Evidence of a cerebrovascular postarteriole windkessel with delayed compliance

The history and role of long duration stimulation in fMRI

During the past 20 years, BOLD fMRI has developed towards a central and fundamental tool in neuroscience. It has been shown that the BOLD response provides an indicator of neuronal activity in the brain. Consequently, for an accurate interpretation of findings in BOLD MRI experiments and to draw meaningful conclusions about the temporal evolution of neural events, a deep understanding of the nature of the BOLD contrast has become of essential importance. Since the dynamics of the major direct determinants of the BOLD signal (CBF, CBV and CMRO(2)) range between seconds and minutes, long duration stimulation was an early key strategy needed to study and understand the BOLD characteristics. This paper summarizes and discusses the thoughts and rationales of the long duration stimulation studies.

The BOLD post-stimulus undershoot, one of the most debated issues in fMRI

This paper provides a brief overview of how we got involved in fMRI work and of our efforts to elucidate the mechanisms underlying BOLD signal changes. The phenomenon discussed here in particular is the post-stimulus undershoot (PSU), the interpretation of which has captivated many fMRI scientists and is still under debate to date. This controversy is caused both by the convoluted physiological origin of the BOLD effect, which allows many possible explanations, and the lack of comprehensive data in the early years. BOLD effects reflect changes in cerebral blood flow (CBF), volume (CBV), metabolic rate of oxygen (CMRO(2)), and hematocrit fraction (Hct). However, the size of such effects is modulated by vascular origin such as intravascular, extravascular, macro and microvascular, venular and capillary, the relative contributions of which depend not only on the spatial resolution of the measurements, but also on stimulus duration, on magnetic field strength and on whether spin echo (SE) or gradient echo (GRE) detection is used. The two most dominant explanations of the PSU have been delayed vascular compliance (first venular, later arteriolar, and recently capillary) and sustained increases in CMRO(2), while post-activation reduction in CBF is a distant third. MRI has the capability to independently measure CBF and arteriolar, venous, and total CBV contributions in humans and animals, which has been of great assistance in improving the understanding of BOLD phenomena. Using currently available MRI and optical data, we conclude that the predominant PSU origin is a sustained increase in CMRO(2). However, some contributions from delayed vascular compliance are likely, and small CBF undershoot contributions that are difficult to detect with current arterial spin labeling technology can also not be excluded. The relative contribution of these different processes, which are not mutually exclusive and can act together, is likely to vary with stimulus duration and type.

A review of the development of Vascular-Space-Occupancy (VASO) fMRI

Vascular-Space-Occupancy (VASO) fMRI is a non-invasive technique to detect brain activation based on changes in Cerebral Blood Volume (CBV), as opposed to conventional BOLD fMRI, which is based on changes in blood oxygenation. This technique takes advantage of the T1 difference between blood and surrounding tissue, and uses an inversion recovery pulse sequence to null blood signal while maintaining part of the tissue signal. The VASO signal intensity can thus be considered proportional to 1-CBV. When neural activation causes CBV to increase, the VASO signal will show a decrease, allowing the detection of activated regions in the brain. Activation-induced changes in VASO signal, ∆S/S, are in the order of -1%. Absolute quantification of ∆CBV requires additional assumptions on baseline CBV and water contents of the parenchyma and blood. The first VASO experiment was conducted approximately 10 years ago. The original goal of nulling the blood signal was to isolate and measure extravascular BOLD effects, thus a long TE of 50 ms was used in the inversion recovery experiment. Instead of a positive signal change, a slight decrease in signal was observed, which became more pronounced when TE was shortened to 10 ms. These findings led to the hypothesis of a CBV signal mechanism and the development of VASO fMRI. Since its discovery, VASO has been validated by comparison with MION-CBV studies in animals and has been used in humans and animals to understand metabolic and hemodynamic changes during brain activation and physiologic challenges. With recent development of more sensitive VASO acquisitions, the availability of arterial-based VASO sequences, and improvement in spatial coverage, this technique is finding its place in neuroscience and clinical studies.

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.

Measurements and modeling of transient blood flow perturbations induced by brief somatosensory stimulation

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

Quantitative MRI of cerebral arterial blood volume

Baseline cerebral arterial blood volume (CBV_a) and its change are important for potential diagnosis of vascular dysfunctions, the determination of functional reactivity, and the interpretation of BOLD fMRI. To quantitative measure baseline CBV_a non-invasively, we developed arterial spin labeling methods with magnetization transfer (MT) or bipolar gradients by utilizing differential MT or diffusion properties of tissue vs. arteries. Cortical CBV_a of isoflurane-anesthetized rats was 0.6 – 1.4 ml/100 g. During 15-s forepaw stimulation, CBV_a change was dominant, while venous blood volume change was minimal. This indicates that the venous CBV increase may be ignored for BOLD quantification for a stimulation duration of less than 15 s. By incorporating BOLD fMRI with varied MT effects in a cat visual cortical layer model, the highest ΔCBV_a was observed at layer 4, while the highest BOLD signal was detected at the surface of the cortex, indicating that CBV_a change is highly specific to neural activity. The CBV_a MRI techniques provide quantified maps, thus, may be valuable tools for routine determination of vessel viability and function, as well as the identification of vascular dysfunction.

