# An interpretable generative multimodal neuroimaging-genomics framework for
decoding Alzheimer’s disease

Giorgio Dolci1,2, Federica Cruciani1, Md Abdur Rahaman2, Anees Abrol2, Jiayu
Chen2, Zening Fu2,
Ilaria Boscolo Galazzo1, Gloria Menegaz1,+, and Vince D. Calhoun2,+,
for the Alzheimer’s Disease Neuroimaging Initiative∗

1Department of Engineering for Innovation Medicine, University of Verona,
Verona, Italy
2Tri-Institutional Center for Translational Research in Neuroimaging and Data
Science (TReNDS),
Georgia State University, Georgia Institute of Technology, Emory University,
Atlanta, GA, USA

+V.D. Calhoun and G. Menegaz equally contributed as last authors to this work.
∗Data used in preparation of this article were obtained from the Alzheimer’s
Disease
Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the
investigators within the ADNI
contributed to the design and implementation of ADNI and/or provided data but
did not participate in analysis
or writing of this report. A complete listing of ADNI investigators can be
found at:
http://adni.loni.usc.edu/wp-
content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf

###### Abstract

Alzheimer’s disease (AD) is the most prevalent form of dementia, affecting
millions worldwide with a progressive decline in cognitive abilities. The AD
continuum encompasses a prodormal stage known as Mild Cognitive Impairment
(MCI), where patients may either progress to AD (MCIc) or remain stable
(MCInc).

Understanding the underlying mechanisms of AD requires complementary analysis
derived from different data sources, leading to the development of multimodal
deep learning models. In this study, we leveraged structural and functional
Magnetic Resonance Imaging (sMRI/fMRI) to investigate the disease-induced grey
matter and functional network connectivity changes. Moreover, considering AD’s
strong genetic component, we introduce Single Nucleotide Polymorphisms (SNPs)
as a third channel. Given such diverse inputs, missing one or more modalities
is a typical concern of multimodal methods. We hence propose a novel deep
learning based classification framework where generative module employing
Cycle Generative Adversarial Networks (cGAN) was adopted to impute missing
data within the latent space. Additionally, we adopted an Explainable
Artificial Intelligence (XAI) method, Integrated Gradients (IG), to extract
input features relevance, enhancing our understanding of the learned
representations.

Two critical tasks were addressed: AD detection and MCI conversion prediction.
Experimental results showed that our framework was able to reach the state-of-
the-art in the classification of CN vs AD reaching an average test accuracy of
$0.926\pm 0.02$. For the MCInc vs MCIc task, we achieved an average prediction
accuracy of $0.711\pm 0.01$ using the pre-trained model for CN and AD. The
interpretability analysis revealed that the classification performance was led
by significant grey matter modulations in cortical and subcortical brain areas
well known for their association with AD. Moreover, impairments in sensory-
motor and visual resting state network connectivity along the disease
continuum, as well as mutations in SNPs defining biological processes linked
to amyloid-beta and cholesterol formation clearance and regulation, were
identified as contributors to the achieved performance. Overall, our
integrative deep learning approach shows promise for AD detection and MCI
prediction, while shading light on important biological insights.

_K_ eywords Alzheimer’s disease continuum $\cdot$ Generative model $\cdot$
Imaging genetics $\cdot$ Integrated Gradients

##  1 Introduction

Alzheimer’s disease (AD) is a chronic neurodegenerative disorder that affects
millions of people worldwide (approximately 30 million in 2015 [1]. It is the
most common cause of cognitive impairment, gradually impacting the activities
of a patient’s daily life. It is characterized by the progressive loss of
cognitive and functional abilities, including memory, language, and executive
functions [2], with a temporal progression. Amyloid accumulation represents
the first event, followed by tau accumulation, hypometabolism (assessed with
Positron Emission Tomography (PET)), atrophy, and cognitive decline [3, 4]. It
is hence evident that the pathology changes of AD actually begin several years
before the first clinical symptoms. Therefore, a timely AD diagnosis is highly
beneficial for optimizing patient care and enabling appropriate therapeutic
interventions. Mild cognitive impairment (MCI) is the intermediate stage from
normal cognitive function to AD, hence representing an opportunity for an
early targeting of the disease. However, it includes a very heterogeneous
class of patients, including subjects that will likely convert to AD, known as
MCI converters (MCIc), with an estimated annual conversion rate around the
$16.5\%$ [5], and subjects that remain stable after several years, being part
of the MCI non-converters (MCInc) group [6].

Among the available neuroimaging technologies, structural Magnetic Resonance
Imaging (sMRI) and resting-state functional MRI (rs-fMRI) have provided
unprecedented opportunities for deriving biomarkers allowing the early
diagnosis of AD. For instance, sMRI is currently a key part of the diagnostic
criteria for the differential diagnosis and longitudinal monitoring of
patients with dementia, enabling the estimation of brain atrophy. Several
studies have consistently observed both global and local atrophic changes in
AD, lying along the hippocampal pathway (entorhinal cortex, hippocampus,
parahippocampal gyrus, and posterior cingulate cortex) in the early stages of
the disease, while atrophy in temporal, parietal and frontal neocortices
emerges at later stages being associated with neuronal loss as well as with
language, visuospatial and behavioral impairments [7, 8]. Rs-fMRI, in turn,
indirectly measures the neural activity by detecting changes in the Blood
Oxygenation Level Dependent (BOLD) signals, which depend on the neurovascular
coupling [9]. In particular, investigating functional connectivity (FC; inter-
regional coupling), functional network connectivity (FNC; inter-network
coupling), and functional networks from BOLD rs-fMRI provides a means for
understanding the mechanisms and relevance of the functional relationships
across brain regions. A growing body of rs-fMRI studies suggests that failure
of specific resting-state networks (RSNs) is closely related to AD, with the
default-mode network (DM) and the salience network (SN) playing a pivotal role
and being disrupted before clinically evident symptoms [10]. Specific
alterations in these functional networks have been reported in AD patients,
with prominent FC decreased within the DM and increased FC in the SN [11, 12].
Moreover, disconnections within and between the different RSNs have been
consistently demonstrated, particularly over long connection distances [13].
All of these factors have contributed to the widespread view of AD as a
disconnection syndrome being characterized by a cascading network failure,
beginning in the posterior DM and then shifting to other systems containing
prominent connectivity hubs, possibly associated with amyloid accumulation
[14]. Moreover, increased evidence supports the view that tau depositions are
also related to functional brain architecture and FC changes, supporting the
view of transneuronal tau propagation in AD [15].

Moreover, AD also features a strong genetic component. Strategies to extract
linked genotype traits are commonly based on Single Nucleotide Polymorphism
(SNPs) analysis [16], representing variations of single nucleotides in DNA
sequences that vary from person to person [16] and are present in at least
$1\%$ of the population. Several Genome-Wide Association Studies (GWAS) have
identified more than 40 AD-associated genes/loci, which are likely to increase
the risk of developing the disease [17, 18, 19]. Among them the apolipoprotein
E (APOE) gene, in particular the $\epsilon 4$ allele, PICALM, CLU, ABCA7, and
CR$1$ are the most important genes being associated with AD risk factor or the
progression from MCI to AD [20], [21], [22], [23], [24], [25], [26, 27].

This great heterogeneity of available biomarkers offers a unique opportunity
to explore various aspects of the disease continuum. Each biomarker provides
valuable information about specific characteristics, enabling a multifaceted
investigation of AD which calls for methods that can effectively integrate and
leverage complementary information. In this regard, artificial intelligence,
particularly Deep Learning (DL), emerges as a promising technology to tackle
this complex task. By employing multiple layers of processing, DL models allow
extracting progressively high-level and more informative features from input
data. Moreover, the inclusion of multiple data sources into a single model can
uncover complex and deep non-linear associations between the input features
from a multimodal perspective [28]. As a result, multimodality is gaining
significant popularity representing the key approach to gain valuable insights
into complex and multifaceted neurodegenerative diseases such as AD [29],
[30], [31]. However, despite the promising foreseen of such an approach,
multiple drawbacks are present and represent the focus of the current
research. The main concern resides in missing data management. Particularly in
the biomedical domain, it is very common to incur in missing values or
acquisitions for certain subjects or entire study cohorts due to different
reasons, such as missing acquisition, corrupted data, and patients dropout
from a study [32], privacy and expensive tests. Additionally, the
interpretability of a model’s predictions is a central characteristic of
decision-aiding models, which is still not pervasively addressed. In the past
years, many high-performing prediction models have been proposed lacking a
clear rationale to be effectively considered for practical use. Strong and
validated explanations associated with a given prediction are fundamental for
increasing trust in the results as well as their applicability in a real-world
scenario. Innovative and viable missing modality management as well as
interpretability are the key attributes that a multimodal model for diagnosis
detection should have.

Diving into missing data management, the simplest and most common solutions
consist either of discarding samples with missing modalities, or filling the
missing values with zeros [33], and computing imputations based on data
interpolation [34]. Such solutions are evidently suboptimal since they could
significantly reduce the number of training samples, already small when
addressing biomedical-related tasks, or introduce important biases in the data
and the model due to the interpolation or the zero filling. Alternative
methods to exploit the information of all the available subjects were
proposed. A possible approach is the complementation of incomplete data
representation, which consists in extracting a latent representation from both
the complete and incomplete modalities, avoiding the need for data imputation
[35, 36]. Most recent approaches aim at generating missing data either in the
input space [37] or in an intermediate latent representation [38, 39] relying
on generative models such as Generative Adversarial Networks (GANs) [40] and
their variants, or Variational Autoencoders [41]. This last approach has been
successfully applied to the AD continuum investigation. It allows the
exploitation of the availability of multimodal data for capturing the
relationship among different data sources in the latent space, enabling the
generation of one modality from another. Generative models, hence, appear as
the route to be followed when dealing with missing data. Interestingly, the
recently proposed Cycle-consistent GANs (Cycle-GANs) [42] have shown
impressive results in various knowledge translation tasks since they offer a
flexible and effective approach for learning mappings across different domains
without relying on paired data.

