Interaction among autoregulation, CO2 reactivity, and intracranial pressure: a mathematical model

Time-domain methods for quantifying dynamic cerebral blood flow autoregulation: Review and recommendations. A white paper from the Cerebrovascular Research Network (CARNet)

Cerebral Autoregulation (CA) is an important physiological mechanism stabilizing cerebral blood flow (CBF) in response to changes in cerebral perfusion pressure (CPP). By maintaining an adequate, relatively constant supply of blood flow, CA plays a critical role in brain function. Quantifying CA under different physiological and pathological states is crucial for understanding its implications. This knowledge may serve as a foundation for informed clinical decision-making, particularly in cases where CA may become impaired. The quantification of CA functionality typically involves constructing models that capture the relationship between CPP (or arterial blood pressure) and experimental measures of CBF. Besides describing normal CA function, these models provide a means to detect possible deviations from the latter. In this context, a recent white paper from the Cerebrovascular Research Network focused on Transfer Function Analysis (TFA), which obtains frequency domain estimates of dynamic CA. In the present paper, we consider the use of time-domain techniques as an alternative approach. Due to their increased flexibility, time-domain methods enable the mitigation of measurement/physiological noise and the incorporation of nonlinearities and time variations in CA dynamics. Here, we provide practical recommendations and guidelines to support researchers and clinicians in effectively utilizing these techniques to study CA.

The conducted vascular response as a mediator of hypercapnic cerebrovascular reactivity: A modelling study

It is well established that the cerebral blood flow (CBF) shows exquisite sensitivity to changes in the arterial blood partial pressure of CO2 ( [Formula: see text] ), which is reflected by an index termed cerebrovascular reactivity. In response to elevations in [Formula: see text] (hypercapnia), the vessels of the cerebral microvasculature dilate, thereby decreasing the vascular resistance and increasing CBF. Due to the challenges of access, scale and complexity encountered when studying the microvasculature, however, the mechanisms behind cerebrovascular reactivity are not fully understood. Experiments have previously established that the cholinergic release of the Acetylcholine (ACh) neurotransmitter in the cortex is a prerequisite for the hypercapnic response. It is also known that ACh functions as an endothelial-dependent agonist, in which the local administration of ACh elicits local hyperpolarization in the vascular wall; this hyperpolarization signal is then propagated upstream the vascular network through the endothelial layer and is coupled to a vasodilatory response in the vascular smooth muscle (VSM) layer in what is known as the conducted vascular response (CVR). Finally, experimental data indicate that the hypercapnic response is more strongly correlated with the CO2 levels in the tissue than in the arterioles. Accordingly, we hypothesize that the CVR, evoked by increases in local tissue CO2 levels and a subsequent local release of ACh, is responsible for the CBF increase observed in response to elevations in [Formula: see text] . By constructing physiologically grounded dynamic models of CBF and control in the cerebral vasculature, ones that integrate the available knowledge and experimental data, we build a new model of the series of signalling events and pathways underpinning the hypercapnic response, and use the model to provide compelling evidence that corroborates the aforementioned hypothesis. If the CVR indeed acts as a mediator of the hypercapnic response, the proposed mechanism would provide an important addition to our understanding of the repertoire of metabolic feedback mechanisms possessed by the brain and would motivate further in-vivo investigation. We also model the interaction of the hypercapnic response with dynamic cerebral autoregulation (dCA), the collection of mechanisms that the brain possesses to maintain near constant CBF despite perturbations in pressure, and show how the dCA mechanisms, which otherwise tend to be overlooked when analysing experimental results of cerebrovascular reactivity, could play a significant role in shaping the CBF response to elevations in [Formula: see text] . Such in-silico models can be used in tandem with in-vivo experiments to expand our understanding of cerebrovascular diseases, which continue to be among the leading causes of morbidity and mortality in humans.

Intracranial pressure-flow relationships in traumatic brain injury patients expose gaps in the tenets of models and pressure-oriented management

Background

The protocols and therapeutic guidance established for treating traumatic brain injuries (TBI) in neurointensive care focus on managing cerebral blood flow (CBF) and brain tissue oxygenation based on pressure signals. The decision support process relies on assumed relationships between cerebral perfusion pressure (CPP) and blood flow, pressure-flow relationships (PFRs), and shares this framework of assumptions with mathematical intracranial hemodynamic models. These foundational assumptions are difficult to verify, and their violation can impact clinical decision-making and model validity.

Method

A hypothesis- and model-driven method for verifying and understanding the foundational intracranial hemodynamic PFRs is developed and applied to a novel multi-modality monitoring dataset.

Results

Model analysis of joint observations of CPP and CBF validates the standard PFR when autoregulatory processes are impaired as well as unmodelable cases dominated by autoregulation. However, it also identifies a dynamical regime -or behavior pattern- where the PFR assumptions are wrong in a precise, data-inferable way due to negative CPP-CBF coordination over long timescales. This regime is of both clinical and research interest: its dynamics are modelable under modified assumptions while its causal direction and mechanistic pathway remain unclear.

Conclusions

Motivated by the understanding of mathematical physiology, the validity of the standard PFR can be assessed a) directly by analyzing pressure reactivity and mean flow indices (PRx and Mx) or b) indirectly through the relationship between CBF and other clinical observables. This approach could potentially help personalize TBI care by considering intracranial pressure and CPP in relation to other data, particularly CBF. The analysis suggests a threshold using clinical indices of autoregulation jointly generalizes independently set indicators to assess CA functionality. These results support the use of increasingly data-rich environments to develop more robust hybrid physiological-machine learning models.