Quantitative functional MRI: concepts, issues and future challenges

Since its inception 20 years ago, functional magnetic resonance imaging (fMRI) of the human brain based on the blood oxygenation level dependent (BOLD) contrast phenomenon has proliferated and matured. Today it is the predominant functional brain imaging modality with the majority of applications being in basic cognitive neuroscience where it has primarily been used as a tool to localize brain activity. While the magnitude of the BOLD response is often used in these studies as a surrogate for the level of neuronal activity, the link between the two is, in fact, quite indirect. The BOLD response is dependent upon hemodynamic (blood flow and volume) and metabolic (oxygen consumption) responses as well as acquisition details. Furthermore, the relationship between neuronal activity and the hemodynamic response, termed neurovascular coupling, is itself complex and incompletely understood. Quantitative fMRI techniques have therefore been developed to measure the hemodynamic and metabolic responses to modulations in brain activity. These methods have not only helped clarify the behaviour and origins of the BOLD signal under normal physiological conditions but they have also provided a potentially valuable set of tools for exploring pathophysiological conditions. Such quantitative methods will be critical to realize the potential of fMRI in a clinical context, where simple BOLD measurements cannot be uniquely interpreted, and to enhance the power of fMRI in basic neuroscience research. In this article, recent advances in human quantitative fMRI methods are reviewed, outstanding issues discussed and future challenges and opportunities highlighted.

A theoretical framework for estimating cerebral oxygen metabolism changes using the calibrated-BOLD method: modeling the effects of blood volume distribution, hematocrit, oxygen extraction fraction, and tissue signal properties on the BOLD signal

Calibrated blood oxygenation level dependent (BOLD) imaging, a technique used to measure changes in cerebral O(2) metabolism, depends on an accurate model of how the BOLD signal is affected by the mismatch between changes in cerebral blood flow (CBF) and cerebral metabolic rate of O(2) (CMRO(2)). However, other factors such as the cerebral blood volume (CBV) distribution at rest and with activation also affect the BOLD signal. The Davis model originally proposed for calibrated BOLD studies (Davis et al., 1998) is widely used because of its simplicity, but it assumes CBV changes are uniformly distributed across vascular compartments, neglects intravascular signal changes, and ignores blood-tissue signal exchange effects as CBV increases and supplants tissue volume. More recent studies suggest that venous CBV changes are smaller than arterial changes, and that intravascular signal changes and CBV exchange effects can bias estimated CMRO(2). In this paper, recent experimental results for the relationship between deoxyhemoglobin and BOLD signal changes are integrated in order to simulate the BOLD signal in detail by expanding a previous model to include a tissue compartment and three blood compartments rather than only the venous blood compartment. The simulated data were then used to test the accuracy of the Davis model of calibrated BOLD, demonstrating that the errors in estimated CMRO(2) responses across the typical CBF-CMRO(2) coupling range are modest despite the simplicity of the assumptions underlying the original derivation of the model. Nevertheless, the accuracy of the model can be improved by abandoning the original physical meaning of the two parameters α and β and treating them as adjustable parameters that capture several physical effects. For a 3Tesla field and a dominant arterial volume change with activation, the accuracy of the Davis model is improved with new values of α=0.14 and β=0.91.

Linear coupling of undershoot with BOLD response in ER-fMRI and nonlinear BOLD response in rapid-presentation ER-fMRI

In event-related (ER) BOLD-fMRI brain activation studies, understanding the relationship between the elicited BOLD signal and its underlying neuronal activity is essential for any quantitative interpretation of the neural events from the BOLD measurements. This requires a better understanding of the dynamic BOLD response. Besides the neuronal activity-induced positive BOLD response, the dynamic response is also characterized by a profound post-stimulus undershoot. The relationship between the positive response and the post-stimulus undershoot, however, remains poorly understood. Earlier studies using block-design paradigms with long stimulation durations (>10s) do not suggest a quantitative relationship. Using an ER paradigm, this study revealed a linear coupling between the positive BOLD response and the post-stimulus undershoot across the human visual cortex. The voxelwise linear coupling across the visual cortex strongly supports a homogeneous hemodynamic response in ER paradigms, though the BOLD response magnitude varies substantially over a wide range across the visual cortex. Although underlying neuronal activity is responsible for a BOLD response, the blood volume fraction affects the magnitude of the BOLD response; the larger the blood volume fraction, the larger the magnitude. This effect needs to be accounted for in any quantitative interpretation of the BOLD measurements. In the absence of nonlinear neuronal activities, the nonlinear vascular response renders the estimated BOLD responses smaller in rapid presentation (RP) ER paradigms compared to that in ER paradigms, and this reduction effect also needs to be considered when interpreting the estimated BOLD responses in RP-ER paradigms. Interestingly, this nonlinear effect might be simply accounted for by a scaling factor across the visual cortex.

