Pilot Study of Distinct Graphs Models in Analysis of Brain Aging in

Resting-State Functional Connectivity Networks

M. A. G. Carvalho

1,2,3 a

and R. Frayne

2,3,4,5 b

School of Technology, University of Campinas, Brazil

Radiology and Clinical Neurosciences, Hotchkiss Brain Institute, Univ. of Calgary, Canada

Seaman Family MR Research Centre, Foothills Medical Centre, Calgary, Canada

Biomedical Engineering Graduate Program, University of Calgary, Canada

Calgary Image Processing and Analysis Centre, Foothills Medical Centre, Calgary, Canada

Keywords:

Graph Model (GM), Graph Metrics, Resting-State Functional Magnetic Resonance Imaging, Brain Networks,

Aging.

Abstract:

Graphs have been used successfully to represent and analyze brain networks for many decades. Such structural

and functional studies are important for revealing interactions between distinct areas of the brain that, for ex-

ample, are associated with the performance of a speciﬁc task or the onset of a cognitive disorder like dementia.

In this pilot study, resting-state functional magnetic resonance imaging data were acquired in a sex-balanced

sample of 10 young (20.1 ± 2.1 years) and 10 old (65.6 ± 0.4 years), presumed healthy, adults. We examined

the effects of age on whole-brain resting-state functional connectivity (RSFC) networks. We examined two

main graph modeling approaches to analyze RSFC networks. These approaches employ different strategies or

graph models for thresholding over the complete network or examining changes in graph density. We com-

puted and compared one graph metric, the modularity, that was derived from the RSFC network graph models.

Considering the need for a model that must preserve the network’s connectivity, strategies that use spanning

trees as seeds to gradually increase the graph’s density seem more appropriate to represent brain networks.

1 INTRODUCTION

Neuroimaging techniques have become more accessi-

ble and frequently used in recent years and have facil-

itate the emergence of human brain studies, including

investigations of brain aging. Such aging studies at-

tempt to understand how the healthy brain transforms

morphologically or functionally across the lifespan.

Considering that in many countries people are living

longer, it is important to ﬁrst study healthy aging if

we are to then attempt to understand pathological ag-

ing. This knowledge can then help understand and

mitigate impacts of illnesses like cognitive loss and

dementia. Functional magnetic resonance imaging

(fMRI) is a widely employed, non-invasive method

to investigate functional organization of and organi-

zational change in the brain during aging. Resting-

state fMRI (rs-fMRI) methods process the sponta-

neous ﬂuctuations in the blood oxygen levels (or the

https://orcid.org/0000-0002-1941-6036

https://orcid.org/0000-0003-0358-1210

BOLD signal - blood oxygen level–dependent) that

occur even in the absence of a stimulus or activation

task (Lv et al., 2018).

To describe the brain functional organization, i.e.,

its underlying functional connectivity, studies have

modeled the brain as a highly structured network,

known as the connectome (Hrybouski et al., 2021).

Graph theory approaches naturally arise as a method

for representing human brain networks. In the mathe-

matical sense, a graph G is an ordered pair G = (V,E)

deﬁned by a set of nodes (or vertices) V and set

of edges (or links) E connecting the nodes (Chung,

2019). The use of graphs to represent networks is im-

portant as it enables characterization and analysis of

brain functional organization using a variety of graph

metrics.

This initial study aims to explore the computation

of modularity graph metric according to distinct graph

models (GMs). Such metric characterize relevant as-

pect of resting-state functional connectivity (RSFC)

networks. We conducted an experiment using four

348

Carvalho, M. A. G. and Frayne, R.

Pilot Study of Distinct Graphs Models in Analysis of Brain Aging in Resting-State Functional Connectivity Networks.

DOI: 10.5220/0013261200003911

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 18th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2025) - Volume 1, pages 348-356

ISBN: 978-989-758-731-3; ISSN: 2184-4305

GMs, corresponding to representations for RFSC net-

works, widely reported in the literature. This work

makes contributions in the following areas:

• We present an up-to-date review of the literature

of GM representations of the RSFC networks.

• We analyzed RSFC networks using a graph metric

calculated for different GMs in order to improve

understanding of the potential and limitations of

each model.

