Evidence of a cerebrovascular postarteriole windkessel with delayed compliance

Experimentally constrained circuit model of cortical arteriole networks for understanding flow redistribution due to occlusion and neural activation

Computations are described which estimate flows in all branches of the cortical surface arteriole network from two-photon excited fluorescence (2PEF) microscopy images which provide the network topology and, in selected branches red blood cell (RBC) speeds and lumen diameters. Validation is done by comparing the flow predicted by the model with experimentally measured flows and by comparing the predicted flow redistribution in the network due to single-vessel strokes with experimental observations. The model predicts that tissue is protected from RBC flow decreases caused by multiple occlusions of surface arterioles but not penetrating arterioles. The model can also be used to study flow rerouting due to vessel dilations and constrictions.

Seizure epicenter depth and translaminar field potential synchrony underlie complex variations in tissue oxygenation during ictal initiation

Whether functional hyperemia during epileptic activity is adequate to meet the heightened metabolic demand of such events is controversial. Whereas some studies have demonstrated hyperoxia during ictal onsets, other work has reported transient hypoxic episodes that are spatially dependent on local surface microvasculature. Crucially, how laminar differences in ictal evolution can affect subsequent cerebrovascular responses has not been thus far investigated, and is likely significant in view of possible laminar-dependent neurovascular mechanisms and angioarchitecture. We addressed this open question using a novel multi-modal methodology enabling concurrent measurement of cortical tissue oxygenation, blood flow and hemoglobin concentration, alongside laminar recordings of neural activity, in a urethane anesthetized rat model of recurrent seizures induced by 4-aminopyridine. We reveal there to be a close relationship between seizure epicenter depth, translaminar local field potential (LFP) synchrony and tissue oxygenation during the early stages of recurrent seizures, whereby deep layer seizures are associated with decreased cross laminar synchrony and prolonged periods of hypoxia, and middle layer seizures are accompanied by increased cross-laminar synchrony and hyperoxia. Through comparison with functional activation by somatosensory stimulation and graded hypercapnia, we show that these seizure-related cerebrovascular responses occur in the presence of conserved neural-hemodynamic and blood flow-volume coupling. Our data provide new insights into the laminar dependency of seizure-related neurovascular responses, which may reconcile inconsistent observations of seizure-related hypoxia in the literature, and highlight a potential layer-dependent vulnerability that may contribute to the harmful effects of clinical recurrent seizures. The relevance of our findings to perfusion-related functional neuroimaging techniques in epilepsy are also discussed.

Multiparametric measurement of cerebral physiology using calibrated fMRI

The ultimate goal of calibrated fMRI is the quantitative imaging of oxygen metabolism (CMRO₂), and this has been the focus of numerous methods and approaches. However, one underappreciated aspect of this quest is that in the drive to measure CMRO₂, many other physiological parameters of interest are often acquired along the way. This can significantly increase the value of the dataset, providing greater information that is clinically relevant, or detail that can disambiguate the cause of signal variations. This can also be somewhat of a double-edged sword: calibrated fMRI experiments combine multiple parameters into a physiological model that requires multiple steps, thereby providing more opportunity for error propagation and increasing the noise and error of the final derived values. As with all measurements, there is a trade-off between imaging time, spatial resolution, coverage, and accuracy. In this review, we provide a brief overview of the benefits and pitfalls of extracting multiparametric measurements of cerebral physiology through calibrated fMRI experiments.

The roadmap for estimation of cell-type-specific neuronal activity from non-invasive measurements

The computational properties of the human brain arise from an intricate interplay between billions of neurons connected in complex networks. However, our ability to study these networks in healthy human brain is limited by the necessity to use non-invasive technologies. This is in contrast to animal models where a rich, detailed view of cellular-level brain function with cell-type-specific molecular identity has become available due to recent advances in microscopic optical imaging and genetics. Thus, a central challenge facing neuroscience today is leveraging these mechanistic insights from animal studies to accurately draw physiological inferences from non-invasive signals in humans. On the essential path towards this goal is the development of a detailed 'bottom-up' forward model bridging neuronal activity at the level of cell-type-specific populations to non-invasive imaging signals. The general idea is that specific neuronal cell types have identifiable signatures in the way they drive changes in cerebral blood flow, cerebral metabolic rate of O2 (measurable with quantitative functional Magnetic Resonance Imaging), and electrical currents/potentials (measurable with magneto/electroencephalography). This forward model would then provide the 'ground truth' for the development of new tools for tackling the inverse problem-estimation of neuronal activity from multimodal non-invasive imaging data.This article is part of the themed issue 'Interpreting BOLD: a dialogue between cognitive and cellular neuroscience'.

Retinal Vascular and Oxygen Temporal Dynamic Responses to Light Flicker in Humans

Purpose

To mathematically model the temporal dynamic responses of retinal vessel diameter (D), oxygen saturation (SO₂), and inner retinal oxygen extraction fraction (OEF) to light flicker and to describe their responses to its cessation in humans.

Methods

In 16 healthy subjects (age: 60 ± 12 years), retinal oximetry was performed before, during, and after light flicker stimulation. At each time point, five metrics were measured: retinal arterial and venous D (D_A, D_V) and SO₂ (SO_2A, SO_2V), and OEF. Intra- and intersubject variability of metrics was assessed by coefficient of variation of measurements before flicker within and among subjects, respectively. Metrics during flicker were modeled by exponential functions to determine the flicker-induced steady state metric values and the time constants of changes. Metrics after the cessation of flicker were compared to those before flicker.

Results

Intra- and intersubject variability for all metrics were less than 6% and 16%, respectively. At the flicker-induced steady state, D_A and D_V increased by 5%, SO_2V increased by 7%, and OEF decreased by 13%. The time constants of D_A and D_V (14, 15 seconds) were twofold smaller than those of SO_2V and OEF (39, 34 seconds). Within 26 seconds after the cessation of flicker, all metrics were not significantly different from before flicker values (P ≥ 0.07).

Conclusions

Mathematical modeling revealed considerable differences in the time courses of changes among metrics during flicker, indicating flicker duration should be considered separately for each metric. Future application of this method may be useful to elucidate alterations in temporal dynamic responses to light flicker due to retinal diseases.

