A time-invariant visco-elastic windkessel model relating blood flow and blood volume

Time-Series Modeling and Forecasting of Cerebral Pressure-Flow Physiology: A Scoping Systematic Review of the Human and Animal Literature

The modeling and forecasting of cerebral pressure-flow dynamics in the time-frequency domain have promising implications for veterinary and human life sciences research, enhancing clinical care by predicting cerebral blood flow (CBF)/perfusion, nutrient delivery, and intracranial pressure (ICP)/compliance behavior in advance. Despite its potential, the literature lacks coherence regarding the optimal model type, structure, data streams, and performance. This systematic scoping review comprehensively examines the current landscape of cerebral physiological time-series modeling and forecasting. It focuses on temporally resolved cerebral pressure-flow and oxygen delivery data streams obtained from invasive/non-invasive cerebral sensors. A thorough search of databases identified 88 studies for evaluation, covering diverse cerebral physiologic signals from healthy volunteers, patients with various conditions, and animal subjects. Methodologies range from traditional statistical time-series analysis to innovative machine learning algorithms. A total of 30 studies in healthy cohorts and 23 studies in patient cohorts with traumatic brain injury (TBI) concentrated on modeling CBFv and predicting ICP, respectively. Animal studies exclusively analyzed CBF/CBFv. Of the 88 studies, 65 predominantly used traditional statistical time-series analysis, with transfer function analysis (TFA), wavelet analysis, and autoregressive (AR) models being prominent. Among machine learning algorithms, support vector machine (SVM) was widely utilized, and decision trees showed promise, especially in ICP prediction. Nonlinear models and multi-input models were prevalent, emphasizing the significance of multivariate modeling and forecasting. This review clarifies knowledge gaps and sets the stage for future research to advance cerebral physiologic signal analysis, benefiting neurocritical care applications.

Characterizing the time course of cerebrovascular reactivity in multiple sclerosis

BACKGROUND AND PURPOSE

Changes in cerebral perfusion occur early in relapsing and progressive multiple sclerosis (MS) patients, though whether cerebral blood flow (CBF) can be altered by therapy is unknown. We sought to characterize the time course of change in CBF (cerebral vascular reactivity [CVR]), following intravenous (IV) acetazolamide (ACZ) in whole brain and within various gray and white matter brain regions in MS patients.

METHODS

We enrolled five relapsing MS patients on injectable therapies. Participants received a 1000 mg IV bolus of ACZ and CBF was measured using pseudocontinuous arterial spin labeling MRI. To quantify differences in time course between patients, we calculated the numerical integration of CVR over time using the trapezoidal rule to estimate area under the curve (AUC(CVR) ).

RESULTS

A change in whole brain CBF of 30%-65% was seen in all participants at 15 minutes after ACZ challenge. CBF increases >20% above baseline were sustained for 90 minutes within whole-brain, normal-appearing white matter and total T2-hyperintense lesioned tissue. AUC(CVR) values for both gray (cortical and deep gray matter) and white (normal-appearing and T2-lesioned) matter regions were similar between patients.

CONCLUSION

Our findings show a prolonged time course in vascular reactivity after ACZ stimulus in MS patients with a similar time course for both gray and white matter brain regions, including in previously injured tissue. Our preliminary results suggest that blood flow can be augmented in the established MS lesion suggesting that even previously injured tissue might be responsive to treatment.

Imaging faster neural dynamics with fast fMRI: A need for updated models of the hemodynamic response

Fast fMRI enables the detection of neural dynamics over timescales of hundreds of milliseconds, suggesting it may provide a new avenue for studying subsecond neural processes in the human brain. The magnitudes of these fast fMRI dynamics are far greater than predicted by canonical models of the hemodynamic response. Several studies have established nonlinear properties of the hemodynamic response that have significant implications for fast fMRI. We first review nonlinear properties of the hemodynamic response function that may underlie fast fMRI signals. We then illustrate the breakdown of canonical hemodynamic response models in the context of fast neural dynamics. We will then argue that the canonical hemodynamic response function is not likely to reflect the BOLD response to neuronal activity driven by sparse or naturalistic stimuli or perhaps to spontaneous neuronal fluctuations in the resting state. These properties suggest that fast fMRI is capable of tracking surprisingly fast neuronal dynamics, and we discuss the neuroscientific questions that could be addressed using this approach.

