Functional and structural reorganization in brain tumors: a machine learning approach using desynchronized functional oscillations

Abstract

Neuroimaging studies have allowed for non-invasive mapping of brain networks in brain tumors. Although tumor core and edema are easily identifiable using standard MRI acquisitions, imaging studies often neglect signals, structures, and functions within their presence. Therefore, both functional and diffusion signals, as well as their relationship with global patterns of connectivity reorganization, are poorly understood. Here, we explore the functional activity and the structure of white matter fibers considering the contribution of the whole tumor in a surgical context. First, we find intertwined alterations in the frequency domain of local and spatially distributed resting-state functional signals, potentially arising within the tumor. Second, we propose a fiber tracking pipeline capable of using anatomical information while still reconstructing bundles in tumoral and peritumoral tissue. Finally, using machine learning and healthy anatomical information, we predict structural rearrangement after surgery given the preoperative brain network. The generative model also disentangles complex patterns of connectivity reorganization for different types of tumors. Overall, we show the importance of carefully designing studies including MR signals within damaged brain tissues, as they exhibit and relate to non-trivial patterns of both structural and functional (dis-)connections or activity.

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communications biology Article
https://doi.org/10.1038/s42003-024-06119-3
Functional and structural reorganization
in brain tumors: a machine learning
approach using desynchronized
functional oscillations
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Joan Falcó-Roget 1, Alberto Cacciola 2, Fabio Sambataro 3&AlessandroCrimi 1,4
Neuroimaging studies have allowed for non-invasive mapping of brain networks in brain tumors.
Although tumor core and edema are easily identifiable using standard MRI acquisitions, imaging
studies often neglect signals, structures, and functions within their presence. Therefore, both
functional and diffusion signals, as well as their relationship with global patterns of connectivity
reorganization, are poorly understood. Here, we explore the functional activity and the structure of
white matter fibers considering the contribution of the whole tumor in a surgical context. First, we find
intertwined alterations in the frequency domain of local and spatially distributed resting-state
functional signals, potentially arising within the tumor. Second, we propose a fiber tracking pipeline
capable of using anatomical information while still reconstructing bundles in tumoral and peritumoral
tissue. Finally, using machine learning and healthy anatomical information, we predict structural
rearrangement after surgery given the preoperative brain network. The generative model also
disentangles complex patterns of connectivity reorganization for different types of tumors. Overall, we
show the importance of carefully designing studies including MR signals within damaged brain
tissues, as they exhibit and relate to non-trivial patterns of both structural and functional (dis-)
connections or activity.
Functional networks of brain tumor patients, as obtained from functional
magnetic resonance imaging (fMRI), show clear altered patterns of local and
global disconnections1that follow functional rather than spatial distance to
tumor location2. Consistent with these findings, a separate study also
reported functional abnormalities that overlap with unaffected structural
areas3. In addition, large-scale theoretical models of functional activity
demonstrated differences in inhibitory connections between networks
having similar structural features4,5. However, all these findings do not
address the question of how the functional signal itself is modified by the
presence of the tumor nor how it relates to potential desynchronizations in
resting-state networks.
The oscillatory nature of functional time series has been widely
exploited to entangle brain regions involved in a wide range of cognitive
scenarios6. These functional co-activations, or connections7,arecomputed
by assessing temporal correlations which, by mathematical construction,
rely on the oscillatory frequencies present in the signals. We hypothesized
that the level of participation of each of those frequencies would be severely
modified by the presence of a brain tumor. If this were true, we could
quantify how these deviations propagate, or at least correlate, to alterations
in the functional connections of resting-state networks similar to what was
shown for a system of coupled oscillators8,9. Thereupon, we analyze local and
brain-wide Fourier-transformed functional time series and study how their
power spectrum singularities account for network anomalie sin brain tumor
patients.
A parallel line of research has recently focused on the use of diffusion
magnetic resonance imaging (dMRI) in a wide variety of brain diseases10,11.
Despite promising progress in the use of dMRI to resolve brain tumor
microstructure12, tumoral tissue is usually contaminated with cerebrospinal
1Brain and More Lab, Computer Vision, Sano Centre for Computational Medicine, Kraków, Poland. 2Brain Mapping Lab, Department of Biomedical, Dental
Sciences and Morphological and Functional Imaging, University of Messina, Messina, Italy. 3Department of Neuroscience, University of Padova, Padua, Italy.
4Faculty of Computer Science, AGH University of Krakow, Kraków, Poland. e-mail: j.roget@sanoscience.org;a.crimi@sanoscience.org
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fluid and gray matter abnormalities, therefore posing a challenge to existing
fiber reconstruction methods. Although several intra-lesion fiber tracking
methods have been developed, their usage is still scarce. Successfully
removing the contribution of cerebrospinal fluid requires the use of low
angular resolution tensor diffusion models unable to resolve complex white
matter regions13,14, or disregarding multi-shell acquisition schemes which
can improve fiber orientation estimation when employing for instance
constrained spherical deconvolution approaches15.Arguably,thelackof
acceptance may be built upon the detrimental effects of disregarding the
aforementioned MRI acquisition protocols and/or diffusion signal model-
ing approaches16, due to a longer acquisition time that is often not suitab le in
the clinical setting. We propose and describe a hybrid pipeline using a single-
shell-3-tissue algorithm17 only in the tumoral area of the brain. Afterward,
we merge the resulting connectivity matrix with the one obtained using a
multi-shell algorithm in healthy tissue, exploiting the best features of each
method and minimizing the impact of their downsides.
Unlike functional network studies, the knowledge of structural net-
works in brain tumors is, to some extent, unclear. Previous groups failed to
find significant tumor-dependent differences between patients and healthy
subjects4,18, suggesting that network integration and segregation are mostly
preserved. However, gliomas significantly altered the structural topology of
the ipsilesional but not the contralesional hemisphere19. In addition, small
structural differences vanished after surgery5, implying that high-precision
surgical interventions allow for spontaneous recovery of canonical
organization.
A promising line of network neuroscience, commonly referred to as
Spectral Graph Theory, builds on the idea that structural connections might
be the source upon which functional activity and behavior rely on20.Like-
wise, structural constraints can be used to model hemodynamics while
potentially revealing effective connections21. Yet, the bonds between struc-
tural and functional connections remain, not surprisingly, an open
problem22,23. Unveiling mechanisms of structural plasticity evolution is,
therefore, a key step toward understanding the impact of disruptions and
recovery in both structural and functional connectomes. In this direction,
and as a last contribution, we present a machine learning prediction study
on how structural connections self-arrange after surgical resection of brain
tumors.
Nonetheless, a certain number of challenges need to be addressed.
Brain tumors, as well as their resections, critically affect elements of the
network that may be far away from the damaged region itself18. Notwith-
standing their success in representation learning and generative
problems24,25, graph neural networks struggle with complex network
topologies26 due to difficulties in aggregating information from long-range
connections. Dehmamy and colleagues showed how this can be bypassed by
designing modular networks. However, this path inevitably leads to com-
plex data-hungry architectures27 that cannot be trained in sensitive clinical
scenarios where data is scarce. Interestingly, fully connected layers, besides
being easier to train, naturally combine knowledge regardless of neighbor
proximity26,28. Thus, we build on the idea thathealthy structural c onnections
could be used to inform and guide predictions. We propose to use anato-
mical constraints in a Bayesian framework combined with fully connected
layers to produce detailed graphs that share both visual similarities and
network topological characteristics with the ground truth.
In summary, we present several contributions in both functional and
diffusion MRI domains in the presence of a brain tumor. Initially, we study
BOLD signals within the tumor and how they relate to abnormal patterns of
brain-wide resting-state connectivity and complexity. Secondly, we present
our attempt to consider fiber tracking within the lesion combined with
whole-brain tractography. Lastly, we study how the fibers in the lesion, as
well as surgery, impact the structural connectivity after tumor resection.
Results
Tumor and default mode network functional signals
We first addressed the question of whether functional signals were present
inside the lesion. The segmented masks included all parts of the tumor, from
the necrotic issue to the edema (see Methods). For this study, resting-state
fMRIs were available (21 controls and 25 patients). We extractedfunctional
signals from inside the lesioned parts of the brain and compared them with
functional activity from the same region in control subjects (Fig. 1a, see also
Methods). There were no straightforward differences concerning Blood-
Oxygen-Level-Dependent (BOLD) signals from regions belonging to the
Default Mode Network (DMN) in the control group (Fig. 1b, see also
Methods).