Moving to model interpretability, it is well established that with increasing
model complexity, interpretability decreases drastically. However, in order to
better understand the mechanisms that underlie the AD continuum and allow the
models to be applied in clinical and real-life applications, it is vital to
understand the reasons behind a certain output. In this case, Explainable
Artificial Intelligence (XAI), becomes essential to understand why a given
model made a certain prediction. XAI encompasses post-hoc methods that allow
the assignment of an importance score to each feature, reflecting its role in
the classification task. This means finally opening the ‘black box’ of complex
models hopefully increasing their exploitability in clinical practice. XAI is
starting to be applied in multimodal frameworks to study neurodegenerative and
psychiatric diseases. Few works could be found adopting simple gradient-based
or feature perturbation methods [43, 44, 45]. On top of this, another
overlooked yet stringent aspect is the strong validation of XAI methods and
the obtained explanations. The evaluation of explanation methods is still
under-investigated, however, since explainability is meant to increase
confidence in AI, it is vital to systematically analyze the obtained results
referring also to the prior knowledge derived from the state-of-the-art.

In this rapidly evolving landscape, where multimodality holds a central role,
we aim at shading light on the importance of the complementary information
that could be derived from advanced biomarkers such as brain FC and SNPs
mutations, together with the well-established brain atrophy measures derived
from sMRI in detecting AD-related modulations. With this purpose, we will
present a novel multimodal framework for AD detection and MCI conversion
prediction which addresses (i) heterogeneous data integration (ii) missing
data management, and (iii) interpretability. Regarding the former, our
framework allows the integration of heterogeneous data featuring different
dimensionality, e.g., 3D volumes and vectorized data, and nature, meaning from
multi-domain, e.g., imaging and genetics. Concerning the second, we propose an
approach that allows generating missing modalities in the latent space
obtained after input feature reduction, ensuring high accuracy in
reconstructing latent features while minimizing computational demands. The
goal is to define a framework that can be generalized to any missing modality,
without requiring to have at least one specific modality shared by all the
subjects in the considered population. Finally, we aimed at emphasizing the
interpretability of the proposed framework in order to reinforce its
transparency and reliability by conducting a post-hoc interpretability
analysis, supplemented by a robust validation step, which enables to precisely
discern the contribution of each input feature to the classification of
subjects in the AD continuum.

##  2 Material and Methods

###  2.1 Dataset

Data used in the preparation of this article were obtained from the
Alzheimer’s Disease Neuroimaging Initiative (ADNI) database
(https://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 MRI, PET, other
biological markers, and clinical and neuropsychological assessment can be
combined to measure the progression of MCI and early AD. For up-to-date
information, see www.adni-info.org.

An accurate and extensive subject selection was performed to retain, for each
subject, the baseline timepoint for all the selected imaging modalities, that
is sMRI and rs-fMRI. The respective genetic variants (SNPs) were then
selected, if available. The final study cohort included $1911$ subjects,
divided into healthy controls (CN), AD, MCI non-converter (MCInc), and MCI
converter (MCIc). In detail, following the classification available on the
ADNI website, an MCI subject was considered as MCIc if dementia was diagnosed
at any timepoint after MCI diagnosis.

Table 1 shows the AD and CN study cohorts demographic information highlighting
the subjects sharing modalities, in particular, sMRI-fMRI and sMRI-SNPs. Table
2 details the MCI study cohort highlighting the percentage of missing data for
each considered modality.

Table 1: Demographic information of the AD and CN study cohort. MMSE = Mini-
Mental State Examination; wild (W) and mutated (M) alleles in APOE e4: $0$ =
homozygous (W/W), $1$ = heterozygous (W/M), $2$ = homozygous (M/M).

CN AD Cohorts All subjects sMRI and fMRI sMRI and SNPs All subjects sMRI and
fMRI sMRI and SNPs Count $644$ $321$ $253$ $332$ $66$ $152$ Age (y) $73.6\pm
6.6$ $72.4\pm 7.1$ $76.4\pm 5.4$ $75.1\pm 7.9$ $74.7\pm 8.1$ $75.8\pm 7.7$
Gender (M/F) $284/360$ $117/204$ $137/116$ $181/151$ $35/31$ $84/68$ MMSE
$29.1\pm 1.1$ $29.1\pm 1.2$ $29.1\pm 1.1$ $23.1\pm 2.2$ $22.6\pm 2.6$ $23.3\pm
2.0$ APOE e$4$ ($0/1/2$) $455/168/21$ $224/87/10$ $189/57/7$ $109/156/67$
$19/34/13$ $49/76/27$

Table 2: Demographic information and missing data percentage of the MCI study cohort. MMSE = Mini-Mental State Examination; wild (W) and mutated (M) alleles in APOE4: $0$ = homozygous (W/W), $1$ = heterozygous (W/M), $2$ = homozygous (M/M). | MCInc | MCIc
---|---|---
Count | 646 | 289
Age (y) | $73\pm 8.5$ | $74\pm 8.5$
Gender (M/F) |  $374$/$272$ |  $172$/$117$
MMSE | $27.9\pm 1.8$ | $26.9\pm 1.8$
APOE4 ($0/1/2$) | $377/205/64$ | $103/143/43$
Missing SNPs (%) | $59.6\%$ | $30.8\%$
Missing fMRI (%) | $60.1\%$ | $92.0\%$

3D T1-w MRI and rs-fMRI acquisitions were considered as imaging input channels
and were acquired with the following sequence parameters: $1$) sagittal
accelerated MPRAGE, TR/TE = shortest, TI = $900$ ms, flip angle = $9^{\circ}$,
Field Of View = $256\times 256$ mm2, spatial resolution = $1\times 1\times 1$
mm3, slices = $176-211$), $2$) rs-fMRI: TR/TE =$3000/30$ ms, FA =
$90^{\circ}$, FOV = $220\times 220\times 163$ mm3, $3.4$-mm isotropic voxel
size. $200$ fMRI volumes were acquired in almost all subjects, with minimal
variations in a small subset (e.g., $197$ or $195$ volumes). More details
about the data acquisition can be found in [46]. Concerning the genetic data,
DNA samples were genotyped using Illumina Human610-Quad or Illumina
HumanOmniExpress BeadChip.

###  2.2 Preprocessing and feature engineering

The sMRI volumes preprocessing included tissue segmentation in Gray Matter
(GM), White matter and Cerebrospinal fluid (CSF) using the modulated
normalization algorithm. Only the GM volume was considered for this study, to
which a smoothing using a Gaussian kernel (FWHM = $6$mm) was applied. Quality
control (QC) included discarding images that exhibited low correlation with
individual and/or group level masks. The full preprocessed GM volume was used
as input for the sMRI channel resulting in an input size of $121\times
145\times 121$ for each subject.

The rs-fMRI data was preprocessed using the statistical parametric mapping
toolbox (SPM12, http://www.fil.ion.ucl.ac.uk/spm/) including rigid body motion
correction to correct subject head motion, slice-timing correction, warping to
the standard MNI space using the EPI template, resampling to ${(3mm)}^{3}$
isotropic voxels, and smoothing using a Gaussian kernel (FWHM = 6mm),
following the preprocessing proposed in [47]. QC procedure was the same as for
sMRI. Fifty-three independent components (ICs) covering the whole brain were
extracted using spatially constrained ICA with the Neuromark_fMRI_$1.0$
template (available in the GIFT software;
http://trendscenter.org/software/gift). For each subject, a correlation matrix
was then created computing the Pearson correlation between the ICs time
courses, resulting in a $53$x$53$ static functional network connectivity
(sFNC) matrix. This was divided in $7$ RSNs, named: (i) Sub-cortical network
(SC); (ii) Auditory network; (iii) Sensorimotor network (SM); (iv) Visual
network (VI); (v) Cognitive-control network (CC); (vi) Default-mode network
(DM); and, (vii) Cerebellar network (CB) (please, refer to Supplementary Table
2 for more information). The upper triangular matrix was then vectorized
resulting in an input vector of 1378 features for each subject.

Moving to the genomics data, pre-imputation QC was performed to remove Single
Nucleotide Polymorphisms (SNPs) with minor allele frequency (MAF) $<0.05$,
call rate $<0.98$, and Hardy Weinberg Equilibrium $<10^{-3}$ (details in
https://www.synapse.org/#!Synapse:syn2290704/wiki/64710). Imputation was
performed with the same reference panel. Only the SNPs with imputation
$r^{2}>0.4$ were included. Linkage disequilibrium (LD)-based pruning with
$r^{2}=0.8$ in a window of $50$kb was applied, yielding $445838$ SNPs for
further analyses [48]. A feature selection leveraging on the genome-wide
association study (GWAS) on AD conducted by [17] was carried on to include all
the relevant SNPs having GWAS p-values less than $1$e-04. A total of $565$
polymorphisms was selected and a value between 0 and 2 was assigned based on
the presence of mutated alleles. In detail defining wild and mutated alleles
respectively as W and M a score of $0$ means wild homozygous alleles (W/W), a
score of $1$ indicates heterozygous alleles (W/M) and a score of $2$ defines
mutated homozygous alleles (M/M).

###  2.3 Classification tasks

Following the aim of this study, the proposed architecture was devised with a
twofold classification aim: (1) AD detection, that is the differentiation of
AD and CN subjects, also referred as Task 1 and (2) MCI conversion prediction,
that is the stratification of MCIc and MCInc patients, also referred as Task
2. In detail, the network was trained and tested on Task 1 and subsequently
used to solve Task 2 allowing to assess its ability in discriminating
different stages of disease and also in capturing and highlighting shared
patterns across the different categories.

###  2.4 Framework architectures

The proposed framework builds on our previous work [30] and is shown in Figure
1. In detail, the architecture for disease detection consists of three
modules: i) Feature reduction module, which performs a CNN-based feature
extraction to derive a lower dimensionality latent space, separately for each
input channel ii) Generative module that, in the eventuality of missing
modalities, actuates a generative process in the latent space transferring the
knowledge from one domain to another; iii) Data fusion & classification module
that fuses the latent features obtained for the three modalities and then
performs the classification. Post-hoc interpretability analysis was then
carried on in order to retrieve feature contributions to the classification
task. The three modules will be detailed in the following paragraphs.

