Explainable AI-based Deep-SHAP for mapping the multivariate relationships between regional neuroimaging biomarkers and cognition.

BACKGROUND: Mild cognitive impairment (MCI)/Alzheimer's disease (AD) is associated with cognitive decline beyond normal aging and linked to the alterations of brain volume quantified by magnetic resonance imaging (MRI) and amyloid-beta (Aß) quantified by positron emission tomography (PET). Yet, the complex relationships between these regional imaging measures and cognition in MCI/AD remain unclear. Explainable artificial intelligence (AI) may uncover such relationships. METHOD: We integrate the AI-based deep learning neural network and Shapley additive explanations (SHAP) approaches and introduce the Deep-SHAP method to investigate the multivariate relationships between regional imaging measures and cognition. After validating this approach on simulated data, we apply it to real experimental data from MCI/AD patients. RESULTS: Deep-SHAP significantly predicted cognition using simulated regional features and identified the ground-truth simulated regions as the most significant multivariate predictors. When applied to experimental MRI data, Deep-SHAP revealed that the insula, lateral occipital, medial frontal, temporal pole, and occipital fusiform gyrus are the primary contributors to global cognitive decline in MCI/AD. Furthermore, when applied to experimental amyloid Pittsburgh compound B (PiB)-PET data, Deep-SHAP identified the key brain regions for global cognitive decline in MCI/AD as the inferior temporal, parahippocampal, inferior frontal, supratemporal, and lateral frontal gray matter. CONCLUSION: Deep-SHAP method uncovered the multivariate relationships between regional brain features and cognition, offering insights into the most critical modality-specific brain regions involved in MCI/AD mechanisms.

Dysregulated Salience Network Control over Default-Mode and Central-Executive Networks in Schizophrenia Revealed Using Stochastic Dynamical Causal Modeling.

Introduction: Neuroimaging studies suggest that the human brain consists of intrinsically organized, large-scale neural networks. Among these networks, the interplay among the default-mode network (DMN), salience network (SN), and central-executive network (CEN) has been widely used to understand the functional interaction patterns in health and disease. This triple network model suggests that the SN causally controls over the DMN and CEN in healthy individuals. This interaction is often referred to as SN's dynamic regulating mechanism. However, such interactions are not well understood in individuals with schizophrenia. Methods: In this study, we leveraged resting-state functional magnetic resonance imaging data from schizophrenia (n = 67) and healthy controls (n = 81) and evaluated the directional functional interactions among DMN, SN, and CEN using stochastic dynamical causal modeling methodology. Results: In healthy controls, our analyses replicated previous findings that SN regulates DMN and CEN activities (Mann-Whitney U test; p < 10-8). In schizophrenia, however, our analyses revealed a disrupted SN-based controlling mechanism over the DMN and CEN (Mann-Whitney U test; p < 10-16). Conclusions: These results indicate that the disrupted controlling mechanism of SN over the other two neural networks may be a candidate neuroimaging phenotype in schizophrenia.

Predicting cognitive dysfunction and regional hubs using Braak staging amyloid-beta biomarkers and machine learning.

Mild cognitive impairment (MCI) is a transitional stage between normal aging and early Alzheimer's disease (AD). The presence of extracellular amyloid-beta (Aß) in Braak regions suggests a connection with cognitive dysfunction in MCI/AD. Investigating the multivariate predictive relationships between regional Aß biomarkers and cognitive function can aid in the early detection and prevention of AD. We introduced machine learning approaches to estimate cognitive dysfunction from regional Aß biomarkers and identify the Aß-related dominant brain regions involved with cognitive impairment. We employed Aß biomarkers and cognitive measurements from the same individuals to train support vector regression (SVR) and artificial neural network (ANN) models and predict cognitive performance solely based on Aß biomarkers on the test set. To identify Aß-related dominant brain regions involved in cognitive prediction, we built the local interpretable model-agnostic explanations (LIME) model. We found elevated Aß in MCI compared to controls and a stronger correlation between Aß and cognition, particularly in Braak stages III-IV and V-VII (p < 0.05) biomarkers. Both SVR and ANN, especially ANN, showed strong predictive relationships between regional Aß biomarkers and cognitive impairment (p < 0.05). LIME integrated with ANN showed that the parahippocampal gyrus, inferior temporal gyrus, and hippocampus were the most decisive Braak regions for predicting cognitive decline. Consistent with previous findings, this new approach suggests relationships between Aß biomarkers and cognitive impairment. The proposed analytical framework can estimate cognitive impairment from Braak staging Aß biomarkers and delineate the dominant brain regions collectively involved in AD pathophysiology.

Self-interaction correction in water-ion clusters.