The remainder of this paper is organized as fol-

lows: In Section 2 the literature survey protocol is

presented. We then summarize our ﬁndings regard-

ing the graph representation used to model RSFC net-

works. Section 3 describes our experiment method-

ology, expanding on the important details required to

build distinct GMs. Section 4 summarizes our results

and discusses the broader implications of our ﬁnd-

ings. Finally, Section 5 concludes the paper with ﬁnal

remarks and a discussion of remaining issues.

2 LITERATURE REVIEW

In this section we explain how we identify key works

in the peer-reviewed literature on RSFC brain net-

works of healthy individuals.

We used the three-staged methodology in order to

select relevant papers that explored graph theory, i.e.,

uses GMs to characterize and analyze RSFC networks

in aging (Figure 1).

Figure 1: Three-stage protocol to select papers dealing with

the representation of RSFC networks through graph models.

The paper extraction intended to answer the fol-

lowing questions:

1. What are the main graph approaches used to rep-

resent RSFC networks?

2. Concerning the identiﬁed approaches, what are

the strategies or variations regarding to the graph

models?

3. What other graph properties (or graph types) are

important in characterizing RSFC networks?

2.1 Exploring Existing Reviews

In this stage we collect three recent review or system-

atic review papers, listed in Table 1, that works with

graph theory to characterize and analyze RSFC net-

works in aging.

The three review and systematic review papers

identiﬁed a number of broad-based studies focused on

brain aging in healthy individuals that analyzed RSFC

networks. Combined, they cited a total of twenty-

six papers that speciﬁed modeling of RSFC networks

using graph theory. Only paper that explicitly men-

tioned using graph metrics were included. We ex-

cluded reports that focused on addressing speciﬁc dis-

eases, trauma or that studied the effects of medica-

tions, other treatments or therapies. We also excluded

reports not written in English. Twenty-ﬁve of these

papers were selected (see list in Table 2) and one arti-

cle was excluded (one study obtained rs-fMRI data in

hypercapnia (Hou et al., 2019)).

2.2 Supplementary Screening and

Inclusion/Exclusion Criteria

Because the most recent of the three review and

systematic review examined papers published before

June 2021 (Deery et al., 2023), a supplementary

search was conducted, according to a three-step pro-

tocol as described in (Kitchenham, 2004), in order to

include articles between June 2021 and June 2024.

The supplementary search was performed using

two complementary databases: 1) IEEE Xplore

(en-

gineering and computer science literature) and 2)

PubMed

(biomedicine literature) using the research

query: “(aging) AND (brain) AND (network) AND

(functional connectivity) AND (review OR systematic

review)”. The inclusion criteria initially considered

only papers focusing on brain aging evaluated with

RSFC networks analysis.

Were used the same inclusion and exclusion crite-

ria applied in previous stage. Finally, we have iden-

tiﬁed an additional six papers published after May

2021.

2.3 Studies: Identiﬁcation and

Summary

These 31 selected articles, including both stages,

cover a period between 2007 and 2024, and constitute

our source of primary studies. Those papers were an-

alyzed in detail, speciﬁcally examining the GM used.

After analysis, we have classiﬁed each approach

concerning the use of graph theory on three types

of graph (GT - Graph Type) and four types of

graph model (GM) (see Table 2). The GTs were:

https://ieeexplore.ieee.org/Xplore/home.jsp

https://pubmed.ncbi.nlm.nih.gov/

Pilot Study of Distinct Graphs Models in Analysis of Brain Aging in Resting-State Functional Connectivity Networks

349

Table 1: Review and systematic review papers selected on stage 1.

Year Paper Title Ref

2023 The older adult brain is less modular, more integrated, and less

efﬁcient at rest: A systematic review of large-scale resting-state

functional brain networks in aging

(Deery et al., 2023)

2021 Resting-state networks in the course of aging-differential in-

sights from studies across the lifespan vs. amongst the old

(Jockwitz and

Caspers, 2021)

2020 Functional brain connectivity changes across the human life

span: From fetal development to old age

(Edde et al., 2020)

Table 2: Summary of graph based methods, summarizing study design, graph type (GT) and graph model (GM). Publications

extracted from Ref (Deery et al., 2023),(Jockwitz and Caspers, 2021), and (Edde et al., 2020), and updated to June 2024.