Figure 1: Schematic representation of the proposed framework. Given three
input modalities, structural Magnetic Resonance Imaging (sMRI), functional MRI
(fMRI) and Single Nucleotide Polymorphisms (SNPs), the framework is
articulated in three different modules: i) A feature reduction module where
the input channels are transformed in their low dimensionality latent
representations; ii) A generative module where, if necessary, the missing
modalities are imputed transferring the knowledge from one domain to another;
iii) A data fusion & classification module where the latent features are fused
together and then classified using a Multilayer Perceptron. Finally, post-hoc
interpretability analysis is performed relying on Integrated Gradients (IG)
method for feature attribution derivation.

##### Feature reduction module

The feature reduction module consists of three different CNNs, one for each
input channel, leading to a latent low dimensionality representation
consisting of $100$ latent features for each channel. The sMRI channel was
analyzed through a 3D CNN defined by three successive convolutional blocks,
each composed of two consecutive convolutional layers (filter sizes of
$3\times 3\times 3$ for the first four convolutional layers and $2\times
2\times 2$ for the last two, number of filters: $64$, $64$, $64$, $128$,
$128$, and $128$, respectively, for the six convolutional layers) and one max-
pooling layer, followed by four fully-connected layers (FCLs) (number of
nodes: $1536$, $768$, $384$, and $192$, respectively).
The rs-fMRI channel was analyzed through a $1$D CNN, composed by four
convolutional layers (filter sizes $5\times 5\times 5$, number of filters:
$64$, $128$, $128$, and $128$, respectively), two max-pooling layers and two
FCLs (number of nodes: $384$ and $100$, respectively).
Finally, for genetic data, a $1$D CNN was employed, consisting of three
convolutional blocks, each including a sequence of convolutional layers
(filter sizes $3\times 3\times 3$, number of filters: $64$, $64$, and $128$,
respectively, for the three convolutional layers), batch-normalization and
max-pooling, followed by three FCLs (number of nodes: $1024$, $512$, and
$128$, respectively).
The ReLU activation function [49] was used for all the layers of these three
CNNs.

##### Generative module

The generative module allows imputing the missing modalities in the latent
space given the others, when necessary. This task is possible thanks to the
injection in the complete framework of four pre-trained generators derived
from two different cGANs [42]. The first, the sMRI-SNPs-cGAN allows imputing
the latent genetics features transferring the knowledge from the latent sMRI
one and vice-versa, and the second, the sMRI-fMRI-cGAN, transfers the
knowledge again from the latent sMRI features to generate the respective rs-
fMRI ones, and vice-versa. An architecture fMRI-SNPs-cGAN was not developed
since the number of subjects that shared both modalities was not sufficient.

The cGANs were built and trained prior to the full framework. In detail, to
obtain the pretrained generators, the first step required to obtain the
channels’ latent representations (i.e., the $100$ features vector for each
modality) needed to subsequently train the cGANs. This was necessary since, as
already highlighted, the proposed framework performs the data generation
directly in the latent space and not in the original input space. Since the
subset of subjects having all three modalities was not numerous enough to
train a classification model, two separate bi-modal models were developed, one
having sMRI and SNPs (sMRI-SNPs-NN) as input channels and the other having
sMRI and rs-fMRI as input channels (sMRI-fMRI-NN). Fig. 2a shows the schematic
representation of the sMRI-fMRI-NN, as a reference example. In order to obtain
the same latent features as the complete framework, the feature reduction for
each channel and the data fusion & classification modules of these bi-modal
models were the same as the ones adopted in the complete framework, and
described in the previous paragraph. Once the latent vectors were obtained,
they were given as input to two cGANs, namely sMRI-fMRI-cGAN and sMRI-SNPs-
cGAN, one for each bi-modal model, and hence for each information transfer,
from sMRI to rs-fMRI and from sMRI to SNPs, respectively. Fig. 2b shows the
sample sMRI-fMRI-cGAN architecture used to generate sMRI from rs-fMRI and
vice-versa. The generators are composed of six FCLs (number of nodes: $256$,
$512$, $512$, $1024$, $512$, and $100$, respectively) activated by a ReLU
activation function. The discriminators consisted of four FCLs (number of
nodes: $256$, $128$, $64$, and $1$, respectively) activated by the LeakyRelu
function [49], alternated with three dropout layers (dropout probability:
$0.3$). The same architecture was considered for the sMRI-SNPs-cGAN.

Figure 2: Schematic representation of a sample bi-modal framework (sMRI-fMRI-
NN) followed by the respective cGAN (sMRI-fMRI-cGAN). (a) The sMRI-fMRI-NN is
composed of two different modules: feature reduction module, equal to the
respective module for each channel in the full framework, and data fusion &
classification module where the latent features are fused together and then
classified. (b) After training, the latent features of both modalities
obtained from the feature reduction module were extracted for each subject and
given as input for the training of the associated cGAN, whose loss is
described in (c) and (d).

##### Data fusion & classification module

The data fusion & classification module consists of a fusion layer and a
classifier. In this module, the latent features obtained either from the data
reduction module or the data generation module (for the subjects with missing
modalities) are fused together through vector concatenation, resulting in
$300$ features. A Multilayer Perceptron (MLP) composed of three FCLs (number
of nodes: $150$, $75$, and $2$, respectively) activated by the ReLU function
was then used for classification. Softmax was used as activation function for
the output layer, allowing to obtain the classification probability associated
with the input data.

###  2.5 Training scheme

Figure 3: Framework training scheme. The training was performed in two steps:
Step 1 involved the training of two bi-modal models (sMRI-fMRI-NN and sMRI-
SNPs-NN, Step 1a) and the respective cGANs (sMRI-fMRI-cGAN and sMRI-SNPs-cGAN,
Step 1b); Step 2 was needed for the training of the complete multimodal
framework.

Figure 3 illustrates the training workflow of the entire framework. As already
specified, the training phase was not performed end-to-end but was divided
into two steps, necessary for the correct training of the generation module:
(i) Step 1: Training of bi-modal models and cGANs; (ii) Step 2: Training of
the full multimodal framework.

Hyperparameter tuning was performed empirically. The number of layers,
channels, nodes, and the filters’ size were tuned considering the single-
modality architectures for the classification (Task 1) before training the
multimodal framework. The weights of the CNNs and classifier, used in both bi-
modal models and the final pipeline, were initialed as follows: the 3D CNN for
sMRI, the 1D CNN for SNPs, and the classifier were initialized using the
Xavier Uniform distribution, while the weights of the 1D CNN for rs-fMRI were
initialized using the Xavier Normal distribution. The weights of the
generators and discriminators were initialized following a Xavier Normal
distribution [50] for both the sMRI-fMRI-cGAN and sMRI-SNPs-cGAN. The weights
initialization was independent between Step 1 and Step 2.

##### Training Step 1: Bi-modal models and cGANs

In the training Step 1 the two sMRI-fMRI-NN and sMRI-SNPs-NN bi-modal models
were trained for the AD and CN classification (Step 1a, Fig. 3) in order to
subsequently extract the latent features to be fed to the two cGANs, sMRI-
fMRI-cGAN and sMRI-SNPs-cGAN(Step 1b, Fig. 3). More in-depth, the bi-model
models and subsequently the cGANs were trained relying on the AD and CN
subjects sharing respectively the sMRI and rs-fMRI acquisition and the sMRI
and SNPs acquisition, presented in Table 1. A $10$-folds stratified Cross
Validation (CV) procedure for a total of $40$ epochs, Adam optimizer [51] with
a learning rate of $0.0001$, and mini-batch technique considering a batch size
of $14$ and $9$ were selected respectively for the training of the sMRI-fMRI-
NN and the sMRI-SNPs-NN. Weighted Cross Entropy (CE) was considered as the
loss function. Differently from the classical CE, it allows computing a weight
guaranteeing higher value to the less numerous class, to address the
unbalanced classes issue. The best model in terms of validation accuracy was
retained for both the NNs and was used to obtain the $100$ latent features for
each subject and for each modality. In detail, the sMRI-fMRI-NN and the sMRI-
SNPs-NN achieved an average validation accuracy of $0.890\pm 0.03$ and
$0.864\pm 0.03$, and then the best models in terms of accuracy for both bi-
modal models were retained for extracting the $100$ latent features vectors
obtained at the end of each feature reduction module for each subject.

The newly obtained feature set was then used to train the two cGANs. A mini-
batch technique, keeping the same subjects in each batch as the bi-modal
models, was used for both the sMRI-fMRI-cGAN and the sMRI-SNPs-cGAN training.
Adam optimizer with a learning rate of $0.0001$ was used to train the
generators for a total of $600$ epochs. As in [42], the adversarial losses
were considered as optimization targets for each cGAN and are represented in
Fig. 2c. In detail, considering the sMRI-fMRI-cGAN as reference, given $s$ and
$f$ the latent feature vector for the sMRI and rs-fMRI, $G_{fs}$ and $G_{sf}$
the generators to obtain $s$ from $f$ and vice-versa and $D_{s}$ and $D_{f}$
the discriminators to distinguish the $s$ from the generated $\hat{s}$ and the
$f$ from the generated $\hat{f}$, respectively, the adversarial loss penalizes
the $D_{s}$ and $D_{f}$ errors in discriminating between $\hat{s}=G_{fs}(f)$
and $s$, and $\hat{f}=G_{sf}(s)$ and $f$, respectively. The major issue
arising when considering this loss solely is that with a large enough
capacity, the generators $G_{fs}$ and $G_{sf}$ can map the same set of input
images to any random permutation of images in the target domain (latent
features in our case) [42]. The cycle consistency losses were hence introduced
to limit the space of possible mapping functions by also penalizing the
difference between $f$ and $G_{sf}(G_{fs}(f))$, and between $s$ and
$G_{fs}(G_{sf}(s))$, respectively, hence completing the cycle (Fig. 2d).

The four pre-trained generators, two for the sMRI-fMRI-cGAN and two for the
sMRI-SNPs-cGAN, were then extracted and injected in the latent space of the
proposed multimodal framework for the on-line generation of the missing
modalities during the full framework training.