We were interested in characterizingthe relationship between BOLD
oscillations present inside the masked lesion and brain areas known to be
functionally active and coherent (i.e., belonging to DMN regions) in
resting conditions29. Thus, to test whether and how functional activity
inside tumors was related to global signals, we first studied how brain
tumors themselves shaped those global signals. Direct comparison of
averaged time series was not possible since arbitrary dephasings intro-
duced artifacts (see Fig. S1a). Therefore, we analyzed functional series
from regions belonging to the DMN in the frequency domain (see
Methods). Alterations in the total power as well as the distribution of such
power across frequencies were present in some subjects but not in others
(Fig. 1c; see also Figs. S2–5a). The autocorrelation functions between time
signals exhibited similar shapes for short time lags (Fig. 1b inset). We
observed that left-skewed power distributions tended to have higher
autocorrelations than right-skewed power distributions (Fig. S4c inset)
suggesting slower time series maintained temporal coherence for longer
times. For longer lags, however, all signals lost this coherence. This
inspired the definition of a score capable of distinguishing patients dis-
playing faster oscillations from patientswho showed the opposite. We will
expand on this idea in the next section.
A similar phenomenon was observed when pair-wise correlations
between DMN regions were compute d to reconstruct the network (Fig. 1d).
Extensive research in network measures allowed us to estimate the com-
plexity of networks based on the distribution of the correlations (see
Methods). Briefly, we devised the ΘRichness score as the difference, in the
module, between the distribution of correlations building the network and a
uniform distribution30. Differences in the ΘRichness between patients and
healthy networks were also found to be inconsistent across subjects (Fig. 1e;
see also Figs. S2–5c). As a final step, we inspected signals from the same
regions belonging to the DMN of both patients and control subjects, again
finding no clear traces of tumoral damage in DMN functional sig-
nals (Fig. 1f).
In summary, functional signals from tumors and DMNs did not show
significant changes in terms of complexity. However, they displayed
alterationsbothinthepowerdomainandinthedistributionoffunctional
connections.
Temporal dynamics and default mode network reorganization
To further characterize DMN signals in brain tumors bypassing phase and
noise artifacts (perhaps unsuccessfully removed by the preprocessing
pipeline), we designed a scalar score based on the cumulative power dis-
tribution of the time series. This Dynamics Alteration Score (DAS), inspired
by previous work on periodic modeling of fMRI time series31,wasableto
differentiate between slower or faster oscillations of BOLD signals (see
Methods; see also Fig. S1). Overall, the dynamics of DMN in patients were
found to be positive, negative, or zero. We measured the similarity of the
patients and control networks with a node similarity score (see Methods)
andobservedthatitissignificantly anti-correlated with the magnitude of the
DAS (r=−0.506, df = 23, p= 0.01, two-tailed exact test; Fig. 2a). We studied
the similarity as a function of the direction in the alteration expecting it
would decrease regardless of the change in dynamics for large scores.
Indeed, we found a clear inverted “U-shaped”pattern that agreed with the
interpretation that altered dynamics is a contributing factor in network
reorganization (Fig. 2a Inset). Negative DAS was positively correlated with
similarity (r>0, p= 0.006, df = 11, one-tailed permutation test) while
positive DAS exhibited the opposite trend (r<0, p= 0.083, df= 14, one-
tailed permutation test).
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Additionally, we found a small but strong difference in the magnitude
of the change in ΘRichness between healthy and brain tumor networks
(ΔΘjj¼0:086, p< 0.001, df = 23, one-tailed t-test; p= 0.054, one-tailed U-
test). Opposite to this, the direction of this change (i.e., considering increases
or decreases) was non-significantly different than zero (p= 0.067, df = 23,
two-tailed t-test; p= 0.286 two-tailed U-test). Negative DAS implied the
presence of higher frequencies of oscillations challenging the existence of
coordinated oscillations. Consistent with this, alterations in the BOLD
dynamics significantly correlated with changes in functional complexity
(r= 0.514, df = 23, p= 0.009, two-tailed exact test; Fig. 2b). An equivalent
trend appeared when considering absolute alterations (r= 0.413, df = 23,
p= 0.04, two-tailed exact test).
In conclusion, we found that changes in the signal oscillations of the
DMN regions translated into significantly different patterns of functional
connections. Slower signals increased the complexity of the patients’net-
work while faster oscillations decreased it. Crucially, the appearance of any
sort of disturbance in the BOLD dynamics was associated with a poorer
similarity with the DMN from healthy subjects. In the following section, we
explore how and where these alterations may arise in brain tumor patients.
Local and distributed functional signals arising from brain tumors
We asked whether spatial proximity between the tumor and the DMN could
explain desynchronization. The magnitude of alteration in the dynamics of
DMN was not correlated with the mean Euclidean distance (p= 0.583,
df = 23, two-tailed exact test) nor with the total overlap (p= 0.29, df = 23,
two-tailed exact test) between tumor and DMN centroids (Fig. 2c).
Next, to assess whether intra-tumor functional activity was both
existent and relevant, we compared the DAS computed from the DMN with
that obtained from intra-lesion signals (see Methods). The alterations in the
signals from the tumor and the DMN of the same patient were highly and
significantly correlated (r= 0.696, df = 23, p< 0.001, two-tailed exact test;
Fig. 2d). This result ultimately linked what happened inside the tumoral
tissue with what was observed across spatially distributed brain regions.
That is, abnormalities in the signals were shared between lesioned and
unaffected regions. We also compared the properties of the BOLD signal
inside the tumor with the same regions in healthy subjects. Alterations in
lesioned areas were observable in the power of the signal ( P
jj
>0,p= 0.031,
df = 23, one-tailed t-test) but they were significantly more pronounced in
the dynamics (Fig. 2e; DAS
jj
>0, p< 0.001, df = 23 one-tailed t-test).
a
b
c
d
e
f
Fig. 1 | sub-PAT07 Edema and DMN functional signals. a Mean functional signal
(BOLD) measured inside the edema of a patient (red) as compared to signals from
the same region in healthy subjects (gray). Similar signals were also found in all
subjects inspected. The time axis is shown in time steps rather than seconds.
bFunctional signals from 5 example regions belonging to the DMN of control
subject 10 (randomly selected). Colors code for regions assigned to the same com-
munity through the Louvain Community detection algorithm. No qualitative dif-
ference is found between the raw time series inside the edema of a patient and regions
of the DMN of a healthy subject. cCumulative power (lines), power distribution
(bars), autocorrelation function (ACF), and total power relative to healthy subjects
(histogram) for the patient (red) and mean of controls (blue) functional signals of the
regions in the DMN. Error bars [mean ± SEM] indicate the results for the control
population, while “*”codes for statistical significance. The relative power was
obtained by averaging over subjects and DMN regions and taking healthy subjects as
the baseline (i.e., equal to 1). dFunctional DMN from the same patient and mean of
control subjects (see Methods). eFunctional complexity as measured by the dis-
tribution of correlations for the patient’s network (red) and the mean of control
(blue) [mean ± SEM] (see Methods). fFunctional signal of two randomly selected
regions from the same patient (red) as opposed to all the control subjects (light blue).
No apparent difference is found between raw time series across regions, subjects, and
patients.
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ab
c
efg
d
Fig. 2 | Linking DMN and tumor BOLD signals. Pearson Correlations and the
corresponding pvalues are shown. Error bars correspond to the mean ± SEM.
aCorrelations between node similarity as measured by the Pearson correlation
coefficient and the Dynamics Alteration Score (DAS) from the Default Mode Net-
work (DMN). The inset shows how alterations in the dynamics shape the organi-
zation of the network regardless of the direction of the displacement of the frequency
spectrum. bAlterations in dynamics correlate with alterations in network com-
plexity. Change in the complexity of the patients’DMN with respect to the healthy
pool (Directionality ΔΘ and Magnitude |ΔΘ|) as a function of the DAS. cScatter plot
showing the null correlation of DAS with distance and overlap between lesion and
the DMN centroids. dA strong linear trend was found between alterations inside the
patients’tumor and alterations in the DMN as measured by the DAS. The orange line
corresponds to the significant linear fit (two-tailed exact test), and the shaded areas
mark the 95% confidence interval. eDifferences in total power relative to healthy
subjects (LEFT) and dynamics (RIGHT). Only the absolute values were significantly
different from zero. fScatter plot of the two components found via Fast Independent
Component Analysis applied to the DAS differences between patients and control
subjects. The same two clusters (red, and blue) were consistently found with a
K-means score of -1.2. gTOP, Alteration in dynamics between different groups of
tumors. BOTTOM, Logistic regression between DAS and periventricular (PV)
tumor patients. Qualitative inspection reveals a tendency for periventricular tumors
to display slower BOLD dynamics, although they were found to be non-significant
presumably due to the small number of samples (N=5,p= 0.31, one-tailed U-test).
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As opposed to changes in network organization and complexity (Fig. 2a),
there was no statistical relationship between alterations in the intensity and
the oscillations (r=−0.113, df = 23, p= 0.588, two-tailed exact test).