Arterial blood stealing as a mechanism of negative BOLD response: From the steady-flow with nonlinear phase separation to a windkessel-based model

Blood Oxygen Level Dependent (BOLD) signal indirectly characterizes neuronal activity by measuring hemodynamic and metabolic changes in the nearby microvasculature. A deeper understanding of how localized changes in electrical, metabolic and hemodynamic factors translate into a BOLD signal is crucial for the interpretation of functional brain imaging techniques. While positive BOLD responses (PBR) are widely considered to be linked with neuronal activation, the origins of negative BOLD responses (NBR) have remained largely unknown. As NBRs are sometimes observed in close proximity of regions with PBR, a blood "stealing" effect, i.e., redirection of blood from a passive periphery to the area with high neuronal activity, has been postulated. In this study, we used the Hagen-Poiseuille equation to model hemodynamics in an idealized microvascular network that account for the particulate nature of blood and nonlinearities arising from the red blood cell (RBC) distribution (i.e., the Fåhraeus, Fåhraeus-Lindqvist and the phase separation effects). Using this detailed model, we evaluate determinants driving this "stealing" effect in a microvascular network with geometric parameters within physiological ranges. Model simulations predict that during localized cerebral blood flow (CBF) increases due to neuronal activation-hyperemic response, blood from surrounding vessels is reallocated towards the activated region. This stealing effect depended on the resistance of the microvasculature and the uneven distribution of RBCs at vessel bifurcations. A parsimonious model consisting of two-connected windkessel regions sharing a supplying artery was proposed to simulate the stealing effect with a minimum number of parameters. Comparison with the detailed model showed that the parsimonious model can reproduce the observed response for hematocrit values within the physiological range for different species. Our novel parsimonious model promise to be of use for statistical inference (top-down analysis) from direct blood flow measurements (e.g., arterial spin labeling and laser Doppler/Speckle flowmetry), and when combined with theoretical models for oxygen extraction/diffusion will help account for some types of NBRs.

Identification of Negative BOLD Responses in Epilepsy Using Windkessel Models

Alongside positive blood oxygenation level–dependent (BOLD) responses associated with interictal epileptic discharges, a variety of negative BOLD responses (NBRs) are typically found in epileptic patients. Previous studies suggest that, in general, up to four mechanisms might underlie the genesis of NBRs in the brain: (i) neuronal disruption of network activity, (ii) altered balance of neurometabolic/vascular couplings, (iii) arterial blood stealing, and (iv) enhanced cortical inhibition. Detecting and classifying these mechanisms from BOLD signals are pivotal for the improvement of the specificity of the electroencephalography–functional magnetic resonance imaging (EEG-fMRI) image modality to identify the seizure-onset zones in refractory local epilepsy. This requires models with physiological interpretation that furnish the understanding of how these mechanisms are fingerprinted by their BOLD responses. Here, we used a Windkessel model with viscoelastic compliance/inductance in combination with dynamic models of both neuronal population activity and tissue/blood O₂ to classify the hemodynamic response functions (HRFs) linked to the above mechanisms in the irritative zones of epileptic patients. First, we evaluated the most relevant imprints on the BOLD response caused by variations of key model parameters. Second, we demonstrated that a general linear model is enough to accurately represent the four different types of NBRs. Third, we tested the ability of a machine learning classifier, built from a simulated ensemble of HRFs, to predict the mechanism underlying the BOLD signal from irritative zones. Cross-validation indicates that these four mechanisms can be classified from realistic fMRI BOLD signals. To demonstrate proof of concept, we applied our methodology to EEG-fMRI data from five epileptic patients undergoing neurosurgery, suggesting the presence of some of these mechanisms. We concluded that a proper identification and interpretation of NBR mechanisms in epilepsy can be performed by combining general linear models and biophysically inspired models.

An object-oriented computational model to study cardiopulmonary hemodynamic interactions in humans

BACKGROUND AND OBJECTIVE

This work introduces an object-oriented computational model to study cardiopulmonary interactions in humans.