Physiological origin for the BOLD poststimulus undershoot in human brain: vascular compliance versus oxygen metabolism

The poststimulus blood oxygenation level-dependent (BOLD) undershoot has been attributed to two main plausible origins: delayed vascular compliance based on delayed cerebral blood volume (CBV) recovery and a sustained increased oxygen metabolism after stimulus cessation. To investigate these contributions, multimodal functional magnetic resonance imaging was employed to monitor responses of BOLD, cerebral blood flow (CBF), total CBV, and arterial CBV (CBV(a)) in human visual cortex after brief breath hold and visual stimulation. In visual experiments, after stimulus cessation, CBV(a) was restored to baseline in 7.9±3.4 seconds, and CBF and CBV in 14.8±5.0 seconds and 16.1±5.8 seconds, respectively, all significantly faster than BOLD signal recovery after undershoot (28.1±5.5 seconds). During the BOLD undershoot, postarterial CBV (CBV(pa), capillaries and venules) was slightly elevated (2.4±1.8%), and cerebral metabolic rate of oxygen (CMRO(2)) was above baseline (10.6±7.4%). Following breath hold, however, CBF, CBV, CBV(a) and BOLD signals all returned to baseline in ∼20 seconds. No significant BOLD undershoot, and residual CBV(pa) dilation were observed, and CMRO(2) did not substantially differ from baseline. These data suggest that both delayed CBV(pa) recovery and enduring increased oxidative metabolism impact the BOLD undershoot. Using a biophysical model, their relative contributions were estimated to be 19.7±15.9% and 78.7±18.6%, respectively.

Assessment of temporal state-dependent interactions between auditory fMRI responses to desired and undesired acoustic sources

A confounding factor in auditory functional magnetic resonance imaging (fMRI) experiments is the presence of the acoustic noise inherently associated with the echo planar imaging acquisition technique. Previous studies have demonstrated that this noise can induce unwanted neuronal responses that can mask stimulus-induced responses. Similarly, activation accumulated over multiple stimuli has been demonstrated to elevate the baseline, thus reducing the dynamic range available for subsequent responses. To best evaluate responses to auditory stimuli, it is necessary to account for the presence of all recent acoustic stimulation, beginning with an understanding of the attenuating effects brought about by interaction between and among induced unwanted neuronal responses, and responses to desired auditory stimuli. This study focuses on the characterization of the duration of this temporal memory and qualitative assessment of the associated response attenuation. Two experimental parameters--inter-stimulus interval (ISI) and repetition time (TR)--were varied during an fMRI experiment in which participants were asked to passively attend to an auditory stimulus. Results present evidence of a state-dependent interaction between induced responses. As expected, attenuating effects of these interactions become less significant as TR and ISI increase and in contrast to previous work, persist up to 18s after a stimulus presentation.

Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain.

Determinants of human cerebral pressure-flow velocity relationships: new insights from vascular modelling and Ca²⁺ channel blockade

The fundamental determinants of human dynamic cerebral autoregulation are poorly understood, particularly the role of vascular compliance and the myogenic response. We sought to 1) determine whether capacitive blood flow associated with vascular compliance and driven by the rate of change in mean arterial blood pressure (dMAP/dt) is an important determinant of middle cerebral artery velocity (MCAv) dynamics and 2) characterise the impact of myogenic blockade on these cerebral pressure-flow velocity relations in humans. We measured MCAv and mean arterial pressure (MAP) during oscillatory lower body negative pressure (n =8) at 0.10 and 0.05 Hz before and after cerebral Ca²⁺ channel blockade (nimodipine). Pressure-flow velocity relationships were characterised using transfer function analysis and a regression-based Windkessel analysis that incorporates MAP and dMAP/dt as predictors of MCAv dynamics. Results show that incorporation of dMAP/dt accounted for more MCAv variance (R² 0.80-0.99) than if only MAP was considered (R2 0.05-0.90). The capacitive gain relating dMAP/dt and MCAv was strongly correlated to transfer function gain (0.05 Hz, r =0.93, P<0.01; 0.10 Hz, r =0.91, P<0.01), but not to phase or coherence. Ca²⁺ channel blockade increased the conductive gain relation between MAP and MCAv (P<0.05), and reduced phase at 0.05 Hz (P<0.01). Capacitive and transfer function gain were unaltered. The findings suggest capacitive blood flow is an important determinant of cerebral haemodynamics that bears strong relations to some metrics of dynamic cerebral autoregulation derived from transfer function analysis, and that Ca²⁺ channel blockade enhances pressure-driven resistive blood flow but does not alter capacitive blood flow. the causes and effects of cerebrovascular diseases such as stroke and dementia.