Dimensionality reduction via Fast Independent Component Analysis
was applied to cluster differences between patients and control subjects. The
same two clusters were consistently found with a K-means score of ~ −1.2,
although no apparent groups were observable (Fig. 2f). As such, we hypo-
thesized that the alteration in power distributions might be explained by
tumor features. We divided subjects into two groups according to 5 tumor
features: location (brain lobe), size (with respect to the sample median),
histology (based on histological features of the resected tissue), grade (based
on the cell appearance and differentiation in the sampled tumor, which
reflect tumor aggressiveness, i.e., the ability to grow, infiltrate and recur) and,
periventricular (when located at the borders of the ventricles). If the tumor
intersected the ventricles, we expected the cerebrospinal fluid to penetrate
the lesion thus severely disturbing and slowing the signal recovered. Tumors
intersecting the ventricles showed a large positive DAS, although non-
significant (Fig. 2gTOP;p= 0.31, one-tailed U-test). However, given its
larger magnitude and greater significance with respect to all other groups,
we provide a possible explanation of its meaning in the discussion. A logistic
regression also displayed a reasonable determination coefficient and pattern
(R2= 0.8), but the small number of periventricular tumors did not allow for
further quantitative assessment (Fig. 2gBOTTOM).
As a final note, we report that the tumor with the highest DAS was a
grade II ependymoma located in the temporal lobe and intersecting with the
left lateral ventricle. The tumor with the lowest (and negative) DAS corre-
sponded with a grade I meningioma located in the frontal-skull base not
intersecting the ventricles.
Structural brain networks containing intra-tumoral and
peritumoral fibers
As a first step towards reliable fiber tracking inside brain tumors, we
designed a combined approach that used two different (previously vali-
dated) constrained spherical deconvolution fiber orientation function
(FOD) reconstruction algorithms (Fig. 3a). As suspected15, the multi-shell
approach caused overdamping of the diffusion signal within the lesion
mask (Fig. S6). In combinationwith this, the altered anatomical properties
surrounding the lesion imposed an artificial early stop to streamlines that
could, if diffusion signal was available, penetrate or circumvallate the
tumor (Fig. 3b; see also Supplementary Material). Instead, the careful
combination of FODs and the relaxation of anatomical constraints in the
peritumoral tissue allowed our pipeline to reconstruct well-known white-
matter pathways that were otherwise truncated (Fig. 3c). Importantly,
these emerging tracts appeared as natural extensions of those stopped by
the lesion.
However, validation of any fiber tracking pipeline is difficult due to the
lack of a unique ground truth. Nonetheless, we inspected the scale-free
properties of the weighted degree distributions of the reconstructed net-
works. For every healthy subject and patient, we fit the tail of these dis-
tributions to a power law, characterized by a single exponent α(see the
Supplementary Material). Distributions showed scale-free properties with
acceptable Kolmogorov-Smirnov distances for different scaling ranges
confirming a power law organization in the asymptotic limit
(α22;3
½
;D2½0:15;0:22,σ2½0:09;0:62). Crucially, differences in the
power law distribution of the healthy networks compared to the lesioned
networks obtained with our pipeline were comparable to the differences of
the networks obtained with a canonical multi-shell multi-tissue pipeline
(Fig. S6d; p> 0.05, two-tailed Wilcoxon test,two-tailedU-test).Yet,the
differences in the distributions between our hybrid approach and the multi-
shell multi-tissue one increased with tumor size. An ordinary linear squared
model showed a significant correlation (R2= 0.439, F= 5.484, p= 0.006)
between alterations in the power law behavior and several tumor features.
Tumor size was the most significant predictor (p= 0.005, df = 21, two-tailed
t-test). Thus, differences between our pipeline and the standard approach
disappeared with small tumors (Fig. S6).
Structural predictions after tumor resection
One of our main goals was to design a method capable of predicting how
structural graphs will look after major surgical procedures while still elu-
cidating the confounding effects of connectivity reorganization. Previous
work showed that linear models could surprisingly capture the fundamental
properties of structural graphs32. We evaluated a Fully Connected NETwork
(FCNET) against a Huber Regressor and a null model. The choice of a
Huber Regressor was motivated by its robustness to outliers and the pre-
sence of heterogeneous data points. Testing against null models helps in
avoiding circular analysis33, therefore we also benchmarked FCNET against
an untrained linear generator. Both the outputs of the Huber and null
generators were weighted by the same anatomical prior as the FCNET. For
each model and fold, we tested the left-out network with 6 different metrics
(see Methods). The results for each score are shown in Table 1for the mean
and in Table S1 for each subject in the dataset.
FCNET significantly outperforms the null model in all evaluation
metrics (p< 0.001 two-tailed U-test). When tested against the Huber
regressor, FCNET outperformed it in the metrics assessing numerical
reconstructions (p< 0.05 two-tailed U-test; for MSE and MAE) as well as
metrics assessing similarity (p~ 0.05 two-tailed U-test; for PCC and CS).
However, when tested for topological accuracy, FCNET did not improve
with respect to the Huber regressor measured by the Kullback-Leiber (KL)
and Jensen-Shanon (JS) divergences (p> 0.4, two-tailed U-test). Despite not
being trained on preserving topological features, both FCNET and Huber
captured structural properties since both models significantly decreased the
KL (p< 0.001, F> 300, one-way ANOVA; p< 0.001, F> 30, Kruskal-Wallis
test) and JS (p< 0.001, F> 300, df
between
=2,df
within
= 54, one-way ANOVA;
p< 0.001, F> 30, Kruskal-Wallis test) divergences of the weight probability
distributions between predicted and ground truth networks (see Methods).
None of the models was trained using a regularization method to
prevent negative connections. Surprisingly, however, FCNET generated
negative connections that accounted for less than 25% and they were all
between 0 and −0.5. Since these values are in log scale, they would account
for a connection of less than 1 and get filtered by the anatomical threshold.
We show the generated post-surgery networks and residuals of three ran-
domly selected subjects in Fig. 4.
Subject-specific predictions
The connections within brain networks are highly heterogeneous in the
context of a brain tumor. Herein, we imposed anatomical prior to act as a
regularization method. However, a highly restrictive prior resulted in a
complete loss of subject specificity despite FCNET achieving lower recon-
struction errors. After some trials, we found that an optimal (or nearly
optimal) prior was able to discard enough connections while still capturing
some inter-subject variability of the networks (Fig. 4red squares; see also
Fig. S7). However, model generalization does not allow for a perfect fittoall
data points (Fig. 4right column).
Next, we asked whether FCNET was simply overfitting a small subset
of similar subjects. We calculated the z-score of each metric with respect to
the 19 folds cross-validated subjects (see Methods). For all metrics, we found
that ~65% of all z-scores lied in the ±σrange and ~95% fell in the ±2σ.Even
more, when repeating the training with different starting weights, all sub-
jects but 2 showed different scores (Fig. 5a); they were not uniquely classified
as outliers and therefore were considered in all the subsequent analysis
(p> 0.05, df = 17, two-tailed Grubbs test). As a further checkpoint to ensure
that the model was not overfitting to a specific subset of similar subjects (i.e.,
patients with similar tumors), we tested for the normality of the z-scores,
thus finding that all of them had a significant linear correlation (r>0.9,
p<0.01 two-tailed t-test) between the theoretical and observed quan-
tiles (Fig. 5b).
We used four metrics to evaluate the model’s output measured the
numerical similarity between the ground truth and predictions. Not
surprisingly, they exhibited high pair-wise correlations (|r| > 0.8 and
p< 0.01, two-tailed permutation test), therefore post hoc analyses on one
score were generalizable to all. Unlike MSE and MAE, both the PCC and
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b
c
d
T1w Tumor mask
Healthy tissue
5TT Image Modified 5TT
Image
dwi
MSMT
SS3T FODf Merge
Lesion tracts
Whole-brain
ACT
Lesion CM
Healthy CM
CM Merging
strategy
1. Greedy
2. Mean
3. ...
Lesioned
structural brain
network
a
e
Whole-brain SIFT2
Lesion SIFT2
Fig. 3 | Reconstruction of brain structural networks. a Summary of the workflow
designed to generate the tractograms in the presence of a brain tumor. Multi-shell
multi-tissue (MSMT) reconstruction methods are run together with anatomically
constrained tractography (ACT) to obtain the “healthy”fibers without including
lesioned tissue. Fiber orientation functions inside the lesions are obtained by run-
ning the single-shell 3-tissue (SS3T) method only inside the lesioned regions (Tumor
mask). Fiber orientation functions (FODs) from both methods are then merged.
Connections originating, terminating, or traversing oedemic tissue are tracked with
the iFOD2 probabilistic algorithm by only seeding inside the lesion. A maximum
angle and FOD amplitude cutoff stopping criteria are used. Both tractograms are
used to obtain a weighted connectivity matrix with the outputs of streamline filtering
(i.e., SIFT2). As a final step, the lesion and healthy structural matrices are merged
using a customized formula (e.g., greedy). bAxial, coronal, and sagittal planes
(thickness of 1 mm) of the tractogram from sub-PAT16 obtained with a simple
multi-shell multi-tissue without masking the tumor (see Methods). 1 mm thick
cropping point is (x,y,z) = (35, −17,−3) mm in MNI space. cTractogram from sub-
PAT16 identical coordinates and thickness as in (b) but having used the hybrid
method outlined in (a). Importantly, large cortico-spinal and superior longitudinal
fasciculus peritumoral fiber bundles are now visible. Overview of the whole brain
tractogram of the same subject with a simple MSMT approach (d) and our hybrid
pipeline (e).