Determining Excitatory and Inhibitory Neuronal Activity from Multimodal fMRI Data Using a Generative Hemodynamic Model

Hemodynamic responses, in general, and the blood oxygenation level-dependent (BOLD) fMRI signal, in particular, provide an indirect measure of neuronal activity. There is strong evidence that the BOLD response correlates well with post-synaptic changes, induced by changes in the excitatory and inhibitory (E-I) balance between active neuronal populations. Typical BOLD responses exhibit transients, such as the early-overshoot and post-stimulus undershoot, that can be linked to transients in neuronal activity, but they can also result from vascular uncoupling between cerebral blood flow (CBF) and venous cerebral blood volume (venous CBV). Recently, we have proposed a novel generative hemodynamic model of the BOLD signal within the dynamic causal modeling framework, inspired by physiological observations, called P-DCM (Havlicek et al., 2015). We demonstrated the generative model's ability to more accurately model commonly observed neuronal and vascular transients in single regions but also effective connectivity between multiple brain areas (Havlicek et al., 2017b). In this paper, we additionally demonstrate the versatility of the generative model to jointly explain dynamic relationships between neuronal and hemodynamic physiological variables underlying the BOLD signal using multi-modal data. For this purpose, we utilized three distinct data-sets of experimentally induced responses in the primary visual areas measured in human, cat, and monkey brain, respectively: (1) CBF and BOLD responses; (2) CBF, total CBV, and BOLD responses (Jin and Kim, 2008); and (3) positive and negative neuronal and BOLD responses (Shmuel et al., 2006). By fitting the generative model to the three multi-modal experimental data-sets, we showed that the presence or absence of dynamic features in the BOLD signal is not an unambiguous indication of presence or absence of those features on the neuronal level. Nevertheless, the generative model that takes into account the dynamics of the physiological mechanisms underlying the BOLD response allowed dissociating neuronal from vascular transients and deducing excitatory and inhibitory neuronal activity time-courses from BOLD data alone and from multi-modal data.

An efficient multistage algorithm for full calibration of the hemodynamic model from BOLD signal responses

We propose a computational strategy that falls into the category of prediction/correction iterative-type approaches, for calibrating the hemodynamic model. The proposed method is used to estimate consecutively the values of the two sets of model parameters. Numerical results corresponding to both synthetic and real functional magnetic resonance imaging measurements for a single stimulus as well as for multiple stimuli are reported to highlight the capability of this computational methodology to fully calibrate the considered hemodynamic model.

Comparing brain graphs in which nodes are regions of interest or independent components: A simulation study

BACKGROUND

A key challenge in building a brain graph using fMRI data is how to define the nodes. Spatial brain components estimated by independent components analysis (ICA) and regions of interest (ROIs) determined by brain atlas are two popular methods to define nodes in brain graphs. It is difficult to evaluate which method is better in real fMRI data.

NEW METHOD

Here we perform a simulation study and evaluate the accuracies of a few graph metrics in graphs with nodes of ICA components, ROIs, or modified ROIs in four simulation scenarios.

RESULTS

Graph measures with ICA nodes are more accurate than graphs with ROI nodes in all cases. Graph measures with modified ROI nodes are modulated by artifacts. The correlations of graph metrics across subjects between graphs with ICA nodes and ground truth are higher than the correlations between graphs with ROI nodes and ground truth in scenarios with large overlapped spatial sources. Moreover, moving the location of ROIs would largely decrease the correlations in all scenarios.

COMPARISON WITH EXISTING METHOD (S)

Evaluating graphs with different nodes is promising in simulated data rather than real data because different scenarios can be simulated and measures of different graphs can be compared with a known ground truth.

CONCLUSION

Since ROIs defined using brain atlas may not correspond well to real functional boundaries, overall findings of this work suggest that it is more appropriate to define nodes using data-driven ICA than ROI approaches in real fMRI data.

Noninvasive optical monitoring of critical closing pressure and arteriole compliance in human subjects

The critical closing pressure ( CrCP) of the cerebral circulation depends on both tissue intracranial pressure and vasomotor tone. CrCP defines the arterial blood pressure ( ABP) at which cerebral blood flow approaches zero, and their difference ( ABP -  CrCP) is an accurate estimate of cerebral perfusion pressure. Here we demonstrate a novel non-invasive technique for continuous monitoring of CrCP at the bedside. The methodology combines optical diffuse correlation spectroscopy (DCS) measurements of pulsatile cerebral blood flow in arterioles with concurrent ABP data during the cardiac cycle. Together, the two waveforms permit calculation of CrCP via the two-compartment Windkessel model for flow in the cerebral arterioles. Measurements of CrCP by optics (DCS) and transcranial Doppler ultrasound (TCD) were carried out in 18 healthy adults; they demonstrated good agreement (R = 0.66, slope = 1.14 ± 0.23) with means of 11.1 ± 5.0 and 13.0 ± 7.5 mmHg, respectively. Additionally, a potentially useful and rarely measured arteriole compliance parameter was derived from the phase difference between ABP and DCS arteriole blood flow waveforms. The measurements provide evidence that DCS signals originate predominantly from arteriole blood flow and are well suited for long-term continuous monitoring of CrCP and assessment of arteriole compliance in the clinic.

Foundations of layer-specific fMRI and investigations of neurophysiological activity in the laminarized neocortex and olfactory bulb of animal models

Laminar organization of neuronal circuits is a recurring feature of how the brain processes information. For instance, different layers compartmentalize different cell types, synaptic activities, and have unique intrinsic and extrinsic connections that serve as units for specialized signal processing. Functional MRI is an invaluable tool to investigate laminar processing in the in vivo human brain, but it measures neuronal activity indirectly by way of the hemodynamic response. Therefore, the accuracy of high-resolution laminar fMRI depends on how precisely it can measure localized microvascular changes nearest to the site of evoked activity. To determine the specificity of fMRI responses to the true neurophysiological responses across layers, the flexibility to invasive procedures in animal models has been necessary. In this review, we will examine different fMRI contrasts and their appropriate uses for layer-specific fMRI, and how localized laminar processing was examined in the neocortex and olfactory bulb. Through collective efforts, it was determined that microvessels, including capillaries, are regulated within single layers and that several endogenous and contrast-enhanced fMRI contrast mechanisms can separate these neural-specific vascular changes from the nonspecific, especially cerebral blood volume-weighted fMRI with intravenous contrast agent injection. We will also propose some open questions that are relevant for the successful implementation of layer-specific fMRI and its potential future directions to study laminar processing when combined with optogenetics.