Fluctuating and sensory-induced vasodynamics in rodent cortex extend arteriole capacity

Neural activity in the brain is followed by localized changes in blood flow and volume. We address the relative change in volume for arteriole vs. venous blood within primary vibrissa cortex of awake, head-fixed mice. Two-photon laser-scanning microscopy was used to measure spontaneous and sensory evoked changes in flow and volume at the level of single vessels. We find that arterioles exhibit slow (<1 Hz) spontaneous increases in their diameter, as well as pronounced dilation in response to both punctate and prolonged stimulation of the contralateral vibrissae. In contrast, venules dilate only in response to prolonged stimulation. We conclude that stimulation that occurs on the time scale of natural stimuli leads to a net increase in the reservoir of arteriole blood. Thus, a "bagpipe" model that highlights arteriole dilation should augment the current "balloon" model of venous distension in the interpretation of fMRI images.

Temporal dynamics and spatial specificity of arterial and venous blood volume changes during visual stimulation: implication for BOLD quantification

Determination of compartment-specific cerebral blood volume (CBV) changes is important for understanding neurovascular physiology and quantifying blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI). In isoflurane-anesthetized cats, we measured the spatiotemporal responses of arterial CBV (CBV(a)) and total CBV (CBV(t)) induced by a 40-second visual stimulation, using magnetization transfer (MT)-varied BOLD and contrast-agent fMRI techniques at 9.4 T. To determine the venous CBV (CBV(v)) change, we calculated the difference between CBV(t) and CBV(a) changes. The dynamic response of CBV(a) was an order of magnitude faster than that of CBV(v), while the magnitude of change under steady-state conditions was similar between the two. Following stimulation offset, ΔCBV(a) showed small poststimulus undershoots, while ΔCBV(v) slowly returned to baseline. The largest CBV(a) and CBV(t) response occurred after 10 seconds of simulation in cortical layer 4, which we identified as the stripe of Gennari by T(1)-weighted MRI. The CBV(v) response, however, was not specific across the cortical layers during the entire stimulation period. Our data indicate that rapid, more-specific arterial vasodilation is followed by slow, less-specific venous dilation. Our finding implies that the contribution of CBV(v) changes to BOLD signals is significant for long, but not short, stimulation periods.

BOLD temporal dynamics of rat superior colliculus and lateral geniculate nucleus following short duration visual stimulation

BACKGROUND

The superior colliculus (SC) and lateral geniculate nucleus (LGN) are important subcortical structures for vision. Much of our understanding of vision was obtained using invasive and small field of view (FOV) techniques. In this study, we use non-invasive, large FOV blood oxygenation level-dependent (BOLD) fMRI to measure the SC and LGN's response temporal dynamics following short duration (1 s) visual stimulation.

METHODOLOGY/PRINCIPAL FINDINGS

Experiments are performed at 7 tesla on Sprague Dawley rats stimulated in one eye with flashing light. Gradient-echo and spin-echo sequences are used to provide complementary information. An anatomical image is acquired from one rat after injection of monocrystalline iron oxide nanoparticles (MION), a blood vessel contrast agent. BOLD responses are concentrated in the contralateral SC and LGN. The SC BOLD signal measured with gradient-echo rises to 50% of maximum amplitude (PEAK) 0.2±0.2 s before the LGN signal (p<0.05). The LGN signal returns to 50% of PEAK 1.4±1.2 s before the SC signal (p<0.05). These results indicate the SC signal rises faster than the LGN signal but settles slower. Spin-echo results support these findings. The post-MION image shows the SC and LGN lie beneath large blood vessels. This subcortical vasculature is similar to that in the cortex, which also lies beneath large vessels. The LGN lies closer to the large vessels than much of the SC.

CONCLUSIONS/SIGNIFICANCE

The differences in response timing between SC and LGN are very similar to those between deep and shallow cortical layers following electrical stimulation, which are related to depth-dependent blood vessel dilation rates. This combined with the similarities in vasculature between subcortex and cortex suggest the SC and LGN timing differences are also related to depth-dependent dilation rates. This study shows for the first time that BOLD responses in the rat SC and LGN following short duration visual stimulation are temporally different.

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.

Exploring the post-stimulus undershoot with spin-echo fMRI: implications for models of neurovascular response

As a consequence of neural stimulation the blood oxygenation-level dependent (BOLD) contrast in gradient-echo echo-planar imaging (GE-EPI) based functional MRI (fMRI) leads to an increased MR signal in activated brain regions. Following this, a BOLD signal undershoot below baseline is generally observed with GE-EPI. The origin of this undershoot has been the focus of many investigations using fMRI and optical modalities, but the underlying mechanisms remain disputed. Here, we investigate the BOLD undershoot following visual stimulation by using a purely T₂-weighted fMRI sequence at 1.5 and 3 T. By taking advantage of the field strength dependency of the T₂ BOLD contrast and complete absence of static dephasing effects due to the pure spin echoes, one can draw conclusions about the origin of the BOLD undershoot and test the hypotheses in the literature. We observe a significant undershoot at both field strengths, with constant undershoot-to-main response ratio. This provides strong evidence that the undershoot is caused by BOLD changes due to elevated post-stimulus deoxyhaemoglobin concentration in the small vessels. 'Delayed vascular compliance' as suggested by the well-known Balloon and Windkessel models does not appear capable of explaining the undershoot. Our results also suggest that blood volume changes in arterioles and capillaries, for which there is consistent evidence from optical imaging studies, cannot alone cause the undershoot. This has important implications for models of neurovascular response and provides further support for the decoupling of changes in the rate of oxygen metabolism and blood flow. In addition, we found that an 'arteriolar balloon' (delayed arterial compliance) may provide a plausible explanation for the temporal characteristics of the BOLD undershoot.