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CS are normalized between -1 and 1 making it desirable regarding
reproducibility. Without loss of generality, we based the following analysis
on the PCC.
FCNET’s sensitivity to tumor size
Structural disconnections are typically correlated with the size of the lesion
and cognitive deficits34; thus, we hypothesized that large tumors would
decrease the performance of the network. Considering all subjects, corre-
lations between accuracy and size werenotfoundtobestatisticallysig-
nificant (Fig. 5c; r=0.0183, p> 0.5, df = 17, two-tailed permutation test).
However, we redid the same analysis without the three largest tumors as
they appeared to be abnormally large. Those tumors had volumes greater
than 60 cm3and their mean value was considered an outlier (p< 0.01, two-
tailed Grubbs Test). In this scenario, correlations drastically increased both
in value and significance (r=−0.336, p= 0.04, df = 14, two-tailed permu-
tation test); yet, when disregarding the fourth largest tumor, relative changes
in correlations were less pronounced (r=−0.451, p< 0.01, df = 13, two-
tailed permutation test).
To settle whether the effect of size was indeed present, we divided all
patients, including the three largest ones, into two groups using the median
of the whole dataset (Fig. 5d; P50 = 12.95 cm3). Subjects with small tumors
(size < median) showed higher PCCs (0.825 ±0.007 [mean ± SEM]) than
subjects with large tumors (0.792 ± 0.013 [mean ± SEM]) (p= 0.03, df = 17,
one-tailed t-test; p= 0.03, one-tailed U-test).
In conclusion, the highly non-linear generative model was sensitively
worse when considering large tumors. However, there seemed to exist
confounding effects distorting the relationship. In the next section, we
explored those in more detail.
Table 1 | Model results (mean ± SEM)
Model MSE MAE PCC CS KL JS
FCNET 1.91 ± 0.07 0.83 ± 0.01 0.807 ± 0.008 0.859 ± 0.006 9.09 ± 0.12 0.68 ± 0.01
Huber 2.14 ± 0.07 0.87 ± 0.02 0.785 ± 0.007 0.841 ± 0.006 9.18 ± 0.13 0.69 ± 0.01
Null 8.09 ± 0.17 1.61 ± 0.03 0.004 ± 0.002 0.005 ± 0.003 13.13 ± 0.07 0.814 ± 0.003
The Fully Connected NETwork (FCNET) was tested using a Leave One Out cross-validation scheme in 6 metrics (MSE: Mean Squared Error; MAE: Mean Absolute Error; PCC: Pearson Correlation
Coefficient; CS: Cosine Similarity; KL Kullback-Leiber and JS: Jensen-Shannon Divergences). In addition, wetested against two benchmark models: Huber andNull regressors. FCNET showed a significant
improvement in all metrics evaluated. Both Huber and Null models were also tested in the same framework, that is, the predicted likelihoods weighted by the same anatomical prior (see Methods). Bold
numbers indicate better performance; lower is better for MSE, MAE, KL, and JS while higher is better for CS and PCC.
Fig. 4 | FCNET’s network generation. Three sub-
jects were randomly selected to be displayed as visual
proof that FCNET captures the essential properties
of the post-surgery graphs. The residuals show the
absolute difference between the predicted and
ground truth networks. Negative connections were
dropped for visualization purposes since they cru-
cially affected the color scale but not the structure.
FCNET can capture some specific inter-subject
variabilities (augmented red squares) despite being
trained on highly heterogeneous data. Connection
strength is measured as log 1 þwðÞwhere wis the
native connectivity derived from the tractograms.
PAT03: meningioma grade I, location parietal right,
78.44 cm3. PAT15: meningioma grade I, location
frontal right, 2.13 cm3PAT28: oligodendroglioma
grade II, location frontal left, 11.49 cm3.
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ab
cd
ef
Fig. 5 | FCNET’s selective predictions. a,bNormality assumptions on the whole
pool of metrics used to test the model in each 1-fold (MSE: Mean Squared Error;
MAE: Mean Absolute Error; PCC: Pearson Correlation Coefficient; CS: Cosine
Similarity; KL Kullback-Leiber and JS: Jensen-Shannon Divergences). Boxplot of
zscores in (a). Shaded areas represent the Inter Quartile Range (Q3–Q1) and the
solid black line depicts the median. Marked subjects (PAT20 and PAT26) were not
classified as outliers for all the metrics used (p~ 0.15, Grubbs one-tailed test). Q–Q
plot for each metric in (b). The dashed black line shows the expected y = x relation.
The significance for each regression was assessed (r> 0.95 and p< 0.01). c,dImpact
of tumor size in the predicted graphs. Correlations between PCC and tumor size in
(c) considering all but the three largest patients (orange) and considering all subjects
(orange+blue). Differences in the PCC [mean ± SEM] between small and large
tumors in (d). The subdivision was made based on the median of the set
(P50 = 12.95 cm3). eDifferences in the PCC [mean ± SEM] between tumor type and
tumor grade (p= 0.037, one-tailed U-test). fDifferences in the PCC [mean ± SEM]
between tumor locations.
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Potential confounding effects on structural connectivity
reorganization
The histology of the tumor greatly influences clinical considerations such as
survival rates or possible treatment strategies. Meningiomas tend to exert
pressure on the healthy brain tissues in opposite to gliomas which show
more infiltrative behaviors. However, we did not find significant differences
(Fig. 5e; p= 0.29, df = 17, two-tailed t-test; p= 0.3, two-tailed U-test) in the
PCC between meningiomas (0.814 ± 0.002 [mean ± SEM]) and gliomas
(0.795 ± 0.007 [mean ± SEM]). Predictions were slightly better for low-
grade tumors (0.816 ± 0.001 [mean ± SEM]) than high-grade(0.794 ± 0.003
[mean ± SEM]) but without reaching statistical significance (p= 0.15, two-
tailed U-test).
Since not all regions of the brain are equally important in terms of
structural connectivity, we also tested if the location of the tumor had an
impact on the predictions. The dataset included 12 patients with frontal and
7 patients with temporal or parietal tumors. We found differences in per-
formance between frontal and non-frontal tumors (Fig. 5f). Despite not
being significant (p= 0.12, two-tailed U-test), frontal tumors showed higher
PCC (0.817 ± 0.002 [mean ± SEM]) than temporal and parietal together
(0.789 ± 0.003 [mean ± SEM]).
Lastly, and contrary to what we observed in functional dynamics,
the results of FCNET were not sensitive to whether the tumor intersected the
ventricles (p= 0.82, two-tailed U-test).
Topological predictions
We also tested the topology of the generated networks by computing the
weight probability distribution. The loss function used to train all models
did not have any topological term, but the generated networks shared global
properties with the ground truth as measured by the KL and JS divergences
in Table 1. The generated graphs showed a biological lognormal weight
distribution with a small number of highly connected nodes (Fig. 6;seealso
Supplementary Materials).
Discussion
The focus of the present work is to quantitatively study functional and
diffusion MRI signals in the presence of brain tumors. Importantly, unlike
previous studies, we focus on the signal present within the lesion and how it
explains connectivity reorganization in both imaging modalities. We show
that when functional time series are compared in the frequency spectrum,
the distribution of oscillatory frequencies is strongly related to how resting-
state connections are re-wired within the DMN. We also observe that the
power spectrum within the brain tumor regions (including edema) is
strongly related to an oscillatory decoupling between the distributed and
active brain regions. Moreover, we designed a hybrid tractography pipeline
capable of combining anatomical constraints and diffusion signal from the
lesioned tissue. Finally, we use the reconstructed networks before and after
brain surgery to train a machine learning model able to extract information
about non-normative patterns of structural reorganization.
We also set out to determine whether functional activity was present
within the brain tumor. We find qualitatively similar signals between
healthy and tumor tissues. However, the fact that there is a non-zero tumor
functional signal is not indicative of its relevance. Therefore, to explore the
functional sanity of the signals found, we first look at the existing differences
in DMN between patients and healthy controls.
Functional connections rely on temporal correlations between time
signals which are entirely dependent on the phase as well as the active
frequencies in the temporal signals7. Because of this mathematical con-
struction, we hypothesized that the most descriptive feature of Blood-
Oxygen-Level-Dependent (BOLD) time series would be the power dis-
tributions across frequencies. For this purpose, we designed a DAS that can
capture not only how different two power distributions are, but also how
these differences are related with the relative dynamics of those signals (see
Methods; see also Figs. 1candS1–S5). Intriguingly, the alteration in the
signal dynamics (measured by the DAS), strongly correlated with network
closeness (measured by node similarity; Fig. 2a).
