Parameter Sensitivity and Experimental Validation for Fractional-Order Dynamical Modeling of Neurovascular Coupling

Goal: Neurovascular coupling is a fundamental mechanism linking neural activity to cerebral blood flow (CBF) response. Modeling this coupling is very important to understand brain functions, yet challenging due to the complexity of the involved phenomena. One key feature that different studies have reported is the time delay that is inherently present between the neural activity and cerebral blood flow, which has been described by adding a delay parameter in standard models. An alternative approach was recently proposed where the framework of fractional-order modeling is employed to characterize the complex phenomena underlying the neurovascular. Thanks to its nonlocal property, a fractional derivative is suitable for modeling delayed and power-law phenomena. Methods: In this study, we analyzed and validated an effective fractional-order for the effective modeling and characterization of the neurovascular coupling mechanism. To show the added value of the fractional order parameters of the proposed model, we perform a parameter sensitivity analysis of the fractional model compared to its integer counterpart. Moreover, the model was validated using neural activity-CBF data related to both event and block design experiments that were acquired using electrophysiology and laser Doppler flowmetry recordings, respectively. Results: The validation results show the aptitude and flexibility of the fractional-order paradigm in fitting a more comprehensive range of well-shaped CBF response behaviors while maintaining a low model complexity. Comparison with the standard integer-order models shows the added value of the fractional-order parameters in capturing various key determinants of the cerebral hemodynamic response, e.g., post-stimulus undershoot. Conclusions: This investigation authenticates the ability and adaptability of the fractional-order framework to characterize a wider range of wellshaped cerebral blood flow responses while preserving low model complexity through a series of unconstrained and constrained optimizations

Increasing robustness of pairwise methods for effective connectivity in Magnetic Resonance Imaging by using fractional moment series of BOLD signal distributions

Estimating causal interactions in the brain from functional magnetic resonance imaging (fMRI) data remains a challenging task. Multiple studies have demonstrated that all current approaches to determine direction of connectivity perform poorly even when applied to synthetic fMRI datasets. Recent advances in this field include methods for pairwise inference, which involve creating a sparse connectome in the first step, and then using a classifier in order to determine the directionality of connection between of every pair of nodes in the second step. In this work, we introduce an advance to the second step of this procedure, by building a classifier based on fractional moments of the BOLD distribution combined into cumulants. The classifier is trained on datasets generated under the Dynamic Causal Modeling (DCM) generative model. The directionality is inferred based upon statistical dependencies between the two node time series, e.g. assigning a causal link from time series of low variance to time series of high variance. Our approach outperforms or performs as well as other methods for effective connectivity when applied to the benchmark datasets. Crucially, it is also more resilient to confounding effects such as differential noise level across different areas of the connectome.Comment: 41 pages, 12 figure

Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics

Loss of cortical integration and changes in the dynamics of electrophysiological brain signals characterize the transition from wakefulness towards unconsciousness. The common mechanism underlying these observations remains unknown. In this study we arrive at a basic model, which explains these empirical observations based on the theory of phase transitions in complex systems. We studied the link between spatial and temporal correlations of large-scale brain activity recorded with functional magnetic resonance imaging during wakefulness, propofol-induced sedation and loss of consciousness, as well as during the subsequent recovery. We observed that during unconsciousness activity in frontal and thalamic regions exhibited a reduction of long-range temporal correlations and a departure of functional connectivity from the underlying anatomical constraints. These changes in dynamics and anatomy-function coupling were correlated across participants, suggesting that temporal complexity and an efficient exploration of anatomical connectivity are inter-related phenomena. A model of a system exhibiting a phase transition reproduced our findings, as well as the diminished sensitivity of the cortex to external perturbations during unconsciousness. This theoretical framework unifies different empirical observations about brain activity during unconsciousness and predicts that the principles we identified are universal and independent of the causes behind loss of awareness.Comment: to appear in Journal of the Royal Society Interfac

Measurements and Modeling of Transient Blood Flow Perturbations Induced by Brief Somatosensory Stimulation

