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

The difference between the rate of change of cerebral blood volume (CBV) and cerebral blood flow (CBF) following stimulation is thought to be due to circumferential stress relaxation in veins (Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679–689). In this paper we explore the visco-elastic properties of blood vessels, and present a dynamic model relating changes in CBF to changes in CBV. We refer to this model as the visco-elastic windkessel (VW) model. A novel feature of this model is that the parameter characterising the pressure–volume relationship of blood vessels is treated as a state variable dependent on the rate of change of CBV, producing hysteresis in the pressure–volume space during vessel dilation and contraction. The VW model is nonlinear time-invariant, and is able to predict the observed differences between the time series of CBV and that of CBF measurements following changes in neural activity. Like the windkessel model derived by Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679–689, the VW model is primarily a model of haemodynamic changes in the venous compartment. The VW model is demonstrated to have the following characteristics typical of visco-elastic materials: (1) hysteresis, (2) creep, and (3) stress relaxation, hence it provides a unified model of the visco-elastic properties of the vasculature. The model will not only contribute to the interpretation of the Blood Oxygen Level Dependent (BOLD) signals from functional Magnetic Resonance Imaging (fMRI) experiments, but also find applications in the study and modelling of the brain vasculature and the haemodynamics of circulatory and cardiovascular systems.

Evidence for a reversal with age in the pattern of near-wall blood flow around aortic branches

The changes that occur with age in the distribution of atherosclerotic lesions around arterial branch points challenge accepted theories relating disease to haemodynamic stresses. We investigated whether flow near branch points changes with age in a way that can account for the different lesion distributions. Flow around 20 branches from immature and mature aortas was investigated by examining the length:width ratio and orientation of endothelial nuclei; these properties depend on the magnitude and direction of near-wall flows, respectively. There were significant changes in the pattern of nuclear shape with age, consistent with a reversal in the pattern of shear around branches. In control regions away from branches, there were no such changes. The role of haemodynamic stresses in atherogenesis may require re-evaluation in the light of these results. (C) 2003 Elsevier Ireland Ltd. All rights reserved.

Evidence for a reversal with age in the pattern of near-wall blood flow around aortic branches

The changes that occur with age in the distribution of atherosclerotic lesions around arterial branch points challenge accepted theories relating disease to haemodynamic stresses. We investigated whether flow near branch points changes with age in a way that can account for the different lesion distributions. Flow around 20 branches from immature and mature aortas was investigated by examining the length:width ratio and orientation of endothelial nuclei; these properties depend on the magnitude and direction of near-wall flows, respectively. There were significant changes in the pattern of nuclear shape with age, consistent with a reversal in the pattern of shear around branches. In control regions away from branches, there were no such changes. The role of haemodynamic stresses in atherogenesis may require re-evaluation in the light of these results.

Model estimation of cerebral hemodynamics between blood flow and volume changes: A data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

A model of the dynamic relationship between blood flow and volume changes during brain activation

The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level-dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBV proportional to CBFPhi has been used extensively in the literature. Two similar models, the Balloon (Buxton et al., 1998) and the Windkessel (Mandeville et al., 1999), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.

Negative blood oxygen level dependence in the rat: a model for investigating the role of suppression in neurovascular coupling

Modern neuroimaging techniques rely on neurovascular coupling to show regions of increased brain activation. However, little is known of the neurovascular coupling relationships that exist for inhibitory signals. To address this issue directly we developed a preparation to investigate the signal sources of one of these proposed inhibitory neurovascular signals, the negative blood oxygen level-dependent (BOLD) response (NBR), in rat somatosensory cortex. We found a reliable NBR measured in rat somatosensory cortex in response to unilateral electrical whisker stimulation, which was located in deeper cortical layers relative to the positive BOLD response. Separate optical measurements (two-dimensional optical imaging spectroscopy and laser Doppler flowmetry) revealed that the NBR was a result of decreased blood volume and flow and increased levels of deoxyhemoglobin. Neural activity in the NBR region, measured by multichannel electrodes, varied considerably as a function of cortical depth. There was a decrease in neuronal activity in deep cortical laminae. After cessation of whisker stimulation there was a large increase in neural activity above baseline. Both the decrease in neuronal activity and increase above baseline after stimulation cessation correlated well with the simultaneous measurement of blood flow suggesting that the NBR is related to decreases in neural activity in deep cortical layers. Interestingly, the magnitude of the neural decrease was largest in regions showing stimulus-evoked positive BOLD responses. Since a similar type of neural suppression in surround regions was associated with a negative BOLD signal, the increased levels of suppression in positive BOLD regions could importantly moderate the size of the observed BOLD response.