The integrity of resting-state activity of the brain has been associated
with cognitive function6. Based on this paradigm, numerous studies have
explored how functional damage translates into cognitive impairment1,3–5,35.
As a clear demonstration of the resilience of the brain to damage, all of them
reported a continuous rather than binary decrease in cognitive performance.
Brain networks undergo rearrangement to minimize the impact of lesions,
and this rewiring follows specificconstraints
36.Fromelectro-
encephalography recordings, Wolthuisandcolleaguesfoundthelevelof
topological similarity to be predictive of post-surgery cognitive skills35,
suggesting once again that understanding how the brain responds to lesions
is crucial to predict the impact of surgical procedures on cognitive function.
ab
Fig. 6 | FCNET’s topological accuracy. Black thick lines show the mean weight
probability distribution predicted by FCNET (a) and the HUBER regressor (b).
The dashed red line shows the mean weight probability distribution of the real post-
surgery graphs. Shaded background bars show the predicted distributions for each
subject in the dataset.
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To this purpose, we computed the complexity of the DMN and found
significant alterations in magnitude with variable directionality across
patients. Approximately half of the patients display increased network
complexity while the rest exhibited the opposite pattern (Fig. 2b). What
these two non-contradictory findings suggest is that different tumors and/or
patients react differently when considering DMN reorganization which
inevitably leads to different network complexities. A strong positive trend
exists between the presence of slower oscillations (DAS > 0) and higher
complexities (Fig. 2b). We may speculate that faster time series resemble
noisy temporal structures lacking temporal coherence, therefore, resulting
in a more uniform distribution of functional connections. In contrast, for
slower functional dynamics, more complex networks would naturally arise.
However, as stated by the proponents of the measure used here30,high
complexity does not imply an optimal segregation-integration balance
promoting small-world topologies and their subsequent advantages in
information propagation37.
We also try to answer the origin of these desynchronizations.Current
knowledge states that structural closeness is not sufficient to understand
disruptions in patterns of functional disconnections1–3. In accordance
with this, changes in BOLD dynamics were not explainable by the spatial
overlap nor distance between lesions and DMN (Fig. 2c). Interestingly,
dynamic alterations in DMN regions increased rather linearly with the
distance to the tumor, from faster oscillations in nearby tumors to slower
ones in spatially separated lesions (r= 0.442, p= 0.027, two-tailed exact
test). However, distance does not account for the difference in network
rearrangements given that dissimilarity increases for both slower and
faster dynamics.
Instead, DMN desynchronization is better explained by frequency
shifts inside brain tumors (Fig. 2d). Current neuroscience methods struggle
to address questions of causality, but for the sake of completeness and
transparency of the results shown, we provide a speculative causal line to the
findings reported. A plausible explanation would be to consider that the
tumors themselves are altering the neural dynamics locally. Then, such
alterations would propagate through spatially distributed brain regions,
perhaps supported by structural connections20,21,23,38, causing a global DMN
desynchronization. To try and compensate, BOLD correlations between
regions would rearrange themselves to spare the functionality. Network
similarities and topologies across subjects would change, as found by pre-
vious studies1–3,35, without greatly altering their complexity. However, DASs
could not disentangle whether the tumor altered the signal and that
alteration spread to the DMN or the opposite. The relationship between the
alterations in the DMN and the tumor remained unchanged when con-
sidering only the tumor core or the non-necrotic tissue of the lesion for
patients with gliomas (Figs. S8–S9).
Finally, periventricular tumors display a higher (positive) DAS than
non-periventricular tumors. These differences do not reach statistical sig-
nificance but are approximately five times larger in magnitude with respect
to other groups. An increase in the volume of cerebral and lymphatic fluids
inside the tumor may be the source of a larger desynchronization in the
BOLD signal. Further research is required to determine whether this is
associated with worse survival ratesinhigher-gradegliomas,suchas
glioblastomas39,40. Rather, tumors growing within the ventricles may result
in obstruction of CSF flow leading to ventricular dilation and affecting CSF
dynamics in ways that need not resemble the ones we reported.
Structural brain networks, commonly referred to as structural con-
nectomes, should be reconstructed with special care to avoid false positive
connections. Moreover, in the presence of pathological tissue, fiber recon-
struction methods suffer from cerebrospinal fluid contamination due to the
inflammation of neuronal tissue. Novel algorithms based on high angular
resolution imaging are specifically designed to minimize the effects of this
contamination but neglect substantial information (i.e., multi-shell diffu-
sion data)15. In this regard, we designed a hybrid pipeline to use each method
where it is best suited (Fig. S6) while, if available, using all the diffusion shells
acquired. The SS3T method needs to be used only inside the tumor hence
only discarding multiple diffusion shells in the lesion area. Further research
should try to assess whether independently running SS3T with each shell
can be combined or not.
On the other hand, Anatomically Constrained Tractography (ACT)
has been shown to increase the correspondence between generated
streamlines and real fiber bundles, but its usage is not suited for tumoral
regions. Automatic segmentation algorithms often delineate tumors with
gray matter causing premature stopping of tracking algorithms19.Tobypass
this effect, Aerts and colleagues5artificially copied the segmented brain
tissue from the contra-lateral hemisphere to the damaged region. However,
this strategy neglected the fact that a brain tumor could have critically altered
the white and gray matter structures invalidating the proposed copied
segmentation (Fig. S6a). Alternatively, these constraints can be dropped at
the price of losing anatomical correspondence between the tractogram and
the white matter pathways15.
In this direction, our pipeline used anatomical constraints outside
tumors while entirely relying on the diffusion signal inside the tumor.
Importantly, the relaxation of the anatomical constraints in peritumoral
tissue together with the incorporation of intra-tumor FODs yielded well-
known tracks that were otherwise truncated (Fig. 3b, c; see also Figs.
S10–S13). Brain tumors are heterogeneous in size and location; thus, it is
important to emphasize that our pipeline gradually reduces to a “standard”
setting the smaller the tumor is. We studied the scale-free properties of the
structural networks derived from our pipeline and observed that they
asymptotically converged to the properties of networks derived without
considering peritumoral fibers (Fig. S6d). For example, if a tumor were of
small size and located mostly within gray matter, most of the peritumoral
fibers would remain unaffected. However, in more critical cases, such as the
ones shown here, the artificial truncation of streamlines derived from
canonical approaches results in a larger percentage of disconnections than
our hybrid pipeline (Fig. 3d, e). Crucially, network neuroscience studies
might rely on these artificial disconnections to report structural dis-
connections without truly assessing whether they are indeed present or
introduced3,19. Furthermore, the deletion of important fiber tracks could
have detrimental effects on surgical planning given the evermore common
use of tractography in pre-operative settings41, needing personalized models
that consider microstructural properties of the tumors for more accurate
tracking alternatives12.
Alternative solutions to fiber tracking inside brain tumors include
multicompartment diffusion tensor models but given their impossibility to
resolve complex white matter structures as well as using diffusion signal
from a single shell, we chose not to use them13,14.
As a last contribution, with the reconstructed structural networks, we
train a machine learning model to predict connectivity rearrangement after
brain surgery. Brain tumors display high heterogeneity including size,
location, histology, grade, and infiltration in gray matter areas, among
others. Consequently, networks of brain tumor patients also show great
variability (Fig. 4). Furthermore, interindividual variability in terms of brain
plasticity and network rearrangement after surgery represents another
relevant source of complexity when trying to understand and predict the
organization of brain networks42.
To reduce the impact of both factors, previous work43–46 guiding pre-
dictions in a different context with networks from healthy subjects achieved
good results, even when considering simple methods32. As such, we designed
aflexible anatomical prior that was used to filter unplausible connections.
We framed the problem in the Bayesian domain, which permits this prior to
be backpropagated during the training phase (see Supplementary Material).
Then, highly plausible connections arenaturallygivenmoreimportance
when minimizing the loss function while, at the same time, successfully
discarding improvable edges.
Neural architecture design in deep learning is itself an exciting and
constantly evolving field. Nonetheless, it is well known how the choice of a
specific architecture introduces a bias47. A natural choice for predicting brain
connectivity is graph neural networks. However, as stated in the introduc-
tion they are not exempt of problems26. T oo vercome them, we design a one-
hidden layer non-linear regressor.
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Fully connected layers have achieved great success in prediction studies
of both clinical48 and relational features28 when adequately corrected for
overfitting confounds. The model was trained with intercalated validation
steps and its performance was evaluated using Leave One Out cross-
validation. The generative model achieved lower reconstruction errors than
the chosen benchmarks (Table 1;seealsoFig.4). We also trained the same
model using brain networks obtained without the hybrid tracking pipeline
(see Methods). Interestingly, results were slightly worse (Table S2; see also
Table S3), suggesting that our hybrid method is equivalent if not better than
current state-of-the-art fiber reconstruction pipelines.
