SC and twPC networks in LMCI and AD compared to the HC group included the left hippocampus to the left fusiform gyrus, the right hippocampus and the right medial orbitofrontal gyrus, the right entorhinal cortex and the right fusiform gyrus. Regions involved in altered twPC networks consisted of both major disease hubs in previously published tau‐PET studies as well as known regions involved in pathways with tau‐dMRI associations. While SC and twPC networks contain common edges that are highly relevant, their corresponding affected networks also contain large non‐overlapping parts (see purple and yellow edges in connectograms of Figure 6). They, therefore, provide complementary information, and both types of connectivities can be useful to develop multi‐modal biomarkers to differentiate disease stages.

Secondly, the coupling between twPC and SC was examined at the node level. The majority of brain regions showed significant negative correlations between SC and twPC. Areas with strong negative correlations suggest that in areas with damaged structural connections, increased tau is likely to be observed, and vice versa. The couplings were stable across all groups, except for the left hippocampus, which showed decreased SC‐twPC coupling in AD participants compared to the HC group. This finding suggests that SC‐twPC coupling is not a sensitive indication of disease stage. Further research may be needed to investigate whether SC‐twPC coupling is sensitive to decline in cognitive performance.

Note that in the case of SC, within‐hemisphere connections (diagonal blocks of the matrix) tend to be stronger, reflecting the biological basis of structural connections; this, therefore, leads to high contrast between diagonal and off‐diagonal blocks. However, the twPC, generated by sampling tau‐PET constrained by structural connections, exhibits the opposite pattern (Figure 3). twPC is given by the endpoint‐to‐endpoint geometric mean PET values, and therefore can lead to high values even with moderate SC. Of note, this relative contrast between within‐ and between‐hemispheres did not bias the NBS findings (which focus instead on the group difference of the connectivity matrices); in fact, for our study, despite the higher between‐hemisphere twPC values, greater differences in within‐hemisphere twPC across groups were observed using NBS, especially in AD cases.

4.4. twPC method considerations

4.4.1. Track‐weighting statistics for twPC

The chosen metric for assigning a PET intensity‐weighted value to each streamline in the current study was the geometric mean of the PET values at the track endpoints. The endpoints were chosen rather than the entire fibre streamlines because fibre‐tracking terminates at the white matter/grey matter interface. The intensity values at the endpoints represent a suitable measure of the PET tracer uptake within the brain regions connected by that streamline. Using the geometric mean, instead of the arithmetic mean, aims to provide a more effective summary statistic, especially when the intensities at the two endpoints differ greatly. Compared to arithmetic means, the distribution of the geometric mean is more left‐skewed (Figure S5). By using the geometric mean, the sampled track‐weighted PET value of a small and a large value would be smaller than using the arithmetic mean. This reduces the chance of a twPC value being dominated by a particularly high tau value at one end of a fibre track. Note, however, that, as for the case of the TWI framework (Calamante et al., 2012), the approach can be easily extended to other metrics. For example, for PET tracers that accumulate in white matter, computing an alternative metric (e.g. sum or mean of values along the streamline) might be preferable. The proposed twPC method should be then considered more a framework than a specific guideline for implementation.

4.4.2. Edge weighting statistics for twPC

The edges of the twPC were computed by calculating a weighted average (weighted according to the SIFT2 weights) of the twPET values for all streamlines between every pair of nodes—see Equation (1). This allows the edge values to be relatively independent of the absolute value of track density to best preserve the information extracted from PET imaging, while still making each streamline contribute in proportion to its SIFT2 value, as that represents the appropriate weighting based on SC (Smith et al., 2015). The exception would be if no fibre track passed through two nodes, in which case the twPC would be 0 accordingly. If the sum or product were chosen instead of the mean, the twPC would be proportional to the values of SC.