The influence of carbon dioxide on cerebral metabolism and oxygen consumption: combining multimodal monitoring with dynamic systems modelling

Hypercapnia increases cerebral blood flow. The effects on cerebral metabolism remain incompletely understood although studies show an oxidation of cytochrome c oxidase, Complex IV of the mitochondrial respiratory chain. Systems modelling was combined with previously published non-invasive measurements of cerebral tissue oxygenation, cerebral blood flow, and cytochrome c oxidase redox state to evaluate any metabolic effects of hypercapnia. Cerebral tissue oxygen saturation and cytochrome oxidase redox state were measured with broadband near infrared spectroscopy and cerebral blood flow velocity with transcranial Doppler ultrasound. Data collected during 5-min hypercapnia in awake human volunteers were analysed using a Fick model to determine changes in brain oxygen consumption and a mathematical model of cerebral hemodynamics and metabolism (BrainSignals) to inform on mechanisms. Either a decrease in metabolic substrate supply or an increase in metabolic demand modelled the cytochrome oxidation in hypercapnia. However, only the decrease in substrate supply explained both the enzyme redox state changes and the Fick-calculated drop in brain oxygen consumption. These modelled outputs are consistent with previous reports of CO2 inhibition of mitochondrial succinate dehydrogenase and isocitrate dehydrogenase. Hypercapnia may have physiologically significant effects suppressing oxidative metabolism in humans and perturbing mitochondrial signalling pathways in health and disease.

Mechanisms of reduced cerebral blood flow in cerebral edema and elevated intracranial pressure

A mechanism of elevated intracranial pressure (ICP) in cerebral edema and its effects on cerebral blood flow (CBF) are presented in this paper. To study and demonstrate these effects, a mathematical model of intracranial hydrodynamics was developed. The model simulates the intracranial hydrodynamics and the changes that occur when cerebral edema predominates. To account for an edema pathology, the model includes resistances to cerebrospinal fluid (CSF) and interstitial fluid (ISF) flows within the parenchyma. The resistances change as the intercellular space becomes smaller due to swelling of brain cells. The model demonstrates the effect of changes in these resistances on ICP and venous resistance to blood flow by accounting for the key interactions between pressure, volume, and flow in the intracranial compartments in pathophysiological conditions. The model represents normal intracranial physiology as well as pathological conditions. Simulating cerebral edema with increased resistance to cerebral ISF flow resulted in elevated ICP, increased brain volume, markedly reduced ventricular volume, and decreased CBF as observed in the neurointensive care patients. The model indicates that in high ICP values, alternation of the arterial-arteriolar resistance to flow minimally affects CBF, whereas at low ICP they have a much greater effect on CBF. The model demonstrates and elucidates intracranial mechanisms related to elevated ICP.NEW & NOTEWORTHY Study goal was to elucidate the role of "bulk flow" of ISF through brain parenchyma. A model was developed to simulate fluid shifts in brain edema, ICP elevation, and their effect on CBF. Bulk flow resistance affected by edema elevates ICP and reduces CBF. Bulk flow affects transmural pressure and volume distribution in brain compartments. Changes in bulk flow resistance result in increase of venous resistance to flow and decrease in CBF.

Predicting pregnancy specific uterine vascular reactivity: A data driven computational model of shear-dependent, myogenic, and mechanical radial artery features

The entire maternal circulation adapts to pregnancy, and this adaption is particularly extensive in the uterine circulation where the major vessels double in size to facilitate an approximately 15-fold increase in blood supply to this organ over the course of pregnancy. Several factors may play a role in both the remodelling and biomechanical function of the uterine vasculature including the paracrine microenvironment, passive properties of the vessel wall, and active components of vascular function (incorporating the myogenic response and response to shear stress induced by intravascular blood flow). However, the interplay between these factors, and how this plays out in an organ-specific manner to induce the extent of remodelling observed in the uterus is not well understood. Here we present an integrated assessment of the uterine radial arteries, likely rate-limiters to flow of oxygenated maternal blood to the placental surface, via computational modelling and pressure myography. We show that uterine radial arteries behave differently to other systemic vessels (higher compliance and shear mediated constriction) and that their properties change with the adaptation to pregnancy (higher myogenic tone, higher compliance, and ability to tolerate higher flow rates before constricting). Together, this provides a useful tool to improve our understanding of the role of uterine vascular adaptation in normal and abnormal pregnancies and highlights the need for vascular bed specific investigations of vascular function in health and disease.

Investigating the role of pericytes in cerebral autoregulation: a modeling study

The brain's inability to store nutrients for more than a few seconds makes it one of the most tightly regulated systems in the body. Driven by metabolic demand, cerebral autoregulation (CA) ensures a constant cerebral blood flow (CBF) over a ±50% change in arterial blood pressure (ABP) from baseline. Recent evidence suggests that pericytes, contractile cells in the capillary bed, play a previously-ignored regulatory role. To elucidate the CA phenomenon, the role of oxygen metabolism, pericyte activity and neural signaling in CBF modulation were quantified. Driven by nutrient metabolism in the tissue and pressure sensitivity in the vasculature, the model introduced here successfully replicates CA. To highlight the role of different vessel sizes, vessels with a diameter above 1 mm were represented using a lumped parameter model while the microvasculature was illustrated as a branching tree network model. This novel approach elucidated the relationship between the microvasculature's nutrient supply and arterial regulation. Capillary responses to local increases in neuronal activity were experimentally determined, showing that pericytes can increase the diameter of the adjacent vessel by 2.5% in approximately 1 s. Their response was quantified and included in the computational model as an active component of the capillary bed. To compare the efficacy model presented here to existing ones, four feedback mechanisms were tested. To simulate dynamic CBF regulation a 10% increase in ABP was imposed. This resulted in a 23.79%-34.33% peak increase in CBF, depending on the nature of the feedback mechanism of the model. The four feedback mechanisms that were studied significantly differ in the response time, ultimately highlighting that capillaries play a fundamental role in the rapid regulation of CBF. Conclusively, this study indicates that while pericytes do not greatly alter the peak CBF change, they play a fundamental role in the speed of regulation.