Advances in functional imaging of the human cerebellum

PURPOSE OF REVIEW

A quarter century of functional neuroimaging has provided a number of insights into the function of the human cerebellum. However, progress has been relatively slow, partly because cerebellar imaging poses a number of unique challenges for functional magnetic resonance imaging (fMRI). This review provides a guide to problems and recent solutions in the design, analysis and interpretation of neuroimaging studies of the human cerebellum.

RECENT FINDINGS

One major problem in the interpretation of functional imaging studies is that it is still unclear what type of neural activity is reflected in the cerebellar blood-oxygenation-level-dependent signal. We summarize recent work that has provided partly contradictory insights. We then highlight some technical challenges, specifically the susceptibility to physiological artifacts, and recently developed techniques to account for them. Furthermore, the small size and functional heterogeneity of the cerebellum poses a challenge for normalization and atlas methods, which demands different analysis techniques than those used in the neocortex. Finally, we highlight some novel results assessing anatomical and functional connectivity with the neocortex.

SUMMARY

Although these results clearly show the limitations of current approaches, they also show the potential of anatomical and functional MRI for the study of the human cerebellum.

Contribution of arterial Windkessel in low-frequency cerebral hemodynamics during transient changes in blood pressure

The Windkessel properties of the vasculature are known to play a significant role in buffering arterial pulsations, but their potential importance in dampening low-frequency fluctuations in cerebral blood flow has not been clearly examined. In this study, we quantitatively assessed the contribution of arterial Windkessel (peripheral compliance and resistance) in the dynamic cerebral blood flow response to relatively large and acute changes in blood pressure. Middle cerebral artery flow velocity (MCA(V); transcranial Doppler) and arterial blood pressure were recorded from 14 healthy subjects. Low-pass-filtered pressure-flow responses (<0.15 Hz) during transient hypertension (intravenous phenylephrine) and hypotension (intravenous sodium nitroprusside) were fitted to a two-element Windkessel model. The Windkessel model was found to provide a superior goodness of fit to the MCA(V) responses during both hypertension and hypotension (R² = 0.89 ± 0.03 and 0.85 ± 0.05, respectively), with a significant improvement in adjusted coefficients of determination (P < 0.005) compared with the single-resistance model (R² = 0.62 ± 0.06 and 0.61 ± 0.08, respectively). No differences were found between the two interventions in the Windkessel capacitive and resistive gains, suggesting similar vascular properties during pressure rise and fall episodes. The results highlight that low-frequency cerebral hemodynamic responses to transient hypertension and hypotension may include a significant contribution from the mechanical properties of vasculature and, thus, cannot solely be attributed to the active control of vascular tone by cerebral autoregulation. The arterial Windkessel should be regarded as an important element of dynamic cerebral blood flow modulation during large and acute blood pressure perturbation.

Similarities and differences in arterial responses to hypercapnia and visual stimulation

Despite the different origins of cerebrovascular activity induced by neurogenic and nonneurogenic conditions, a standard assumption in functional studies is that the consequence on the vascular system will be mechanically similar. Using a recently developed arterial spin labeling method, we examined arterial blood volume, arterial-microvascular transit time, and cerebral blood flow (CBF) in the gray matter and in areas with large arterial vessels under hypercapnia, visual stimulation, and a combination of the two. Spatial heterogeneity in arterial reactivity was observed between conditions. During hypercapnia, large arterial volume changes contributed to CBF increase and further downstream, there were reductions in the gray matter transit time. These changes were not significant during visual stimulation, and during the combined condition they were moderated. These findings suggest distinct vascular mechanisms for large and small arterial segments that may be condition specific. However, the power relationships between gray matter arterial blood volume and CBF in hypercapnia (α=0.69±0.24) and visual stimulation (α=0.68±0.20) were similar. Assuming consistent capillary and venous volume responses across these conditions, these results offer support for a consistent total CBV-flow relationship typically assumed in blood oxygen-level dependent calibration techniques.