4.4.3. Cluster‐defining thresholds for NBS

Due to the exploratory nature of the present study, supra‐thresholds of $p<.001$ and $p<.005$ (included in Figures S6 and S7) were chosen for SC and twPC to examine whether overlapping edges and nodes occur between SC and twPC. The behaviour of twPC in response to supra‐thresholds was similar to typical SCs, with decreased supra‐thresholds often yielding larger altered networks. The actual t‐values used in the NBS toolbox vary slightly depending on the corresponding degree of freedom (sample sizes). T‐values of 3.2 and 2.8 correspond to p‐values around .001 and .005 respectively, which are among the range of supra‐thresholds applied in previous NBS studies (Wang et al., 2018). Note that while the majority of results and trends were consistent between the two supra‐thresholds, there were some differences. Noticeably, only at a supra‐threshold of $p<.005$ was an increased twPC network identified in LMCI participants compared to AD (Figure S7). In future studies, a threshold‐free NBS (Vinokur et al., 2015) method or a network filtering algorithm may be useful to apply on the twPC to further optimise the NBS analysis. We, however, used the standard NBS approach in the current study, as that remains the most widely used NBS variant—and also given that twPC is a new method, and the traditional NBS provides a simpler and more tested approach to tuning parameters.

4.4.4. Image smoothing

Similar to the approach used for track‐weighted functional connectivity (Calamante et al., 2013), a further step used here to improving sampling accuracy during end‐point measurements was the use of spatial smoothing as a pre‐processing step; this helps ensure a more representative summary of adjacent tau distributions around the end‐points of individual fibre tracks. Image smoothing is used as a preliminary sampling step because only PET values at fibre endpoints were sampled. Various filter sizes were initially tested, and a median filter of 5 mm was empirically found to provide a reasonable level of smoothing without considerable loss of anatomical resolution. Smoothing is highly recommended, since if it is not applied, track‐weighted PET values will be highly influenced by local noise. Too large a filter, however, runs the risk of sampling many values of adjacent nodes. Thus, when choosing the filter size, the atlas should also be taken into consideration. In the case of an atlas with smaller brain regions, the filter size should be reduced accordingly. Another recommended step is to apply partial volume correction prior to generating twPC in PET images with relatively low spatial resolution. This additional step would improve the accuracy of the generated twPC, especially because the PET values are sampled around the fibre track endpoints, which are typically at the interface between grey and white matter regions where partial volume effects may be significant.

4.5. Comparison with other PET connectomes

In addition to the metabolic connectivity methods introduced in the introduction, other data‐driven approaches, such as the work by Vogel et al. (2018), also aimed to derive network information from static PET data. This method provides valuable insights into the clustering of tracer accumulation in PET images, elucidating groups of key regions, which exhibit certain similarities with the information obtained through the twPC. Note that while existing approaches contribute to capturing network‐based molecular information, the twPC approach uniquely incorporates SC information derived from dMRI fibre‐tracking. This integration serves as a guiding framework for the sampling of tau‐PET values in grey matter regions connected by white matter pathways, introducing a novel dimension that explicitly links structural pathways as a reference for interpreting molecular connectivity patterns. Drawing a direct comparison across all these methods is challenging because existing PET‐based connectomes did not incorporate any MRI information.

4.6. Limitations and future directions

There were a few limitations to the present study. First, similar to other studies using the ADNI database, the data quality can vary considerably. This problem was especially prominent in the PET data, which was acquired across a variety of sites with different PET/CT scanner models with different performance characteristics. Different image reconstruction and filtering algorithms were applied, which resulted in variable PET image spatial resolution and quality. These variabilities affected the quality of PET/MRI registration as well as quantitative accuracy. Moreover, since the PET and MRI were acquired separately on different scanners and during different sessions, changes might have occurred between these sessions. During the data selection, the maximum interval between the PET and MRI sessions was capped at 1 year, and the median time interval was 30 days. These limitations could be resolved by acquiring datasets with more harmonised protocols and possibly using a simultaneous PET/MRI scanner in future studies. Despite these limitations, ADNI does provide a powerful resource to investigate multi‐modal imaging and clinical data for preclinical disease, those with MCI and those with established AD. Also, it is noted that the groups examined here were classified on the basis of clinical characteristics and not according to AD biomarkers. Furthermore, the baseline clinical characteristics may not match the corresponding time of the imaging sessions. While this may have influenced findings within and across groups, it is noted that the focus was on the MRI and PET biomarkers and that doing this within clinical disease is potentially more applicable to clinical practice, particularly in areas where access to biomarkers is not possible or feasible. Nonetheless, a further limitation was the relatively small number of participants in each group, particularly for the diseased groups. Importantly, despite these small numbers, several statistically significant results were obtained, suggesting the proposed method can have high sensitivity to detect an effect. The use of larger groups will only increase the sensitivity to detect more subtle effects.