Cerebral blood flow, cerebrovascular reactivity and their influence on ventilatory sensitivity

NEW FINDINGS

What is the topic of this review? Cerebrovascular reactivity to CO₂ , which is a principal factor in determining ventilatory responses to CO₂ through the role reactivity plays in determining cerebral extra- and intracellular pH. What advances does it highlight? Recent animal evidence suggests central chemoreceptor vasculature may demonstrate regionally heterogeneous cerebrovascular reactivity to CO₂ , potentially as a protective mechanism against excessive CO₂ washout from the central chemoreceptors, thereby allowing ventilation to reflect the systemic acid-base balance needs (respiratory changes in P aC O 2 ) rather than solely the cerebral needs. Ventilation per se does not influence cerebrovascular reactivity independent of changes in P aC O 2 .

ABSTRACT

Alveolar ventilation and cerebral blood flow are both predominantly regulated by arterial blood gases, especially arterial P C O 2 , and so are intricately entwined. In this review, the fundamental mechanisms underlying cerebrovascular reactivity and central chemoreceptor control of breathing are covered. We discuss the interaction of cerebral blood flow and its reactivity with the control of ventilation and ventilatory responsiveness to changes in P C O 2 , as well as the lack of influence of ventilation itself on cerebrovascular reactivity. We briefly summarize the effects of arterial hypoxaemia on the relationship between ventilatory and cerebrovascular response to both P C O 2 and P O 2 . We then highlight key methodological considerations regarding the interaction of reactivity and ventilatory sensitivity, including the following: regional heterogeneity of cerebrovascular reactivity; a pharmacological approach for the reduction of cerebral blood flow; reactivity assessment techniques; the influence of mean arterial blood pressure; and sex-related differences. Finally, we discuss ventilatory and cerebrovascular control in the context of high altitude and congestive heart failure. Future research directions and pertinent questions of interest are highlighted throughout.

Clinical Decision Support for Traumatic Brain Injury: Identifying a Framework for Practical Model-Based Intracranial Pressure Estimation at Multihour Timescales

BACKGROUND

The clinical mitigation of intracranial hypertension due to traumatic brain injury requires timely knowledge of intracranial pressure to avoid secondary injury or death. Noninvasive intracranial pressure (nICP) estimation that operates sufficiently fast at multihour timescales and requires only common patient measurements is a desirable tool for clinical decision support and improving traumatic brain injury patient outcomes. However, existing model-based nICP estimation methods may be too slow or require data that are not easily obtained.

OBJECTIVE

This work considers short- and real-time nICP estimation at multihour timescales based on arterial blood pressure (ABP) to better inform the ongoing development of practical models with commonly available data.

METHODS

We assess and analyze the effects of two distinct pathways of model development, either by increasing physiological integration using a simple pressure estimation model, or by increasing physiological fidelity using a more complex model. Comparison of the model approaches is performed using a set of quantitative model validation criteria over hour-scale times applied to model nICP estimates in relation to observed ICP.

RESULTS

The simple fully coupled estimation scheme based on windowed regression outperforms a more complex nICP model with prescribed intracranial inflow when pulsatile ABP inflow conditions are provided. We also show that the simple estimation data requirements can be reduced to 1-minute averaged ABP summary data under generic waveform representation.

CONCLUSIONS

Stronger performance of the simple bidirectional model indicates that feedback between the systemic vascular network and nICP estimation scheme is crucial for modeling over long intervals. However, simple model reduction to ABP-only dependence limits its utility in cases involving other brain injuries such as ischemic stroke and subarachnoid hemorrhage. Additional methodologies and considerations needed to overcome these limitations are illustrated and discussed.

Joint time-frequency analysis of dynamic cerebral autoregulation using generalized harmonic wavelets

OBJECTIVE

To develop a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) for dynamic cerebral autoregulation (DCA) performance quantification.

APPROACH

We considered two groups of human subjects to develop and validate the method: 55 healthy volunteers and 35 stroke-free subjects with unilateral internal carotid artery stenosis (CAS). We determined the mean and coherence-weighted average of the phase shift (PS) of appropriately defined GHW-based transfer functions, based on data points over the joint time-frequency domain. We compared agreement of standard transfer function analysis (TFA) and GHW analyses in healthy subjects using Bland-Altman plots. We assessed sensitivity of each metric to detect the presumed side-to-side difference in DCA function in CAS subjects (with decreased PS on the occluded side), using McNemar's chi square test to compare each metric to the standard TFA approach. An alternative Morlet wavelet-based approach was also considered.

MAIN RESULTS

The GHW and TFA methods exhibited strong agreement in healthy subjects. Among CAS subjects, GHW metrics outperformed TFA and Morlet wavelet-based approaches in identifying expected side-to-side differences: TFA sensitivity was 40.0% (95%CI 23.9-57.9), Morlet 60.0% (95%CI 42.1-76.1), and GHW  >70% for both metrics (GHW mean PS sensitivity 74.3, 95%CI 56.7-87.5, p   =  0.0027 versus TFA; GHW coherence-weighted PS sensitivity 71.4, 95%CI 53.7-85.4, p   =  0.0009 versus TFA).

SIGNIFICANCE

In comparison to the widely used stationary Fourier transform-based TFA and to Morlet wavelet-based analysis, our data suggest that the GHW-based analysis performs better in identifying DCA asymmetry between the two cerebral hemispheres in patients with high grade unilateral carotid stenosis. Our method may provide enhanced confidence in employing DCA metrics as a sensitive diagnostic tool for detecting impaired DCA function in a variety of pathological settings.