METHODS

Modeling was performed in object-oriented programing language Matlab Simscape, where model components are connected with each other through physical connections. Constitutive and phenomenological equations of model elements are implemented based on their non-linear pressure-volume or pressure-flow relationship. The model includes more than 30 physiological compartments, which belong either to the cardiovascular or respiratory system. The model considers non-linear behaviors of veins, pulmonary capillaries, collapsible airways, alveoli, and the chest wall. Model parameters were derisved based on literature values. Model validation was performed by comparing simulation results with clinical and animal data reported in literature.

RESULTS

The model is able to provide quantitative values of alveolar, pleural, interstitial, aortic and ventricular pressures, as well as heart and lung volumes during spontaneous breathing and mechanical ventilation. Results of baseline simulation demonstrate the consistency of the assigned parameters. Simulation results during mechanical ventilation with PEEP trials can be directly compared with animal and clinical data given in literature.

CONCLUSIONS

Object-oriented programming languages can be used to model interconnected systems including model non-linearities. The model provides a useful tool to investigate cardiopulmonary activity during spontaneous breathing and mechanical ventilation.

A Potential Tool for the Study of Venous Ulcers: Blood Flow Responses to Load

Venous ulcers are deep wounds that are located predominantly on the lower leg. They are prone to infection and once healed have a high probability of recurrence. Currently, there are no effective measures to predict and prevent venous ulcers from formation. Hence, the goal of this work was to develop a Windkessel-based model that can be used to identify hemodynamic parameters that change between healthy individuals and those with wounds. Once identified, these parameters have the potential to be used as indicators of when internal conditions change, putting the patient at higher risk for wound formation. In order to achieve this goal, blood flow responses in lower legs were measured experimentally by a laser Doppler perfusion monitor (LDPM) and simulated with a modeling approach. A circuit model was developed on the basis of the Windkessel theory. The hemodynamic parameters were extracted for three groups: legs with ulcers (“wounded”), legs without ulcers but from ulcer patients (“nonwounded”), and legs without vascular disease (“healthy”). The model was executed by two independent operators, and both operators reported significant differences between wounded and healthy legs in localized vascular resistance and compliance. The model successfully replicated the experimental blood flow profile. The global and local vascular resistances and compliance parameters rendered quantifiable differences between a population with venous ulcers and healthy individuals. This work supports that the Windkessel modeling approach has the potential to determine patient specific parameters that can be used to identify when conditions change making venous ulcer formation more likely.

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.

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.

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.

Development of functional in vivo imaging of cerebral lenticulostriate artery using novel synchrotron radiation angiography

The lenticulostriate artery plays a vital role in the onset and development of cerebral ischemia. However, current imaging techniques cannot assess the in vivo functioning of small arteries such as the lenticulostriate artery in the brain of rats. Here, we report a novel method to achieve a high resolution multi-functional imaging of the cerebrovascular system using synchrotron radiation angiography, which is based on spatio-temporal analysis of contrast density in the arterial cross section. This method provides a unique tool for studying the sub-cortical vascular elasticity after cerebral ischemia in rats. Using this technique, we demonstrated that the vascular elasticity of the lenticulostriate artery decreased from day 1 to day 7 after transient middle cerebral artery occlusion in rats and recovered from day 7 to day 28 compared to the controls (p < 0.001), which paralleled with brain edema formation and inversely correlated with blood flow velocity (p < 0.05). Our results demonstrated that the change of vascular elasticity was related to the levels of brain edema and the velocity of focal blood flow, suggesting that reducing brain edema is important for the improvement of the function of the lenticulostriate artery in the ischemic brain.

Neurovascular deconvolution of optical signals as a proxy for the true neuronal inputs

Since the Kalman filter and Monte Carlo techniques, much theoretical work has been put into the development of signal deconvolution tools. Among recent developments taking place in neuroscience are Dynamic Expectation Maximization, Generalized Filtering and the Cubature Kalman Filter. While there are exciting prospects to use these tools for Dynamic Causal Modeling and other analyses of networks, there has been comparatively little work to validate the algorithms on controlled experimental data. In this work, the latest evolution of these tools, the square-root cubature Kalman smoother (SCKS), is tested for its effectiveness on multimodal neurovascular data. Multispectral intrinsic optical imaging and electrophysiological measurements of Wistar rats are used in combination with somatosensory stimulation. The Buxton-Friston (B-F) balloon model is then deconvolved with the SCKS algorithm to obtain the estimated neuronal inputs u(t) from the hemodynamic measurements (flow, oxy- and deoxygenated hemoglobin).