Of note, no data leakage was present between the training Step 1 (bi-modal
models and cGANs) and the training Step 2 (full multimodal framework) since
Step 2 involved end-to-end training of subjects with no missing modalities
(i.e., using input data for these subjects only) and generative models trained
in Step 1b for deriving latent features for subjects with missing modalities
only. Of note, the full cohort of subjects was not used to train the bi-modal
models and corresponding cGANs (Step 1a and 1b), only relying on those
subjects sharing the modalities under analysis (sMRI and rs-fMRI for sMRI-
fMRI-NN/cGAN, and sMRI and SNPs for sMRI-SNPs-NN/cGAN).

The cycle consistency loss was used in both sMRI-fMRI-cGAN and sMRI-SNPs-cGAN
in order to assess the performance of the generators in imputing missing
modalities using the Mean Absolute Error (MAE).

##### Training Step 2: Full multimodal framework

The full multimodal framework including the three input channels, sMRI, rs-
fMRI, and SNPs, was trained for classification Task 1, AD detection, relying
on the complete AD and CN data cohort.

Subjects were split into training and testing sets, respectively, including
the $80\%$-$20\%$ of the study cohort. The testing set was kept unseen until
the last testing phase. A stratified $10$-fold CV procedure was applied to the
training set. A mini-batch strategy ($12$ subjects in each batch) was adopted
during training. Adam optimizer with a learning rate of $0.0001$ was chosen
and the model was trained for a total of $70$ epochs. Weighted CE was
considered as the loss function. During this training phase, the four pre-
trained cGAN generators’ weights were kept frozen. Indeed, during the
backpropagation phase, only the weights of the feature reduction module and
the data fusion and classification module were updated.

####  2.5.1 Testing and performance evaluation

The best model, in terms of validation accuracy, obtained from the CV
procedure of training Step 2 was considered for the testing phase for the two
classification tasks presented in Section 2.3. The testing set retained from
the AD and CN study cohort splitting was used for classification Task 1, AD
detection. The full MCI cohort, never considered during the training phase,
hence kept completely unseen by the model, was considered as a testing set for
the classification Task 2, MCI conversion prediction. The framework was
finally evaluated in terms of accuracy (ACC), precision (PRE), recall (REC),
F$1$ score, Area Under Precision Recall Curve (AUPRC), and Area Under the
Curve (AUC) on both testing sets for the two classification tasks.

Five independent runs reshuffling the train and test sets were performed for
probing the generalization capabilities of the model, and the average test
performance over the different runs was retained. All the training and testing
described were performed in Python, specifically relying on the Pytorch
library [52].

##  3 Post-hoc interpretability analysis

The post-hoc interpretability analysis was performed relying on Integrated
Gradients (IG) [53], aiming at obtaining attribution maps describing the
relevance score associated with each input feature on the different input
channels. IG maps were derived for the subjects in the testing set of the best
model over the five generalization runs for both the classification tasks
(Task 1: AD detection and Task 2: MCI prediction conversion, which coincides
with the full MCI cohort). A brief introduction of the IG method and its
properties followed by the attribution analysis performed for each input
channel will be given in the following sections.

###  3.1 Integrated Gradients (IG)

Integrated Gradients (IG) [53] is an interpretability method allowing to find
the relevance of the input features with respect to the prediction of the
model without requiring any modification to the network under analysis. It is
a Baseline Attribution Method (BAM) [54]. To obtain feature attributions, IG
computes the path integral of the gradients along the straightline path from a
given baseline $x^{\prime}$ to the input $x$ [53] following the equation

$\centering
IG_{i}(x)::=(x_{i}-x_{i}^{\prime})\times\int_{\alpha=0}^{1}\frac{\partial
F(x^{\prime}_{i}+\alpha\times(x_{i}-x^{\prime}_{i}))}{\partial
x_{i}}d\alpha\@add@centering$ (1)

where $F$ is the model and $\alpha$ is a factor ranging in [$0,1$],
determining the steps along the straightline path from $x$ to $x^{\prime}$.

This method is gaining high popularity among the post-hoc interpretability
methods since it satisfies three important axioms: (i) Sensitivity, for which
a null score is given to the input features which do not contribute to the
prediction; (ii) Implementation invariance, hence given a certain input, the
derived attributions for two functionally equivalent networks are as well
equivalent; and (iii) Completeness, which ensures that the attributions
approximately add up to the difference between the input and the baseline
prediction scores [53].

Following the definition, IG attribution scores can assume both positive and
negative values. The higher or lower the value of a given feature is, the
higher its contribution to the prediction outcome is, either with a positive
or negative effect.

It is evident how the baseline choice impacts on the obtained attribution
maps. Some recent studies have investigated this issue in order to raise
awareness among the users and show the impact of different baselines on the IG
scores obtained for the same input and model [55, 56, 57]. Of note, the main
requirement for the baseline is to represent a neutral input for the model
under investigation. In other words, it should produce a zero score or,
equivalently, around $0.5$ prediction probability for both classes resulting
from the activation function of the final classification layer. For the
proposed framework, a triplet of neutral baselines, one for each input
modality, was selected after exhaustive empirical research, defined as
follows: (i) $3$D matrix of zeros for sMRI; (ii) 1D vector of zeros for rs-
fMRI; and (iii) 1D vector of Gaussian noise for SNPs, which allowed on average
to obtain random classification scores.

###  3.2 IG feature attribution analysis

IG allows obtaining attribution maps for each input and channel, which lay in
the same input space. In our study IG was applied on the testing set of each
classification task, resulting in a triplet of attribution maps representing
sMRI, rs-fMRI, and SNPs feature attributions lying in the same space as the
input data, for each subject and task. The different maps will be referred to
as sMRI-IG, fMRI-IG, and SNPs-IG in what follows.

####  3.2.1 Neuroimaging

In order to retain the most relevant features, an initial sMRI-IG map
thresholding was carried on, selecting only the attribution values exceeding
in absolute value the $99.5^{th}$ percentile of the respective IG values
distribution voxelwise. The average sMRI-IG values for $55$ cortical and
subcortical brain regions based on the Harvard-Oxford atlas [58] were then
extracted for all the subjects in the testing sets of both classification
tasks. Only the regions where at least $99\%$ of the subjects had average
values exceeding the percentile threshold were kept for subsequent analysis.

Moving to the fMRI-IG, only the connections whose attribution scores were in
absolute value above the $98^{th}$ percentile of the respective IG value
distribution connection-wise were considered for further analysis. Different
thresholds were chosen between the IG maps due to the different input sizes.

A statistical group-based analysis was then performed considering the
attribution maps derived for each class, namely CN, MCInc, MCIc, and AD.
Shapiro-Wilk test of normality [59] was initially performed on the sMRI-IG and
fMRI-IG derived features, revealing non-normally distributed features. The
non-parametric Kruskal-Wallis test [60] was hence performed to check the
statistical difference across the four classes considered in each feature
derived either from rs-fMRI (most relevant connections resulting from fMRI-IG)
or sMRI (most relevant brain regions derived from the sMRI-IG). When
significance was found, the pairwise Wilcoxon Rank Sum Test [61] was performed
between all the possible couples of the four considered groups (AD-CN, AD-
MCIc, AD-MCInc, CN-MCIc, CN-MCInc, MCIc-MCInc) and adjusted for multiple
comparisons with Bonferroni correction. All the statistical analyses were
performed in R.

####  3.2.2 Genetics

Only the SNPs with attribution greater than the $65^{th}$ percentile of the
SNPs-IG distribution, hence those having positive attribution, were kept. The
Ensembl Variant Effect Predictor (VEP) tool [62] was used to annotate the
selected SNPs in their corresponding genes. Web interface of VEP
(https://useast.ensembl.org/Tools/VEP) and default settings were used to run
the analysis. Selected settings included finding the co-located known variants
and 1000 Genomes global minor allele frequency as frequency data for co-
located variants parameters. No filtering was applied to the analysis to not
exclude relevant biological data. Enrichment analysis was then performed using
the clusterProfiler package in R [63] to derive the most important biological
processes in which the annotated genes were represented. A background of
$16714$ genes was selected by annotating the whole SNPs-set of the GWAS study
used for feature selection of the input data. The enrichment results were
corrected with the Benjamini-Hochberg procedure. The SNPs annotation, as well
as the enrichment analysis, was computed only on the classes of patients,
namely the AD, MCInc, and MCIc individuals.

##  4 Results

Classification performance and IG attribution analysis results will be firstly
presented separately for classification Task 1 and Task 2. An overview of the
overall group-based analysis will then follow.

###  4.1 Task 1: AD detection

The generators for both sMRI-fMRI-cGAN and sMRI-SNPs-cGAN models were tested
by computing the MAE across the validation sets to compare the true latent
space and the reconstructed one. For the sMRI-fMRI-cGAN, the generators
achieved a MAE of $0.065\pm 0.01$ and $0.074\pm 0.01$ for the fMRI and the
sMRI modalities, respectively. Meanwhile, the sMRI-SNPs-cGAN generators
reached a MAE of $0.506\pm 0.04$ and $0.333\pm 0.10$ for SNPs and sMRI data,
respectively.

The proposed framework reached $0.926\pm 0.02$ in ACC, $0.910\pm 0.05$ in PRE,
$0.876\pm 0.03$ in REC, $0.891\pm 0.03$ in F$1$ score, $0.829\pm 0.03$ in
AUPRC, and $0.960\pm 0.01$ in AUC for the differentiation between AD and CN
subjects. Of note, the best model over the five generalization runs reached
$0.964$ in ACC, $0.984$ in PRE, $0.909$ in REC, $0.945$ in F$1$, $0.876$ in
AUPRC, and $0.970$ in AUC.

####  4.1.1 Feature relevance

Figure 4: Overview of IG attribution maps for the classification Task 1, AD
detection. All the IG maps are presented for the correctly classified CN and
AD subjects in the testing set. A. Average sMRI-IG maps, thresholded to retain
IG scores exceeding the $99.5^{th}$ percentile and overlaid to MNI$152$
template; B. Average fMRI-IG derived connectograms, thresholded to retain the
connections with an associated IG score over the $98^{th}$ percentile; C.
Average SNPs-IG scores highlighting the SNPs with an associated positive IG
score exceeding the $65^{th}$ percentile, SNPs are grouped by chromosome.