Morphological changes of intracranial pressure quantifies vasodilatory effect of verapamil to treat cerebral vasospasm

INTRODUCTION

After aneurysmal subarachnoid hemorrhage (SAH), both proximal and distal cerebral vasospasm can contribute to the development of delayed cerebral ischemia. Intra-arterial (IA) vasodilators are a mainstay of treatment for distal arterial vasospasm, but no methods of assessing the efficacy of interventions in real time have been established.

OBJECTIVE

To introduce a new method for continuous intraprocedural assessment of endovascular treatment for cerebral vasospasm.

METHODS

The premise of our approach was that distal cerebral arterial changes induce a consistent pattern in the morphological changes of intracranial pressure (ICP) pulse. This premise was demonstrated using a published algorithm in previous papers. In this study, we applied the algorithm to calculate the likelihood of cerebral vasodilation (VDI) and cerebral vasoconstriction (VCI) from intraprocedural ICP signals that are synchronized with injection of the IA vasodilator, verapamil. Cerebral blood flow velocities (CBFVs) on bilateral cerebral arteries were studied before and after IA therapy.

RESULTS

192 recordings of patients with SAH were reviewed, and 27 recordings had high-quality ICP waveforms. The VCI was significantly lower after the first verapamil injection (0.47±0.017) than VCI at baseline (0.49±0.020, p<0.001). A larger dose of injected verapamil resulted in a larger and longer VDI increase. CBFV of the middle cerebral artery increases across the days before the injection of verapamil and decreases after IA therapy.

CONCLUSION

This study provides preliminary validation of an algorithm for continuous assessment of distal cerebral arterial changes in response to IA vasodilator infusion in patients with vasospasm and aneurysmal SAH.

Redox Regulation of the Microcirculation

The microcirculation maintains tissue homeostasis through local regulation of blood flow and oxygen delivery. Perturbations in microvascular function are characteristic of several diseases and may be early indicators of pathological changes in the cardiovascular system and in parenchymal tissue function. These changes are often mediated by various reactive oxygen species and linked to disruptions in pathways such as vasodilation or angiogenesis. This overview compiles recent advances relating to redox regulation of the microcirculation by adopting both cellular and functional perspectives. Findings from a variety of vascular beds and models are integrated to describe common effects of different reactive species on microvascular function. Gaps in understanding and areas for further research are outlined. © 2020 American Physiological Society. Compr Physiol 10:229-260, 2020.

Meaning of Intracranial Pressure-to-Blood Pressure Fisher-Transformed Pearson Correlation-Derived Optimal Cerebral Perfusion Pressure: Testing Empiric Utility in a Mechanistic Model

OBJECTIVES

Time-averaged intracranial pressure-to-blood pressure Fisher-transformed Pearson correlation (PRx) is used to assess cerebral autoregulation and derive optimal cerebral perfusion pressure. Empirically, impaired cerebral autoregulation is considered present when PRx is positive; greater difference between time series median cerebral perfusion pressure and optimal cerebral perfusion pressure (ΔCPP) is associated with worse outcomes. Our aims are to better understand: 1) the potential strategies for targeting optimal cerebral perfusion pressure; 2) the relationship between cerebral autoregulation and PRx; and 3) the determinants of greater ΔCPP.

DESIGN

Mechanistic simulation using a lumped compartmental model of blood pressure, intracranial pressure, cerebral autoregulation, cerebral blood volume, PaCO2, and cerebral blood flow.

SETTING

University critical care integrative modeling and precision physiology research group.

SUBJECTS

None, in silico studies.

INTERVENTIONS

Simulations in blood pressure, intracranial pressure, PaCO2, and impairment of cerebral autoregulation, with examination of "output" cerebral perfusion pressure versus PRx-plots, optimal cerebral perfusion pressure, and ΔCPP.

MEASUREMENTS AND MAIN RESULTS

In regard to targeting optimal cerebral perfusion pressure, a shift in mean blood pressure or mean intracranial pressure with no change in mean blood pressure, with intact cerebral autoregulation, impacts optimal cerebral perfusion pressure. Second, a positive PRx occurs even with intact cerebral autoregulation. In relation to ΔCPP, for a given input blood pressure profile, with constant intracranial pressure, altering the degree of impairment in cerebral autoregulation or the level of PaCO2 maintains differences to within ±5 mm Hg. Change in intracranial pressure due to either an intermittently prolonged pattern of raised intracranial pressure or terminal escalation shows ΔCPP greater than 10 mm Hg and less than -10 mm Hg, respectively.

CONCLUSIONS

These mechanistic simulations provide insight into the empiric basis of optimal cerebral perfusion pressure and the significance of PRx and ΔCPP. PRx and optimal cerebral perfusion pressure deviations do not directly reflect changes in cerebral autoregulation but are, in general, related to the presence of complex states involving well-described clinical progressions with raised intracranial pressure.

Real-Time Noninvasive Intracranial State Estimation Using Unscented Kalman Filter

Intracranial pressure (ICP) monitoring is desirable as a first-line measure to assist decision-making in cases of increased ICP. Clinically, non-invasive ICP monitoring is also required to avoid infection and hemorrhage in patients. The relationships among the arterial blood pressure (ABP), ICP, cerebral blood flow, and its velocity ( [Formula: see text]) measured by transcranial Doppler ultrasound measurement have been reported. However, real-time non-invasive ICP estimation using these modalities is less well documented. This paper presents a novel algorithm for real-time and non-invasive ICP monitoring with [Formula: see text] and ABP, called direct-current (DC)-ICP. The technique was compared with invasive ICP for 10 acute-brain-injury patients admitted to Cheju Halla Hospital and Gangnam Severance Hospital from July 2017 to June 2018. The inter-subject correlation coefficient between true and estimate was 0.75 and the AUCs of the ROCs for prediction of increased ICP for the DC-ICP methods were 0.83. Thus, [Formula: see text] monitoring can facilitate reliable real-time ICP tracking with our novel DC-ICP algorithm, which can provide valuable information under clinical conditions.