A dynamic model of neurovascular coupling: Implications for blood vessel dilation and constriction

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

A dynamic causal model of the coupling between pulse stimulation and neural activity

We present a dynamic causal model that can explain context-dependent changes in neural responses, in the rat barrel cortex, to an electrical whisker stimulation at different frequencies. Neural responses were measured in terms of local field potentials. These were converted into current source density (CSD) data, and the time series of the CSD sink was extracted to provide a time series response train. The model structure consists of three layers (approximating the responses from the brain stem to the thalamus and then the barrel cortex), and the latter two layers contain nonlinearly coupled modules of linear second-order dynamic systems. The interaction of these modules forms a nonlinear regulatory system that determines the temporal structure of the neural response amplitude for the thalamic and cortical layers. The model is based on the measured population dynamics of neurons rather than the dynamics of a single neuron and was evaluated against CSD data from experiments with varying stimulation frequency (1–40 Hz), random pulse trains, and awake and anesthetized animals. The model parameters obtained by optimization for different physiological conditions (anesthetized or awake) were significantly different. Following Friston, Mechelli, Turner, and Price (2000), this work is part of a formal mathematical system currently being developed (Zheng et al., 2005) that links stimulation to the blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal through neural activity and hemodynamic variables. The importance of the model described here is that it can be used to invert the hemodynamic measurements of changes in blood flow to estimate the underlying neural activity.

Long duration stimuli and nonlinearities in the neural–haemodynamic coupling

Recent studies have shown that the haemodynamic responses to brief (<2 secs) stimuli can be well characterised as a linear convolution of neural activity with a suitable haemodynamic impulse response. In this paper, we show that the linear convolution model cannot predict measurements of blood flow responses to stimuli of longer duration (>2 secs), regardless of the impulse response function chosen. Modifying the linear convolution scheme to a nonlinear convolution scheme was found to provide a good prediction of the observed data. Whereas several studies have found a nonlinear coupling between stimulus input and blood flow responses, the current modelling scheme uses neural activity as an input, and thus implies nonlinearity in the coupling between neural activity and blood flow responses. Neural activity was assessed by current source density analysis of depth-resolved evoked field potentials, while blood flow responses were measured using laser Doppler flowmetry. All measurements were made in rat whisker barrel cortex after electrical stimulation of the whisker pad for 1 to 16 secs at 5 Hz and 1.2 mA (individual pulse width 0.3 ms).

Association of vitamin D status with arterial blood pressure and hypertension risk: a mendelian randomisation study

BACKGROUND: Low plasma 25-hydroxyvitamin D (25[OH]D) concentration is associated with high arterial blood pressure and hypertension risk, but whether this association is causal is unknown. We used a mendelian randomisation approach to test whether 25(OH)D concentration is causally associated with blood pressure and hypertension risk. METHODS: In this mendelian randomisation study, we generated an allele score (25[OH]D synthesis score) based on variants of genes that affect 25(OH)D synthesis or substrate availability (CYP2R1 and DHCR7), which we used as a proxy for 25(OH)D concentration. We meta-analysed data for up to 108 173 individuals from 35 studies in the D-CarDia collaboration to investigate associations between the allele score and blood pressure measurements. We complemented these analyses with previously published summary statistics from the International Consortium on Blood Pressure (ICBP), the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) consortium, and the Global Blood Pressure Genetics (Global BPGen) consortium. FINDINGS: In phenotypic analyses (up to n=49 363), increased 25(OH)D concentration was associated with decreased systolic blood pressure (β per 10% increase, -0·12 mm Hg, 95% CI -0·20 to -0·04; p=0·003) and reduced odds of hypertension (odds ratio [OR] 0·98, 95% CI 0·97-0·99; p=0·0003), but not with decreased diastolic blood pressure (β per 10% increase, -0·02 mm Hg, -0·08 to 0·03; p=0·37). In meta-analyses in which we combined data from D-CarDia and the ICBP (n=146 581, after exclusion of overlapping studies), each 25(OH)D-increasing allele of the synthesis score was associated with a change of -0·10 mm Hg in systolic blood pressure (-0·21 to -0·0001; p=0·0498) and a change of -0·08 mm Hg in diastolic blood pressure (-0·15 to -0·02; p=0·01). When D-CarDia and consortia data for hypertension were meta-analysed together (n=142 255), the synthesis score was associated with a reduced odds of hypertension (OR per allele, 0·98, 0·96-0·99; p=0·001). In instrumental variable analysis, each 10% increase in genetically instrumented 25(OH)D concentration was associated with a change of -0·29 mm Hg in diastolic blood pressure (-0·52 to -0·07; p=0·01), a change of -0·37 mm Hg in systolic blood pressure (-0·73 to 0·003; p=0·052), and an 8·1% decreased odds of hypertension (OR 0·92, 0·87-0·97; p=0·002). INTERPRETATION: Increased plasma concentrations of 25(OH)D might reduce the risk of hypertension. This finding warrants further investigation in an independent, similarly powered study.