RESULTS

The estimated neuronal inputs are compared to the stimulation protocol and a sensitivity and specificity analysis is carried out. SCKS succeeds in recovering most of the stimulations. Next, the estimated inputs are compared to actual measures of neuronal activity: local field potentials (LFPs) and multiunit activity (MUA). Good sensitivity of the technique is obtained with both LFPs and MUA over the whole recordings, with the area of the ROC curves favoring LFPs. A weak correlation between SCKS estimated inputs and LFPs is found outside stimulation periods, significant at one standard deviation. Finally, the accuracy of state reconstructions is studied and SCKS reconstructed states are highly concordant with measured states.

Arteries dominate volume changes during brief functional hyperemia: evidence from mathematical modelling

Variations in local neural activity are accompanied by rapid, focal changes in cerebral blood flow and volume. While a range of observations have shown that dilation occurs in cerebral arteries, there is conflicting evidence about the significance of volume changes in post-arteriole vessels. Here, we reconcile the competing observations using a new mathematical model of the hemodynamic response. First, we followed a 'top down' approach, without constraining the model, but using experimental observations at progressively more detailed scales to ensure physiological behaviour. Then, we blocked dilation of post-arteriole vessels, and predicted observations at progressively more aggregated scales (a 'bottom up' approach). Predictions of blood flow, volume, velocity, and vessel diameter changes were consistent with experimental observations. Interestingly, the model predicted small, slow increases in capillary and venous diameter in agreement with recent in vivo data. Blocking dilation in these vessels led to erroneous volume predictions. The results are further evidence that arteries make up the majority of blood volume increases during brief functional activation. However, dilation of capillaries and veins appears to be increasingly significant during extended stimulation. These are important considerations when interpreting results from different neurovascular imaging modalities.

Experimental animal models for studies on the mechanisms of blast-induced neurotrauma

A blast injury is a complex type of physical trauma resulting from the detonation of explosive compounds and has become an important issue due to the use of improvised explosive devices (IED) in current military conflicts. Blast-induced neurotrauma (BINT) is a major concern in contemporary military medicine and includes a variety of injuries that range from mild to lethal. Extreme forces and their complex propagation characterize BINT. Modern body protection and the development of armored military vehicles can be assumed to have changed the outcome of BINT. Primary blast injuries are caused by overpressure waves whereas secondary, tertiary, and quaternary blast injuries can have more varied origins such as the impact of fragments, abnormal movements, or heat. The characteristics of the blast wave can be assumed to be significantly different in open field detonations compared to explosions in a confined space, such an armored vehicle. Important parameters include peak pressure, duration, and shape of the pulse. Reflections from walls and armor can make the prediction of effects in individual cases very complex. Epidemiological data do not contain information of the comparative importance of the different blast mechanisms. It is therefore important to generate data in carefully designed animal models. Such models can be selective reproductions of a primary blast, penetrating injuries from fragments, acceleration movements, or combinations of such mechanisms. It is of crucial importance that the physical parameters of the employed models are well characterized so that the experiments can be reproduced in different laboratory settings. Ideally, pressure recordings should be calibrated by using the same equipment in several laboratories. With carefully designed models and thoroughly evaluated animal data it should be possible to achieve a translation of data between animal and clinical data. Imaging and computer simulation represent a possible link between experiments and studies of human cases. However, in order for mathematical simulations to be completely useful, the predictions will most likely have to be validated by detailed data from animal experiments. Some aspects of BINT can conceivably be studied in vitro. However, factors such as systemic response, brain edema, inflammation, vasospasm, or changes in synaptic transmission and behavior must be evaluated in experimental animals. Against this background, it is necessary that such animal experiments are carefully developed imitations of actual components in the blast injury. This paper describes and discusses examples of different designs of experimental models relevant to BINT.