Spatiotemporal evolution of the functional magnetic resonance imaging response to ultrashort stimuli

The specificity of the hemodynamic response function (HRF) is determined spatially by the vascular architecture and temporally by the evolution of hemodynamic changes. The stimulus duration has additional influence on the spatiotemporal evolution of the HRF, as brief stimuli elicit responses that engage only the local vasculature, whereas long stimuli lead to the involvement of remote vascular supply and drainage. Here, we used functional magnetic resonance imaging to investigate the spatiotemporal evolution of the blood oxygenation level-dependent (BOLD), cerebral blood flow (CBF), and cerebral blood volume (CBV) HRF to ultrashort forelimb stimulation in an anesthetized rodent model. The HRFs to a single 333-μs-long stimulus were robustly detected and consisted of a rapid response in both CBF and CBV, with an onset time (OT) of 350 ms and a full width at half-maximum of 1 s. In contrast, longer stimuli elicited a dispersive transit of oxygenated blood across the cortical microvasculature that significantly prolonged the evolution of the CBV HRF, but not the CBF. The CBF and CBV OTs suggest that vasoactive messengers are synthesized, released, and effective within 350 ms. However, the difference between the BOLD and CBV OT (∼100 ms) was significantly smaller than the arteriolar-venular transit time (∼500 ms), indicating an arterial contribution to the BOLD HRF. Finally, the rapid rate of growth of the active region with stimulus elongation suggests that functional hyperemia is an integrative process that involves the entire functional cortical depth. These findings offer a new view into the spatiotemporal dynamics of functional hemodynamic regulation in the brain.

Oscillations in cerebral blood flow and cortical oxygenation in Alzheimer's disease

In Alzheimer's disease (AD) cerebrovascular function is at risk. Transcranial Doppler, near-infrared spectroscopy, and photoplethysmography are noninvasive methods to continuously measure changes in cerebral blood flow velocity (CBFV), cerebral cortical oxygenated hemoglobin (O(2)Hb), and blood pressure (BP). In 21 patients with mild to moderate AD and 20 age-matched controls, we investigated how oscillations in cerebral blood flow velocity (CBFV) and O(2)Hb are associated with spontaneous and induced oscillations in blood pressure (BP) at the very low (VLF = 0.05 Hz) and low frequencies (LF = 0.1 Hz). We applied spectral and transfer function analysis to quantify dynamic cerebral autoregulation and brain tissue oxygenation. In AD, cerebrovascular resistance was substantially higher (34%, AD vs. control: Δ = 0.69 (0.25) mm Hg/cm/second, p = 0.012) and the transmission of very low frequency (VLF) cerebral blood flow (CBF) oscillations into O(2)Hb differed, with increased phase lag and gain (Δ phase 0.32 [0.15] rad; Δ gain 0.049 [0.014] μmol/cm/second, p both < 0.05). The altered transfer of CBF to cortical oxygenation in AD indicates that properties of the cerebral microvasculature are changed in this disease.

Basal cerebral blood volume during the poststimulation undershoot in BOLD MRI of the human brain

One of the characteristics of the blood oxygenation level-dependent (BOLD) magnetic resonance imaging (MRI) response to functional challenges of the brain is the poststimulation undershoot, which has been suggested to originate from a delayed recovery of either cerebral blood volume (CBV) or cerebral metabolic rate of oxygen to baseline. Using bolus-tracking MRI in humans, we recently showed that relative CBV rapidly normalizes after the end of stimulation. As this observation contradicts at least part of the blood-pool contrast agent studies performed in animals, we reinvestigated the CBV contribution by dynamic T1-weighted three-dimensional MRI (8 seconds temporal resolution) and Vasovist at 3 T (12 subjects). Initially, we determined the time constants of individual BOLD responses. After injection of Vasovist, CBV-related T1-weighted signal changes revealed a signal increase during visual stimulation (1.7% ± 0.4%), but no change relative to baseline in the poststimulation phase (0.2% ± 0.3%). This finding renders the specific nature of the contrast agent unlikely to be responsible for the discrepancy between human and animal studies. With the assumption of normalized cerebral blood flow after stimulus cessation, a normalized CBV lends support to the idea that the BOLD MRI undershoot reflects a prolonged elevation of oxidative metabolism.

MEG and fMRI Fusion for Non-Linear Estimation of Neural and BOLD Signal Changes

The combined analysis of magnetoencephalography (MEG)/electroencephalography and functional magnetic resonance imaging (fMRI) measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the blood oxygenation level dependent (BOLD) response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater signal-to-noise ratio, that confirms the expectation arising from the nature of the experiment. The highly non-linear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources.

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.

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.

Functional neuroimaging: a physiological perspective

Metabolic physiology and functional neuroimaging have played important and complementary roles over the past two decades. In particular, investigations of the mechanisms underlying functional neuroimaging signals have produced fundamental new insights into hemodynamic and metabolic regulation. However, controversies were also raised as regards the metabolic pathways (oxidative vs. non-oxidative) for meeting the energy demand and driving the increases in cerebral blood flow (CBF) during brain activation. In a recent study, with the concurrent functional MRI-MRS measurements, we found that task-evoked energy demand was predominately met through oxidative metabolism (approximately 98%), despite a small increase in cerebral metabolic rate of oxygen (12–17%). In addition, the task-induced increases in CBF were most likely mediated by anaerobic glycolysis rather than oxygen demand. These observations and others from functional neuroimaging support the activation-induced neuron-astrocyte interactions portrayed by the astrocyte-neuron lactate shuttle model. The concurrent developments of neuroimaging methods and metabolic physiology will also pave the way for the future investigation of cerebral hemodynamics and metabolism in disease states.