Despite complying with normality assumptions, the reconstruction
errors for two subjects were consistently low and high. An interesting
paradigm in statistics emphasizes those data points that deviate from the
trend. When looked from this perspective, the potential of deep learning
models to uncover complex patterns translates into the increased ability to
detect individual data points that deviate from, now more complex non-
linear, statistical relationships.
The accuracy of the FCNET prediction was correlated with tumor size,
achievinghigherscoresforsmalltumors(Fig.5c, d). The chances of
affecting long-distance structural connections naturally increase with the
size of the tumor. Long-distance connections are expected to carry high
metabolic costs36. Moreover, long-range connections in structural networks
have been shown to emerge during the early stages of development in C.
elegans49, mice hippocampal circuits50, and primates51, although the debate
is still active in the latter case. Therefore, directly reestablishing a long-range
connection (i.e., end-to-end) to preserve rich-club and small-world
topologies5might not be feasible. A possible way to circumvent these con-
straints would require several indirect connections leading to complex as
well as non-normative patterns elusive to the model trained.
All but one patient suffered from grade I meningiomas, while all
gliomas were of grades II and III. Interestingly, FCNET’s prediction accu-
racy is less sensitive to tumor histology than grade. According to previous
studies, tumor grade and histology have the greatest influence on survival
rates in high-grade (III–IV) glioma patients52. Joint understanding of sur-
vival rates and connection rewiring is challenging, due to poorly established
structure-function relationships. Given the results shown, however, we
suggest that grade instead of histology is a better indicator of normative
patterns of connection reestablishment. In addition, the last years have been
characterized by increasing evidence on the mutational profile impact of
survival rate of gliomas53.Thismeansthatgliomascanhavecompletely
different survival rates according to their molecular profile53,54.
The location of the tumor did have an impact on theprediction score,
although it was borderline significant. The predictions for frontal tumors
showed slightly higher accuracies. Frontal areas are associated with higher
metabolic activity55 causing energy expenditure, shaping as well as
increasing the costs of network rewiring56. On the other hand, frontal
regions are also the endpoints of fiber bundles, mainly involving both
short- and long-rangeconnections. Consequently, these two factors might
compensate for each other, allowing for rather normalized patterns of
network rewiring easily captured by the prediction model. However, it is
difficult to assert the validity of this result as frontal tumors represented
slightly more than half of the total. Thus, FCNET might very well be
overfitting to these patients although we are inclined to discard this
hypothesis given the precautions taken into consideration(Fig. 5a; see also
Methods).
In contrast to the functional results discussed previously, the accuracy
was independent of the periventricular features. This is understandable
since the ventricles contain cerebrospinal fluid and no biologically relevant
streamlines could be reconstructed within the ventricular system.
Interestingly, despite not being trained on it, predictions from both the
FCNET and the alternative model show essential topological properties
found in brain networks. The predictive model generates weighted networks
that, opposite to their simpler unweighted siblings, follow lognormal rather
than scale-free distributions (Fig. 6; see also Supplementary Materials). This
effect has been found in numerous studies on mice and macaques57,58,
suggesting that rapid decay and high variance in connection strength arise
from distance-dependent wiring costs59.
The main limitation of this study is the small sample size and t helac k of
an external validation dataset. Heterogeneity could also impact the results.
Despite not showing inter-group differences in the time interval between
scans, individual trajectories should also be considered, and thus investi-
gated in more detail. However, to overcome the heterogeneity present in the
data, we conducted some independent analyses for several groups. As such,
all statistical results should be interpreted with extreme caution. None-
theless, small sample sizes are found very often in studies dealing with
patients with brain tumors1–5,41 possibly due to current standardized pro-
tocols disregarding pre-surgery functional acquisitions, rather simple dif-
fusion sequences and the lack of multi-site initiatives60–62.Also,carefully
designed metrics can pinpoint existing phenomena, as is often seen in
medical case studies. Further work should also reveal the predictive potential
of the score used in this work regarding cognitive impairment and perhaps
local control and survival.
In terms of the machine learning model accuracy and reliability, due to
a small sample size, we were limited as to which Deep Learning methods
were usable. Recent progress in Geometric Deep Learning and Graph
Representation Learning24,25 have yielded very promising results which are
already showing great potential in medical imaging applications. Further-
more, it has been proven that topological guidance of graph neural networks
drastically increases accuracy in highly heterogeneous data27. However, all
thesemethodsrequirehugedatasetswhichmaynotbeavailablefor
medically sensitive problems such as the one studied here. Even more, the
topology and structure of networks suffering from brain tumors are not yet
clearly understood, introducing a new layer of complexity as to what
measures should be used to guide the training. Nonetheless, further work
should find an optimal compromise to exploit these useful features in
smaller datasets.
To summarize, detailed analysis in the frequency domain revealed local
and distributed abnormalities in resting-state time series and connections
while establishing a potential causal link between them. We also proposed a
pipeline for fiber tracking that used more diffusion signal than previous
attempts, as well as anatomical constraints. Lastly, we used these structural
networks, which included intra-tumor streamlines and connections, to train
a machine learning model to predict and study structural brain con-
nectomes after surgery. The model achieved competent accuracies, dis-
closed tumor-dependent plasticity patterns, and preserved biological
topologies. In summary, our results showed that brain tumors are both
functionally and structurally dynamic, strengthening the need for more
targeted MRI and neuro-oncology studies.
Methods
Acquisition and usage of MRIs
A detailed explanation of the participants as well as the acquisition of the
data is already available63; nonetheless, for the sake of transparency, we
briefly present some crucial aspects. Subjects were asked to undergo MR
scans both in pre- and post-surgery sessions. Out of the 36 subjects that
agreed to take part in the pre-surgery session (11 healthy [58.6 ± 10.6 years],
14 meningioma [60.4 ± 12.3 years] and 11 glioma [47.5 ± 11.3 years]), 28
were scanned after surgery (10 healthy [59.6 ± 10.3 years], 12 meningioma
[57.9 ± 11.0 years] and 7 glioma [50.7 ± 11.7 years]). The post-surgery scan
session took place during the first medical consultation at the hospital after
the surgical intervention (mean: 7.9 months, range: 5.2–10.7 months). There
were no differences in the time intervals between the groups (meningioma
[243 ± 12 days], glioma [223 ± 15 days], p=0.328,two-tailedU-test).As a
result, 19 pre- and post-surgery pairs of structural connectomes were usable
as training and testing data. All brain tumors were classified as grade I, II,
and III according to the World Health Organization. All ethical regulations
relevant to human research participants were followed63.
Each MR session consisted of a T1-MPRAGE anatomical scan
(160 slices, TR = 1750 ms, TE =4.18ms, field of view = 256 mm, flip
angle = 9o, voxel size 1 × 1 × 1 mm3, acquisition time of 4:05 min) followed
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by a multi-shell HARDI acquisition (60 slices, TR = 8700 ms, TE = 110 ms,
field of view = 240 mm, voxel size 2.5 × 2.5 × 2.5 mm3, acquisition time of
15:14 min, 101–102 directions b=0,700,1200,2800s/mm
2) together with
two reversed phase-encoding b=0s/mm
2blips to correct susceptibility-
induced distortions64. Resting-state functional echo-planar imaging data
were obtained (42 slices, TR = 2100 ms, TE =27ms,field of view = 192 mm,
flip angle = 90o, voxel size 3 × 3 × 3 mm3, acquisition time of 6:24 min). The
TR was accidentally changed to 2400 ms after 4 control subjects, 5
meningioma patients and 2 glioma patients were scanned changing the
times of acquisition to 7:19 min. For all the subsequent Fourier analyses, this
TR mismatch is solved by adding zero padding and truncating the shorter
time series to ensure that equivalent spectrums were sampled by the Python
methods (for further details see Supplementary Material).
Additionally, segmented lesions including the edema, non-enhan-
cing, enhancing, and necrotic areas were available. Tumor masks were
obtained with a combination of manualdelineation, disconnectome63, and
the Unified Segmentation withLesion toolbox4. To identify the tumor core
of gliomas, two clinicians with more than thirty and ten years of experi-
ence performed and independently validated the segmentations using 3D
slicer. Data only allowedfor the identification of the tumor cores; hence we
subtracted the resulting cores from the whole lesion to obtain a “non-
necrotic”region for each of the patients diagnosed with a glioma-
like tumor.