Proper interpretation of BOLD fMRI and other common functional imaging methods requires an understanding of neurovascular coupling. We used laser speckle-contrast optical imaging to measure blood-flow responses in rat somatosensory cortex elicited by brief (2 s) forepaw stimulation. Results show a large increase in local blood flow speed followed by an undershoot and possible late-time oscillations. The blood flow measurements were modeled using the impulse response of a simple linear network, a four-element windkessel. This model yielded excellent fits to the detailed time courses of activated regions. The four-element windkessel model thus provides a simple explanation and interpretation of the transient blood-flow response, both its initial peak and its late-time behavior

Optical Cerebral Blood Flow Monitoring of Mice to Men

This thesis describes cerebral hemodynamic monitoring with the optical techniques of diffuse optical spectroscopy (DOS) and diffuse correlation spectroscopy (DCS). DOS and DCS both employ near-infrared light to investigate tissue physiology millimeters to centimeters below the tissue surface. DOS is a static technique that analyzes multispectral tissue-scattered light intensity signals with a photon diffusion approach (Chapter 2) or a Modified Beer-Lambert law approach (Chapter 3) to derive tissue oxy- and deoxy-hemoglobin concentrations, which are in turn used to compute tissue oxygen saturation and blood volume (Section 2.13). DCS is a qualitatively different dynamic technique that analyzes rapid temporal fluctuations in tissue-scattered light with a correlation diffusion approach to derive tissue blood flow (Chapter 4). Further, in combination these measurements of blood flow and blood oxygenation provide access to tissue oxygen metabolism (Section 7.6). The new contributions of my thesis to the diffuse optics field are a novel analysis technique for the DCS signal (Chapter 5), and a novel approach for separating cerebral hemodynamic signals from extra-cerebral artifacts (Chapter 6). The DCS analysis technique extends the Modified Beer-Lambert approach for DOS to the DCS measurement. This new technique has some useful advantages compared to the correlation diffusion approach. It facilitates real-time flow monitoring in complex tissue geometries, provides a novel route for increasing DCS measurement speed, and can be used to probe tissues wherein light transport is non-diffusive (Chapter 5). It also can be used to filter signals from superficial tissues. For separation of cerebral hemodynamic signals from extra-cerebral artifacts, the Modified Beer-Lambert approach is employed in a pressure modulation scheme, which determines subject-specific contributions of extra-cerebral and cerebral tissues to the DCS/DOS signals by utilizing probe pressure modulation to induce variations in extra-cerebral hemodynamics while cerebral hemodynamics remain constant (Chapter 6). In another novel contribution, I used optical techniques to characterize neurovascular coupling at several levels of cerebral ischemia in a rat model (Chapter 7). Neurovascular coupling refers to the relationship between increased blood flow and oxygen metabolism and increased neuronal activity in the brain. In the rat, localized neuronal activity was increased from functional forepaw stimulation. Under normal flow levels, I (and others) observed that the increase in cerebral blood flow (surrogate for oxygen delivery) from forepaw stimulation exceeded the increase in cerebral oxygen metabolism by about a factor of 2. My measurements indicate that this mismatch between oxygen delivery and consumption are more balanced during ischemia (Chapter 7). In Chapters 2 and 3, I review the underlying theory for the photon diffusion model and the Modified Beer-Lambert law for DOS analysis. I also review the correlation diffusion approach for analyzing DCS signals in Chapter 4. My hope is that readers new to the field will find these background chapters helpful

Development of a novel diffuse correlation spectroscopy platform for monitoring cerebral blood flow and oxygen metabolism: from novel concepts and devices to preclinical live animal studies

