ArcheD, a residual neural network for prediction of cerebrospinal fluid amyloid‐beta from amyloid PET images

Detection and measurement of amyloid‐beta (Aβ) in the brain is a key factor for early identification and diagnosis of Alzheimer's disease (AD). We aimed to develop a deep learning model to predict Aβ cerebrospinal fluid (CSF) concentration directly from amyloid PET images, independent of tracers, brain reference regions or preselected regions of interest. We used 1870 Aβ PET images and CSF measurements to train and validate a convolutional neural network (“ArcheD”). We evaluated the ArcheD performance in relation to episodic memory and the standardized uptake value ratio (SUVR) of cortical Aβ. We also compared the brain region's relevance for the model's CSF prediction within clinical‐based and biological‐based classifications. ArcheD‐predicted Aβ CSF values correlated with measured Aβ CSF values (r = 0.92; q < 0.01), SUVR (rAV45 = −0.64, rFBB = −0.69; q < 0.01) and episodic memory measures (0.33 < r < 0.44; q < 0.01). For both classifications, cerebral white matter significantly contributed to CSF prediction (q < 0.01), specifically in non‐symptomatic and early stages of AD. However, in late‐stage disease, the brain stem, subcortical areas, cortical lobes, limbic lobe and basal forebrain made more significant contributions (q < 0.01). Considering cortical grey matter separately, the parietal lobe was the strongest predictor of CSF amyloid levels in those with prodromal or early AD, while the temporal lobe played a more crucial role for those with AD. In summary, ArcheD reliably predicted Aβ CSF concentration from Aβ PET scans, offering potential clinical utility for Aβ level determination.

Population Health of the University of Helsinki (AT); Academy of Finland, Grant/Award Numbers: 314639, 320109, 345988, 322675, 328890 Edited by: Yoland Smith more significant contributions (q < 0.01).Considering cortical grey matter separately, the parietal lobe was the strongest predictor of CSF amyloid levels in those with prodromal or early AD, while the temporal lobe played a more crucial role for those with AD.In summary, ArcheD reliably predicted Aβ CSF concentration from Aβ PET scans, offering potential clinical utility for Aβ level determination.
K E Y W O R D S Alzheimer's disease, amyloid, cerebrospinal fluid, deep learning, PET