Pre-processing of MRIs
High-resolution anatomical T1 weighted images were skull-stripped65,
corrected for bias field inhomogeneities66, registered to MNI space67,and
segmented into 5 tissue-type images68. Diffusion-weighted images suffer
from many artifacts all of which were appropriately corrected. Images were
also skull-stripped65, corrected for susceptibility-induced distortions64,
denoised69, freed from Gibbs ringing artifacts70 and corrected for eddy-
currents and motion artifacts71. The preprocessed images were then co-
registered to its corresponding anatomical template (already in MNI
space)67, resampled to a 1.5 mm3voxel size and eventually corrected for bias
field inhomogeneities66. After motion correction as well as registration to the
MNI template, the B-matrix was appropriately rotated72.
Functional data was preprocessed with fMRIprep73 and the eXten-
sible Connectivity Pipeline (XCP-D)74 which are two BIDS-compatible
apps that perform all recommended processing steps to correct for dis-
tortion artifacts in functional data. Regression of global signal has been
shown to improve denoising in BOLD series without excessive loss of
community structure75. In total,36 nuisance regressors were selected from
the nuisance confound matrices of fMRIPrep output which included six
motion parameters, global signal, the mean white matter, the mean CSF
signal with their temporal derivatives, and the quadratic expansion of six
motion parameters, tissues signals and their temporal derivatives76.
Volumes with framewise displacement higher than 0.3 mm were regres-
sed out. Although smoothed time series were available, our analysis did
not consider them. All specific steps were common to all subjects, both
control and brain tumor patients. All images (T1s, T1 segmentations,
diffusion, lesion masks and functional) were eventually co-registered to
MNI space for comparison.
Assessment of default mode network and tumoral BOLD Signals
BOLD signals belonging to the DMN were identified with the Gordon
functional Parcellation77. More precisely, each one of the 41 regions classi-
fied as “Default”by the parcellation image was used as a binary mask to
extract the time series from the functional image. For each subject (patient
and control), the pair-wise Pearson correlation coefficient between time
series was computed to obtain a functional connectivity matrix. The spatial
overlap between DMNs and tumor masks was computed by summing all
the voxels in the lesion mask belonging to one of these 41 regions. To
normalize this score, we divided the resulting number by the number of
voxels belonging to each one of the 41 regions labeled as “Default”.Note
that, with this definition, an overlap of 1 would mean the presence of a
tumor the size of the entire DMN.
Overlap ¼jTumor \DMNj
DMN
jj ð1Þ
Moreover, the spatial distance between the center of mass tumor and
the DMN was computed by averaging the Euclidean distances to the center
of mass of each one of the DMN nodes.
The DMN of the patients was compared to the mean of the healthy
networks with two different metrics to assess (1) differences node-wise and
(2) the Richness of the networks. Node similarity was assessed by computing
the mean Pearson correlation between the same nodes in two different
networks. For that, each row in the adjacency matrices was treated as a
vector and compared with the same row of all matrices from the healthy
subjects. After iterating through all nodes in the DMN, the mean and
standard errors were computed for comparison. Furthermore, to assess the
complexity of a given network, we computed the absolute difference
between the distribution of correlations building the network and a uniform
distribution30. We refer to this score as ΘRichness:
Θ¼1m
2ðm1ÞX
m
μ¼1
Pμrij

1
m






ð2Þ
where m¼15 is the number of bins of the histogram estimating the dis-
tribution of correlations in the network Pμðrij Þ.Zamora-Lópezand
ccolleagues showed the robustness of the quantity in Eq. (2) with regard
to the value of the parameter m. However, sensible choices range from 10 to
20 to ensure a sufficiently rich approximation of Pμðrij Þ.Thechangesin
richness ΔΘ across patients were obtained by computing the difference
relative to the richness of the mean DMN obtained from control
subjects: ΔΘ ¼ΘPatient ΘHealthy.
A similar procedure was followed to study BOLD signals inside the
lesioned tissue. For each patient, the binary mask containing the edema was
used to extract the time series from the patient, as well as from all control
subjects. Consequently, BOLD signals in lesioned regions of the brain were
comparable to 11 healthy signals from the same region. No network was
computable in this case, making the use of Eq. (2) pointless.
Fourier analysis of BOLD signals
To compare time series between subjects, we computed the Real Fast Fourier
Transform of the BOLD series. This allowed us to compare the power
spectrum of two or more signals regardless of, for example, the dephasing
between them. Let Aωbe the amplitude of the component with frequency ω.
Then, the total power of the signal can easily be obtained by summing the
squared amplitudes of all the components:
PT¼X
8ω
Aω



2
ð3Þ
With the Fourier decomposition, we could also characterize the power
distribution of the signals as a function of the frequency. Analogous to Eq.
(3), we summed the squared amplitudes corresponding to frequencies inside
a bin of amplitude Δω.
Pωc¼100
PT
X
8ω2½ωcΔω;ωc
Aω



2ð4Þ
Since each signal had a different PT,tocomparebetweensubjectsand/
or regions, we divided the result by the total power PTand multiplied by 100
to make it a percentage. Arbitrarily, we chose the parameter Δωfor each
subject so that each bin included 10% of the total power. The qualitative
results did not depend on the exact choice of the bin width.
Similarly, we computed the cumulative power distribution CPωby
summing all the squared amplitude coefficients up to a certain
threshold. For consistency, we measured the CPωas a percentage score
https://doi.org/10.1038/s42003-024-06119-3 Article
Communications Biology | (2024) 7:419 12
Content courtesy of Springer Nature, terms of use apply. Rights reserved

and chose the thresholds to be multiples of exact percentages i.e.,
ω0/10%;20%;...).
CPωc¼100
PT
X
8ω2½0;ωc
Aω



2ð5Þ
Both the power distribution Pωand cumulative power distribution
CPωcan be used to compare dynamics between time series, but they have
the inconvenience of not being scalar numbers. Furthermore, computing
any distance-like metric (i.e., KL divergence) between these distributions
across subjects would not yield any information of whether BOLD signals
had slower dynamics (more power located in low frequencies) or the
opposite (i.e., DMN in healthy and patient).
To overcome this, we designed a DAS between time series based on the
difference between two cumulative power distributions. It is worth noting
that in the limit Δω!0, the summations in Eqs. (2), (3), and (4) become
integrals simplifying the following mathematical expressions. The DAS
between two BOLD signals i;jwas computed as the area between the two
cumulative power distributions:
DAS i;j

¼ZdωCPi
ωCPj
ω

¼DASðj;iÞð6Þ
Finding a positive DASði;jÞwould mean that time series ihad slower
dynamics than time series jsince more power is accumulated in lower
frequencies with respect to the total. Throughout this manuscript, DASs
were defined as the difference in power distribution between patients and
the healthy cohort. For a simplified and, hopefully comprehensive, example,
we kindly refer the reader to Fig. S1. To characterize a specificDMN,all
these measures were computed for each region separately and then averaged
[mean ± SEM]. As opposed to the ΘRichness, the DAS was computable
both for DMNs and tumors since it only required two temporal series rather
than a complete distribution. To compute absolute values of this score, the
DAS for each region (or tumor) was made strictly positive. Only then
average between regions and subjects was performed. Notably, these two
operations are not interchangeable.
For the score defined in Eq. (6) to make sense, the Real Fast Fourier
Transform of the time series needed to be computed using the same fre-
quency intervals, which, in short, implied that the time duration of the
signals needed to be equal. For functional images with different TRs,this was
solved by adding zero-padding to the shortest signal to match the same time
duration (Fig. S14). Further permutation analyses on a reduced subset of
subjects with identical TRs confirmed the tendencies reported in the text
(Fig. S15).
Reconstruction of tumoral structural brain networks
To ensure a detailed subject-specific network, we used a state-of-the-art
pipeline to obtain brain graphs while at the same time not neglecting tracts
inside lesioned regions of the brain (i.e., brain tumors). We combined two
reconstruction methods, yielding two different tractograms and three
connectivity matrices. Roughly, the first tractogram aims at reconstructing
white matter fibers using non-contaminated diffusion signal, while the
second one carefully assesses the presence of meaningful diffusion signal in
perilesional and lesioned tissue. Later, for each tractogram, a personalized
connectivity matrix can be obtained and combined to yield a unique
abstraction of the brain in surgical contexts. A schematic workflow of the
pipeline is in Fig. 3a, and a detailed account of the parameters is in Table 2.
The first branch of the method consisted of a well-validated set of steps
to reconstruct the network without considering lesioned regions of the
brain. To ensure this was the case, we used a binary brain mask that did not
include the segmented lesion (i.e., we subtracted the lesion from the brain
binary mask). This step was added for consistency with the logic of not
tracking within the lesion. Nonetheless, the steps were repeated without this
mask and the results were found to be almost identical (Fig. S6). This was
expected as multi-shell methods highly disregard cerebrospinal fluid
contamination inside the lesion15. The lesion mask was added to the 5 tissue-
type image to be considered as pathological tissue78.Withinthismask,for
each b-value shell and tissue type (white matter, gray matter, and cere-
brospinal fluid) a response function was estimated79;andthefiber orien-
tation distribution functions (FODs) were built and intensity normalized
using a multi-shell multi-tissue (MSMT) constrained spherical deconvo-
lution approach80. Within the same binary mask excluding potentially
damaged tissue, anatomically constrained whole-brain probabilistic trac-
tography was performed using dynamic seeding, backtracking, and the
iFOD2 algorithm68,81. The total number of streamlines was set to 8 million
minus the number of streamlines intersecting the lesion (see below). We
used spherical-deconvolution informed filtering to assign a weight to each
generated streamline and assess their contribution to the initial diffusion
image82.Finally,ahealthy structural connectivity matrix was constructed by
counting the number of weighted streamlines between each pair of regions o f
interest as delineated by the third version of the Automated Anatomical
Label atlas83.