Fig. 4 shows the average IG maps obtained for the AD detection task and for
each input channel, averaged over the correctly classified subjects per class
(test set). The jet colorbar was used to highlight the attribution scores,
where red and blue correspond to positive and negative attribution values,
respectively. In detail, Fig. 4A shows the average sMRI-IG maps for the
correctly classified CN and AD patients, overlaid onto the MNI$152$ template
(1.5 mm). A thresholding was applied in order to visualize only the relevance
scores above the $99.5^{th}$ percentile of the relevance distribution,
followed by a Gaussian smoothing with FWHM = 3 mm for visualization purposes.
It is evident that the subcortical regions, in particular the hippocampus, are
associated with high IG scores in absolute value, with the highest positive
(negative) values for CN (AD). Cortical regions generally showed almost null
relevance for both the CN and the AD-derived sMRI-IG maps. Of note, higher
absolute values were found for the AD maps compared with the CN ones.

Moving to the fMRI-IG qualitative analysis, Fig. 4B shows the average
connectograms for CN and AD subjects, including only the connections above the
$98^{th}$ percentile of the relevance distribution. The ICs-brain region
correspondences are detailed in Supplementary Table $2$.

The most relevant RSNs were the primary information processing-related
networks (SM and VI) followed by multisensory integration networks (CC and
DM), and cerebellum (CB), showing high relevance for both the CN and the AD-
derived fMRI-IG. In particular, the $53$% of the most relevant connections for
the CN group belong to the SM network, as opposed to the $38$% found for the
AD-derived fMRI-IG maps. On the other hand, the VI was highly involved for AD
subjects, with the $28$% of relevant connections belonging to this RSN,
differently from the CN where only $2$ VI ICs resulted as relevant. Of note, a
total of $15$ ICs were marked as relevant for both the CN and the AD-derived
fMRI-IG, but with an opposite sign.

More in detail of the relevant connections between the different ICs, the CN
subjects showed positive relevant intra-network connections in the CB and SM
RSNs, with particularly high scores for the connections involving the
post/paracentral and parietal gyri (ICs $9,10,11,12,13$). Inter-network
positively relevant connections were also found between the SM and the CB, and
the SM and the CC RSNs. Only two negative IG scores were instead retrieved,
related to an intra-network connection in the VI network and to an inter-
network connection between CC and DM.

A similar pattern was found for the AD fMRI-IG relevant connections but with
generally opposite IG-associated scores. In detail, negative relevance was
mainly found for both the intra- and inter-network connections encompassing
the SM and CB RSNs, with an intra-connection in SM (ICs $11-12$) showing the
highest negative relevance between the same ICs highlighted with the opposite
sign in the CN. On the contrary, positive relevance was recorded for the
connections between multiple VI ICs, in particular involving right middle
occipital gyrus (IC $21$) with cuneus (IC $20$), inferior occipital gyrus (IC
$23$), and middle temporal gyrus (IC $25$) as well as the inter-network
connections VI-DM and CC-DM, with the latter being the most relevant one.

Finally, concerning the SNPs-IG qualitative analysis, Fig. 4C presents a
Manhattan plot including only the SNPs with an attributed positive IG score
higher than the $65^{th}$ percentile, grouped by chromosome. The y-axis
reports the associated IG score. A complementary trend between the IG values
associated with the SNPs was found between the two classes. This was
particularly evident for Chr $1$, $7$, $11$, $14$, $15$ and $19$. A generally
high involvement of the Chr $7$, $8$, $11$, $14$, and $19$ was present for
both the AD and CN, with the majority of SNPs selected in these Chr showing
high IG scores, either positively or negatively. Of interest, the most
relevant SNPs, with positive IG were found in Chr $4$, $7$, and $8$ for the CN
and in Chr $12$ and $14$ for the AD. On the contrary, the most negatively
relevant SNPs for CN were found in Chr $14$ and $19$, as opposed to AD where
they were mainly in Chr $1$, $6$, and $7$.

###  4.2 Task 2: MCI conversion prediction

The MCI prediction task was performed by testing the full MCI cohort on the
best model obtained for the AD detection task, for each one of the five
independent runs. This allowed to assess its viability in predicting MCI
conversion to AD, by correctly stratifying MCIc and MCInc subjects, without
being trained for the specific task. This procedure allowed to reach an ACC of
$0.711\pm 0.01$, a PRE of $0.558\pm 0.03$, a REC of $0.610\pm 0.03$, $0.581\pm
0.01$ in F$1$ score, $0.470\pm 0.02$ in AUPRC,and finally an AUC of $0.755\pm
0.01$ for the differentiation between MCIc and MCInc. Regarding the
performance retrieved using the best model trained on the classification Task
1, we achieved $0.711$ in ACC, $0.612$ in PRE, $0.550$ in REC, $0.579$ in F$1$
score, $0.505$ in AUPRC, and $0.766$ in AUC.

####  4.2.1 Feature relevance

Figure 5: Overview of IG attribution maps for the classification Task 2, MCI
conversion prediction. All the IG maps are presented for the correctly
classified MCIc and MCInc subjects in the testing set. A. Average sMRI-IG
maps, thresholded to retain IG scores exceeding the $99.5^{th}$ percentile
overlaid to MNI$152$ template; B. Average fMRI-IG derived connectograms,
thresholded to retain the connection with an associated IG score over the
$98^{th}$ percentile; C. Average SNPs-IG scores highlighting the SNPs with an
associated positive IG score exceeding the $65^{th}$ percentile, grouped by
chromosome.

In parallel with the results shown for Task 1, Fig. 5 shows a summary of the
IG results obtained for the MCI conversion prediction task. The same
visualization techniques presented for Task 1 were applied also for this
figure. The maps were averaged over the correctly classified subjects for each
class, the jet colorbar was used to highlight the attribution scores, and
thresholding was applied to retain only the values above the $99.5^{th}$,
$98^{th}$ and $65^{th}$ percentile of the relevance distribution, respectively
for the sMRI-IG, fMRI-IG, and the SNPs-IG. The sMRI-IG maps were smoothed and
overlaid onto the MNI$152$ template. In detail, Fig. 5A shows the average
sMRI-IG maps for the correctly classified MCIc and MCInc patients. Similarly
to what was shown for Task 1, the subcortical regions held the highest
relevance, with the hippocampus being clearly highlighted as the most
important region with positive attributions for MCInc and negative values for
MCIc. Cortical regions did not show particular relevance, except for some
temporal and occipital areas, which however showed low IG scores.

Moving to the fMRI-IG, Fig. 5B shows the averaged connectograms. In accordance
with Task 1, the same five RSNs resulted as the most relevant also for the MCI
prediction conversion task, namely the SM, VI, CC, DM and CB. The MCInc fMRI-
IG showed more involvement of VI ($25$% of the relevant ICs), compared with
the MCIc one ($14$% of the relevant ICs). On the contrary, the MCIc IG
connectome showed a higher number of ICs belonging to the CC network ($4$ ICs)
compared to the two found for the MCInc one. Of note, the two connectograms
had $11$ common connections with opposite trends.

More in details of the relevant connections between the different ICs, of
interest, the most relevant connections between the ICs in the SM were exactly
the same for MCIc and MCInc, with opposite signs, and mainly involved the
post/paracentral and parietal gyri (ICs $9,10,11,12,13$), as for Task 1.
Moreover, the fMRI-IG for the MCInc subjects showed positive relevance also
for the intra-network connections in the CB, and for the inter-network
connections involving CB-SM and CC-SM. On the other hand, negative relevance
was found for the intra-network connections in the VI, mainly involving
occipital, lingual, calcarine, middle temporal gyri, and cuneus areas (ICs
$17-24$, $18-20$, $21-25$, $23-24$), and for the inter-network connections
between VI and DM, and CC and DM. A slightly different pattern was found for
the MCIc fMRI-IG, whose relevant connections generally had a negative IG-
associated score. In detail, intra-network connections with negative scores
were found for SM and CB, as already presented, while inter-network negative
connections were depicted for VI-CC, VI-DM, and SM-DM. Of interest, negative
connections between CC and SM were also retrieved, never reported for the
other classes in the study. Positive attribution was found only for an intra-
network connection in the VI (ICs $23-24$) and a connection between CC and DM
(ICs $28-45$).

Finally, concerning the SNPs-IG, Fig. 5C presents a Manhattan plot
highlighting the SNPs with an attributed positive IG score higher than the
$65^{th}$ percentile. As expected and as already seen for the other
modalities, a complementary trend between the IG values associated with the
SNPs was found for the two classes, with positive weights being associated
with the MCInc and negative weights associated with the MCIc for the same SNPs
and vice-versa. This was particularly evident for Chr $1$, $2$, $7$, $14$,
$15$ and $17$. A generally high involvement of the Chr $11$ and $17$ was
present for both the MCIc and MCInc, with the majority of SNPs showing high IG
scores. Of interest, the most relevant SNPs, with positive IG were found in
Chr $17$ for the MCInc and in Chr $15$ for the MCIc. On the contrary, the most
negatively relevant SNPs for MCInc were found in Chr $14$, $15$, and $17$, as
opposed to the MCIc where they were mainly in Chr $1$, $2$, and $7$.

Figure 6: Overview of the neuroimaging statistical analysis. A. Boxplots
showing the CN, AD, MCInc, and MCIc correctly classified subjects distribution
in the most relevant cortical and subcortical brain regions, resulting from
the sMRI-IG; B. sMRI-IG Wilcoxon test results for each group comparison and
each brain region, divided into cortical and subcortical regions; C. fMRI-IG
Wilcoxon test results for each group comparison for each relevant brain
connection divided into extra- (upper) and intra-network (lower) connectivity.
The p-values for B. and C. are reported in negative logarithmic scale, dark
red the most significant. White cells represent no statistical significance.

###  4.3 Group-based statistical IG analysis

The IG scores obtained for the four groups of subjects in the study were
analyzed together in order to quantify the differences and similarities
outlined in the qualitative analysis. In what follows, the statistical
analyses will be presented separately for the neuroimaging (sMRI and rs-fMRI)
and the genetic channels.

##### Neuroimaging channels

Figure 7: Enrichment analysis results. The top $15$ biological processes are
reported for the three classes of patients, namely AD, MCIc, and MCInc
(columns). The enrichment analysis was performed over the genes annotated from
the SNPs-IG. The colorbar represents the associated p-value, dark red the
lowest, while the number of genes involved is reported as the bar height. The
* symbol indicates the biological processes statistically significant after
p-value correction.

