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. 2020 Oct 15;41(15):4155-4172.
doi: 10.1002/hbm.25105. Epub 2020 Aug 23.

Finding specificity in structural brain alterations through Bayesian reverse inference

Franco Cauda  1   2   3 , Andrea Nani  1   2   3 , Donato Liloia  1   2   3 , Jordi Manuello  1   2   3 , Enrico Premi  4   5 , Sergio Duca  1 , Peter T Fox  6   7 , Tommaso Costa  1   2   3
Affiliations

Finding specificity in structural brain alterations through Bayesian reverse inference

Franco Cauda et al. Hum Brain Mapp. .

Abstract

In the field of neuroimaging reverse inferences can lead us to suppose the involvement of cognitive processes from certain patterns of brain activity. However, the same reasoning holds if we substitute "brain activity" with "brain alteration" and "cognitive process" with "brain disorder." The fact that different brain disorders exhibit a high degree of overlap in their patterns of structural alterations makes forward inference-based analyses less suitable for identifying brain areas whose alteration is specific to a certain pathology. In the forward inference-based analyses, in fact, it is impossible to distinguish between areas that are altered by the majority of brain disorders and areas that are specifically affected by certain diseases. To address this issue and allow the identification of highly pathology-specific altered areas we used the Bayes' factor technique, which was employed, as a proof of concept, on voxel-based morphometry data of schizophrenia and Alzheimer's disease. This technique allows to calculate the ratio between the likelihoods of two alternative hypotheses (in our case, that the alteration of the voxel is specific for the brain disorder under scrutiny or that the alteration is not specific). We then performed temporal simulations of the alterations' spread associated with different pathologies. The Bayes' factor values calculated on these simulated data were able to reveal that the areas, which are more specific to a certain disease, are also the ones to be early altered. This study puts forward a new analytical instrument capable of innovating the methodological approach to the investigation of brain pathology.

Keywords: Alzheimer's disease; Bayes' factor; alteration specificity; brain disorders; pain; reverse probability; schizophrenia; voxel-based morphometry.

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Conflict of interest statement

The authors report no competing interests.

Figures

FIGURE 1
FIGURE 1
Top: Base rates reports of how many pathologies of the VBM BrainMap database cause alterations in every area of the brain. Areas highlighted in red are those in which more than the 90% of pathologies cause at least an alteration. Middle and bottom: Association test (expressed in z points) over the term ‘Pain’ performed with Neurosynth and compared with a Bayes' factor (expressed in normalized BF values) map calculated with equiprobable priors over BrainMap data (see Table S6 for the specific numeric visualization). Left panel: Radar map illustrating the comparison between the network‐based decomposition of previous results expressed in z mean points (Neurosynth) and Bayes' factor values
FIGURE 2
FIGURE 2
Top right: Bayes' factor (BF) map of Alzheimer's disease calculated with equiprobable priors over BrainMap data. Top left: Bayes' factor map of Alzheimer's disease calculated with equiprobable priors over BrainMap data, compensated for the different representativeness of pathologies in the database. Bottom right: Bayes' factor (BF) map of schizophrenia calculated with equiprobable priors over BrainMap data. Bottom left: Bayes' factor map of schizophrenia calculated with equiprobable priors over BrainMap data, compensated for the different representativeness of pathologies in the database. Middle: Radar maps illustrating the comparison between the network‐based decomposition of previous results expressed in mean Bayes' factor values. Bayes' factor maps are expressed in normalized BF values. See Table S4 and S5 for the specific numeric visualization
FIGURE 3
FIGURE 3
Bayes' factor (BF) and the temporal evolution of pathologies. Top left: Starting nodes of the target pathology (Alzheimer's disease, AD). Middle: Temporal evolution (expressed in arbitrary time points) both of the target pathology and of all the other simulated pathologies. Colors from green to violet show the areas that are altered from early to late phases of the simulated pathological spread. Bottom: BF values calculated on synthetic data. Right panel: Comparison between the areas showing a BF > 10 and the starting points of the simulated target pathology
FIGURE 4
FIGURE 4
Right panel: Comparison between the results of the Bayes' information criterion (BIC), expressed in S value (see Methods section), performed over the term 'Pain' and the Bayes' factor (BF) map calculated with equiprobable priors over BrainMap data. Left panel: Radar map illustrating the comparison between the network‐based decomposition of previous results expressed in mean BIC and BF values. Bayes' factor maps are expressed in normalized BF values. See Table S6 for the specific numeric visualization
FIGURE 5
FIGURE 5
Left panel: Fail‐safe results of the Bayes' factor calculated over pain data. Areas colored from blue to red show increasing resistances to progressively greater injections of noise in the data set. Middle panel: Fail‐safe results of the Bayes' factor calculated over Alzheimer's disease data. Areas colored from blue to red show increasing resistances to progressively greater injections of noise in the data set. Right panel: Fail‐safe results of the Bayes' factor calculated over schizophrenia data. Areas colored from blue to red show increasing resistances to progressively greater injections of noise in the data set
FIGURE 6
FIGURE 6
Fail‐safe results of the Bayes' factor (BF) of three data sets (i.e., pain, Alzheimer's disease, and schizophrenia) obtained from the correlational values between the BF map calculated without injections of noise and BF maps calculated with progressively increasing injections of noise. Colors from blue to red indicate increasing values of standard deviation between the r values calculated in the different runs of the fail‐safe procedure
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