To minimise image quality variability and to acquire a reasonable sample size, a less advanced single‐shell Siemens diffusion imaging protocol was chosen for the dMRI data selection. The diffusion gradient schemes of the basic ADNI3 diffusion protocols had slight variability across Siemens, Phillips and the GE scanners. The diffusion data acquired from the Siemens scanners were selected because the data quality and the gradient encoding were highly standardised. Two participants were excluded from the analysis due to failed distortion correction. Future studies involving larger sample sizes should help increase the power to detect abnormalities in twPC analysis.

Similar to the limitations of connectivity studies, the cluster‐defining suprathresholds could influence the results significantly. A threshold‐free approach was not chosen in the present study in order to explore the behaviour of the newly proposed PET connectivity method using more widely accepted techniques. The accuracies of both the SC and twPC would depend on the tractography processing. To minimise this source of error, in this study, we followed the state‐of‐the‐art tractography methods to process single‐shell multi‐tissue dMRI (Dhollander & Connelly, 2016), which included (Calamante, 2019): distortion correction (Schilling et al., 2019), dMRI model for fibre orientations that are robust to crossing fibres (Tournier et al., 2007), probabilistic tractography algorithm (Tournier et al., 2012) with anatomical constrains (Smith et al., 2012) and streamline filtering for tractography quantification (Smith et al., 2012).

A limitation of this study is the potential mediating role of amyloid, as the participants exhibited mixed amyloid status. Amyloid imaging was not included in the present study because the studies of associations between SC and amyloid‐PET were found to have mixed results (Mito et al., 2018). Further research with larger sample sizes and comprehensive assessments of amyloid burden, including longitudinal evaluations, is necessary to better understand the potential confounding effects and unravel the intricate interplay between amyloid pathology, tau pathology and SC disruptions in individuals with MCI and AD.

Our current study focuses on the method development of the novel twPC and demonstrated its applications in AD using NBS. Another analysis approach with high potential would be incorporating graph theory measures, which could provide valuable insights into the network characteristics and potential pathways of pathology propagation. However, twPC, being unique in capturing molecular information while constrained by structural connections, presents a novel challenge in defining the meanings of graph metrics within this specific framework. Applying a comprehensive graph theoretical analysis requires careful examination of whether the traditional interpretations of graph metrics still hold in this new context. The prospect of graph theory analyses remains an exciting avenue for future research.

5. CONCLUSIONS

The present study offers a new twPC approach at the subject level, which can be used to examine the intricate interplay between molecular information (imaged by PET) and SC (imaged by dMRI). Applied in the AD spectrum, our findings reveal distinct topological changes in SC and twPC networks from early MCI to late stages of AD. Decreased SC and increased twPC in specific brain regions were revealed, emphasising the complexity of network changes during cognitive decline. Changes in network edges involve critical brain areas, including the bilateral hippocampus, fusiform gyrus and entorhinal cortex, which underscores the differential impact of molecular and structural changes on disease progression. The twPC method can be used as a flexible framework to bring crucial insights into the relationship between molecular distributions and structural connections in neurodegenerative disorders.

AUTHOR CONTRIBUTIONS

Zhuopin Sun, Steven Meikle, and Fernando Calamante contributed to the study conception and design. Software development and data analysis were performed by Zhuopin Sun. Zhuopin Sun, Steven Meikle and Fernando Calamante contributed to optimisation of the proposed method. All authors contributed to the interpretation of the findings from the ADNI data. The first draft of the manuscript was written by Zhuopin Sun and all authors contributed to critical revision of subsequent versions of the manuscript. All authors read and approved the final manuscript.

FUNDING INFORMATION

This research was funded by the Engineering and Information Technologies Research Scholarship granted by the University of Sydney to ZS.

CONFLICT OF INTEREST STATEMENT

The authors have no relevant financial or non‐financial interests to disclose.

Supporting information

Data S1. Implementation with Mrtrix3, FSL installed.

Data S2. Supplementary information.

Sun, Z. , Naismith, S. L. , Meikle, S. , Calamante, F. , & for the Alzheimer's Disease Neuroimaging Initiative (2024). A novel method for PET connectomics guided by fibre‐tracking MRI: Application to Alzheimer's disease. Human Brain Mapping, 45(4), e26659. 10.1002/hbm.26659

DATA AVAILABILITY STATEMENT

Data sharing is not applicable to this article as no new data were created or analyzed in this study.