| INTRODUCTION
Early detection and diagnosis of Alzheimer's disease (AD) can help in the prevention of dementia and in identifying at-risk individuals for clinical drug or lifestyle intervention trials.Even though AD is characterized by both clinical symptoms and neuropathological changes, diagnostic guidelines have been based on clinical symptoms, in particular on episodic memory impairment (Jack et al., 2011;McKhann et al., 1984).However, clinical classification based on symptoms is neither sensitive nor specific for AD, as cognitive impairment can be caused by other neurodegenerative diseases or other reasons (Erickson et al., 2022;Jack et al., 2018;Sperling et al., 2013).Approximately 10-30% of those with clinically defined AD do not have AD-specific neuropathological changes of amyloid-beta (Aβ) plaques and neurofibrillary tangles of hyperphosphorylated tau on autopsy (Nelson et al., 2011).Moreover, about 30% of cognitively healthy individuals have substantial AD-related neuropathological changes (Aizenstein et al., 2008;Knopman et al., 2003).
Acknowledging the inconsistency between cognitive status and AD-related brain pathology, the biological classification of AD is based solely on biomarkers and defines AD independently of the cognitive status (Jack et al., 2011).The AT(N) frameworkand its extension ATX(N)are based on biological hallmarks of AD: Aβ (A), tau (T) related pathology and also neurodegeneration (N) (Jack et al., 2018) and potential novel biomarkers (X) (Hampel, Cummings, et al., 2021).Aggregation of Aβ can start even decades before the onset of the first clinical symptoms, whereas tau protein deposition begins much later and closer to the first clinical symptoms (Jack et al., 2010).Based on Aβ and tau measurements in cerebrospinal fluid (CSF) and positron emission tomography (PET) and determination of neurodegeneration via PET or magnetic resonance imaging (MRI) scans, the AT(N) framework yields eight biomarker profiles, which separate the AD continuum from non-AD pathologic changes and normal AD biomarkers (Jack et al., 2018).In the biological framework, it is the Aβ positivity that is needed to define an individual on the Alzheimer's continuum (Jack et al., 2018).Further, cognitive status is evaluated independently of the biomarker profile and is used for disease staging.Although biomarkers are currently supplementary in clinical practice of AD definition (Arias et al., 2024;Ashton et al., 2024;Jack et al., 2018) and/or limited to memory clinics, biological classification is intended to improve the definition, classification and diagnosis of AD as a unique neurodegenerative disease (Hampel et al., 2022).
Large neuroimaging datasets with PET measurements of AD biomarkers provide an excellent opportunity to further evaluate the AT(N) framework (Weber et al., 2021).Deep learning (DL) models have shown high accuracy in classifying AD and its progression from MRI and PET images (Jo et al., 2019).The majority of the models have used MRI or PET scans to predict clinical disease stages, early disease detection or disease progression (Choi et al., 2020;Ding et al., 2019;Jo et al., 2020;Lin et al., 2021).Only a few studies have aimed to predict AD with amyloid biomarkers (Kim et al., 2019;Reith et al., 2020Reith et al., , 2021)).However, these models were trained to quantify the standardized uptake value ratios (SUVR), to classify amyloid status and to predict a change in amyloid pathology on future scans.So far, models have not been trained to predict continuous Aβ (based on CSF) from the amyloid PET (independent of the Aβ tracer type, preselected regions of interest, brain reference region and SUVR definition) (Palmqvist et al., 2015;Spallazzi et al., 2019).Such a prediction studies the link between the localization of amyloid in the brain and CSF amyloid levels across the entire continuum of biomarker aggregation.In the case PET imaging is done in clinical practice, ArcheD would allow using only one biomarker, thus decreasing clinicians' workload, avoiding invasive CSF sampling and following challenging CSF measurement standardization.
In this study, we propose a convolutional neural network model ("ArcheD") with residual connections to predict Aβ CSF concentration from amyloid PET images.Residual deep networks have been used in PET image analyses previously (Shah et al., 2022), but here we aimed to assess their applicability in predicting fluid biomarker levels from PET images.Our approach allows probing the model and input amyloid PET images to reveal the brain regions that contribute most to the predicted CSF amyloid concentrations.ArcheD does not use any prespecified cortical (or other) brain regions, but instead adopts a hypothesis-free approach leveraging all information available in PET images.To examine our approach, we compared our method's performance with SUVR, a measure that determines cortical amyloid aggregation in relation to the cerebellum, a commonly used reference region (Heeman et al., 2020;Jack et al., 2013).We also studied our model in relation to episodic memory including immediate and delayed recall measures.We further investigated the model and brain regions separately in sub-groups based on both clinical and biological classification of AD.To scrutinize the trained neural network model, we extracted brain regions that the model considers informative for CSF prediction and compared them between clinical and biological classes.