Fig. 6A shows the boxplots representing the distribution of the average IG
values for each subject in the most relevant cortical and subcortical brain
regions (ROIs). Of note, only those regions where at least the $99\%$ of the
subjects had an IG value were selected for these analyses. The complete
acronym list is reported in Supplementary Table 1. A general agreement between
the CN and the MCInc subjects, as well as between the AD and the MCIc patients
is evident in all the considered ROIs, with the AD/MCIc subjects showing a
generally higher variance. As expected from the qualitative analysis, the Hipp
and the Amy resulted as the highest relevant ROIs, as well as the ones showing
the highest distance between the groups, with high positive attribution for
the CN and the MCInc, and strong negative attribution for the AD and MCIc.
Among the other subcortical ROIs, the Acc showed a notable relevance for all
the groups, with the MCInc and CN having negative scores and the MCIc and AD
positive ones. Cau and Put had an associated high positive relevance for AD
and MCIc, while almost null scores for the other two groups. Interestingly,
among the cortical regions, the TOF was the most relevant region for both the
MCIc and AD (positive IG scores) and the MCInc and CN (negative IG scores).
The highest distance between the group IG scores distributions was found for
PhGa, followed by the TFCp with the AD and MCIc having high negative scores.
On the contrary, the OFG, the POpC, and the PaGp showed high positive
relevance for AD and MCIc patients associated with negative scores for the CN
and MCInc.

In order to evaluate whether these differences were significant, a Kruskal-
Wallis test was performed separately for each ROI, considering the four groups
together. The significant ROIs (all except the Ins and the TP) were further
analyzed to investigate the group-related differences through the Wilcoxon
Rank Sum test. Results are shown in Fig. 6B. The heatmap reports the
Bonferroni corrected p-values ($6$ pairwise comparisons) in logarithmic scale
and reverse hot colorbar (yellow/red correspond to higher/lower p-value, white
stands for the non-significant comparisons). The most significant differences
were found between MCIc and MCInc in the subcortical ROIs, resulting as
generally significant (except for Put and Pall) with the lowest p-values being
recorded for Hipp and Amy. Moreover, significant differences were also
recorded for the temporal (PcC, PhGa, PaGp, TFCp) and occipital (TOF, OFG,
POpC) cortical regions, with the most significant difference being recorded
for PcC and PhGa. A coherent significance pattern was found between the
contrasts MCIc-CN, MCInc-AD, and the CN-AD with generally higher p-values. Of
interest, no statistically significant differences were found in the sMRI-IG
scores distributions between AD and MCIc patients, except for PcC, TFCp, and
POpC, while some significant differences were found between CN and MCInc but
with relatively high p-values.

The same statistical analysis was carried out for fMRI-IG, considering all the
most relevant connections resulting from the fMRI-IG scores for all the
considered classes. The connections between IC$18$ (VI) – IC$14$ (SM) and
IC$44$ (DM) – IC$17$ (VI) did not reach significance at the Kruskal-Wallis
test, therefore they were excluded from the post-hoc analysis. The Bonferroni-
corrected pairwise tests (Wilcoxon rank sum) are reported in Fig. 6C,
separately for intra- and inter-network connections, with the p-values being
represented in logarithmic scale. The related boxplots are reported in
Supplementary Fig. $1$. Opposed to the sMRI-IG significance pattern, the most
significant differences were found between the CN-AD and MCInc-AD contrasts,
which showed significant differences for almost all the connections
considered. In particular, for the MCInc-AD contrast, significant intra-
network connections were part of the SM, involving connections in the parietal
lobe, and in the VI RSNs. Concerning the inter-network connection,
significance was found between ICs in the DM, part of the cingulate gyrus
(IC47, IC45), and ICs in the CC or VI RSNs, as well as between ICs in the SM,
located in the parietal lobe and ICs in the CC or CB RSNs. MCIc-CN and MCInc-
MCIc showed the same significant pattern as the CN-AD contrast, showing
generally higher p-values. Of interest, as for the sMRI-IG statistical
analysis, no significant differences were detected for the contrasts MCIc-AD
and MCInc-CN, except for two connections between CB and SM (IC51-IC9 and the
IC51-IC12 respectively for the MCInc-CN and the MCIc-AD).

##### Genetic channel

Finally, Figure 7 shows the biological processes derived from enrichment
analysis for AD, MCIc and MCInc classes, considering for the gene annotation
step only the SNPs having positive attributions higher than the $65^{th}$
percentile. Supplementary Tables $3$, $4$, and $5$ show additional
information, such as the most frequent genes, the GO index, and the
corresponding raw and adjusted p-value for each significant biological
process. The most significant biological processes were found for MCIc. Among
these were biological processes related to amyloid-beta ($A\beta$), e.g., the
amyloid-beta formation and amyloid-beta metabolic process. Of interest, other
biological processes relevant to MCIc were related to the cholesterol and
lipoprotein/phospholipid, such as cholesterol efflux, regulation of sterol
transport, regulation of cholesterol transport, protein-lipid complex
assembly, phospholipid efflux, and plasma lipoprotein particle organization.
The AD-related biological processes were principally related to A$\beta$
regulation, such as regulation of metalloendopeptidase activity involved in
amyloid precursor protein catabolic process, negative regulation of
metalloendopeptidase activity involved in amyloid precursor protein catabolic
process, positive regulation of amyloid fibril formation, negative regulation
of amyloid precursor protein catabolic process, regulation of aspartic-type
endopeptidase activity involved in amyloid precursor protein catabolic
process, and regulation of amyloid-beta formation (the last three were not
statistically significant after correction, but they were considering the raw
p-value). The most frequent genes present in these biological processes, for
both AD and MCIc, and hence being among the SNPs-IG annotated ones, were APOE,
PICALM, SORL1, ABCA7, APOC1, and APOA2. The MCInc-related biological processes
showed a major difference from the other two groups. In detail, the biological
pathways were mostly related to the regulation of the complement activation or
immune response, B cells, and leukocytes. For this group and the obtained
biological processes, the most frequent genes were CR1, CR1L, FCER1G, ERCC1,
and PLCG2.

##  5 Discussion

With this work, we proposed a novel multimodal generative and interpretable
method, which holds the potential of addressing missing data management while
focusing on model interpretability. We specifically applied this method to the
crucial tasks of diagnosing AD and assessed its viability in detecting also
MCI conversion to AD. By integrating neuroimaging (sMRI and rs-fMRI) and
genetics (SNPs) data through DL-based feature extraction, we introduced a
novel multimodal data fusion framework, relying on input data not yet
simultaneously investigated in the AD continuum in the current literature.
Incomplete data is handled by generating missing modalities in the latent
space, obtained after feature reduction. This ensures high accuracy in
reconstructing latent features while minimizing computational demands. To
accomplish this, we relied on pre-trained generators from two cGANs, one
trained to generate sMRI and SNPs data, and the other to generate sMRI and rs-
fMRI modalities. The approach is however generalizable to any missing
modality. The framework is trained to detect AD in a cohort including CN and
AD subjects, while its generalization capabilities were then tested by
predicting MCI conversion to AD in an independent study cohort. Furthermore,
we meticulously conducted a post-hoc interpretability analysis, supplemented
by a robust validation step, consolidating the findings’ impact in the field.
In this section we will first give a technical discussion focused on the
classification accuracies and the missing data management, we will then
discuss the interpretability analysis and the obtained results from a more
neuroscientific point of view.

Table 3: Comparison of the proposed model with other state-of-the-art methods
dealing with missing modalities for AD detection and MCI conversion tasks.

(a) AD detection task. Accuracy (ACC), precision (PRE), and recall (REC)
metrics are reported on the test set or averaged during the cross-validation
phase ($mean\pm std$).

Authors Modalities Study cohort Input data Missing data rate Missing data
management ACC REC PRE XAI [33] sMRI, Genetics, Clinics 1406 PAT (266 AD, 699
MCI), 598 CN Full MRI volume WGS data, Set of clinical scores $\sim 67\%$
missing sMRI $\sim 61\%$ missing SNP Feature exclusion if the 70% had missing
value Zero filling for the others $0.630^{*}$ $0.780^{\dagger}$ $0.570^{*}$
$0.780^{\dagger}$ $0.620^{*}$ $0.770^{\dagger}$ Yes [35] sMRI, FDG-PET 85 AD,
90 CN ROI based features $50\%$ missing PET Auto-Encoder for the
complementation of complete and incomplete latent representation $0.836\pm
0.08$ n.d. n.d. No [38] sMRI, FDG-PET 352 AD, 427 CN sMRI and PET volumes
$30\%$ missing PET Task-induced pyramid and attention generative adversarial
network (TPA-GAN) $0.927$ $0.917$ n.d. No [64] sMRI, FDG-PET 160 AD, 210 CN
ROI based features for VBM, FDG 50% missing PET GAN with attention layer in
latent space $0.914\pm 0.19$ $0.881\pm 0.11$ n.d. Yes Proposed framework sMRI,
fMRI, Genetics $332$ AD, $664$ CN GM volume sFNC matrix, SNPs $\sim 59\%$
missing fMRI $\sim 57\%$ missing SNPs Multiple cGANs to generate missing
latent representation $0.926\pm 0.02$ $0.876\pm 0.03$ $0.910\pm 0.05$ Yes

(b) MCI conversion prediction. Accuracy (ACC), precision (PRE), and recall
(REC) metrics are reported on the test set.