IRON fMRI measurements of CBV and implications for BOLD signal

Changes in cerebral blood volume (CBV) and blood magnetization each induce changes in the transverse relaxation rate of MRI signal that are associated with changes in cerebral activity. BOLD signal, the preeminent method for non-invasive localization of task-induced brain function in human subjects, reflects a combination of changes in CBV and blood magnetization. Intravenous injection of paramagnetic contrast media, usually iron oxide particles surrounded by larger macromolecules, can overwhelm the BOLD response and sensitize signal to blood plasma volume, a method we have deemed "IRON" fMRI. The practical advantage of this technique is the ability to optimize blood magnetization at any echo time, enabling high detection power and the use of short echo times; for these reasons, IRON fMRI has become a valuable imaging tool in animal models. The temporal response of blood plasma volume is quite different from blood flow and BOLD signal; thus, CBV has been identified as a prominent source of transient features of the BOLD response. This article reviews the methodological advantages of the IRON method and how CBV measurements have informed our understanding of the BOLD response.

Dynamic models of BOLD contrast

This personal recollection looks at the evolution of ideas about the dynamics of the blood oxygenation level dependent (BOLD) signal, with an emphasis on the balloon model. From the first detection of the BOLD response it has been clear that the signal exhibits interesting dynamics, such as a pronounced and long-lasting post-stimulus undershoot. The BOLD response, reflecting a change in local deoxyhemoglobin, is a combination of a hemodynamic response, related to changes in blood flow and venous blood volume, and a metabolic response related to oxygen metabolism. Modeling is potentially a way to understand the complex path from changes in neural activity to the BOLD signal. In the early days of fMRI it was hoped that the hemodynamic/metabolic response could be modeled in a unitary way, with blood flow, oxygen metabolism, and venous blood volume-the physiological factors that affect local deoxyhemoglobin-all tightly linked. The balloon model was an attempt to do this, based on the physiological ideas of limited oxygen delivery at baseline and a slow recovery of venous blood volume after the stimulus (the balloon effect), and this simple model of the physiology worked well to simulate the BOLD response. However, subsequent experiments suggest a more complicated picture of the underlying physiology, with blood flow and oxygen metabolism driven in parallel, possibly by different aspects of neural activity. In addition, it is still not clear whether the post-stimulus undershoot is a hemodynamic or a metabolic phenomenon, although the original venous balloon effect is unlikely to be the full explanation, and a flow undershoot is likely to be important. Although our understanding of the physics of the BOLD response is now reasonably solid, our understanding of the underlying physiological relationships is still relatively poor, and this is the primary hurdle for future models of BOLD dynamics.

Biophysical model estimation of neurovascular parameters in a rat model of healthy aging

Neuronal, vascular and metabolic factors result in a deterioration of the cerebral hemodynamic response with age. The interpretation of neuroimaging studies in the context of aging is rendered difficult due to the challenge in untangling the composite effect of these modifications. In this work we integrate multimodal optical imaging in biophysical models to investigate vascular and metabolic changes occurring in aging. Multispectral intrinsic optical imaging of an animal model of healthy aging, the LOU/c rat, is used in combination with somatosensory stimulation to study the modifications of the hemodynamic response with increasing age. Results are fitted with three macroscopic biophysical models to extract parameters, providing a phenomenological description of vascular and metabolic changes. Our results show that 1) biophysical parameters are estimable from multimodal data and 2) parameter estimates in this population change with aging.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network. Part II: flow variations induced by global or localized modifications of arteriolar diameters

In a companion paper (Lorthois et al., Neuroimage, in press), we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking into account the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, volumes of functional vascular territories, regional flow at voxel and network scales, etc. Using the same approach, we study flow reorganizations induced by global arteriolar vasodilations (an isometabolic global increase in cerebral blood flow). For small to moderate global vasodilations, the relationship between changes in volume and changes in flow is in close agreement with Grubb's law, providing a quantitative tool for studying the variations of its exponent with underlying vascular architecture. A significant correlation between blood flow and vascular structure at the voxel scale, practically unchanged with respect to baseline, is demonstrated. Furthermore, the effects of localized arteriolar vasodilations, representative of a local increase in metabolic demand, are analyzed. In particular, localized vasodilations induce flow changes, including vascular steal, in the neighboring arteriolar trunks at small distances (<300 μm), while their influence in the neighboring veins is much larger (about 1 mm), which provides an estimate of the vascular point spread function. More generally, for the first time, the hemodynamic component of various functional neuroimaging techniques has been isolated from metabolic and neuronal components, and a direct relationship with several known characteristics of the BOLD signal has been demonstrated.