| Data and participants
We studied 1252 individuals' PET data on brain amyloid and CSF measurements of amyloid-β 1-42 peptide and phosphorylated tau 181P provided by the Alzheimer's Disease Neuroimaging Initiative (ADNI).
Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu).The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD.The primary goal of ADNI has been to test whether serial magnetic resonance imaging (MRI), positron emission tomography (PET), other biological markers and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimer's disease (AD).For up-to-date information, see https://adni.loni.usc.edu/.(Petersen et al., 2010).
We used PET and MRI scans, CSF measurements, ADNI clinical classifications, episodic memory measurements and demographics data (adni.loni.usc.edu).Amyloid PET scans were obtained with different tracers (i.e., Pittsburgh compound B, Florbetapir, Florbetaben) depending on the ADNI study phase, and pre-processed by the ADNI PET imaging corelab (i.e., 'co-reg, avg, standardized image and voxel size').In addition to imaging data, we used the cortical composite standardized uptake value ratios (SUVR) (Kinahan & Fletcher, 2010;Landau et al., 2015) normalized by the whole cerebellum as a reference region, and added it as a standard amyloid measurement from PET in our model's performance evaluation.
As some participants had several clinical visits, a total of 1870 amyloid PET images were obtained.Among them individuals had AD (n = 190), amnestic mild cognitive impairment (aMCI) due to AD (n = 928), subjective memory complaints (SMC) (n = 145) or were cognitively normal (CN) (n = 607) based on the ADNI clinical classification (Table S2).The clinical classifications in ADNI are based on the Clinical Dementia Rating (CDR), the Mini-Mental State Examination (MMSE) and delayed recall of 1 paragraph from the Logical Memory (LM) II of the Wechsler Memory Scale-Revised (Petersen et al., 2010).In addition to clinical classifications, we used immediate and delayed recall measures from the LM Story A and also immediate (total words in trials 1-5) and delayed recall measures of the Rey Auditory Verbal Learning Test (AVLT): these tests were used as continuous measures of episodic memory.
As a result, we obtained four biological classes: participants with negative amyloid and tau proteins' CSF measurements based on cut-off values (A-T-); amyloid negative, tau positive group (A-T+); amyloid positive, tau negative group (A + T-); amyloid and tau positive group (A + T+).We used only A and T in our biological classification, whereas the neurodegeneration (N) component was not included because it is not currently needed for the biological classification of AD-related pathology (Jack et al., 2018).
To integrate values from the different CSF measurement methods, we trained linear regression and third-degree polynomial regression models to rescale AlzBio3 values to Roche Elecsys based on 1072 samples with both values available (858 training samples, 214 test samples).The model that maximized the coefficient of determination (R 2 ) and accuracy of positive and negative amyloid classification using cut-off values in the test dataset was selected for further analysis.

| A deep neural network model to predict CSF values from PET scans
We developed a deep convolutional neural network model called "ArcheD", which utilizes residual connections (He et al., 2016) to predict logarithmic Aβ CSF values from amyloid PET scans.The residual connections allow for a deeper model to be trained, which has been shown to improve performance (He et al., 2016).Our model architecture includes one initial convolution-pooling block followed by two residual-pooling blocks, two fully connected layers and a linear regression node (Figure 1).Each residual block contains a sequence of convolutional, batch normalization and rectified linear activation function (ReLU) activation layers.
ArcheD contains 35 layers and approximately 10.7 millions parameters.To train the model, we used the Adam optimization algorithm (Kingma & Ba, 2014) with an initial learning rate of 0.0001 to minimize the mean squared error (MSE) of observed and predicted CSF values.The model was trained for a maximum of 150 epochs with a minibatch size of four, and stopped early if loss in the validation dataset did not decrease for 15 epochs.
We used 60% of the dataset for training (n = 1197), 20% for validation (n = 299) and 20% for testing the model (n = 374).To increase the size of the training dataset with data augmentation, we either applied Gaussian noise (σ = 0,5,10,15,20,25%; six possible augmentations) or flipped the image by X or Y axes (two possible augmentations).To generate an augmented image from a training dataset image, one of the eight possible augmentations was selected with an equal probability.In the end, we obtained a total of 14,352 original and augmented brain scans constituting the augmented training data.To evaluate the robustness of ArcheD in data not used in training, we used a test dataset.ArcheD code is available at GITHUB (https://github.com/artagmaz/arched.git).

| Guided backpropagation relevance maps
To explore which brain regions contribute the most to ArcheD's predictions of amyloid CSF measurements from amyloid PET scans, we used the guided backpropagation technique (Springenberg et al., 2014).This approach quantifies how much model outputs change in response to perturbing model inputs.In PET imaging data, we used guided backpropagation to extract the contribution (relevance value) of each input voxel to CSF prediction.Guided backpropagation creates more specific relevance value maps compared to the classic backpropagation approach by replacing negative gradients with zero in ReLU activation layers during backward passes (Rieke et al., 2018) (Figure 2.1).
To compare the relevance maps between individuals and AD classes, we co-registered PET scans and corresponding relevance maps to individuals' MRI and MNI152 templates with the AntsPy package (Avants et al., 2009) (Figure 2.2).Since all PET images and relevance maps were described in the same coordinate space, we were able to create average PET and relevance maps for all samples and separate AD classes.We used the neuromorphometrics atlas to derive regions-of-interest (ROIs) (Bakker et al., 2015) (Table S1, Figure 2.3) and compared their relevance to the model decision-making between classes (Figure 2.4).The relevance value per ROI was normalized to the size of the region to evaluate how relevant the average voxel of each area is for CSF predictions.