Study GT GM

Ref Design 1 2 3 1 2 3 4

(Hrybouski et al., 2021) CS - - - -

(Grady et al., 2016) CS - - - - -

(Geerligs et al., 2015) CS - - - -

(Gallen et al., 2016) CS - - - - -

(Iordan et al., 2018) CS - - - -

(Betzel et al., 2014) CS - - - - -

(Chan et al., 2014) CS - - - - -

(Stumme et al., 2020) CS - - - - -

(Alcauter et al., 2015) CS - - - - -

(Asis-Cruz et al., 2015) CS - - - -

(Marek et al., 2015) CS - - - - -

(Song et al., 2014) CS - - - -

(Thomason et al., 2014) CS - - - - -

(van den Heuvel et al., 2018) CS - - - - -

(Varangis et al., 2019) CS - - - - -

(Bagarinao et al., 2019) CS - - - - -

(Cao et al., 2014) CS - - - - -

(Li et al., 2016) CS - - - - -

(Onoda and Yamaguchi, 2013) CS - - - - - -

(Sala-Llonch et al., 2014) CS - - - -

(Meunier et al., 2009) CS - - - - -

(Achard and Bullmore, 2007) CS - - - - -

(Lehmann et al., 2021)

∗

CS - - - - -

(Foo et al., 2021)

∗

CS - - - - -

(Wang et al., 2024)

∗

CS - - - - -

(Moretto et al., 2022)

∗

CS - - - - -

(Filippi et al., 2023)

∗

CS - - - - -

(Chong et al., 2019) CS/L - - - - -

(Wen et al., 2019) L - - - - -

(Xiao et al., 2016) L - - - - -

(Pedersen et al., 2021)

∗

L - - - - -

∗

= Additional paper identiﬁed in supplementary screening

GTs were: GT1-binary graph, GT2-weighted graph, only positive

values, and GT3-weighted graph, positive and negative values.

GMs were: GM1-thresholding operation approach, GM2-spanning tree

initial seed approach, GM3-density approach, and GM4-entire graph.

CS = Cross-Sectional; L = Longitudinal

BIOIMAGING 2025 - 12th International Conference on Bioimaging

350

GT1) binary graph (14/31, 45.2%), GT2) weighted

graph, only positive values (12/31, 38.7%), and GT3)

weighted graph, positive and negative values (10/31,

32.2%). Some papers work with multiple GT, which

can result in a sum greater than 30. The use of bi-

nary graphs was associated with the evaluation of as-

pects of the network topology. This observation is

related to the scope of the study, i.e., being able to

evaluate only aspects of the network topology, as in

the case of using binary graphs, or when it was neces-

sary to evaluate more speciﬁc graph properties, such

as strength and shortest path length. The detailed re-

view also identiﬁed an alternative GM aimed at inves-

tigating brain hubs, i.e., highly connected regions of

the neurocognitive functional networks (Filippi et al.,

2023). This approach was recently used to obtain new

adjacency matrices from the analysis of the distance

of any brain region, according to the degree of step-

wise connectivity and the seed area (i.e., hubs).

The models included GM1) based on a threshold-

ing operation (ﬁxed value or range) (8/31, 25.8%),

GM2) based on the construction of a spanning tree

and the addition of successive edges (1/31, 3.2%),

GM3) based on the pre-deﬁned values of graph den-

sity range (14/31, 45.2%), and GM4) based on the

entire and non-sparse graph (7/31, 22.6%).

The ﬁrst model (GM1) used thresholding. One of

the main challenges in applying strategies that use a

thresholding process is deﬁning the threshold itself, as

this operation may include irrelevant or disregard rel-

evant information from the RSFC network (van den

Heuvel et al., 2017). One way to mitigate the im-

pact of using a single threshold is to apply a range

of values. Indeed, most studies use a threshold range

(Asis-Cruz et al., 2015)(van den Heuvel et al., 2018)

(Chong et al., 2019). In Bagarinao (Bagarinao et al.,

2019), for example, a threshold range [0.20,0.40] was

used. We also found studies that used a single thresh-

old (Alcauter et al., 2015)(Xiao et al., 2016). One

aspect that is not always explicitly reported was the

fact that the thresholding process can generate dis-

connected RSFC networks. In this situation, the cal-

culation of graph metrics were performed separately

on either each connected component or only on the

largest connected component.