Authors Modalities Study cohort Input data Missing data rate Missing data
management Trained on the specific task ACC REC PRE XAI [34] $10$ modalities
including imaging and clinics 86 MCIc 237 MCInc Tabular features $\sim 8\%$
missing features Mean imputation and imputation by the EM Yes $0.670$ n.d.
n.d. No [37] sMRI, FDG-PET 76 MCIc 128 MCInc GM volume PET volumes $50\%$
missing PET 3D encoder-decoder network to generate the full PET volume Yes
$0.657$ n.d. n.d. No [39] sMRI, FDG-PET Genetics 157 MCIc 205 MCInc ROI based
features for PET and MRI, SNPs $51\%$ missing PET Latent representation
learning without missing data imputation Yes $0.743$ n.d. n.d. Yes [38] sMRI,
FDG-PET 234 MCIc 342 MCInc sMRI and PET volumes $30\%$ missing PET Task-
induced pyramid and attention generative adversarial network (TPA-GAN) Yes
$0.753$ $0.708$ n.d. No Proposed framework sMRI, fMRI, Genetics 289 MCIc 646
MCInc GM volume sFNC matrix, SNPs $\sim 76\%$ missing fMRI $\sim 45\%$ missing
SNPs Multiple cGANs to generate missing latent representation No $0.711\pm
0.01$ $0.610\pm 0.03$ $0.558\pm 0.03$ Yes

∗ CN vs PAT (AD+MCI) classification relying only on sMRI and SNPs, † Three
classes classification, CN vs MCI vs AD relying on the three modalities

###  5.1 Classification performance and missing data management

Focusing on the Task 1, AD detection, our model reached the state-of-the-art
performance, obtaining an average testing accuracy of $0.926\pm 0.02$, with
the best model reaching an accuracy score of $0.964$. This achievement is even
more noteworthy considering that only $12\%$ of the subjects had complete data
across all three modalities. Of note, our dataset was constructed considering
the subjects that at least had the sMRI modality, however, our proposed
framework showcases the capability to potentially impute all three modalities
by transferring knowledge across domains, not being limited to having at least
one acquisition for all the subjects. Indeed, the injection of the pre-trained
generators, that is the two cGANs, allows both to impute the missing rs-fMRI
or SNPs from the sMRI and the vice-versa, meaning that it would allow deriving
the missing sMRI from the other two modalities if needed. This allows relaxing
the requirement of having at least one acquisition for all the subjects which
is one of the strengths of the proposed model compared with the state-of-the-
art.

Table 3(a) shows the performance of the proposed model compared with the
state-of-the-art in detecting AD, considering works allowing multimodality and
missing data management. The simplest model [33] proposed a DL-based
multimodal method based on sMRI, clinics, and genetics, excluding features if
missing in more than $70\%$ of subjects and filling the remaining missing data
with zeros. Their classification task was different from ours since they
included the MCI subjects in a three-class classification task. While they
achieved an accuracy of $0.780$ for the classification between CN, MCI, and
AD, the accuracy dropped to $0.630$ when classifying CN from the full patient
cohort using only sMRI and genetics. Moreover, the proposed technique has some
drawbacks, mainly linked to the biases introduced in the network, as already
discussed.

Alternatively, methods to exploit the information of all the available
subjects, without explicitly generating the missing modalities were proposed
relying on latent representation learning. [35] developed an Auto-Encoder-
based multi-view missing data completion framework using sMRI and FDG-PET ROI-
based features. Their method achieved a classification accuracy of $0.836$ for
classifying CN versus AD, even with $50\%$ missing PET. Similarly, [64]
proposed a GAN with an attention layer to generate missing FDG-PET from
available MRI features, resulting in a classification accuracy of $0.914\pm
0.19$. While these approaches demonstrated excellent results, their framework
was limited in handling arbitrary missing modalities, allowing only the
completion of missing PET from available sMRI and FDG-PET features.

Finally, [38] presented a task-induced pyramid and attention generative
adversarial network (TPA-GAN) to generate missing FDG-PET data from sMRI,
achieving an accuracy of $0.927$. However, the model was trained and tested on
two independent databases with different acquisition protocols, which on one
side allowed to evaluate the generalizability of the model, but on the other
could bias the results due to the different data source. Moreover, it still
lacked the ability to reconstruct sMRI from FDG-PET data. Despite the
aforementioned limitations, they are currently the state-of-the-art
performance for multimodal MCI conversion prediction, accounting for the 30%
of missing PET data.

To address classification Task 2, we directly tested the model trained for
Task 1 on the MCI cohort. Only the $11\%$ of the dataset shared all the
modalities, making it a challenging scenario. Nevertheless, our framework
achieved an average accuracy of $0.711\pm 0.01$ for the independent test sets.
Although it did not outperform methods specifically trained on this particular
task, it demonstrated competitive results. Other approaches have focused on
different input data and missing data management to solve this task. For
instance, [34] proposed simple machine learning methods with tabular features
and limited imputation techniques, achieving an accuracy of $0.670$ to
stratify MCI subjects. [37] used a GAN to impute missing PET images from sMRI
scans, achieving an accuracy of $0.657$ for discriminating MCInc vs MCIc
patients. Furthermore, [39] proposed a framework for projecting original
features into a latent representation, resulting in an accuracy of $0.743$
considering a 51% of missing PET. Finally, [38] applied the approach already
discussed also to address the classification Task 2, MCI conversion prediction
reaching the best accuracy score of $0.753$.

Despite the promising results obtained by generative models for missing data
imputation, it is essential to acknowledge their shared limitation: they all
relied on having sMRI as a prerequisite to impute PET data, and very few
included genetics or rs-fMRI information in their analyses, which have instead
been demonstrated as relevant biomarkers for AD [10, 15]. In contrast, our
framework does not necessitate a common modality shared by all subjects.
Utilizing two cGANs during the generation phase enables to produce the missing
latent rs-fMRI and/or SNPs from sMRI. In addition, this process is applicable
bidirectionally, allowing the generation of sMRI latent features from either
SNPs or rs-fMRI as well. The versatility of this approach opens the way to its
generalization to additional modalities through training distinct cGANs and
integrating the resulting generators into the complete classification
framework. Furthermore, our model’s performance confirms that generative
models allow to obtain realistic data and learn nonlinear mappings across the
different acquisitions, achieving competitive prediction accuracy also with a
substantial proportion of missing modalities.

###  5.2 Interpretability analyses

In our work we adopted a post-hoc interpretability analysis through IG,
followed by a group-based statistical analysis. More in detail, for each input
modality and each task, relevance maps were extracted and analyzed from a
qualitative and quantitative point of view. We recall that being IG baseline-
based, the feature relevance is to be considered baseline-dependent. The
baseline represents a neutral input to the network, that is an input surrogate
subject that for the network could equivalently belong to one class or the
other. Hence, the baseline chosen should be validated [55, 56, 57]. In a
binary classification, the sign of IG could generally be referred to as an
increase in the associated feature, on the contrary, a negative value could be
associated with a decrease in a feature value.

Interestingly, among the state-of-the-art methods for multimodal AD detection
or MCI conversion prediction, only a few works introduced interpretability
analysis. [33] proposed an interpretable analysis masking one feature at a
time and measuring the drop in accuracy, uncovering that when considering the
three modalities together (namely clinics, sMRI, and genetics) the most
relevant features were AD-related clinical biomarkers, while when considering
solely sMRI and genetics the most relevant features were brain areas such as
the hippocampus and amygdala, with limited relevance of the SNP features.
Concerning DL and generative-based frameworks, [64], thanks to the adoption of
an attention layer in their generation module, obtained feature importance for
the generator and discriminator which allowed to analyze the most relevant
sMRI features for the generation of the missing PET, as well as the most
relevant PET features for the discriminator. However, such relevance was not
widely discussed in the paper and it was only limited to the generation phase
and not to the classification. Finally, [39] exploited the weights learned for
their latent representation learning to derive the input feature importance,
finding relevant regions highly related to AD and MCI diagnosis such as the
hippocampus and amygdala.

In our results, the interpretability analysis revealed similarities between
the MCIc and the AD, as well as between the MCInc and CN, while highlighting
significant differences between the CN and AD, as expected, but also between
MCIc and MCInc which are of high interest since they would allow to identify
early AD biomarkers.

Beginning with the sMRI data, our findings highlighted that sub-cortical
regions carried more informative and relevant information for the final
classification compared to cortical areas. The hippocampus resulted as the
most critical region for all classes under analysis, alongside the amygdala.
In AD and MCIc patients, such regions exhibited negative attribution values,
suggesting a decrease in GM probability, as opposed to positive values in CN
and MCInc subjects. Of interest, the most significant differences in the
relevance assigned to such regions were found between MCIc and MCInc. These
findings were in line with the well-known literature findings and established
hallmarks of AD. Indeed, the pathological process initially affects the
hippocampus and amygdala regions before extending to other nearby structures
[65, 66]. Focusing on MCI, [67] demonstrated that MCIc patients exhibited
higher atrophy in the hippocampus and amygdala compared to MCInc and CN
subjects, which aligns well with our findings. Regarding the caudate region,
[68] and [69] highlighted a negative correlation between caudate and
hippocampus volumes in healthy subjects, and, in addition, the second work
also showed that patients with AD and non-specified dementia have a larger
caudate volume compared to non-dementia subjects. However, this is still
debated in literature with other works suggesting that the caudate is
susceptible to atrophy, resulting in a reduction of GM of this region in AD
patients [70], [71], [72].

The cortical areas had a generally lower relevance to the classification for
all the classes under analysis. The parahippocampal gyrus (anterior division)
and the occipital fusiform gyrus showed the highest attribution scores, with
positive values assigned to CN. This was in line with [73] and [67] findings
which revealed smaller volumes in the anterior parahippocampal area in AD,
MCIc, and MCInc subjects compared to CN individuals. Additionally, [74]
highlighted the importance of the occipital fusiform gyrus in their framework
for AD classification. Moving to the other relevant brain regions, the
precuneus and fusiform cortices showed a reduction of the GM volume in our
results, coherent with what is known from the literature [75], [76], [77].
Overall, our findings on sMRI revealed that the relevance scores were sensible
to an increase in neurodegeneration in some focal brain areas in AD and MCIc
compared with CN and MCInc, which aligns well with the literature findings.

Moving to rs-fMRI attributions, five functional RSNs emerged as highly
relevant for the final classification of both tasks, namely SM, DM, CB, VI,
and CC. The DM has a central role in information integration and processing,
and its involvement in AD is well-known in the current literature, with
several studies consistently demonstrating that this is the first RSN to be
affected by abnormal protein aggregation [78, 14]. In our results, we did not
retrieve intra-network connections in the DM mode. However, for the MCIc
subjects, a negative relevance score, suggesting a decreased FC, was found for
inter-network connections between DM and visual/sensorimotor areas (DM-VI, DM-
SM), while a positive inter-network connection was highlighted between DM and
CC. Conversely, AD subjects revealed a positive relevance for a few
connections between the DM and VI and between the DM and the CC, while one
negative connection was found between DM and SM. These patterns are not
commonly reported in the literature but deserve further investigation since
they could represent compensation connectivity patterns.