| Statistical analyses
We computed Pearson correlations with two-tailed p-values to quantify the strength of the associations between model prediction and CSF Aβ, cortical SUVR and episodic memory measures.We also compared relevance values of brain areas between biological or clinical classes by bootstrapping with a 95% confidence interval, Cohen's d and Welch's t-test.For all multiple comparisons, we computed false discovery rates (FDR) with the Benjamini-Hochberg method.

| Programming environment
Tensorflow 2.4.1 and Python 3.9.7 were used to develop the machine-learning models and perform computational analyses.The models were trained on NVIDIA Tesla V100 GPUs with 16 GB memory.For uploading, augmentation, registration and visualization of PET images we used nibabel, dltk and AntsPy python packages (Avants et al., 2009;Brett et al., 2023;Pawlowski et al., 2017).Functions for guided backpropagation gradient analysis were adapted from https://github.com/jrieke/cnn-interpretability.All R and Python scripts used in the study are provided at https://github.com/artagmaz/arched.git.

| RESULTS
The mean age of the participants was 73.6 years (SD = 7.37) and 49% were women.Detailed descriptive statistics of study participants are presented in Table S2.
F I G U R E 2 Workflow to process PET scans with ArcheD and guided backpropagation to identify characteristics distinguishing brain regions of interest and clinical and biological groups.Created with BioRender.com.

| Fluid biomarker rescaling
We first transformed AlzBio3 CSF values to conform to the range of values present in Roche Elecsys CSF measurements (Shaw & Trojanowski, 2017).Both regression models performed similarly on a held-out portion of the data (linear regression: R 2 test = 68.9%,91.5% accuracy; third-degree polynomial regression: R 2 test = 69.4%,91.5% accuracy) (Table S3, Figure S1).Based on these metrics and visual inspection of the regression models  (Figure 3a), we decided to use a third-degree polynomial regression model to predict Roche Elecsys amyloid measurements for the remaining 1102 samples.

| Training the ArcheD model and overall predictive performance
ArcheD was trained on 14,352 augmented PET scan images to predict logarithmic CSF values.The model achieving the best performance in the validation set was obtained after the eighth epoch of training (mean squared error, MSE = 0.12) (Figure S1).Finally, ArcheD explained 66% of the variance (R 2 ) in the test dataset not used in training (Figure 3b).

| Associations of DL with SUVR and episodic memory measurements
The ArcheD Aβ CSF prediction was correlated with biological and cognitive AD markers (Table 1).A significant association was observed between predicted and clinically measured CSF Aβ, both for all samples and all clinical classes (r > 0.89, q < 0.01).SUVR strongly correlated with all sample subsets' Aβ CSF (r < À0.53, q < 0.01) except for AD samples (r AV45 = À0.42,q < 0.05; r FBB = À0.08,q = 0.76).In the case of episodic memory test results, CSF predictions were generally weaker and mostly non-significant in the AD (n = 190) and SMC (n = 145) groups compared to MCI (n = 928) and CN (n = 607) groups.There was a significant positive correlation in AD samples between predicted Aβ CSF and AVLT immediate recall (r = 0.36; q < 0.01), whereas in those with SMC predicted CSF measurements showed no significant correlations with any of the episodic memory measures (Table 1).All memory test scores for MCI and CN groups were significantly correlated with predicted amyloid CSF measurement (r > 0.16, q < 0.01) (Table 1).