GM2 derives a spanning tree (MST - minimum

spanning tree in that case) as a seed and gradually

include a percentage of edges, as adopted by (Song

et al., 2014). This method represents an interest-

ing approach as it guarantees the connectivity of the

graph. One important point is that the weights of the

edges added in a minimum spanning tree are those

with smaller values, in ascending order, according to

Kruskal’s algorithm (Fornito et al., 2016). Consider-

ing the graph density approach added relevant edges,

i.e., stronger connections, in this case, therefore, it

would be appropriate to work with a maximum span-

ning tree (MaxST).

GM3 consists of deﬁning a range of graph den-

sity values (Grady et al., 2016) (Marek et al., 2015)

and generating representations of the RSFC network.

Graph density is a measure of the ratio between edges

and nodes. The density is 0 for a graph without edges

and 1 for a complete graph. The graph density strat-

egy is similar to spanning trees because with the ex-

ception of not using a seed, it also consists of gradu-

ally adding relevant edges. One limitation is the pos-

sibility of creating disconnected graphs. We found

papers that worked with graph densities that ranged

between 1% and 60% (Grady et al., 2016) and 1%

and 25% (Marek et al., 2015).

The ﬁnal model (GM4) used the entire graph, such

that each entry of the Pearson correlation matrix cor-

responds to an edge in the graph. In (Thomason et al.,

2014), for instance, both positive and negative corre-

lation values were used in order to build the equiva-

lent graph. On the other hand, (Chan et al., 2014) only

positive values of the correlation matrix were used.

Table 3 list the ﬁve most cited articles listed in

Table 2. The most cited of these papers presented

the calculation of local and global efﬁciency graph

metrics, in addition to using a graph model approach

based on graph density (Achard and Bullmore, 2007).

Table 3: Highly cited papers (Source: PubMed).

Ref Total Citations

citations per year

(Achard and Bullmore, 2007) 1113 > 60

(Chan et al., 2014) 399 ≈ 40

(Betzel et al., 2014) 392 ≈ 40

(Geerligs et al., 2015) 348 ≈ 40

(Meunier et al., 2009) 370 ≈ 25

2.4 Considerations on Review Findings

The connectivity of a GM is an important feature in

the analysis of RSFC networks. Graph metric compu-

tation may undergo changes according to the connec-

tivity property, such as corresponding to the value of

the largest connected component. Iordan et al.(Iordan

et al., 2018), for instance, explicitly pointed out the

number of nodes that were disconnected in the graphs

built in his modeling. Meunier et al.(Meunier et al.,

2009) deﬁned the number of connections, in a range

between 100 and 400 edges (or links), in order to

keep the graph connected. An interesting strategy

that guarantees the connectivity of a graph model

is the use of minimum spanning trees (Song et al.,

Pilot Study of Distinct Graphs Models in Analysis of Brain Aging in Resting-State Functional Connectivity Networks

351

2014). A spanning tree is a tree-like subgraph of

a connected graph that includes all vertices. More

consistent results may be found when employing a

maximum spanning tree, instead minimum spanning

tree, because the most relevant edges of the graph are

added in sequence.

To correctly understand the brain aging process

trajectory, it is necessary to explore longitudinal

data. This methodology investigates changes in intra-

individual functional connectivity networks and al-

lows us to understand the compensatory changes car-

ried out by the different RSFC networks in healthy in-

dividuals. Only a few studies (4/30, 13.3%) used lon-

gitudinal data when calculating graph metrics (Chong

et al., 2019)(Wen et al., 2019)(Xiao et al., 2016)(Ped-

ersen et al., 2021). These four studies only exam-

ined one age group and, therefore, have limitations

in terms of extrapolation of results over the adult life

span.

Choosing a GM is not just a question of efﬁciency,

as they all enable RSFC network characterization us-

ing graph metrics via appropriate parameter deﬁni-

tion. Choosing a GM is about knowing the condi-

tions for acquiring and processing rs-fMRI data and

the study sample, avoiding spurious connections and

biases (Rubinov and Sporns, 2010)(Varangis et al.,

2019).

We also observed the existence of distinct nomen-

clatures to represent the number or percentage of

edges in the graph model, as well as in the deﬁnition

of relevant entries (correlation values) of the FC ma-

trix. Considering that the origin of the term thresh-

olding is related to the modiﬁcation of intensity or

amplitude values in a matrix, we propose to use the

simple terminology for the GMs found in the litera-

ture. The described GMs and graph analysis scenarios

can be organized into two major approaches for ana-

lyzing RSFC networks: 1) Thresholding, where the

weighted edges of the corresponding graph must be

greater than a value or a range of values, and 2) Graph

density, where the resulting graph is constructed from

a percentage of connections in the original network,

including the entire graph.