Flow-aligned jets in the magnetospheric cusp: Results from the Geospace Environment Modeling Pilot Program

The extended flight of the Airborne Ionospheric Observatory during the Geospace Environment Modeling (GEM) Pilot program on January 16, 1990, allowed continuous all-sky monitoring of the two-dimensional ionospheric footprint of the northward interplanetary magnetic field (IMF) cusp in several wavelengths. Especially important in determining the locus of magnetosheath electron precipitation was the 630.0-nm red line emission. The most striking morphological change in the images was the transient appearance of zonally elongated regions of enhanced 630.0-nm emission which resembled “rays” emanating from the centroid of the precipitation. The appearance of these rays was strongly correlated with the Y component of the IMF: when the magnitude of By was large compared to Bz, the rays appeared; otherwise, the distribution was relatively unstructured. Late in the flight the field of view of the imager included the field of view of flow measurements from the European incoherent scatter radar (EISCAT). The rays visible in 630.0-nm emission exactly aligned with the position of strong flow jets observed by EISCAT. We attribute this correspondence to the requirement of quasi-neutrality; namely, the soft electrons have their largest precipitating fluxes where the bulk of the ions precipitate. The ions, in regions of strong convective flow, are spread out farther along the flow path than in regions of weaker flow. The occurrence and direction of these flow bursts are controlled by the IMF in a manner consistent with newly opened flux tubes; i.e., when |By| > |Bz|, tension in the reconnected field lines produce east-west flow regions downstream of the ionospheric projection of the x line. We interpret the optical rays (flow bursts), which typically last between 5 and 15 min, as evidence of periods of enhanced dayside (or lobe) reconnection when |By| > |Bz|. The length of the reconnection pulse is difficult to determine, however, since strong zonal flows would be expected to persist until the tension force in the field line has decayed, even if the duration of the enhanced reconnection was relatively short.

On flow reversal boundaries and transpolar voltage in average models of high-latitude convection

The implications of polar cap expansions, contractions and movements for empirical models of high-latitude plasma convection are examined. Some of these models have been generated by directly averaging flow measurements from large numbers of satellite passes or radar scans; others have employed more complex means to combine data taken at different times into large-scale patterns of flow. In all cases, the models have implicitly adopted the assumption that the polar cap is in steady state: they have all characterized the ionospheric flow in terms of the prevailing conditions (e.g. the interplanetary magnetic field and/or some index of terrestrial magnetic activity) without allowance for their history. On long enough time scales, the polar cap is indeed in steady state but on time scales shorter than a few hours it is not and can oscillate in size and position. As a result, the method used to combine the data can influence the nature of the convection reversal boundary and the transpolar voltage in the derived model. This paper discusses a variety of effects due to time-dependence in relation to some ionospheric convection models which are widely applied. The effects are shown to be varied and to depend upon the procedure adopted to compile the model.

Platelet adhesion to podoplanin under flow is mediated by the receptor CLEC-2 and stabilised by Src/Syk-dependent platelet signalling

Platelet-specific deletion of CLEC-2, which signals through Src and Syk kinases, or global deletion of its ligand podoplanin results in blood-filled lymphatics during mouse development. Platelet-specific Syk deficiency phenocopies this defect, indicating that platelet activation is required for lymphatic development. In the present study, we investigated whether CLEC-2-podoplanin interactions could support platelet arrest from blood flow and whether platelet signalling is required for stable platelet adhesion to lymphatic endothelial cells (LECs) and recombinant podoplanin under flow. Perfusion of human or mouse blood over human LEC monolayers led to platelet adhesion and aggregation. Following αIIbβ3 blockade, individual platelets still adhered. Platelet binding occurred at venous but not arterial shear rates. There was no adhesion using CLEC-2-deficient blood or to vascular endothelial cells (which lack podoplanin). Perfusion of human blood over human Fc-podoplanin (hFcPDPN) in the presence of monoclonal antibody IV.3 to block FcγRIIA receptors led to platelet arrest at similar shear rates to those used on LECs. Src and Syk inhibitors significantly reduced global adhesion of human or mouse platelets to LECs and hFcPDPN. A similar result was seen using Syk-deficient mouse platelets. Reduced platelet adhesion was due to a decrease in the stability of binding. In conclusion, our data reveal that CLEC-2 is an adhesive receptor that supports platelet arrest to podoplanin under venous shear. Src/Syk-dependent signalling stabilises platelet adhesion to podoplanin, providing a possible molecular mechanism contributing to the lymphatic defects of Syk-deficient mice.