Magnetic resonance advection imaging of cerebrovascular pulse dynamics

We analyze the pulsatile signal component of dynamic echo planar imaging data from the brain by modeling the dependence between local temporal and spatial signal variability. The resulting magnetic resonance advection imaging maps depict the location of major arteries. Color direction maps allow for visualization of the direction of blood vessels. The potential significance of magnetic resonance advection imaging maps is demonstrated on a functional magnetic resonance imaging data set of 19 healthy subjects. A comparison with the here introduced pulse coherence maps, in which the echo planar imaging signal is correlated with a cardiac pulse signal, shows that the magnetic resonance advection imaging approach results in a better spatial definition without the need for a pulse reference. In addition, it is shown that magnetic resonance advection imaging velocities can be estimates of pulse wave velocities if certain requirements are met, which are specified. Although for this application magnetic resonance advection imaging velocities are not quantitative estimates of pulse wave velocities, they clearly depict local pulsatile dynamics. Magnetic resonance advection imaging can be applied to existing dynamic echo planar imaging data sets with sufficient spatiotemporal resolution. It is discussed whether magnetic resonance advection imaging might have the potential to evolve into a biomarker for the health of the cerebrovascular system.

Time to wake up: Studying neurovascular coupling and brain-wide circuit function in the un-anesthetized animal

Functional magnetic resonance imaging (fMRI) has allowed the noninvasive study of task-based and resting-state brain dynamics in humans by inferring neural activity from blood-oxygenation-level dependent (BOLD) signal changes. An accurate interpretation of the hemodynamic changes that underlie fMRI signals depends on the understanding of the quantitative relationship between changes in neural activity and changes in cerebral blood flow, oxygenation and volume. While there has been extensive study of neurovascular coupling in anesthetized animal models, anesthesia causes large disruptions of brain metabolism, neural responsiveness and cardiovascular function. Here, we review work showing that neurovascular coupling and brain circuit function in the awake animal are profoundly different from those in the anesthetized state. We argue that the time is right to study neurovascular coupling and brain circuit function in the awake animal to bridge the physiological mechanisms that underlie animal and human neuroimaging signals, and to interpret them in light of underlying neural mechanisms. Lastly, we discuss recent experimental innovations that have enabled the study of neurovascular coupling and brain-wide circuit function in un-anesthetized and behaving animal models.

Modelling confounding effects from extracerebral contamination and systemic factors on functional near-infrared spectroscopy

Haemodynamics-based neuroimaging is widely used to study brain function. Regional blood flow changes characteristic of neurovascular coupling provide an important marker of neuronal activation. However, changes in systemic physiological parameters such as blood pressure and concentration of CO2 can also affect regional blood flow and may confound haemodynamics-based neuroimaging. Measurements with functional near-infrared spectroscopy (fNIRS) may additionally be confounded by blood flow and oxygenation changes in extracerebral tissue layers. Here we investigate these confounds using an extended version of an existing computational model of cerebral physiology, ‘BrainSignals’. Our results show that confounding from systemic physiological factors is able to produce misleading haemodynamic responses in both positive and negative directions. By applying the model to data from previous fNIRS studies, we demonstrate that such potentially deceptive responses can indeed occur in at least some experimental scenarios. It is therefore important to record the major potential confounders in the course of fNIRS experiments. Our model may then allow the observed behaviour to be attributed among the potential causes and hence reduce identification errors.

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Confounding of fNIRS haemoglobin signals is simulated using a computational model.

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Model is extended to simulate scalp haemodynamics.

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Changes in blood pressure and CO₂ can mimic and mask functional activation.

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Experimental recording of systemic factors is recommended to aid interpretation.

Modeling of Cerebral Oxygen Transport Based on In vivo Microscopic Imaging of Microvascular Network Structure, Blood Flow, and Oxygenation

Oxygen is delivered to brain tissue by a dense network of microvessels, which actively control cerebral blood flow (CBF) through vasodilation and contraction in response to changing levels of neural activity. Understanding these network-level processes is immediately relevant for (1) interpretation of functional Magnetic Resonance Imaging (fMRI) signals, and (2) investigation of neurological diseases in which a deterioration of neurovascular and neuro-metabolic physiology contributes to motor and cognitive decline. Experimental data on the structure, flow and oxygen levels of microvascular networks are needed, together with theoretical methods to integrate this information and predict physiologically relevant properties that are not directly measurable. Recent progress in optical imaging technologies for high-resolution in vivo measurement of the cerebral microvascular architecture, blood flow, and oxygenation enables construction of detailed computational models of cerebral hemodynamics and oxygen transport based on realistic three-dimensional microvascular networks. In this article, we review state-of-the-art optical microscopy technologies for quantitative in vivo imaging of cerebral microvascular structure, blood flow and oxygenation, and theoretical methods that utilize such data to generate spatially resolved models for blood flow and oxygen transport. These “bottom-up” models are essential for the understanding of the processes governing brain oxygenation in normal and disease states and for eventual translation of the lessons learned from animal studies to humans.

Joint state and parameter estimation of the hemodynamic model by particle smoother expectation maximization method

OBJECTIVE

In this paper, we aimed for the robust estimation of the parameters and states of the hemodynamic model by using blood oxygen level dependent signal.

APPROACH

In the fMRI literature, there are only a few successful methods that are able to make a joint estimation of the states and parameters of the hemodynamic model. In this paper, we implemented a maximum likelihood based method called the particle smoother expectation maximization (PSEM) algorithm for the joint state and parameter estimation.

MAIN RESULTS

Former sequential Monte Carlo methods were only reliable in the hemodynamic state estimates. They were claimed to outperform the local linearization (LL) filter and the extended Kalman filter (EKF). The PSEM algorithm is compared with the most successful method called square-root cubature Kalman smoother (SCKS) for both state and parameter estimation. SCKS was found to be better than the dynamic expectation maximization (DEM) algorithm, which was shown to be a better estimator than EKF, LL and particle filters.

SIGNIFICANCE

PSEM was more accurate than SCKS for both the state and the parameter estimation. Hence, PSEM seems to be the most accurate method for the system identification and state estimation for the hemodynamic model inversion literature. This paper do not compare its results with Tikhonov-regularized Newton-CKF (TNF-CKF), a recent robust method which works in filtering sense.