New optical technologies were developed to continuously measure cerebral blood flow (CBF) and oxygen metabolism (CMRO2) non-invasively through the skull. Methods and devices were created to improve the performance of near-infrared spectroscopy (NIRS) and diffuse correlation spectroscopy (DCS) for use in experimental animals and humans. These were employed to investigate cerebral metabolism and cerebrovascular reactivity under different states of anesthesia and during models of pathological states. Burst suppression is a brain state arising naturally in pathological conditions or under deep general anesthesia, but its mechanism and consequences are not well understood. Electroencephalography (EEG) and cortical hemodynamics were simultaneously measured in rats to evaluate the coupling between cerebral oxygen metabolism and neuronal activity in the burst suppressed state. EEG bursts were used to deconvolve NIRS and DCS signals into the hemodynamic and metabolic response function for an individual burst. This response was found to be similar to the stereotypical functional hyperemia evoked by normal brain activation. Thus, spontaneous burst activity does not cause metabolic or hemodynamic dysfunction in the cortex. Furthermore, cortical metabolic activity was not associated with the initiation or termination of a burst. A novel technique, time-domain DCS (TD-DCS), was introduced to significantly increase the sensitivity of transcranial CBF measurements to the brain. A new time-correlated single photon counting (TCSPC) instrument with a custom high coherence pulsed laser source was engineered for the first-ever simultaneous measurement of photon time of flight and DCS autocorrelation decays. In this new approach, photon time tags are exploited to determine path-length-dependent autocorrelation functions. By correlating photons according to time of flight, CBF is distinguished from superficial blood flow. Experiments in phantoms and animals demonstrate TD-DCS has significantly greater sensitivity to the brain than existing transcranial techniques. Intracranial pressure (ICP) modulates both steady-state and pulsatile CBF, making CBF a potential marker for ICP. In particular, the critical closing pressure (CrCP) has been proposed as a surrogate measure of ICP. A new DCS device was developed to measure pulsatile CBF non-invasively. A novel method for estimating CrCP and ICP from DCS measurement of pulsatile microvascular blood flow in the cerebral cortex was demonstrated in rats.2018-03-08T00:00:00

Clinical correlates of mathematical modeling of cortical spreading depression: Single‐cases study

Introduction: Considerable connections between migraine with aura and cortical spreading depression (CSD), a depolarization wave originating in the visual cortex and traveling toward the frontal lobe, lead to the hypothesis that CSD is underlying migraine aura. The highly individual and complex characteristics of the brain cor‐ tex suggest that the geometry might impact the propagation of cortical spreading depression. Methods: In a single‐case study, we simulated the CSD propagation for five migraine with aura patients, matching their symptoms during a migraine attack to the CSD wavefront propagation. This CSD wavefront was simulated on a patient‐specific tri‐ angulated cortical mesh obtained from individual MRI imaging and personalized dif‐ fusivity tensors derived locally from diffusion tensor imaging data. Results: The CSD wave propagation was simulated on both hemispheres, despite in all but one patient the symptoms were attributable to one hemisphere. The CSD wave diffused with a large wavefront toward somatosensory and prefrontal regions, devoted to pain processing. Discussion: This case‐control study suggests that the cortical geometry may con‐ tribute to the modality of CSD evolution and partly to clinical expression of aura symptoms. The simulated CSD is a large and diffuse phenomenon, possibly capa‐ ble to activate trigeminal nociceptors and to involve cortical areas devoted to pain processing

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Review

Functional ultrasound (fUS) is a hemodynamic-based functional neuroimaging technique, primarily used in animal models, that combines a high spatiotemporal resolution, a large field of view, and compatibility with behavior. These assets make fUS especially suited to interrogating brain activity at the systems level. In this review, we describe the technical capabilities offered by fUS and discuss how this technique can contribute to the field of functional connectomics. First, fUS can be used to study intrinsic functional connectivity, namely patterns of correlated activity between brain regions. In this area, fUS has made the most impact by following connectivity changes in disease models, across behavioral states, or dynamically. Second, fUS can also be used to map brain-wide pathways associated with an external event. For example, fUS has helped obtain finer descriptions of several sensory systems, and uncover new pathways implicated in specific behaviors. Additionally, combining fUS with direct circuit manipulations such as optogenetics is an attractive way to map the brain-wide connections of defined neuronal populations. Finally, technological improvements and the application of new analytical tools promise to boost fUS capabilities. As brain coverage and the range of behavioral contexts that can be addressed with fUS keep on increasing, we believe that fUS-guided connectomics will only expand in the future. In this regard, we consider the incorporation of fUS into multimodal studies combining diverse techniques and behavioral tasks to be the most promising research avenue