Among the other RSNs, the SM was the most present and relevant, showing
negative relevance scores for AD and MCIc for both the intra-connections,
involving post/para central and partial gyri, and inter-connections with the
other relevant RSNs. On the contrary, for the CN and, importantly, for the
MCInc the SM showed positive relevance, leading to significant differences for
both intra- and inter-network connections with the most severe groups (AD and
MCIc). The lowest p-values were found when comparing MCInc vs AD as well as CN
vs AD over the different SM intra-network connections. Inter- and intra-
network SM connections were indeed demonstrated to be affected by AD
pathology, generally showing an overall decreased connectivity in the later
stages of the disease [79], [80], [78]. Moreover, [81] showed that many
pyramidal and extrapyramidal motor impairments affect a substantial portion of
AD patients, even at an early stage of the disease, and progressively worsen
along with cognitive impairment, reflecting a possible decreased connectivity
in the SM network.

Interestingly, the VI RSN was involved in the classification of the different
AD stages. In detail, positive relevance was assigned to AD subjects in both
intra- and inter-connections (VI-DM and VI-CC), while a different pattern was
found for MCInc, which showed negative relevance in almost the same ICs. Of
note, the MCIc did not show high involvement of the VI intra-connections,
while few negative inter-connections were found between VI and the other
relevant RSN (SM, CC, and DM). This revealed another difference between AD and
its prodromal stages, indicating a decrease in VI connectivity in the MCI
stage, particularly evident for the MCInc, which then converts into
hyperconnectivity in the most severe stage, full-blown dementia. The damage in
VI due to AD was previously shown by [78]. In detail, [81] found that
subgroups of AD patients have concomitant eye diseases, and some visual
functions are impaired, which could be caused by impairments in the VI RSN.
Moreover, recent studies demonstrated a hyperconnectivity pattern in the most
severe stages of the disease present in the VI network [82]. Hence, further
investigation would be needed for studying the involvement of VI RSN in the AD
continuum.

Finally, the inter-network connections between the CB and the SM resulted
negatively relevant, hence affected by the disease with a decreased
connectivity in both AD and MCIc, while the same was not recorded for the
MCInc, unraveling a possible impact on this RSN in a later stage compared to
the others.

Moving to the genetic relevance, the significant biological processes for
MCInc, MCIc, and AD were derived from the genes annotated starting from the
most significant SNPs resulting from the interpretability analysis on our two
tasks. Biological processes related to A$\beta$ were found both in AD and
MCIc, and they were related to the regulation and formation of amyloid-beta
structures and amyloid fibrillar, such as amyloid-beta formation, amyloid-beta
metabolic process, and regulation of amyloid-beta formation, and positive
regulation of amyloid fibril formation, which are biological processes related
to AD [83], [84], [85], [86]. Moreover, particularly in MCIc, we found
biological processes related to cholesterol, like regulation of cholesterol
transport, regulation of sterol transport, and cholesterol efflux, which, on a
deeper analysis, were shown as possibly being associated with the AD
continuum. Excess cholesterol deposit in the brain was demonstrated to be
related to an increase of amyloid-beta plaques and amyloid cascade leading to
synaptic plasticity annihilation, promotion of tau phosphorylation, hence
contributing to the risk and pathogenesis of AD, possibly in an early phase
[87, 88]. Regarding the particular genes, APOE, PICALM, APOA2, APOC1, ABCA7,
and SORL1 were the most frequent in the biological processes. Of note, they
all have a relevant impact in the development of AD [45, 89]. In particular,
APOE is notably the major risk factor of AD [90] and is mainly expressed in
both the brain and the liver. More in depth, the ApolipoproteinE is a ligand
receptor-mediated endocytosis of lipoprotein particles [90] and is the major
cholesterol transport and other lipids in the brain [91], [92]. This gene is
hence one of the responsible of the most important biomarkers for AD, namely
amyloid-beta plaques containing amyloid-$\beta$ peptides and the
neurofibrillary tangles containing hyperphosphorylated tau proteins [93].
ABCA7 is one of the most important risk genes for AD [27] that mainly
regulates the processes related to cholesterol and the processing and
clearance of A$\beta$ proteins [94]. ABCA7-expressed proteins have a relevant
role in the control of cholesterol metabolism, then the cholesterol has a
strong influence in the regulation of A$\beta$ synthesis [94, 95].
Additionally, some studies reported also that different variants of ABCA7 are
associated with an increase of A$\beta$ deposition in MCI patients rather than
AD [96], similar to what we found in our results, where the ABCA7 gene was
involved in MCIc biological processes (Supplementary Table 4). Moving to the
other relevant genes, PICALM is involved in the production, modulation, and
clearance of A$\beta$ complexes [23]. Also, for this gene, interactions with
APOE have been demonstrated [24]. Another important gene related to AD is
SORL1. Some studies found associations between AD and this gene [97, 98].
SORL1 is primarily involved in generating A$\beta$. In detail, a reduction of
SORL1 protein in brain tissue increases the production of A$\beta$ protein
[97, 99]. Finally, [24] and [26] highlighted also CR$1$ as relevant factor
related to AD pathogenesis.

###  5.3 Main contributions and outcomes

We proposed an interpretable and generative framework for multimodal AD
detection and MCI conversion prediction. The main contributions of this work
are: (i) reaching the state-of-the-art of multimodal and generative models in
the classification of CN vs AD; (ii) reaching competitive performance in the
classification of MCI cohort using a pretrained framework; (iii) managing
missing data introducing a generation module in the latent space allowing to
impute missing modalities in a lower space with respect to the input space,
and without requiring the presence of at least one modality for all the
subjects; and (iv) proposing an interpretability analysis based on IG, which
to the best of our knowledge was never applied for studying the
neurodegenerative diseases.

The complementary analysis of three different input modalities allowed to
uncover the disease signatures at multiple levels of analysis and contemporary
present. We were indeed able to confirm the presence of atrophy, particularly
involving the hippocampus in later stages (MCIc and AD), together with FNC
impairment, particularly in the information processing-related RSN (SM and
VI). The former showed negative relevance scores, hence suggesting a decreased
inter- and intra-connectivity in both the MCIc and the AD stages, while the
latter, the VI, showed negative relevance in the MCInc stage, being poorly
relevant in the MCIc while being positively attributed in the AD subjects,
suggesting a compensation mechanism leading to a hyperconnectivity in such RSN
in the later stages of the disease. Such brain modulations were present along
with the mutation of relevant SNPs linked to the impairment of different
biological processes related to amyloid and cholesterol regulation and
formation for the MCIc and AD subjects, while mostly related to the complement
activation, B cell processes, and immune response pathways for the MCInc.

####  5.3.1 Limitations and future works

In what follows, the main open issues will be briefly summarized, paving the
way for further research. First, concerning the MCI conversion prediction
task, in this work, our aim was to test the model generalizability by
straightforwardly testing it on the MCI cohort. Training and fine-tuning on
the specific task would allow obtaining better classification results and will
be the object of future analysis. Moreover, being the model intrinsically
multimodal and easily expandable, different channels should be considered,
such as clinical information and PET imaging which have been demonstrated to
be highly discriminative for the disease [4], as well as advanced structural
connectivity metrics derived from diffusion MRI which could help to shed light
on early disease signatures. Moreover, it would be interesting to explore
different subject classifications, either proposing a multiclass prediction or
defining biologically homogeneous groups following the A/T/N (amyloid, tau,
neurodegeneration) system which has been attracting increasing attention in
recent years [100]. Finally, concerning the interpretability analysis, we
strongly point toward deeper exploitation of XAI methods to open the way to
not yet studied associations or mechanisms that are instead captured by the
model. However, we acknowledge that the interpretation of results is not
always straightforward, especially when relying on baseline-based XAI
approaches, where using not well-chosen baselines strongly impacts on the
results. One future aim is, hence, to establish clear rules for the choice of
the baseline, enabling the unambiguous interpretation of the attributions as
well as the investigation of other post-hoc methods pursuing the robustness
and reliability of the interpretation. Moreover, the analysis of the
associations between the different input features would be of high impact,
eventually exploiting causality models to uncover the temporal sequence of the
different biomarkers modulations in the disease continuum.

##  6 Conclusion

In this work, we presented a multimodal generative and interpretable DL-based
framework for AD detection and MCI conversion prediction. Neuroimaging
(structural and functional features) and genetics data were used to address
these classification tasks. The generation of missing modalities in the latent
space using four pre-trained generators of two different cGANs allowed to
obtain competitive classification performance in both tasks. The application
of an interpretability method yielded our model to be interpretable extracting
the relevance of each input feature and revealing the most important ones for
each class, highlighting disease structural, functional, and genetic
signatures and opening the way to further analyses.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

## Acknowledgments

Data collection and sharing for this project was funded by the Alzheimer’s
Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant
U01 AG024904) and DOD ADNI (Department of Defense award number
W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the
National Institute of Biomedical Imaging and Bioengineering, and through
generous contributions from the following: AbbVie, Alzheimer’s Association;
Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.;
Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.;
Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La
Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE
Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research &
Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development
LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.;
NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals
Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical
Company; and Transition Therapeutics. The Canadian Institutes of Health
Research is providing funds to support ADNI clinical sites in Canada. Private
sector contributions are facilitated by the Foundation for the National
Institutes of Health (www.fnih.org). The grantee organization is the Northern
California Institute for Research and Education, and the study is coordinated
by the Alzheimer’s Therapeutic Research Institute at the University of
Southern California. ADNI data are disseminated by the Laboratory for Neuro
Imaging at the University of Southern California.

The study was also funded by NIH grant RF1AG063153 and NSF grant #2112455, as
well as, Fondazione CariVerona (Bando Ricerca Scientifica di Eccellenza 2018,
EDIPO project, num. 2018.0855.2019) and MIUR D.M. 737/2021 “AI4Health:
empowering neurosciences with eXplainable AI methods”.

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