New horizons in neurometabolic and neurovascular coupling from calibrated fMRI

Neurovascular coupling relates changes in neuronal activity to constriction/dilation of microvessels. However neurometabolic coupling, which is less well known, relates alterations in neuronal activity with metabolic demands. The link between the blood oxygenation level dependent (BOLD) signal and neural activity opened doors for functional MRI (fMRI) to be a powerful neuroimaging tool in the neurosciences. But due to the complex makeup of BOLD contrast, researchers began to investigate the relationship between BOLD signal and blood flow and/or volume changes during functional brain activation, which together provided the tools to measure oxygen consumption on the basis of the biophysical model of BOLD. This field is called calibrated fMRI, thereby allowed probing of both neurometabolic and neurovascular couplings for a variety of health conditions in animals and humans. Calibrated fMRI may provide brain disorder biomarkers that could be used for monitoring effective therapies.

A novel approach to calibrate the hemodynamic model using functional Magnetic Resonance Imaging (fMRI) measurements

BACKGROUND

The calibration of the hemodynamic model that describes changes in blood flow and blood oxygenation during brain activation is a crucial step for successfully monitoring and possibly predicting brain activity. This in turn has the potential to provide diagnosis and treatment of brain diseases in early stages.

NEW METHOD

We propose an efficient numerical procedure for calibrating the hemodynamic model using some fMRI measurements. The proposed solution methodology is a regularized iterative method equipped with a Kalman filtering-type procedure. The Newton component of the proposed method addresses the nonlinear aspect of the problem. The regularization feature is used to ensure the stability of the algorithm. The Kalman filter procedure is incorporated here to address the noise in the data.

RESULTS

Numerical results obtained with synthetic data as well as with real fMRI measurements are presented to illustrate the accuracy, robustness to the noise, and the cost-effectiveness of the proposed method.

COMPARISON WITH EXISTING METHOD(S)

We present numerical results that clearly demonstrate that the proposed method outperforms the Cubature Kalman Filter (CKF), one of the most prominent existing numerical methods.

CONCLUSION

We have designed an iterative numerical technique, called the TNM-CKF algorithm, for calibrating the mathematical model that describes the single-event related brain response when fMRI measurements are given. The method appears to be highly accurate and effective in reconstructing the BOLD signal even when the measurements are tainted with high noise level (as high as 30%).

Low-Dimensional Models of "Neuro-Glio-Vascular Unit" for Describing Neural Dynamics under Normal and Energy-Starved Conditions

The motivation of developing simple minimal models for neuro-glio-vascular (NGV) system arises from a recent modeling study elucidating the bidirectional information flow within the NGV system having 89 dynamic equations (1). While this was one of the first attempts at formulating a comprehensive model for neuro-glio-vascular system, it poses severe restrictions in scaling up to network levels. On the contrary, low-­dimensional models are convenient devices in simulating large networks that also provide an intuitive understanding of the complex interactions occurring within the NGV system. The key idea underlying the proposed models is to describe the glio-vascular system as a lumped system, which takes neural firing rate as input and returns an “energy” variable (analogous to ATP) as output. To this end, we present two models: biophysical neuro-energy (Model 1 with five variables), comprising K_ATP channel activity governed by neuronal ATP dynamics, and the dynamic threshold (Model 2 with three variables), depicting the dependence of neural firing threshold on the ATP dynamics. Both the models show different firing regimes, such as continuous spiking, phasic, and tonic bursting depending on the ATP production coefficient, ɛ_p, and external current. We then demonstrate that in a network comprising such energy-dependent neuron units, ɛ_p could modulate the local field potential (LFP) frequency and amplitude. Interestingly, low-frequency LFP dominates under low ɛ_p conditions, which is thought to be reminiscent of seizure-like activity observed in epilepsy. The proposed “neuron-energy” unit may be implemented in building models of NGV networks to simulate data obtained from multimodal neuroimaging systems, such as functional near infrared spectroscopy coupled to electroencephalogram and functional magnetic resonance imaging coupled to electroencephalogram. Such models could also provide a theoretical basis for devising optimal neurorehabilitation strategies, such as non-invasive brain stimulation for stroke patients.

Differences in the Pulsatile Component of the Skin Hemodynamic Response to Verbal Fluency Tasks in the Forehead and the Fingertip

Several studies have claimed that hemodynamic signals measured by near-infrared spectroscopy (NIRS) on the forehead exhibit different patterns during a verbal fluency task (VFT) in various psychiatric disorders, whereas many studies have noted that NIRS signals can reflect task-related changes in skin blood flow. If such a task-related skin hemodynamic response is also observed in the fingertip, a simpler biomarker may be developed. Furthermore, determining the difference in the response pattern may provide physiological insights into the condition. We found that the magnitude of the pulsatile component in skin hemodynamic signals increased on the forehead (p < 0.001 for N = 50, p = 0.073 for N = 8) but decreased on the fingertip (p < 0.001, N = 8) during the VFT, whereas the rate in both areas increased (p < 0.02, N = 8). We also did not find a repetition effect in both the rate and the magnitude on the fingertip, whereas the effect was present in the magnitude (p < 0.02, N = 8) but not in the rate on the forehead. These results suggest that the skin vasomotor system in the forehead could have a different vessel mechanism to psychological tasks compared to the fingertip.

Commentary on the statistical properties of noise and its implication on general linear models in functional near-infrared spectroscopy

Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.

Investigating Human Neurovascular Coupling Using Functional Neuroimaging: A Critical Review of Dynamic Models

The mechanisms that link a transient neural activity to the corresponding increase of cerebral blood flow (CBF) are termed neurovascular coupling (NVC). They are possibly impaired at early stages of small vessel or neurodegenerative diseases. Investigation of NVC in humans has been made possible with the development of various neuroimaging techniques based on variations of local hemodynamics during neural activity. Specific dynamic models are currently used for interpreting these data that can include biophysical parameters related to NVC. After a brief review of the current knowledge about possible mechanisms acting in NVC we selected seven models with explicit integration of NVC found in the literature. All these models were described using the same procedure. We compared their physiological assumptions, mathematical formalism, and validation. In particular, we pointed out their strong differences in terms of complexity. Finally, we discussed their validity and their potential applications. These models may provide key information to investigate various aspects of NVC in human pathology.