A Bayesian framework for the analysis of systems biology models of the brain

Systems biology models are used to understand complex biological and physiological systems. Interpretation of these models is an important part of developing this understanding. These models are often fit to experimental data in order to understand how the system has produced various phenomena or behaviour that are seen in the data. In this paper, we have outlined a framework that can be used to perform Bayesian analysis of complex systems biology models. In particular, we have focussed on analysing a systems biology of the brain using both simulated and measured data. By using a combination of sensitivity analysis and approximate Bayesian computation, we have shown that it is possible to obtain distributions of parameters that can better guard against misinterpretation of results, as compared to a maximum likelihood estimate based approach. This is done through analysis of simulated and experimental data. NIRS measurements were simulated using the same simulated systemic input data for the model in a ‘healthy’ and ‘impaired’ state. By analysing both of these datasets, we show that different parameter spaces can be distinguished and compared between different physiological states or conditions. Finally, we analyse experimental data using the new Bayesian framework and the previous maximum likelihood estimate approach, showing that the Bayesian approach provides a more complete understanding of the parameter space.

Systems biology models are mathematical representations of biological processes that reproduce the overall behaviour of a biological system. They are comprised by a number of parameters representing biological information. We use them to understand the behaviour of biological systems, such as the brain. We do this by fitting the model’s parameter to observed or simulated data; and by looking at how these values change during the fitting process we investigate the behaviour of our system. We are interested in understanding differences between a healthy and an injured brain. Here we outline a statistical framework that uses a Bayesian approach during the fitting process that can provide us with a distribution of parameters rather than single parameter number. We apply this method when simulating the physiological responses between a healthy and a vascular compromised brain to a drop in oxygenation. We then use experimental data that demonstrates the healthy brain response to an increase in arterial CO2 and fit our brain model predictions to the measurements. In both instances we show that our approach provides more information about the overlap between healthy and unhealthy brain states than a fitting process that provides a single value parameter estimate.

Data-Augmented Modeling of Intracranial Pressure

Precise management of patients with cerebral diseases often requires intracranial pressure (ICP) monitoring, which is highly invasive and requires a specialized ICU setting. The ability to noninvasively estimate ICP is highly compelling as an alternative to, or screening for, invasive ICP measurement. Most existing approaches for noninvasive ICP estimation aim to build a regression function that maps noninvasive measurements to an ICP estimate using statistical learning techniques. These data-based approaches have met limited success, likely because the amount of training data needed is onerous for this complex applications. In this work, we discuss an alternative strategy that aims to better utilize noninvasive measurement data by leveraging mechanistic understanding of physiology. Specifically, we developed a Bayesian framework that combines a multiscale model of intracranial physiology with noninvasive measurements of cerebral blood flow using transcranial Doppler. Virtual experiments with synthetic data are conducted to verify and analyze the proposed framework. A preliminary clinical application study on two patients is also performed in which we demonstrate the ability of this method to improve ICP prediction.

Dynamic cerebral autoregulation measurement using rapid changes in head positioning: experiences in acute ischemic stroke and healthy control populations

The ideal technique for dynamic cerebral autoregulation (dCA) assessment in critically ill patients should provide considerable variability in blood pressure (BP) but without the need for patient cooperation. We proposed using rapid head positioning (RHP) over spontaneous BP fluctuations for dCA assessment in patients with acute ischemic stroke (AIS). Cerebral blood velocity (transcranial Doppler), beat-to-beat BP (Finometer), and end-tidal CO2 (capnography) were recorded during 5-min baseline and RHP in 16 controls (8 women and 8 men, mean age: 57 ± 16 yr) and 15 patients with AIS (7 women and 8 men, mean age: 69 ± 8 yr) at two (12 ± 8 days) and three visits (13.3 ± 6.9 h, 4.8 ± 3.2 days, and 93.9 ± 11.5 days from the symptom onset), respectively. All participants were able to complete the RHP protocol without difficulty. Compared with controls, patients with AIS were hypocapnic (all visits, P < 0.0024) and hypertensive ( visit 1, P = 0.011), although BP gradually reduced after the acute phase. RHP demonstrated greater beat-to-beat BP variability (BPV) in controls ( visits 1 and 2, P < 0.001) but not in patients with AIS at any visit. Compared with controls, a reduced autoregulation index (ARI) was demonstrated in patients with AIS, at visit 2 for the baseline recording but not at other visits or during RHP. The area under the receiver-operating curve was 0.53 and 0.54 for baseline and RHP, respectively. The RHP paradigm required minimal patient cooperation and could be considered a feasible alternative for assessing dCA, mainly in conditions leading to increased BPV. The lack of BPV increase in AIS with RHP deserves further investigation.

NEW & NOTEWORTHY This study used rapid head positioning (RHP) to enhance blood pressure (BP) variability (BPV) to improve BP signal-to-noise ratio and reliability of dynamic cerebral autoregulation (dCA). RHP was well accepted by controls and acute ischemic stroke (AIS); the increased BPV induced in controls was not observed in AIS, suggesting BPV at rest was already elevated. RHP did not improve detection of impaired CA in AIS; further work is needed to understand the different responses observed.