From acoustic segmentation to language processing: evidence from optical imaging

During language acquisition in infancy and when learning a foreign language, the segmentation of the auditory stream into words and phrases is a complex process. Intuitively, learners use “anchors” to segment the acoustic speech stream into meaningful units like words and phrases. Regularities on a segmental (e.g., phonological) or suprasegmental (e.g., prosodic) level can provide such anchors. Regarding the neuronal processing of these two kinds of linguistic cues a left-hemispheric dominance for segmental and a right-hemispheric bias for suprasegmental information has been reported in adults. Though lateralization is common in a number of higher cognitive functions, its prominence in language may also be a key to understanding the rapid emergence of the language network in infants and the ease at which we master our language in adulthood. One question here is whether the hemispheric lateralization is driven by linguistic input per se or whether non-linguistic, especially acoustic factors, “guide” the lateralization process. Methodologically, functional magnetic resonance imaging provides unsurpassed anatomical detail for such an enquiry. However, instrumental noise, experimental constraints and interference with EEG assessment limit its applicability, pointedly in infants and also when investigating the link between auditory and linguistic processing. Optical methods have the potential to fill this gap. Here we review a number of recent studies using optical imaging to investigate hemispheric differences during segmentation and basic auditory feature analysis in language development.

Interpreting oxygenation-based neuroimaging signals: the importance and the challenge of understanding brain oxygen metabolism

Functional magnetic resonance imaging is widely used to map patterns of brain activation based on blood oxygenation level dependent (BOLD) signal changes associated with changes in neural activity. However, because oxygenation changes depend on the relative changes in cerebral blood flow (CBF) and cerebral metabolic rate of oxygen (CMRO(2)), a quantitative interpretation of BOLD signals, and also other functional neuroimaging signals related to blood or tissue oxygenation, is fundamentally limited until we better understand brain oxygen metabolism and how it is related to blood flow. However, the positive side of the complexity of oxygenation signals is that when combined with dynamic CBF measurements they potentially provide the best tool currently available for investigating the dynamics of CMRO(2). This review focuses on the problem of interpreting oxygenation-based signals, the challenges involved in measuring CMRO(2) in general, and what is needed to put oxygenation-based estimates of CMRO(2) on a firm foundation. The importance of developing a solid theoretical framework is emphasized, both as an essential tool for analyzing oxygenation-based multimodal measurements, and also potentially as a way to better understand the physiological phenomena themselves. The existing data, integrated within a simple theoretical framework of O(2) transport, suggests the hypothesis that an important functional role of the mismatch of CBF and CMRO(2) changes with neural activation is to prevent a fall of tissue pO(2). Future directions for better understanding brain oxygen metabolism are discussed.

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.

Vascular Origins of BOLD and CBV fMRI Signals: Statistical Mapping and Histological Sections Compared

Comparison of 3T blood oxygenation level dependent (BOLD) and cerebral blood volume (CBV) activation maps to histological sections enables the spatial discrimination of functional magnetic resonance imaging (fMRI) signal changes into different vascular compartments. We use a standard gradient echo-echo planar imaging technique to measure BOLD signal changes in the somatosensory cortex in response to whisker stimulation. Corresponding changes in CBV were estimated following the infusion of a super-paramagnetic contrast agent. We imaged in a tangential imaging plane that covered the cortical surface. Images were associated with post mortem histological sections showing both the surface vasculature and cytochrome oxidase stained whisker barrel cortex. We found a significant BOLD signal change in the large draining veins which occurred in the absence of a corresponding CBV change. Results suggest that in the venous drainage system, ~3mm distant from the area of activity, there is a robust change in blood oxygen saturation with little or no volume change. CBV changes are localised over the somatosensory barrel cortex and overlying arterial supply, supporting the theory that CBV changes are greater in the arterial than in the venous vasculature. This work investigating BOLD signal and underlying hemodynamics provides more information on the vascular origins of these important neuroimaging signals.

Neural activity-induced modulation of BOLD poststimulus undershoot independent of the positive signal

Despite intense research on the blood oxygenation level-dependent (BOLD) signal underlying functional magnetic resonance imaging, our understanding of its physiological basis is far from complete. In this study, it was investigated whether the so-called poststimulus BOLD signal undershoot is solely a passive vascular effect or actively induced by neural responses. Prolonged static and flickering black-white checkerboard stimulation with isoluminant grey screen as baseline condition were employed on eight human subjects. Within the same region of interest, the positive BOLD time courses for static and flickering stimuli were identical over the entire stimulus duration. In contrast, the static stimuli exhibited no poststimulus BOLD signal undershoot, whereas the flickering stimuli caused a strong BOLD poststimulus undershoot. To ease the interpretation, we performed an additional study measuring both BOLD signal and cerebral blood flow (CBF) using arterial spin labeling. Also for CBF, a difference in the poststimulus period was found for the two stimuli. Thus, a passive blood volume effect as the only contributor to the poststimulus undershoot comes short in explaining the BOLD poststimulus undershoot phenomenon for this particular experiment. Rather, an additional active neuronal activation or deactivation can strongly modulate the BOLD poststimulus behavior. In summary, the poststimulus time course of BOLD signal could potentially be used to differentiate neuronal activity patterns that are otherwise indistinguishable using the positive evoked response.