Cortical Network Models of Firing Rates in the Resting and Active States Predict BOLD Responses

Measurements of blood oxygenation level dependent (BOLD) signals have produced some surprising observations. One is that their amplitude is proportional to the entire activity in a region of interest and not just the fluctuations in this activity. Another is that during sleep and anesthesia the average BOLD correlations between regions of interest decline as the activity declines. Mechanistic explanations of these phenomena are described here using a cortical network model consisting of modules with excitatory and inhibitory neurons, taken as regions of cortical interest, each receiving excitatory inputs from outside the network, taken as subcortical driving inputs in addition to extrinsic (intermodular) connections, such as provided by associational fibers. The model shows that the standard deviation of the firing rate is proportional to the mean frequency of the firing when the extrinsic connections are decreased, so that the mean BOLD signal is proportional to both as is observed experimentally. The model also shows that if these extrinsic connections are decreased or the frequency of firing reaching the network from the subcortical driving inputs is decreased, or both decline, there is a decrease in the mean firing rate in the modules accompanied by decreases in the mean BOLD correlations between the modules, consistent with the observed changes during NREM sleep and under anesthesia. Finally, the model explains why a transient increase in the BOLD signal in a cortical area, due to a transient subcortical input, gives rises to responses throughout the cortex as observed, with these responses mediated by the extrinsic (intermodular) connections.

Test-retest reliability of effective connectivity in the face perception network

Computational approaches have great potential for moving neuroscience toward mechanistic models of the functional integration among brain regions. Dynamic causal modeling (DCM) offers a promising framework for inferring the effective connectivity among brain regions and thus unraveling the neural mechanisms of both normal cognitive function and psychiatric disorders. While the benefit of such approaches depends heavily on their reliability, systematic analyses of the within-subject stability are rare. Here, we present a thorough investigation of the test-retest reliability of an fMRI paradigm for DCM analysis dedicated to unraveling intra- and interhemispheric integration among the core regions of the face perception network. First, we examined the reliability of face-specific BOLD activity in 25 healthy volunteers, who performed a face perception paradigm in two separate sessions. We found good to excellent reliability of BOLD activity within the DCM-relevant regions. Second, we assessed the stability of effective connectivity among these regions by analyzing the reliability of Bayesian model selection and model parameter estimation in DCM. Reliability was excellent for the negative free energy and good for model parameter estimation, when restricting the analysis to parameters with substantial effect sizes. Third, even when the experiment was shortened, reliability of BOLD activity and DCM results dropped only slightly as a function of the length of the experiment. This suggests that the face perception paradigm presented here provides reliable estimates for both conventional activation and effective connectivity measures. We conclude this paper with an outlook on potential clinical applications of the paradigm for studying psychiatric disorders. Hum Brain Mapp 37:730-744, 2016. © 2015 Wiley Periodicals, Inc.

Nonlinear extension of a hemodynamic linear model for coherent hemodynamics spectroscopy

In this work, we are proposing an extension of a recent hemodynamic model (Fantini, 2014a), which was developed within the framework of a novel approach to the study of tissue hemodynamics, named coherent hemodynamics spectroscopy (CHS). The previous hemodynamic model, from a signal processing viewpoint, treats the tissue microvasculature as a linear time-invariant system, and considers changes of blood volume, capillary blood flow velocity and the rate of oxygen diffusion as inputs, and the changes of oxy-, deoxy-, and total hemoglobin concentrations (measured in near infrared spectroscopy) as outputs. The model has been used also as a forward solver in an inversion procedure to retrieve quantitative parameters that assess physiological and biological processes such as microcirculation, cerebral autoregulation, tissue metabolic rate of oxygen, and oxygen extraction fraction. Within the assumption of "small" capillary blood flow velocity oscillations the model showed that the capillary and venous compartments "respond" to this input as low pass filters, characterized by two distinct impulse response functions. In this work, we do not make the assumption of "small" perturbations of capillary blood flow velocity by solving without approximations the partial differential equation that governs the spatio-temporal behavior of hemoglobin saturation in capillary and venous blood. Preliminary comparison between the linear time-invariant model and the extended model (here identified as nonlinear model) are shown for the relevant parameters measured in CHS as a function of the oscillation frequency (CHS spectra). We have found that for capillary blood flow velocity oscillations with amplitudes up to 10% of the baseline value (which reflect typical scenarios in CHS), the discrepancies between CHS spectra obtained with the linear and nonlinear models are negligible. For larger oscillations (~50%) the linear and nonlinear models yield CHS spectra with differences within typical experimental errors, but further investigation is needed to assess the effect of these differences. Flow oscillations larger than 10-20% are not typically induced in CHS; therefore, the results presented in this work indicate that a linear hemodynamic model, combined with a method to elicit controlled hemodynamic oscillations (as done for CHS), is appropriate for the quantitative assessment of cerebral microcirculation.

fMRI study of olfaction in the olfactory bulb and high olfactory structures of rats: Insight into their roles in habituation

Cerebral blood volume (CBV) fMRI with ultrasmall superparamagnetic iron oxide particles (USPIO) as a contrast agent was used to investigate olfactory processing in rats. fMRI data were acquired in sixteen 0.75-mm coronal slices covering the olfactory bulb (OB) and higher olfactory regions (HOR), including the anterior olfactory nucleus and piriform cortex. For each animal, multiple consecutive fMRI measurements were made during a 3-h experiment session, with each measurement consisting of a baseline period, an odorant stimulation period, and a recovery period. Two different stimulation paradigms with a stimulation period of 40s or 80s, respectively, were used to study olfactory processing. Odorant-induced CBV increases were robustly observed in the OB and HOR of each individual animal. Olfactory adaptation, which is characterized by an attenuation of responses to continuous exposure or repeated stimulations, has different characteristics in the OB and HOR. For adaptation to repeated stimuli, while it was observed in both the OB and HOR, CBV responses in the HOR were attenuated more significantly than responses in the OB. In contrast, within each continuous 40-s or 80-s odor exposure, CBV responses in the OB were stable and did not show adaptation, but the CBV responses in the HOR were state dependent, with no adaptation during initial exposures, but significant adaptation during following exposures. These results support previous reports that HOR plays a more significant role than OB in olfactory habituation. The technical approach presented in this study should enable more extensive fMRI studies of olfactory processing in rats.