Slow sinusoidal tilt movements demonstrate the contribution to orthostatic tolerance of cerebrospinal fluid movement to and from the spinal dural space

Standing up elicits a host of cardiovascular changes which all affect the cerebral circulation. Lowered mean arterial blood pressure (ABP) at brain level, change in the cerebral venous outflow path, lowered end-tidal PCO2 (PET CO2 ), and intracranial pressure (ICP) modify cerebral blood flow (CBF). The question we undertook to answer is whether gravity-induced blood pressure (BP) changes are compensated in CBF with the same dynamics as are spontaneous or induced ABP changes in a stable position. Twenty-two healthy subjects (18/4 m/f, 40 ± 8 years) were subjected to 30° and 70° head-up tilt (HUT) and sinusoidal tilts (SinTilt, 0°↨60° around 30° at 2.5-10 tilts/min). Additionally, at those three tilt levels, they performed paced breathing at 6-15 breaths/min to induce larger than spontaneous cardiovascular oscillations. We measured continuous finger BP and cerebral blood flow velocity (CBFv) in the middle cerebral artery by transcranial Doppler to compute transfer functions (TFs) from ABP- to CBFv oscillations. SinTilt induces the largest ABP oscillations at brain level with CBFv gains strikingly lower than for paced breathing or spontaneous variations. This would imply better autoregulation for dynamic gravitational changes. We demonstrate in a mathematical model that this difference is explained by ICP changes due to movement of cerebrospinal fluid (CSF) into and out of the spinal dural sack. Dynamic cerebrovascular autoregulation seems insensitive to how BP oscillations originate if the effect of ICP is factored in. CSF-movement in-and-out of the spinal dural space contributes importantly to orthostatic tolerance by its effect on cerebral perfusion pressure.

Spaceflight-Induced Intracranial Hypertension and Visual Impairment: Pathophysiology and Countermeasures

Visual impairment intracranial pressure (VIIP) syndrome is considered an unexplained major risk for future long-duration spaceflight. NASA recently redefined this syndrome as Spaceflight-Associated Neuro-ocular Syndrome (SANS). Evidence thus reviewed supports that chronic, mildly elevated intracranial pressure (ICP) in space (as opposed to more variable ICP with posture and activity on Earth) is largely accounted for by loss of hydrostatic pressures and altered hemodynamics in the intracranial circulation and the cerebrospinal fluid system. In space, an elevated pressure gradient across the lamina cribrosa, caused by a chronic but mildly elevated ICP, likely elicits adaptations of multiple structures and fluid systems in the eye which manifest themselves as the VIIP syndrome. A chronic mismatch between ICP and intraocular pressure (IOP) in space may acclimate the optic nerve head, lamina cribrosa, and optic nerve subarachnoid space to a condition that is maladaptive to Earth, all contributing to the pathogenesis of space VIIP syndrome. Relevant findings help to evaluate whether artificial gravity is an appropriate countermeasure to prevent this seemingly adverse effect of long-duration spaceflight.

An effective model of cerebrovascular pressure reactivity and blood flow autoregulation

Understanding cerebral blood flow dynamics is crucial for the care of patients at risk of poor cerebral perfusion. We describe an effective model of cerebral hemodynamics designed to reveal important macroscopic features of cerebral blood flow without having to resolve the detailed microvasculature of the brain. Based on principles of fluid and elastic dynamics and vascular pressure-reactivity, the model quantifies the physical means by which the vasculature executes autoregulatory reflexes. We demonstrate that the frequency response of the proposed model matches experimental measurements and explains the influence of mechanical factors on the autoregulatory performance. Analysis of the model indicates the existence of an optimal mean arterial pressure which minimizes the sensitivity of the flow to changes in perfusion pressure across the frequency spectrum of physiological oscillations. We highlight the simplicity of the model and its potential to improve monitoring of brain perfusion via real-time computational simulations of cerebro- and cardio-vascular interventions.

Carbogen-induced increases in tumor oxygenation depend on the vascular status of the tumor: A multiparametric MRI study in two rat glioblastoma models

The alleviation of hypoxia in glioblastoma with carbogen to improve treatment has met with limited success. Our hypothesis is that the eventual benefits of carbogen depend on the capacity for vasodilation. We examined, with MRI, changes in fractional cerebral blood volume, blood oxygen saturation, and blood oxygenation level dependent signals in response to carbogen. The analyses were performed in two xenograft models of glioma (U87 and U251) recognized to have different vascular patterns. Carbogen increased fractional cerebral blood volume, blood oxygen saturation, and blood oxygenation level dependent signals in contralateral tissues. In the tumor core and peritumoral regions, changes were dependent on the capacity to vasodilate rather than on resting fractional cerebral blood volume. In the highly vascularised U87 tumor, carbogen induced a greater increase in fractional cerebral blood volume and blood oxygen saturation in comparison to the less vascularized U251 tumor. The blood oxygenation level dependent signal revealed a delayed response in U251 tumors relative to the contralateral tissue. Additionally, we highlight the considerable heterogeneity of fractional cerebral blood volume, blood oxygen saturation, and blood oxygenation level dependent within U251 tumor in which multiple compartments co-exist (tumor core, rim and peritumoral regions). Finally, our study underlines the complexity of the flow/metabolism interactions in different models of glioblastoma. These irregularities should be taken into account in order to palliate intratumoral hypoxia in clinical trials.

Compartmental and Data-Based Modeling of Cerebral Hemodynamics: Nonlinear Analysis

OBJECTIVE

As an extension to our study comparing a putative compartmental and data-based model of linear dynamic cerebral autoregulation (CA) and CO2-vasomotor reactivity (VR), we study the CA-VR process in a nonlinear context.

METHODS

We use the concept of principal dynamic modes (PDM) in order to obtain a compact and more easily interpretable input-output model. This in silico study permits the use of input data with a dynamic range large enough to simulate the classic homeostatic CA and VR curves using a putative structural model of the regulatory control of the cerebral circulation. The PDM model obtained using theoretical and experimental data are compared.