| Relevance of brain areas for model decision-making
To understand which brain regions contributed the most to ArcheD predictions, we compared the relevance of these regions with guided backpropagation.We found that the areas that contributed the most were cerebral (mean relevance 0.251, 95% CI [0.247, 0.255]) and cerebellum white matter (0.207, 95% CI [0.205;0.208])followed by the brain stem, subcortical areas, grey matter regions at the lobar level and cerebellum grey matter, whereas limbic lobe, basal forebrain, ventricles and optic chiasm were substantially less important for the model (Table S4, Figure 4a,b).
We then explored the clustering of ROIs in the ADNI cohort by examining their similarity based on relevance profiles (Figure 4c).This analysis aimed to enhance our understanding of the region-specific contributions to our model.As expected, cerebral and cerebellum white matter, and vessels clustered together.The main cerebral lobes, i.e., frontal, temporal, parietal and occipital lobes were clustered together, as were the brainstem and subcortical regions.The remaining regions formed two clusters containing optic chiasm and ventricles, and basal forebrain and limbic lobe (Figure 4c).

| Region-specific contributions to prediction of CSF in clinical and biological sub-classes
Different brain regions may have different levels of contribution to the model's prediction of CSF values.These differences may also vary as a function of the stage in the AD continuum.Therefore, we compared their relevance values within both clinical (CN, SMC, MCI, AD) and biological (A-T-, A-T+, A + T-, A + T+) classifications.The between-classes analysis showed that there were brain areas that contributed at the same level for all clinical or biological classes (optic chiasm, ventricles and vessels) and areas that were significantly different between classes by relevance value (Figure S3, Figure 5, Table S4).
Significant differences in relevance values between AD/MCI and CN groups were observed in eight ROIs (q < 0.01) (Table S5).Cerebral white matter contributed more to Aβ CSF value predictions in the CN group (AD vs CN Cohen's d = À0.976,A + T + vs A-Td = À1.138;q < 0.01), whereas other regions (cortical lobes, limbic lobe, basal forebrain and subcortical areas) were more important for prediction in the AD and MCI groups (Table S5).Brainstem relevance values differentiated only between MCI and CN groups (Figure 5, Table S5).However, there were no significant differences between SMC and CN groups (Figure 5, Table S5).
Most of the relevance patterns observed for biological classes were concordant with those seen in clinical classes.In all ROIs, except vessels, ventricles and optic chiasm, a marked difference in relevance values was visible between A + T + and A-T-classes (Figure 5, Table S5).In addition, parietal, occipital, frontal, temporal lobes, brain stem, cerebral white matter and subcortical areas differentiated A + T-from the A-T-(q < 0.01) (Figure 5, Table S5).