Arterial impulse model for the BOLD response to brief neural activation

The blood oxygen level dependent (BOLD) signal evoked by brief neural stimulation, the hemodynamic response function (HRF), is a critical feature of neurovascular coupling. The HRF is directly related to local transient changes in oxygen supplied by cerebral blood flow (CBF) and oxygen demand, the cerebral metabolic rate of oxygen (CMRO2). Previous efforts to explain the HRF have relied upon the hypothesis that CBF produces a non-linear venous dilation within the cortical parenchyma. Instead, the observed dynamics correspond to prompt arterial dilation without venous volume change. This work develops an alternative biomechanical model for the BOLD response based on the hypothesis that prompt upstream dilation creates an arterial flow impulse amenable to linear description. This flow model is coupled to a continuum description of oxygen transport. Measurements using high-resolution fMRI demonstrate the efficacy of the model. The model predicts substantial spatial variations of the oxygen saturation along the length of capillaries and veins, and fits the varied gamut of measured HRFs by the combined effects of corresponding CBF and CMRO2 responses. Three interesting relationships among the hemodynamic parameters are predicted. First, there is an offset linear correlation with approximately unity slope between CBF and CMRO2 responses. Second, the HRF undershoot is strongly correlated to the corresponding CBF undershoot. Third, late-time-CMRO2 response can contribute to a slow recovery to baseline, lengthening the HRF undershoot. The model provides a powerful mathematical framework to understand the dynamics of neurovascular and neurometabolic responses that form the BOLD HRF.

Eccentricity mapping of the human visual cortex to evaluate temporal dynamics of functional T1ρ mapping

Recent experiments suggest that T1 relaxation in the rotating frame (T(1ρ)) is sensitive to metabolism and can detect localized activity-dependent changes in the human visual cortex. Current functional magnetic resonance imaging (fMRI) methods have poor temporal resolution due to delays in the hemodynamic response resulting from neurovascular coupling. Because T(1ρ) is sensitive to factors that can be derived from tissue metabolism, such as pH and glucose concentration via proton exchange, we hypothesized that activity-evoked T(1ρ) changes in visual cortex may occur before the hemodynamic response measured by blood oxygenation level-dependent (BOLD) and arterial spin labeling (ASL) contrast. To test this hypothesis, functional imaging was performed using T(1ρ), BOLD, and ASL in human participants viewing an expanding ring stimulus. We calculated eccentricity phase maps across the occipital cortex for each functional signal and compared the temporal dynamics of T(1ρ) versus BOLD and ASL. The results suggest that T(1ρ) changes precede changes in the two blood flow-dependent measures. These observations indicate that T(1ρ) detects a signal distinct from traditional fMRI contrast methods. In addition, these findings support previous evidence that T(1ρ) is sensitive to factors other than blood flow, volume, or oxygenation. Furthermore, they suggest that tissue metabolism may be driving activity-evoked T(1ρ) changes.

A Sensitivity Analysis of fMRI Balloon Model

Functional magnetic resonance imaging (fMRI) allows the mapping of the brain activation through measurements of the Blood Oxygenation Level Dependent (BOLD) contrast. The characterization of the pathway from the input stimulus to the output BOLD signal requires the selection of an adequate hemodynamic model and the satisfaction of some specific conditions while conducting the experiment and calibrating the model. This paper, focuses on the identifiability of the Balloon hemodynamic model. By identifiability, we mean the ability to estimate accurately the model parameters given the input and the output measurement. Previous studies of the Balloon model have somehow added knowledge either by choosing prior distributions for the parameters, freezing some of them, or looking for the solution as a projection on a natural basis of some vector space. In these studies, the identification was generally assessed using event-related paradigms. This paper justifies the reasons behind the need of adding knowledge, choosing certain paradigms, and completing the few existing identifiability studies through a global sensitivity analysis of the Balloon model in the case of blocked design experiment.

A mathematical model relating cortical oxygenated and deoxygenated hemoglobin flows and volumes to neural activity

OBJECTIVE

To describe a toolkit of components for mathematical models of the relationship between cortical neural activity and space-resolved and time-resolved flows and volumes of oxygenated and deoxygenated hemoglobin motivated by optical intrinsic signal imaging (OISI).

APPROACH

Both blood flow and blood volume and both oxygenated and deoxygenated hemoglobin and their interconversion are accounted for. Flow and volume are described by including analogies to both resistive and capacitive electrical circuit elements. Oxygenated and deoxygenated hemoglobin and their interconversion are described by generalization of Kirchhoff's laws based on well-mixed compartments.

MAIN RESULTS

Mathematical models built from this toolkit are able to reproduce experimental single-stimulus OISI results that are described in papers from other research groups and are able to describe the response to multiple-stimuli experiments as a sublinear superposition of responses to the individual stimuli.

SIGNIFICANCE

The same assembly of tools from the toolkit but with different parameter values is able to describe effects that are considered distinctive, such as the presence or absence of an initial decrease in oxygenated hemoglobin concentration, indicating that the differences might be due to unique parameter values in a subject rather than different fundamental mechanisms.

Venous cerebral blood volume increase during voluntary locomotion reflects cardiovascular changes

Understanding how changes in the cardiovascular system contribute to cerebral blood flow (CBF) and volume (CBV) increases is critical for interpreting hemodynamic signals. Here we investigated how systemic cardiovascular changes affect the cortical hemodynamic response during voluntary locomotion. In the mouse, voluntary locomotion drives an increase in cortical CBF and arterial CBV that is localized to the forelimb/hindlimb representation in the somatosensory cortex, as well as a diffuse venous CBV increase. To determine if the heart rate increases that accompany locomotion contribute to locomotion-induced CBV and CBF increases, we occluded heart rate increases with the muscarinic cholinergic receptor antagonist glycopyrrolate, and reduced heart rate with the β1-adrenergic receptor antagonist atenolol. We quantified the effects of these cardiovascular manipulations on CBV and CBF dynamics by comparing the hemodynamic response functions (HRF) to locomotion across these conditions. Neither the CBF HRF nor the arterial component of the CBV HRF was significantly affected by pharmacological disruption of the heart rate. In contrast, the amplitude and spatial extent of the venous component of the CBV HRF were decreased by atenolol. These results suggest that the increase in venous CBV during locomotion was partially driven by peripheral cardiovascular changes, whereas CBF and arterial CBV increases associated with locomotion reflect central processes.