RESULTS

It was found that the PDM model was able to reflect accurately both the simulated static CA and VR curves in the associated nonlinear functions (ANFs). Similar to experimental observations, the PDM model essentially separates the pressure-flow relationship into a linear component with fast dynamics and nonlinear components with slow dynamics. In addition, we found good qualitative agreement between the PDMs representing the dynamic theoretical and experimental CO2-flow relationship.

CONCLUSION

Under the modeling assumption and in light of other experimental findings, we hypothesize that PDMs obtained from experimental data correspond with passive fluid dynamical and active regulatory mechanisms.

SIGNIFICANCE

Both hypothesis-based and data-based modeling approaches can be combined to offer some insight into the physiological basis of PDM model obtained from human experimental data. The PDM modeling approach potentially offers a practical way to quantify the status of specific regulatory mechanisms in the CA-VR process.

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

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

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

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

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

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Model is extended to simulate scalp haemodynamics.

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

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Experimental recording of systemic factors is recommended to aid interpretation.

A Coupled Lumped-Parameter and Distributed Network Model for Cerebral Pulse-Wave Hemodynamics

The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is necessary for cerebral blood flow (CBF) modeling, as well as investigations into pathological conditions. We discuss a one-dimensional (1D) nonlinear model of blood flow in the cerebral arteries coupled to autoregulatory lumped-parameter (LP) networks. The LP networks incorporate intracranial pressure (ICP), cerebrospinal fluid (CSF), and cortical collateral blood flow models. The overall model is used to evaluate changes in CBF due to occlusions in the middle cerebral artery (MCA) and common carotid artery (CCA). Velocity waveforms at the CCA and internal carotid artery (ICA) were examined prior and post MCA occlusion. Evident waveform changes due to the occlusion were observed, providing insight into cerebral vasospasm monitoring by morphological changes of the velocity or pressure waveforms. The role of modeling of collateral blood flows through cortical pathways and communicating arteries was also studied. When the MCA was occluded, the cortical collateral flow had an important compensatory role, whereas the communicating arteries in the circle of Willis (CoW) became more important when the CCA was occluded. To validate the model, simulations were conducted to reproduce a clinical test to assess dynamic autoregulatory function, and results demonstrated agreement with published measurements.

On the roles of vascular smooth muscle contraction in cerebral blood flow autoregulation - a modeling perspective

We here review existing models of vascular smooth muscle cell, endothelial cell and cell-cell communication, which have been developed to better understand vascular tone and blood flow autoregulation. In particular, we discuss models that intended to explain modulation of myogenic tone by intraluminal pressure in resistance arterioles. Modeling efforts in the recent past have witnessed a shift from empirical models to models with mechanistic details that underscore different physical aspects of vascular regulation. Future models should synthesize mechanistic interactions in a hierarchy, from molecular regulation of ion channels to whole organ blood flow control.

Application of Mathematical Modeling for Simulation and Analysis of Hypoplastic Left Heart Syndrome (HLHS) in Pre- and Postsurgery Conditions

This paper is concerned with the mathematical modeling of a severe and common congenital defect called hypoplastic left heart syndrome (HLHS). Surgical approaches are utilized for palliating this heart condition; however, a brain white matter injury called periventricular leukomalacia (PVL) occurs with high prevalence at or around the time of surgery, the exact cause of which is not known presently. Our main goal in this paper is to study the hemodynamic conditions under which HLHS physiology may lead to the occurrence of PVL. A lumped parameter model of the HLHS circulation has been developed integrating diffusion modeling of oxygen and carbon dioxide concentrations in order to study hemodynamic variables such as pressure, flow, and blood gas concentration. Results presented include calculations of blood pressures and flow rates in different parts of the circulation. Simulations also show changes in the ratio of pulmonary to systemic blood flow rates when the sizes of the patent ductus arteriosus and atrial septal defect are varied. These changes lead to unbalanced blood circulations and, when combined with low oxygen and carbon dioxide concentrations in arteries, result in poor oxygen delivery to the brain. We stipulate that PVL occurs as a consequence.

Compartmental and Data-Based Modeling of Cerebral Hemodynamics: Linear Analysis

Compartmental and data-based modeling of cerebral hemodynamics are alternative approaches that utilize distinct model forms and have been employed in the quantitative study of cerebral hemodynamics. This paper examines the relation between a compartmental equivalent-circuit and a data-based input-output model of dynamic cerebral autoregulation (DCA) and CO2-vasomotor reactivity (DVR). The compartmental model is constructed as an equivalent-circuit utilizing putative first principles and previously proposed hypothesis-based models. The linear input-output dynamics of this compartmental model are compared with data-based estimates of the DCA-DVR process. This comparative study indicates that there are some qualitative similarities between the two-input compartmental model and experimental results.

Modelling Blood Flow and Metabolism in the Preclinical Neonatal Brain during and Following Hypoxic-Ischaemia

Hypoxia-ischaemia (HI) is a major cause of neonatal brain injury, often leading to long-term damage or death. In order to improve understanding and test new treatments, piglets are used as preclinical models for human neonates. We have extended an earlier computational model of piglet cerebral physiology for application to multimodal experimental data recorded during episodes of induced HI. The data include monitoring with near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS), and the model simulates the circulatory and metabolic processes that give rise to the measured signals. Model extensions include simulation of the carotid arterial occlusion used to induce HI, inclusion of cytoplasmic pH, and loss of metabolic function due to cell death. Model behaviour is compared to data from two piglets, one of which recovered following HI while the other did not. Behaviourally-important model parameters are identified via sensitivity analysis, and these are optimised to simulate the experimental data. For the non-recovering piglet, we investigate several state changes that might explain why some MRS and NIRS signals do not return to their baseline values following the HI insult. We discover that the model can explain this failure better when we include, among other factors such as mitochondrial uncoupling and poor cerebral blood flow restoration, the death of around 40% of the brain tissue.