| Contribution of grey matter regions to Aβ CSF prediction in clinical and biological classes
Taking into account the high amount of unspecified binding of the amyloid tracers in cerebral and cerebellar white matter, we conducted a closer investigation focusing only on the cortical grey matter (GM) regions (Figure 4b) (Klunk et al., 2004).GM regions are first affected by the neuropathological changes of AD (Thal et al., 2002) and our results indicated that these regions contributed more to the model prediction of later stages of the disease (Figure 5).Therefore, we explored their contribution to AD development in clinical and biological classes.
When comparing relevance value differences between biological or clinical classes, we observed that the most contributing grey matter region differed along the AD continuum (Figure 6b, Table S6).In the CN and SMC groups (based on the clinical classification), the parietal lobe (CN mean 0.101, 95% CI [0.099, 0.103]; SMC 0.101, 95% CI [0.098, 0.104]) was the most significantly contributing region, followed by the temporal, occipital lobes, cerebellum grey matter and frontal lobe (Figure 6b, Table S6).In MCI and AD groups, the relevance values of all regions were higher than in the CN group, and the temporal lobe contributed more than the other lobes (MCI temporal 0.108, 95% CI [0.106, 0.110]; AD temporal 0.126, 95% CI [0.122, 0.131]).
F I G U R E 5 Comparison of mean relevance values per brain region within clinical or biological classifications.The cognitive normal (CN) group was used as a control for clinical classification.A-T-was used as a control for biological classification.***q < 0.01.
We developed a deep neural network model (ArcheD) for the prediction of CSF amyloid biomarker concentration directly from amyloid PET images independent of the amyloid PET tracer.Trained on ADNI PET images and associated Aβ CSF measurements, ArcheD was able to explain 66% of the variance in CSF levels in a test dataset withheld from training.We thus envision using ArcheD to complement the information obtained in an Aβ PET scan by providing an estimate of the Aβ CSF level without a lumbar puncture.
CSF Aβ predicted by our model correlated significantly with cortical amyloid PET SUVR and episodic memory performance.The correlations of measured and predicted Aβ CSF with PET SUVR and episodic memory measurements were highly similar (Hake et al., 2015;Niemantsverdriet et al., 2017) and can be interpreted as additional proof of the model's prediction accuracy.The absence of association in AD and SMC groups with FBB SUVR and episodic memory performance could be explained by the smaller number of participants in these classes compared to group sizes of CN and MCI.In addition, the AD group included individuals with severe AD, resulting in little variation in amyloid levels and episodic memory performance; amyloid levels plateau in the course of AD and there is also little variation in delayed recall measures in those with severe AD (Klunk et al., 2004;Thal et al., 2002).
To understand which brain regions were the most influential in predicting CSF Aβ levels, we investigated the relevance of average voxel per brain region and compared ROIs between each other, and, furthermore, performed these comparisons separately in clinical and biological sub-classes.The cerebellum and cerebral white matter, followed by the subcortical area and brainstem, were identified as the most influential brain regions for model predictions.Some of these regions have unspecific binding of amyloid tracers (Klunk et al., 2004;Matsubara et al., 2016) and can be used as visual control regions to test the tracers' delivery to the brain.They are also not affected by amyloid plaques until the very late AD stage (Klunk et al., 2004;Thal et al., 2002) and can be used as possible reference regions for calculating SUVR (Heeman et al., 2020), even if cerebellum grey and white matter is the gold standard reference region (Klunk et al., 2015).It is likely that our ArcheD model learnt to use these regions as a reference point for CSF prediction and combined them with cortical regions to 'calibrate' amyloid CSF values.Furthermore, supporting evidence comes from the clustering of ROIs based on their relevance profiles (Figure 4c).This clustering distinctly separated white matter and vessels from other brain regions and effectively grouped all grey matter regions and cerebellum grey matter together.
Areas contributing the least to the model's predictions were the limbic lobe, basal forebrain, ventricles and optic chiasm.Despite hippocampus and basal forebrain degeneration being characteristic of early-stage AD (Hampel, Hardy, et al., 2021;Kerbler et al., 2015;Teipel et al., 2018), ArcheD did not consider them informative for CSF prediction.This can be attributed to the small size of these ROIs and the limited spatial resolution of PET scans, resulting in a partial-volume effect (Soret et al., 2007).
Furthermore, we explored whether the same or different regions contributed to CSF prediction in different clinical and biological classes.Relevance of cerebral cortex (including limbic lobe), subcortical, brain stem, basal forebrain, cerebellum white and grey matter regions was significantly greater in those with AD compared to those without AD or in those who were amyloid positive compared to those who were amyloid negative.Cerebral white matter contributed more to CSF prediction in individuals without cognitive impairment (CN, SMC) or in individuals who were amyloid negative (A-T-, A-T+).According to criteria for amyloid PET scan usage, amyloid-positive scans differentiate from amyloidnegative scans based on grey matter cortical uptake that is above the level of nonspecific binding in white matter (Johnson et al., 2013;Richards & Sabbagh, 2014;Wolk et al., 2012).This corresponds to our finding, indicating that cerebral white matter plays a more significant role in CSF prediction for amyloid-negative groups, while cortical regions are more relevant to amyloid-positive individuals.We hypothesized that ArcheD might not only use cerebral white matter as a reference region but also focus on both white and grey matter amyloid binding levels together.
Focusing on cortical GM, we found considerable differences between lobes' relevance values and amyloid deposition level.Temporal and parietal areas contributed the most to the model prediction, whereas occipital and frontal lobes' relevance values were noticeably less.The temporal lobe has been reported to substantially contribute to model decision-making also in other studies of AD classification based on MRI scans (Dyrba et al., 2021;Rieke et al., 2018).However, on PET scans, the parietal, occipital and frontal lobes have higher levels of amyloid aggregation, while the temporal lobe has significantly less amyloid.According to the Aβ pathology studies, parietal and frontal lobes are regions with early amyloid accumulation, which can explain the high biomarker concentration in those regions in our results (Insel et al., 2020;Mattsson et al., 2019).
Despite the temporal lobe being the least amyloidenriched lobe in PET scans, ArcheD highlighted this lobe as the most important cortical region for the amyloid CSF prediction.When we looked at the level of cortical lobes' relevance between different classes, we noticed that the temporal lobe's relevance is more important than other lobes only in MCI, AD and A + T + groups, which indicate later stages in the AD continuum compared to SMC, CN and A-negative groups.In early stages of the disease development, the parietal lobe is the most significant contributor, which is compatible with earlier studies (Insel et al., 2020;Mattsson et al., 2019).
This study presented a novel neural network model that analyses amyloid PET scans, independent of the amyloid tracer used and predicts what the amyloid beta level would be in CSF.The model learned to focus on specific brain regions depending on the AD stage, defined by the biological or clinical classification.These regions aligned well with previous findings on AD progression.
ArcheD has the potential to be used in clinical practice in the future.It can reduce the amount of work for clinicians and potentially prevent patients from lumbar puncture.ArcheD is also straightforward to use, as the PET scan image is the only input to the method.However, our research has some limitations that can be improved in future studies.We had only a limited dataset of PET scans with available CSF measurements, especially of AD individuals, to train the ArcheD model.Larger training datasets would likely yield better predictive performance.Another limiting factor is the strict requirement for input PET images to have dimensions of 160x160x96 voxels.Therefore, users may need to perform preprocessing, such as co-registration, averaging, standardization and voxel size adjustment, similar to ADNI PET imaging corelab, on their own.Our model and findings also need to be validated on external datasets.