Next, to consider fiber bundles that originate and traverse lesioned
tissue, a recent method for reconstruction was used only in the segmented
lesion17. The coined Single-Shell-3-Tissue Constrained Spherical Decon-
volution (SS3T) algorithm uses only one diffusion shell and the unweighted
b= 0 volumes. We used the shell with the highest gradient strength (i.e.,
b= 2800 s/mm2) as it offered the best white-matter contrast15,80.TheseFODs
were reconstructed, and intensity normalized only inside the lesion mask
using the same underlying response function as estimated earlier in the
healthy tissue. We merged the reconstructed FODs with the previously
obtained with the multi-shell algorithm (Fig. 3a CENTER). It is important to
note that both images were in NIFTI format, co-registered, and non-over-
lapping, therefore making this step straightforward. Anatomical constraints
were no longer suited since white- and gray-matter are compromised inside
the lesion and in the perilesional tissue. Even more, regardless of the FOD
reconstruction procedure, the anatomical constraints caused fibers to stop
around the edema since those surrounding voxels were (nearly-)always
segmented as gray matter (see Fig. S6). We used dynamic seeding only
within the masked lesion and whole-brain probabilistic tractography with
backtracking to estimate white-matter fibers within the whole-brain
mask68,81. The number of streamlines was set as the average number of
streamlines intersecting the lesion in the healthy cohort. We superimposed
the lesion on the tractograms of each control subject and tallied the over-
lapping streamlines78. This was important given that each lesion was in a
different location and the natural density of streamlines in that specific
location differed. This subject-specific streamline count controlled that the
tract densities were comparable to the healthy cases (Fig. 3b–e; see also Figs.
S10–S13). Spherical-deconvolution informed filtering82 was applied to
ensure that each streamline adequately contributed to the lesioned diffusion
signal (i.e., filtering was applied inside the lesion mask). Then, a lesion
structural connectivity matrix was constructed similarly to the previous
case.
Nstreamlines in lesion ¼1
Ncontrol X
Ncontrol
i¼1X
streamlines
streamline¼1
11ifstreamline 2Lesion
0otherwise

ð7Þ
Finally, we merged the two available connectivity matrices to recon-
struct a lesioned structural brain network. To do so, we employed a greedy
approach where we took the maximum connectivity strength for each pair
of regions:
ωij ¼max ωhealthy
ij ;ωlesion
ij
 ð8Þ
Thus, for each pre-operative scan, a total of 3 different connectivity
matrices were available: the healthy connections, the (potentially) lesioned
connections, and the full lesioned structural network. The networks from
https://doi.org/10.1038/s42003-024-06119-3 Article
Communications Biology | (2024) 7:419 13
Content courtesy of Springer Nature, terms of use apply. Rights reserved

the control subjects and post-operative scans from patients were recon-
structed using a usual multi-shell multi-tissue pipeline without the binary
lesion-free mask but with the same parameters (see Table 2). Note that the
3rd version of the Automated Anatomically Labeled Atlas has 4 empty
regions out of 170 to maximize compatibility with the previous versions.
Anatomical priors and Bayesian filtration of predictions
As suggested by previous works, guiding learning with healthy cohorts
should be useful to inform predictions43–45. Brain graphs are notoriously
heterogeneous when considering age-related differences. To take this into
account, we selected subjects with significant age overlap between healthy
subjects and patients in both tumor types. However, we did not consider sex
segregation, since structural differences are rather unclear84; even more, the
sample size for each subgroup would be severely reduced. We built a prior
probability distribution of healthy links to guide the predictions using a
thresholded average of the set of connections present in this healthy cohort
(see Supplementary Material). This thresholded average allowed us to
control for the inclusion (or exclusion) of spurious connections, while
minimizing the false positive rate of connections85.
Training and testing the machine learning model
For each reconstructed network, a total of 13695 normalized edges needed
to be reconstructed, thus making the problem ill-posed. Nonetheless, as
argued in the introduction, we hypothesized that a fully connected network
adequately guided with anatomical information could capture essential
properties (see Supplementary Material). We evaluated the model using
Leave One Out Cross Validation, therefore, training and testing a total of 19
models or 19 folds.
The high number of reconstructed fibers yielded high values for the
connectivity between ROIs (~103). To prevent numerical overflow as well as
to enhance differences in lower connections, all weights wwere normalized
by computing log 1 þωðÞbefore feeding them into the artificial deep neural
network.
The model consisted of a 1 hidden layer deep neural network which
was trained minimizing the Mean Squared Error (MSE) between the output
and the ground truth determined from the MRIs (see Supplementary
Material). The weights were optimized using stochastic gradient descent
with a learning rate of 0.01 and 100 epochs to avoid overfitting. Evaluation
metrics included the Mean Absolute Error (MAE), Pearson Correlation
Coefficient (PCC) and the Cosine Similarity (CS) between the flattened
predicted and ground truth graphs. The topology of the generated networks
was evaluated by computing the Kullback-Leiber and Jensen-Shannon
divergences between the weight probability distributions of the generated
and real graphs.
Leave One Out cross-validation was done using 18 connectomes to train
each one of the 19 models. For each model, the training data was randomly
split into train (80%) and validation (20%) sets to prevent overfitting. Vali-
dation steps were run every 20 training epochs. For each fold, the testing of
each model was done in the left-out connectome (Table S1).
Statistical and topological network analysis
Statistical tests and p-value computations were done with Scipy’s stats
module and in-house permutation scripts. Unless stated otherwise, we used
one-tailed hypotheses only when addressing the significance of strictly
positive magnitudes combined with non-parametric methods. Non-
negative magnitudes cannot be tested for negative results and do not need
to satisfy normality.
The Leave One Out cross-validation approach yielded a pool of 19
subjects that were independently tested. For each metric, we computed the
z-score by subtracting the mean and dividing by the standard deviation of
the sample. Despite verifying that all of them were normally distributed, we
ran parametric and non-parametric statistical tests due to the small sample
size. Topological metrics were computed using the Networkx Python
library86. Since the brain graphs were weighted, we computed a weight
probability distribution instead of the more common degree distribution
(see Supplementary Material). To compare the weight probability dis-
tributions of two graphs, we computed the Kullback-Leiber as well as the
Jensen-Shannon divergences. The Jensen-Shannon divergence has the
advantage of being both symmetric and normalized between 0 and 1
therefore interpretable as a distance between two distributions (i.e., pre-
dicted vs ground truth).
Reporting summary
Further information on research design is available in the Nature Portfolio
Reporting Summary linked to this article.
Data availability
The original data is publicly available at OpenNeuro63. The processed data
necessary to reproduce this study is also publicly available87.
Code availability
For the processing of MRIs several softwarepackageswerecombinedand
integrated in a flexible Python 3.9.7 pipeline73,74,78,88–90.Forthemachine
learning model, PyTorch and CUDA libraries were used. The code is
publicly available87.
Received: 15 December 2022; Accepted: 28 March 2024;
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Acknowledgements
We thank Ricardo Budai and Rosmary Blanco for the segmentations of the
tumor nodulesand feedback. The publication wascreated within the project
of the Minister of Science and Higher Education “Support for the activity of
Centers of Excellence established in Poland under Horizon 2020”on the
basis of the contract number MEiN/2023/DIR/3796. This project has
received funding from the European Union’s Horizon 2020 research and
innovation program under grant agreement No 857533. This publication is
supported by Sano project carried out within the International Research
Agendas program of the Foundation for Polish Science, co-financed by the
European Union under the European Regional Development Fund. This
research was supported in part by the PLGrid infrastructure. Computations
have been partially performed on the ARES supercomputer at ACC
Cyfronet AGH.
Author contributions
J.F.-R. and A.Cr. conceptualized the study; J.F.-R. analyzed the data; J.F.-
R., A.Ca., F.S. and A.Cr. wrote the paper.
Competing interests
The authors declare no competing interests.
https://doi.org/10.1038/s42003-024-06119-3 Article
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Peer review information Communications Biology thanks Luoyu Wang,
Lucius Fekonja, Hesheng Liu for their contribution to the peer review of this
work. Primary Handling Editors: Karli Montague-Cardoso and Luke R.
Grinham. A peer review file is available.
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