Modeling fMRI signals can provide insights into neural processing in the cerebral cortex

Every stimulus or task activates multiple areas in the mammalian cortex. These distributed activations can be measured with functional magnetic resonance imaging (fMRI), which has the best spatial resolution among the noninvasive brain imaging methods. Unfortunately, the relationship between the fMRI activations and distributed cortical processing has remained unclear, both because the coupling between neural and fMRI activations has remained poorly understood and because fMRI voxels are too large to directly sense the local neural events. To get an idea of the local processing given the macroscopic data, we need models to simulate the neural activity and to provide output that can be compared with fMRI data. Such models can describe neural mechanisms as mathematical functions between input and output in a specific system, with little correspondence to physiological mechanisms. Alternatively, models can be biomimetic, including biological details with straightforward correspondence to experimental data. After careful balancing between complexity, computational efficiency, and realism, a biomimetic simulation should be able to provide insight into how biological structures or functions contribute to actual data processing as well as to promote theory-driven neuroscience experiments. This review analyzes the requirements for validating system-level computational models with fMRI. In particular, we study mesoscopic biomimetic models, which include a limited set of details from real-life networks and enable system-level simulations of neural mass action. In addition, we discuss how recent developments in neurophysiology and biophysics may significantly advance the modelling of fMRI signals.

Nonparametric hemodynamic deconvolution of FMRI using homomorphic filtering

Functional magnetic resonance imaging (fMRI) is an indirect measure of neural activity which is modeled as a convolution of the latent neuronal response and the hemodynamic response function (HRF). Since the sources of HRF variability can be nonneural in nature, the measured fMRI signal does not faithfully represent underlying neural activity. Therefore, it is advantageous to deconvolve the HRF from the fMRI signal. However, since both latent neural activity and the voxel-specific HRF is unknown, the deconvolution must be blind. Existing blind deconvolution approaches employ highly parameterized models, and it is unclear whether these models have an over fitting problem. In order to address these issues, we 1) present a nonparametric deconvolution method based on homomorphic filtering to obtain the latent neuronal response from the fMRI signal and, 2) compare our approach to the best performing existing parametric model based on the estimation of the biophysical hemodynamic model using the Cubature Kalman Filter/Smoother. We hypothesized that if the results from nonparametric deconvolution closely resembled that obtained from parametric deconvolution, then the problem of over fitting during estimation in highly parameterized deconvolution models of fMRI could possibly be over stated. Both simulations and experimental results demonstrate support for our hypothesis since the estimated latent neural response from both parametric and nonparametric methods were highly correlated in the visual cortex. Further, simulations showed that both methods were effective in recovering the simulated ground truth of the latent neural response.

Coupling mechanism and significance of the BOLD signal: a status report

Functional magnetic resonance imaging (fMRI) provides a unique view of the working human mind. The blood-oxygen-level-dependent (BOLD) signal, detected in fMRI, reflects changes in deoxyhemoglobin driven by localized changes in brain blood flow and blood oxygenation, which are coupled to underlying neuronal activity by a process termed neurovascular coupling. Over the past 10 years, a range of cellular mechanisms, including astrocytes, pericytes, and interneurons, have been proposed to play a role in functional neurovascular coupling. However, the field remains conflicted over the relative importance of each process, while key spatiotemporal features of BOLD response remain unexplained. Here, we review current candidate neurovascular coupling mechanisms and propose that previously overlooked involvement of the vascular endothelium may provide a more complete picture of how blood flow is controlled in the brain. We also explore the possibility and consequences of conditions in which neurovascular coupling may be altered, including during postnatal development, pathological states, and aging, noting relevance to both stimulus-evoked and resting-state fMRI studies.

Modeling the role of osmotic forces in the cerebrovascular response to CO2

Increases in blood osmolarity have been shown to exert a vasodilatory effect on cerebral and other vasculature, with accompanying increases in blood flow. It has also been shown that, through an influence on blood concentration of the bicarbonate ion and pH, changes in blood levels of CO2 can alter blood osmolarity sufficiently to have an impact on vessel diameter. We propose here that this phenomenon plays a previously unappreciated role in CO2-mediated vasodilation, and present a biophysical model of osmotically driven vasodilation. Our model, which is based on literature data describing CO2-dependent changes in blood osmolarity and hydraulic conductivity (Lp) of the blood-brain barrier, is used to predict the change in cerebral blood flow (CBF) associated with osmotic forces arising from a specific hypercapnic challenge. Modeled changes were then compared with actual CBF changes determined using arterial spin-labeling (ASL) MRI. For changes in the arterial partial pressure of CO2 (PaCO2) of 20 mmHg, our model predicted increases of 80% from baseline CBF with a temporal evolution that was comparable to the measured hemodynamic responses. Our modeling results suggest that osmotic forces could play a significant role in the cerebrovascular response to CO2.

Nonlinear Bayesian estimation of BOLD signal under non-Gaussian noise

Modeling the blood oxygenation level dependent (BOLD) signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.

Regulation of blood flow in the retinal trilaminar vascular network

Light stimulation evokes neuronal activity in the retina, resulting in the dilation of retinal blood vessels and increased blood flow. This response, named functional hyperemia, brings oxygen and nutrients to active neurons. However, it remains unclear which vessels mediate functional hyperemia. We have characterized blood flow regulation in the rat retina in vivo by measuring changes in retinal vessel diameter and red blood cell (RBC) flux evoked by a flickering light stimulus. We found that, in first- and second-order arterioles, flicker evoked large (7.5 and 5.0%), rapid (0.73 and 0.70 s), and consistent dilations. Flicker-evoked dilations in capillaries were smaller (2.0%) and tended to have a slower onset (0.97 s), whereas dilations in venules were smaller (1.0%) and slower (1.06 s) still. The proximity of pericyte somata did not predict capillary dilation amplitude. Expression of the contractile protein α-smooth muscle actin was high in arterioles and low in capillaries. Unexpectedly, we found that blood flow in the three vascular layers was differentially regulated. Flicker stimulation evoked far larger dilations and RBC flux increases in the intermediate layer capillaries than in the superficial and deep layer capillaries (2.6 vs 0.9 and 0.7% dilation; 25.7 vs 0.8 and 11.3% RBC flux increase). These results indicate that functional hyperemia in the retina is driven primarily by active dilation of arterioles. The dilation of intermediate layer capillaries is likely mediated by active mechanisms as well. The physiological consequences of differential regulation in the three vascular layers are discussed.

