Convergent cross-mapping (CCM) has attracted increased attention recently due to its capability to detect causality in nonseparable systems under deterministic settings, which may not be covered by the traditional Granger causality. From an information-theoretic perspective, causality is often characterized as the directed information (DI) flowing from one side to the other. As information is essentially nondeterministic, a natural question is: does CCM measure DI flow? Here, we first causalize CCM so that it aligns with the presumption in causality analysis—the future values of one process cannot influence the past of the other, and then establish and validate the approximate equivalence of causalized CCM (cCCM) and DI under Gaussian variables through both theoretical derivations and fMRI-based brain network causality analysis. Our simulation result indicates that, in general, cCCM tends to be more robust than DI in causality detection. The underlying argument is that DI relies heavily on probability estimation, which is sensitive to data size as well as digitization procedures; cCCM, on the other hand, gets around this problem through geometric cross-mapping between the manifolds involved. Overall, our analysis demonstrates that cross-mapping provides an alternative way to evaluate DI and is potentially an effective technique for identifying both linear and nonlinear causal coupling in brain neural networks and other settings, either random or deterministic, or both.

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications.

Mounting evidence suggests that amyloid-β (Aβ) and vascular etiologies are intertwined in the pathogenesis of Alzheimer’s disease (AD). Blood-oxygen-level-dependent (BOLD) signals, measured by resting-state functional MRI (rs-fMRI), are associated with neuronal activity and cerebrovascular hemodynamics. Nevertheless, it is unclear if BOLD fluctuations are associated with Aβ deposition in individuals at high risk of AD. Thirty-three patients with amnestic mild cognitive impairment underwent rs-fMRI and AV45 PET. The AV45 standardized uptake value ratio (AV45-SUVR) was calculated using cerebral white matter as reference, to assess Aβ deposition. The whole-brain normalized amplitudes of low-frequency fluctuations (sALFF) of local BOLD signals were calculated in the frequency band of 0.01–0.08 Hz. Stepwise increasing physiological/vascular signal regressions on the rs-fMRI data examined whether sALFF-AV45 correlations were driven by vascular hemodynamics, neuronal activities, or both. We found that sALFF and AV45-SUVR were negatively correlated in regions of default-mode and visual networks (precuneus, angular, lingual and fusiform gyri). Regions with higher sALFF had less Aβ accumulation. Correlated cluster sizes in MNI space ( r ≈ −0.47) were reduced from 3018 mm³ to 1072 mm³ with stronger cardiovascular regression. These preliminary findings imply that local brain blood fluctuations due to vascular hemodynamics or neuronal activity can affect Aβ homeostasis.

Spontaneous fluctuations of resting-state functional connectivity have been studied in many ways, but grasping the complexity of brain activity has been difficult. Dimensional complexity measures, which are based on Eigenvalue (EV) spectrum analyses (e.g., Ω entropy) have been successfully applied to EEG data, but have not been fully evaluated on functional MRI recordings, because only through the recent introduction of fast multiband fMRI sequences, feasable temporal resolutions are reached. Combining the Eigenspectrum normalization of Ω entropy and the scalable architecture of the so called Multivariate Principal Subspace Entropy (MPSE) leads to a new complexity measure, namely normalized MPSE (nMPSE). It allows functional brain complexity analyses at varying levels of EV energy, independent from global shifts in data variance. Especially the restriction of the EV spectrum to the first dimensions, carrying the most prominent data variance, can act as a filter to reveal the most discriminant factors of dependent variables. Here we look at the effects of healthy aging on the dimensional complexity of brain activity. We employ a large open access dataset, providing a great number of high quality fast multiband recordings. Using nMPSE on whole brain, regional, network and searchlight approaches, we were able to find many age related changes, i.e., in sensorimotoric and right inferior frontal brain regions. Our results implicate that research on dimensional complexity of functional MRI recordings promises to be a unique resource for understanding brain function and for the extraction of biomarkers.

Functional magnetic resonance imaging faces inherent challenges when applied to deep-brain areas in rodents, e.g. entorhinal cortex, due to the signal loss near the ear cavities induced by susceptibility artifacts and reduced sensitivity induced by the long distance from the surface array coil. Given the pivotal roles of deep brain regions in various diseases, optimized imaging techniques are needed. To mitigate susceptibility-induced signal losses, we introduced baby cream into the middle ear. To enhance the detection sensitivity of deep brain regions, we implemented inductively coupled ear-bars, resulting in approximately a 2-fold increase in sensitivity in entorhinal cortex. Notably, the inductively coupled ear-bar can be seamlessly integrated as an add-on device, without necessitating modifications to the scanner interface. To underscore the versatility of inductively coupled ear-bars, we conducted echo-planner imaging-based task functional magnetic resonance imaging in rats modeling Alzheimer’s disease. As a proof of concept, we also demonstrated resting-state-functional magnetic resonance imaging connectivity maps originating from the left entorhinal cortex—a central hub for memory and navigation networks-to amygdala hippocampal area, Insular Cortex, Prelimbic Systems, Cingulate Cortex, Secondary Visual Cortex, and Motor Cortex. This work demonstrates an optimized procedure for acquiring large-scale networks emanating from a previously challenging seed region by conventional magnetic resonance imaging detectors, thereby facilitating improved observation of functional magnetic resonance imaging outcomes.

Mounting evidence suggests that amyloid-β (Aβ) and vascular etiologies are intertwined in the pathogenesis of Alzheimer’s disease. Spontaneous fluctuations of the brain blood-oxygen-level-dependent (BOLD) signal, as measured by resting-state functional MRI (rs-fMRI), have been shown to be associated with neuronal activities as well as cerebrovascular hemodynamics. Nevertheless, it is unclear if rs-fMRI BOLD fluctuations are associated with brain Aβ deposition in individuals with an elevated risk of Alzheimer’s disease. We recruited 33 patients with amnestic mild cognitive impairment who underwent rs-fMRI and positron emission tomography (PET). The Aβ standardized uptake value ratio (SUVR) was calculated with cortical white matter as the reference region to improve sensitivity for cortical Aβ quantification. We calculated the amplitudes of low-frequency fluctuations (ALFF) of local BOLD signals in the frequency band of 0.01-0.08 Hz. Applying physiological/vascular signal regression in stepwise increasing levels on the rs-fMRI data, we examined whether local correlations between ALFF and brain Aβ deposition were driven by vascular hemodynamics, spontaneous neuronal activities, or both. We found that ALFF and Aβ SUVR were negatively correlated in brain regions involving the default-mode and visual networks, with peak correlation at the precuneus, and angular, lingual, and fusiform gyri. Regions with higher ALFF had less Aβ accumulation. The correlated cluster sizes in MNI space were reduced from 3018 mm ³ with no physiological/vascular regression to 1072 mm ³ with strong physiological/vascular regression, with mean cluster r values at approximately -0.47. Results demonstrate that both vascular hemodynamics and neuronal activities, as reflected by BOLD fluctuations, are negatively associated with brain Aβ deposition. These findings further imply that local brain blood fluctuations due to either vascular hemodynamics or neuronal activities can affect Aβ homeostasis.