The change in cerebrovascular reactivity between 3 T and 7 T measured using graded hypercapnia

Mapping cerebrovascular reactivity (CVR) to hypercapnia is important both clinically and for improved understanding of the haemodynamic properties of the BOLD effect. In this work, BOLD/R2 CVR was investigated by using a device which provided small, repeatable and stable steps in PETCO2, whilst maintaining a steady PETO2 level. Significant CVR was observed in both grey and white matter at both 3 and 7 T, whilst an approximately linear relationship found between R2 CVR and field strength has implications for BOLD models and calibration. Grey matter R2 CVR was 0.066+/-0.004 s(-1) mm Hg(-1) at 3 T and 0.141+/-0.008 s(-1) mm Hg(-1) at 7 T. White matter R2 CVR was 0.021+/-0.003 s(-1) mm Hg(-1) at 3 T and 0.040+/-0.007 s(-1) mm Hg(-1) at 7 T.

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.

BOLD-specific cerebral blood volume and blood flow changes during neuronal activation in humans

To understand and predict the blood-oxygenation level-dependent (BOLD) fMRI signal, an accurate knowledge of the relationship between cerebral blood flow (DeltaCBF) and volume (DeltaCBV) changes is critical. Currently, this relationship is widely assumed to be characterized by Grubb's power-law, derived from primate data, where the power coefficient (alpha) was found to be 0.38. The validity of this general formulation has been examined previously, and an alpha of 0.38 has been frequently cited when calculating the cerebral oxygen metabolism change (DeltaCMRo(2)) using calibrated BOLD. However, the direct use of this relationship has been the subject of some debate, since it is well established that the BOLD signal is primarily modulated by changes in 'venous' CBV (DeltaCBV(v), comprising deoxygenated blood in the capillary, venular, and to a lesser extent, in the arteriolar compartments) instead of total CBV, and yet DeltaCBV(v) measurements in humans have been extremely scarce. In this work, we demonstrate reproducible DeltaCBV(v) measurements at 3 T using venous refocusing for the volume estimation (VERVE) technique, and report on steady-state DeltaCBV(v) and DeltaCBF measurements in human subjects undergoing graded visual and sensorimotor stimulation. We found that: (1) a BOLD-specific flow-volume power-law relationship is described by alpha = 0.23 +/- 0.05, significantly lower than Grubb's constant of 0.38 for total CBV; (2) this power-law constant was not found to vary significantly between the visual and sensorimotor areas; and (3) the use of Grubb's value of 0.38 in gradient-echo BOLD modeling results in an underestimation of DeltaCMRo(2).

The Possible Role of CO(2) in Producing A Post-Stimulus CBF and BOLD Undershoot

Comprehending the underlying mechanisms of neurovascular coupling is important for understanding the pathogenesis of neurodegenerative diseases related to uncoupling. Moreover, it elucidates the casual relation between the neural signaling and the hemodynamic responses measured with various imaging modalities such as functional magnetic resonance imaging (fMRI). There are mainly two hypotheses concerning this mechanism: a metabolic hypothesis and a neurogenic hypothesis. We have modified recent models of neurovascular coupling adding the effects of both NO (nitric oxide) kinetics, which is a well-known neurogenic vasodilator, and CO₂ kinetics as a metabolic vasodilator. We have also added the Hodgkin–Huxley equations relating the membrane potentials to sodium influx through the membrane. Our results show that the dominant factor in the hemodynamic response is NO, however CO₂ is important in producing a brief post-stimulus undershoot in the blood flow response that in turn modifies the fMRI blood oxygenation level-dependent post-stimulus undershoot. Our results suggest that increased cerebral blood flow during stimulation causes CO₂ washout which then results in a post-stimulus hypocapnia induced vasoconstrictive effect.

Perturbation of the BOLD response by a contrast agent and interpretation through a modified balloon model

This study used an infusion of a paramagnetic contrast agent to perturb intravascular blood susceptibility and investigate its effect on the BOLD hemodynamic response. A three compartment BOLD signal model combined with a modified balloon model was developed to interpret the MR signal. This model incorporated arterial blood volume in order to simulate signal changes resulting from the contrast agent. The BOLD signal model was fitted to the experimental data to test the hypothesis that arterial blood volume changes during activation. It was found that allowing arterial blood volume to change, rather than assuming this change is negligible as often assumed in the literature, provides a better fit to the experimental data, particularly during the BOLD overshoot. The post-stimulus undershoot was fitted well, regardless of whether the arterial blood volume was allowed to change, by assuming that this feature is due to delayed venous compliance. However the resultant elevation in post-stimulus blood volume decays with an extremely long time constant, taking more than 55 s to recover to baseline following a 4.8 s stimulus. The post-stimulus signal changes measured here could alternatively be described by a post-stimulus elevation in metabolism. An alternative model of oxygen extraction, in place of the Oxygen Limitation model, would be required to test this hypothesis.

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.