We study the importance of self-interaction errors in density functional approximations for various water-ion clusters. We have employed the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in conjunction with the local spin-density approximation, Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and strongly constrained and appropriately normed (SCAN) meta-GGA to describe binding energies of hydrogen-bonded water-ion clusters, i.e., water-hydronium, water-hydroxide, water-halide, and non-hydrogen-bonded water-alkali clusters. In the hydrogen-bonded water-ion clusters, the building blocks are linked by hydrogen atoms, although the links are much stronger and longer-ranged than the normal hydrogen bonds between water molecules because the monopole on the ion interacts with both permanent and induced dipoles on the water molecules. We find that self-interaction errors overbind the hydrogen-bonded water-ion clusters and that FLOSIC reduces the error and brings the binding energies into closer agreement with higher-level calculations. The non-hydrogen-bonded water-alkali clusters are not significantly affected by self-interaction errors. Self-interaction corrected PBE predicts the lowest mean unsigned error in binding energies (≤50 meV/H2O) for hydrogen-bonded water-ion clusters. Self-interaction errors are also largely dependent on the cluster size, and FLOSIC does not accurately capture the subtle variation in all clusters, indicating the need for further refinement.

Exploring and enhancing the accuracy of interior-scaled Perdew-Zunger self-interaction correction.

The Perdew-Zunger self-interaction correction (PZ-SIC) improves the performance of density functional approximations for the properties that involve significant self-interaction error (SIE), as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by local scaling self-interaction correction (LSIC) of the PZ-SIC to the local spin density approximation (LSDA). Here, we propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of the atomic number Z in the asymptotic expansion of the exchange-correlation (xc) energy for atoms. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator zσ, which distinguishes one-electron regions from many-electron regions. LSIC+ applied to the LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof generalized gradient approximation (GGA), and almost close to the strongly constrained and appropriately normed (SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bond, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. To make a locally scaled down SIC to functionals beyond the LSDA requires a gauge transformation of the functional's energy density. The resulting SCAN-sdSIC, evaluated on SCAN-SIC total and localized orbital densities, leads to an acceptable description of many equilibrium properties including the dissociation energies of weak bonds.

Density-related properties from self-interaction corrected density functional theory calculations.

The Perdew-Zunger self-interaction correction (PZ-SIC) removes unphysical electron self-interaction from calculations employing standard density functional approximations. Doing so improves many computed properties, bringing them into better agreement with experimental observations or with results from high-level quantum chemistry calculations. However, while PZ-SIC generally corrects in the right direction relative to the corresponding reference values, in many cases, it over-corrects. For this reason, scaled-down versions of PZ-SIC have been proposed and investigated. These approaches have mostly employed exterior scaling in which SIC correction terms are scaled in the same way at every point in space. Recently, a new local, or interior, scaling SIC method was proposed on non-empirical grounds to restore a property of the exact, but unknown, density functional that is broken in PZ-SIC. In this approach, the scaling at each point depends on the character of the charge density at that point. However, the local scaling can be done in various ways while still restoring the behavior of the exact functional. In this work, we compare and contrast the performance of various interior scaling approaches for addressing over-corrections of calculated molecular dipole moments and atomic polarizabilities and properties that reflect the nature of the electronic charge density.

The Fermi-Löwdin self-interaction correction for ionization energies of organic molecules.

(Semi)-local density functional approximations (DFAs) suffer from self-interaction error (SIE). When the first ionization energy (IE) is computed as the negative of the highest-occupied orbital (HO) eigenvalue, DFAs notoriously underestimate them compared to quasi-particle calculations. The inaccuracy for the HO is attributed to SIE inherent in DFAs. We assessed the IE based on Perdew-Zunger self-interaction correction on 14 small to moderate-sized organic molecules relevant in organic electronics and polymer donor materials. Although self-interaction corrected DFAs were found to significantly improve the IE relative to the uncorrected DFAs, they overestimate. However, when the self-interaction correction is interiorly scaled using a function of the iso-orbital indicator zσ, only the regions where SIE is significant get a correction. We discuss these approaches and show how these methods significantly improve the description of the HO eigenvalue for the organic molecules.

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory.

Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to the leading order (-0.221Z5/3 and -0.021Z ln Z, respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to Ex(N, Z) ≈ -0.354N2/3Z (as known before only for Z ≫ N ≫ 1) and Ec ≈ -0.02N ln N. These asymptotic estimates are most correct for atomic ions with large N and Z ≫ N, but we find that they are qualitatively and semi-quantitatively correct even for small N and N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely predictive approximate density functionals should be designed to recover the correct asymptotics. It is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.

A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction. II. Gauge consistency of the energy density at three levels of approximation.

The Perdew-Zunger (PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly varying (in space) limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC is found here to work excellently for atoms and molecules only with this basic approximation and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work unambiguously shows that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowly varying density limits. It also confirms the relevance of these limits to atoms and molecules.

Stretched or noded orbital densities and self-interaction correction in density functional theory.

Semilocal approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semilocal approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semilocal approximations satisfy, suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus, PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here, in particular, to the strongly constrained and appropriately normed (SCAN) meta-GGA, for which the correlation part is already self-interaction-free. This property makes SCAN a natural first candidate for a generalized SIC.