Simulation study of brain blood flow regulation by intra-cortical arterioles in an anatomically accurate large human vascular network: Part I: methodology and baseline flow

Hemodynamically based functional neuroimaging techniques, such as BOLD fMRI and PET, provide indirect measures of neuronal activity. The quantitative relationship between neuronal activity and the measured signals is not yet precisely known, with uncertainties remaining about the relative contribution by their metabolic and hemodynamic components. Empirical observations have demonstrated the importance of the latter component and suggested that micro-vascular anatomy has a potential influence. The recent development of a 3D computer-assisted method for micro-vascular cerebral network analysis has produced a large quantitative library on the microcirculation of the human cerebral cortex (Cassot et al., 2006), which can be used to investigate the hemodynamic component of brain activation through fluid dynamic modeling. For this purpose, we perform the first simulations of blood flow in an anatomically accurate large human intra-cortical vascular network (~10000 segments), using a 1D non-linear model taking account of the complex rheological properties of blood flow in microcirculation. This model predicts blood pressure, blood flow and hematocrit distributions, as well as volumes of functional vascular territories, and regional flow at voxel and network scales. First, the influence of the prescribed boundary conditions (BCs) on the baseline flow structure is investigated, highlighting relevant lower- and upper-bound BCs. Independent of these BCs, large heterogeneities of baseline flow from vessel to vessel and from voxel to voxel, are demonstrated. These heterogeneities are controlled by the architecture of the intra-cortical vascular network. In particular, a correlation between the blood flow and the proportion of vascular volume occupied by arterioles or venules, at voxel scale, is highlighted. Then, the extent of venous contamination downstream to the sites of neuronal activation is investigated, demonstrating a linear relationship between the catchment surface of the activated area and the diameter of the intra-cortical draining vein.

Quantification of CMRO(2) without hypercapnia using simultaneous near-infrared spectroscopy and fMRI measurements

Estimation of the cerebral metabolic rate of oxygen (CMRO(2)) and cerebral blood flow (CBF) is important to investigate the neurovascular coupling and physiological components in blood oxygenation level-dependent (BOLD) signals quantitatively. Although there are methods that can determine CMRO(2) changes using functional MRI (fMRI) or near-infrared spectroscopy (NIRS), current approaches require a separate hypercapnia calibration process and have the potential to incur bias in many assumed model parameters. In this paper, a novel method to estimate CMRO(2) without hypercapnia is described using simultaneous measurements of NIRS and fMRI. Specifically, an optimization framework is proposed that minimizes the differences between the two forms of the relative CMRO(2)-CBF coupling ratio from BOLD and NIRS biophysical models, from which hypercapnia calibration and model parameters are readily estimated. Based on the new methods, we found that group average CBF, CMRO(2), cerebral blood volume (CBV), and BOLD changes within activation of the primary motor cortex during a finger tapping task increased by 39.5 +/- 21.4%, 18.4 +/- 8.7%, 12.9 +/- 6.7%, and 0.5 +/- 0.2%, respectively. The group average estimated flow-metabolism coupling ratio was 2.38 +/- 0.65 and the hypercapnia parameter was 7.7 +/- 1.7%. These values are within the range of values reported from other literatures. Furthermore, the activation maps from CBF and CMRO(2) were well localized on the primary motor cortex, which is the main target region of the finger tapping task.

Optimisation on the least squares identification of dynamical systems with application to hemodynamic modelling

Dynamic modelling using the traditional least squares method with noisy input/output data can yield biased and sometimes unstable model predictions. This is largely because the cost function employed by the traditional least squares method is based on the one-step-ahead prediction errors. In this paper, the model-predicted-output errors are used in estimating the model parameters. As the cost function is highly nonlinear in terms of the model parameters, the particle swarm optimisation method is used to search for the optimal parameters. We will show that compared with model predictions using the traditional least squares method, the model-predicted-output approach is more robust at dealing with noisy input/output data. The algorithm is applied to identify the dynamic relationship between changes in cerebral blood flow and volume due to evoked changes in neural activity and is shown to produce better predictions than that using the least squares method.