| CONCLUSION
In conclusion, ArcheD was able to predict amyloid CSF values directly from amyloid PET scans in the AD continuum (including cognitively unimpaired individuals with preclinical AD).Predicted CSF values correlated significantly with CSF amyloid, cortical amyloid SUVR and episodic memory performance.Analysing the relevance of brain regions to model's CSF prediction, cerebellar and cerebral white matter, brainstem and subcortical areas were found to contribute the most and may have been used by ArcheD as reference regions for prediction.Upon comparing clinical and biological classes we found that the subcortical areas, brain stem, cerebellum, cerebral cortex and its subregion -the basal forebrain, influenced predictions, especially in the MCI and AD clinical subclasses and A + T-and A + T + biomarker-defined classes.Moreover, cerebral white matter contributed more to clinically normal and biologically defined early-stage groups.Examining cortical regions more closely, we observed a constant higher level of the temporal lobe relevance along the entire AD continuum and assumed that the model prioritized it as a predictor of Aβ CSF.Our model can serve in clinical practice for determining an Aβ CSF state and improving AD early detection.However, further studies are needed to validate and tune the model for clinical use.

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I G U R E 1 Schematic presentation of the ArcheD model architecture.PETpositron emission tomography; CSFcerebrospinal fluid; n1, n2 and n3the number of filters in convolution layers are specified in brackets for both convolutional residual blocks.Created with BioRender.com.
Linear (orange line) and third-degree polynomial (blue line) regression for fluid amyloid rescaling from INNO-BIA AlzBio3 system to Roche Elecsys.Grey lines present cut-off values for Aβ CSF measurement.(b) Comparison of clinically measured Aβ CSF and values predicted by the ArcheD model.CSF values are given as natural logarithms.Lines illustrate the linear relationship between clinical Aβ CSF measurement and prediction of our model: greenlinear relation between real and predicted values of the test dataset; orangelinear relation between real and predicted values of the training dataset.The red diagonal line shows the ideal one-to-one correspondence between observed and predicted values.T A B L E 1 Pearson correlations between Aβ CSF values predicted by model and clinical, imaging and memory markers of AD.

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I G U R E 4 (a) Mean relevance values for brain regions and bootstrapped 95% confidence intervals.Values were multiplied by 1000.(b) Average relevance value and amyloid concentration (SUVR) for the dataset on PET scan.(c) Heatmap of Pearson correlations for relevance values of all brain regions.

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I G U R E 6 (a) Mean relevance values (top) and amyloid concentration (bottom) for grey matter regions and bootstrapped 95% confidence intervals.(b) Relevance level of grey matter regions on different clinical (top) and biological classes (bottom) of AD.