3 METHODS

The modularity analysis pipeline is shown in Fig. 2

and consisted of four main steps described in this sec-

tion.

Figure 2: Overview of processing pipeline.

3.1 Data Acquisition

MR imaging data in this study were acquired as part

of the Calgary Normative Study (CNS) (McCreary

et al., 2020). The CNS is an ongoing longitudi-

nal study, started in 2013, that focuses on collect-

ing quantitative data from community dwelling, pre-

sumed healthy adults (18-90+ years). Several types

of MR neuroimaging were performed in the CNS in-

cluding rs-fMRI. To pilot our methods, we exam-

ined twenty (20) individuals extracted from the CNS

database, ten (10) from a young and ten (10) from an

older group. Table 4 lists the demographics of the

groups.

Table 4: Dataset sample demographics.

Group (Number) Sex Ratio Age (years)

Young (N = 10) 50% Female 20.1 ± 2.1

50% Male

Old (N = 10) 50% Female 65.6 ± 0.4

50% Male

3.2 Image Preprocessing

The preprocessing pipeline consists of the prepara-

tion and analysis of the rs-fMRI images. The pipeline

comprises several key steps: 1) skull striping us-

ing BET, 2) motion correction using MCFLIRT (Mo-

tion Correction FMRIB Linear Image Registration

Tool), 3) interleaved slice-time correction, 4) spatial

smoothing, 5) temporal high-pass ﬁltering, 6) inde-

pendent component analysis (ICA) and 7) functional-

structural registration. Details of the pipeline are de-

scribed in (Sidhu, 2023).

3.3 FC Network Matrices and Graph

Models

From the average BOLD time series, a FC matrix of

size 200×200 was derived for each individual by cal-

culating the Pearson correlation (r) across the time

series (Sidhu, 2023). This matrix size was obtained

BIOIMAGING 2025 - 12th International Conference on Bioimaging

352

from the brain segmentation into 200 anatomical re-

gions using the Schaefer-Yeo atlas. We consider a

brain organization based on the existence of seven rel-

evant modules (Sidhu, 2023): Visual network, Senso-

rimotor network, Frontoparietal network, Dorsal at-

tention network, Limbic network, Ventral attention

network, Default mode network. After analyzing the

quality of the rs-fMRI data, FC matrix entries from

the left and right limbic networks were excluded be-

cause of signal loss resulting from MR susceptibility

artifacts. Fisher’s r–to–z transformation was then ap-

plied to the Pearson correlation values and the main

diagonal of the FC matrix was set to zero to exclude

self connections.

We explored four GMs that can be used to repre-

sent RSFC networks from FC matrices. These GM

were ﬁrst identiﬁed in our systematic review (Table

2):

• GM 1: Thresholding applied a threshold range

directly to the Pearson correlation matrix.

• GM 2: Minimum Spanning Tree was built from

all graphs. Graph connectivity was preserved

and edges were added according to their weight,

choosing ﬁrst to add those with the lower values.

• GM 3: Graph Density used a range of values

for the graph density metric. We gradually add

edges (as a percentage) to the model graph, as in

the previous model.

• GM4: Entire Graph used all positive values of

the Pearson correlation matrix. Each matrix entry

corresponds to an edge of the graph.

We decided to include a ﬁfth GM, GM5, corre-

sponding to a variation of spanning tree called Maxi-

mum Spanning Tree. Unlike the Minimum spanning

tree, this tree is built by considering the strongest con-

nections, as done by the thresholding and graph den-

sity approaches. In that case, edges are added accord-

ing to their weight, choosing ﬁrst to add those with the

higher values. In all cases where a range was used, the

ﬁnal value of the graph metric was the average value

calculated over that range.

3.4 Modularity: Graph Metric

Modularity (Q) measures the relative strength of a

network division into groups. Modularity reﬂects the

existence of subnetworks within the full network.

Q =

∑

I∈M





−

∑

J∈M





(1)

where the network is divided into a set of nonoverlap-

ping modules M and l

is the ratio of all links that

connect nodes in module I with module J. RSFC net-

works with high modularity have dense connections

between nodes within the module but sparse connec-

tions between nodes across different modules. Details

concerning modularity can be found at (Fornito et al.,

2016).