Fundamental relationships between blood pressure and cerebral blood flow in humans

Cerebral blood flow responses to transient blood pressure challenges are frequently attributed to cerebral autoregulation (CA), yet accumulating evidence indicates vascular properties like compliance are also influential. We hypothesized that middle cerebral blood velocity (MCAv) dynamics during or following a transient blood pressure perturbation can be accurately explained by the windkessel mechanism. Eighteen volunteers underwent blood pressure manipulations, including bilateral thigh-cuff deflation and sit-to-stand maneuvers under normocapnic and hypercapnic (5% CO2) conditions. Pressure-flow recordings were analyzed using a windkessel analysis approach that partitions the frequency-dependent resistance and compliance contributions to MCAv dynamics. The windkessel was typically able to explain more than 50% of the MCAv variance, as indicated by R2 values for both the flow recovery and postrecovery phase. The most consistent predictors of MCAv dynamics under the control condition were the windkessel capacitive gain and high-frequency resistive gain. However, there were significant interindividual variations in the composition of windkessel predictors. Hypercapnia consistently reduced the capacitive gain and enhanced the low-frequency (0.04–0.20 Hz) resistive gain for both thigh-cuff deflation and sit-to-stand trials. These findings indicate that 1) MCAv dynamics during acute transient hypotension challenges are dominated by cerebrovascular windkessel properties independent of CA; 2) there is significant heterogeneity in windkessel properties between individuals; and 3) hemodynamic effects of hypercapnia during transient blood pressure challenges primarily reflect changes in windkessel properties rather than pure CA impairment.

Data collection and analysis strategies for phMRI

Although functional MRI traditionally has been applied mainly to study changes in task-induced brain function, evolving acquisition methodologies and improved knowledge of signal mechanisms have increased the utility of this method for studying responses to pharmacological stimuli, a technique often dubbed "phMRI". The proliferation of higher magnetic field strengths and the use of exogenous contrast agent have boosted detection power, a critical factor for successful phMRI due to the restricted ability to average multiple stimuli within subjects. Receptor-based models of neurovascular coupling, including explicit pharmacological models incorporating receptor densities and affinities and data-driven models that incorporate weak biophysical constraints, have demonstrated compelling descriptions of phMRI signal induced by dopaminergic stimuli. This report describes phMRI acquisition and analysis methodologies, with an emphasis on data-driven analyses. As an example application, statistically efficient data-driven regressors were used to describe the biphasic response to the mu-opioid agonist remifentanil, and antagonism using dopaminergic and GABAergic ligands revealed modulation of the mesolimbic pathway. Results illustrate the power of phMRI as well as our incomplete understanding of mechanisms underlying the signal. Future directions are discussed for phMRI acquisitions in human studies, for evolving analysis methodologies, and for interpretative studies using the new generation of simultaneous PET/MRI scanners. This article is part of the Special Issue Section entitled 'Neuroimaging in Neuropharmacology'.

A semi-parametric nonlinear model for event-related fMRI

Nonlinearity in evoked hemodynamic responses often presents in event-related fMRI studies. Volterra series, a higher-order extension of linear convolution, has been used in the literature to construct a nonlinear characterization of hemodynamic responses. Estimation of the Volterra kernel coefficients in these models is usually challenging due to the large number of parameters. We propose a new semi-parametric model based on Volterra series for the hemodynamic responses that greatly reduces the number of parameters and enables "information borrowing" among subjects. This model assumes that in the same brain region and under the same stimulus, the hemodynamic responses across subjects share a common but unknown functional shape that can differ in magnitude, latency and degree of interaction. We develop a computationally-efficient strategy based on splines to estimate the model parameters, and a hypothesis test on nonlinearity. The proposed method is compared with several existing methods via extensive simulations, and is applied to a real event-related fMRI study.

Changes in cortical microvasculature during misery perfusion measured by two-photon laser scanning microscopy

This study aimed to examine the cortical microvessel diameter response to hypercapnia in misery perfusion using two-photon laser scanning microscopy (TPLSM). We evaluated whether the vascular response to hypercapnia could represent the cerebrovascular reserve. Cerebral blood flow (CBF) during normocapnia and hypercapnia was measured by laser-Doppler flowmetry through cranial windows in awake C57/BL6 mice before and at 1, 7, 14, and 28 days after unilateral common carotid artery occlusion (UCCAO). Diameters of the cortical microvessels during normocapnia and hypercapnia were also measured by TPLSM. Cerebral blood flow and the vascular response to hypercapnia were decreased after UCCAO. Before UCCAO, vasodilation during hypercapnia was found primarily in arterioles (22.9%±3.5%). At 14 days after UCCAO, arterioles, capillaries, and venules were autoregulatorily dilated by 79.5%±19.7%, 57.2%±32.3%, and 32.0%±10.8%, respectively. At the same time, the diameter response to hypercapnia in arterioles was significantly decreased to 1.9%±1.5%. A significant negative correlation was observed between autoregulatory vasodilation and the diameter response to hypercapnia in arterioles. Our findings indicate that arterioles play main roles in both autoregulatory vasodilation and hypercapnic vasodilation, and that the vascular response to hypercapnia can be used to estimate the cerebrovascular reserve.

Identification of optimal structural connectivity using functional connectivity and neural modeling

The complex network dynamics that arise from the interaction of the brain's structural and functional architectures give rise to mental function. Theoretical models demonstrate that the structure-function relation is maximal when the global network dynamics operate at a critical point of state transition. In the present work, we used a dynamic mean-field neural model to fit empirical structural connectivity (SC) and functional connectivity (FC) data acquired in humans and macaques and developed a new iterative-fitting algorithm to optimize the SC matrix based on the FC matrix. A dramatic improvement of the fitting of the matrices was obtained with the addition of a small number of anatomical links, particularly cross-hemispheric connections, and reweighting of existing connections. We suggest that the notion of a critical working point, where the structure-function interplay is maximal, may provide a new way to link behavior and cognition, and a new perspective to understand recovery of function in clinical conditions.