4 RESULTS AND DISCUSSIONS

Our objective was to highlight trends in the ﬁve GMs

between the young and old age groups and com-

pare them with literature ﬁndings. For all exper-

iments, we use Python and the networkX library

(https://networkx.org/).

The GMs examined were (section 3.3): GM1 –

thresholding with ﬁfteen steps in the range [0.05,0.4];

GM2 and GM5 – minimum and maximum spanning

trees followed by a gradual addition of edges in the

range of 2% and 40% (Song et al., 2014); GM3 –

graph density using the range [1%,25%]; and GM4

– entire graph(Marek et al., 2015). For all models,

we processed only positive Pearson coefﬁcient values

and computed the modularity (section 3.4) to evalu-

ate age-related change in the GMs. Figure 3 presents

results for all examined GMs.

As we can see in Figure 3, Q decreased in the

old compared to the young group, over a range of dif-

ferent thresholds and edges densities. This was also

observed in GM4, where the mean values obtained for

the young and old groups were 0.1162 and 0.1099, re-

spectively. This ﬁnding is similar to that obtained in

Deery (Deery et al., 2023) who found that in 100% of

studies Q decreased with age.

In the neuroimaging ﬁeld, the construction of

networks and their analyses draws on the concept of

small world networks (Deery et al., 2023). Small-

world networks are deﬁned as networks that are sig-

niﬁcantly more clustered than random networks (Ru-

binov and Sporns, 2010). Except for the GM4 model,

all GMs presents mean modularity values greater than

0.3, an indicative of nonrandom community structure,

i.e., the existence of modular structure of functional

brain networks across the adult lifespan(Song et al.,

2014). Finally, Minimum and Maximum spanning

trees (GM2 and GM5, respectively) present a simi-

lar behavior; however, considering that GM5 includes

ﬁrst the most relevant connections in terms of Pearson

correlation values, this would be the most coherent

choice.

Pilot Study of Distinct Graphs Models in Analysis of Brain Aging in Resting-State Functional Connectivity Networks

353

Figure 3: Modularity values by graph model. for young (black stars) and old individuals (gray circles). Rows are graph

models: GM1, GM2, and GM3, GM4 and GM5 (top to bottom).

5 CONCLUSIONS

We found thirty peer-reviewed papers that addressed

changes in RSFC networks in aging using graphs (Ta-

ble 2. Many additional papers used graphs to study

diseases and disorders, but were outside our selection

criteria. It was possible to identify two approaches

to model brain as graphs: Thresholding operations

(that act on the Pearson correlation values), and ap-

proaches that use a gradual increase in graph density

(that act on the number of edges or links). More stud-

ies only worked with positive Pearson correlation val-

ues, than those using positive and negative values. In

addition, binary graphs were widely used to express

network characteristics, such as modularity and clus-

tering coefﬁcient. Also of note is the maintenance of

the graph connectivity property, observed from its ad-

jacency matrix. Graph connectivity is important be-

cause it allows the application of other mathematical

approaches and more advanced computational tech-

niques. In this context, the model that uses spanning

trees naturally results in connected graphs.

We carried out a pilot experiment that com-

pared a common graph metric (modularity), com-

puted over distinct graph models representing RSFC

networks, to analize existing differences among

groups of young and old healthy individuals. This ex-

periment presents ﬁndings similar to those obtained

in the literature, which indicate that the value of mod-

ularity decreases with aging. We highlight that this

work consists of an exploratory analysis of GMs. An

in-depth study of the full CNS dataset with respect to

brain aging including other parameters is warranted.

Finally, to understand the brain aging process from

a different perspective, we should examine longitu-

dinal data, that is, study changes in intra-individual

functional connectivity networks, considering age as

a continuous variable. This type of study will also al-

low us to understand changes made in different RSFC

networks over age in healthy individuals.

ACKNOWLEDGEMENTS

This study was ﬁnanced in part by the Coordination of

Improvement of Higher Education Personnel - Brazil

(CAPES) - Finance Code 001. Marco Carvalho wish

to express their gratitude to the S

ao Paulo Research

Foundation/Fundac¸

ao de Amparo

a Pesquisa do Es-

tado de S

ao Paulo (FAPESP grant 2023/02302-6). We

also acknowledge the assistance of Kau

e TN Duarte,

Abhi S Sidhu, and Cherly R McCreary, from Univer-

sity of Calgary.

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