BrainSignals Revisited: Simplifying a Computational Model of Cerebral Physiology

Multimodal monitoring of brain state is important both for the investigation of healthy cerebral physiology and to inform clinical decision making in conditions of injury and disease. Near-infrared spectroscopy is an instrument modality that allows non-invasive measurement of several physiological variables of clinical interest, notably haemoglobin oxygenation and the redox state of the metabolic enzyme cytochrome c oxidase. Interpreting such measurements requires the integration of multiple signals from different sources to try to understand the physiological states giving rise to them. We have previously published several computational models to assist with such interpretation. Like many models in the realm of Systems Biology, these are complex and dependent on many parameters that can be difficult or impossible to measure precisely. Taking one such model, BrainSignals, as a starting point, we have developed several variant models in which specific regions of complexity are substituted with much simpler linear approximations. We demonstrate that model behaviour can be maintained whilst achieving a significant reduction in complexity, provided that the linearity assumptions hold. The simplified models have been tested for applicability with simulated data and experimental data from healthy adults undergoing a hypercapnia challenge, but relevance to different physiological and pathophysiological conditions will require specific testing. In conditions where the simplified models are applicable, their greater efficiency has potential to allow their use at the bedside to help interpret clinical data in near real-time.

Spaceflight on the Bion-M1 biosatellite alters cerebral artery vasomotor and mechanical properties in mice

Conditions during spaceflight, such as the loss of the head-to-foot gravity vector, are thought to potentially alter cerebral blood flow and vascular resistance. The purpose of the present study was to determine the effects of long-term spaceflight on the functional, mechanical, and structural properties of cerebral arteries. Male C57BL/6N mice were flown 30 days in a Bion-M1 biosatellite. Basilar arteries isolated from spaceflight (SF) (n = 6), habitat control (HC) (n = 6), and vivarium control (VC) (n = 16) mice were used for in vitro functional and mechanical testing and histological structural analysis. The results demonstrate that vasoconstriction elicited through a voltage-gated Ca(2+) mechanism (30-80 mM KCl) and thromboxane A2 receptors (10(-8) - 3 × 10(-5) M U46619) are lower in cerebral arteries from SF mice. Inhibition of Rho-kinase activity (1 μM Y27632) abolished group differences in U46619-evoked contractions. Endothelium-dependent vasodilation elicited by acetylcholine (10 μM, 2 μM U46619 preconstriction) was virtually absent in cerebral arteries from SF mice. The pressure-diameter relation was lower in arteries from SF mice relative to that in HC mice, which was not related to differences in the extracellular matrix protein elastin or collagen content or the elastin/collagen ratio in the basilar arteries. Diameter, medial wall thickness, and medial cross-sectional area of unpressurized basilar arteries were not different among groups. These results suggest that the microgravity-induced attenuation of both vasoconstrictor and vasodilator properties may limit the range of vascular control of cerebral perfusion or impair the distribution of brain blood flow during periods of stress.

Modeling Cerebral Blood Flow Velocity During Orthostatic Stress

Cerebral autoregulation refers to the physiological process that maintains stable cerebral blood flow (CBF) during changes in arterial blood pressure (ABP). In this study, we propose a simple, nonlinear quantitative model with only four parameters that can predict CBF velocity as a function of ABP. The model was motivated by the viscoelastic-like behavior observed in the data collected during postural change from sitting to standing. Qualitative testing of the model involved analysis of dynamic responses to step-changes in pressure both within and outside the autoregulatory range, while quantitative testing was used to show that the model can fit dynamics observed in data measured from a healthy young and a healthy elderly subject. The latter involved analysis of structural and practical identifiability, sensitivity analysis, and parameter estimation. Results showed that the model is able to reproduce observed overshoot and adaptation and predict the different responses in the healthy young and the healthy elderly subject. For the healthy young subject, the overshoot was significantly more pronounced than for the elderly subject, but the recovery time was longer for the young subject. These differences resulted in different parameter values estimated using the two datasets.

Reproduction of consistent pulse-waveform changes using a computational model of the cerebral circulatory system

Due to the inaccessibility of the cranial vault, it is difficult to study cerebral blood flow dynamics directly. A mathematical model can be useful to study these dynamics. The model presented here is a novel combination of a one-dimensional fluid flow model representing the major vessels of the circle of Willis (CoW), with six individually parameterized auto-regulatory models of the distal vascular beds. This model has the unique ability to simulate high temporal resolution flow and velocity waveforms, amenable to pulse-waveform analysis, as well as sophisticated phenomena such as auto-regulation. Previous work with human patients has shown that vasodilation induced by CO2 inhalation causes 12 consistent pulse-waveform changes as measured by the morphological clustering and analysis of intracranial pressure algorithm. To validate this model, we simulated vasodilation and successfully reproduced 9 out of the 12 pulse-waveform changes. A subsequent sensitivity analysis found that these 12 pulse-waveform changes were most affected by the parameters associated with the shape of the smooth muscle tension response and vessel elasticity, providing insight into the physiological mechanisms responsible for observed changes in the pulse-waveform shape.

Dynamic cerebral autoregulation is acutely impaired during maximal apnoea in trained divers

Aims

To examine whether dynamic cerebral autoregulation is acutely impaired during maximal voluntary apnoea in trained divers.

Methods

Mean arterial pressure (MAP), cerebral blood flow-velocity (CBFV) and end-tidal partial pressures of O₂ and CO₂ (PETO₂ and PETCO₂) were measured in eleven trained, male apnoea divers (28±2 yr; 182±2 cm, 76±7 kg) during maximal “dry” breath holding. Dynamic cerebral autoregulation was assessed by determining the strength of phase synchronisation between MAP and CBFV during maximal apnoea.

Results

The strength of phase synchronisation between MAP and CBFV increased from rest until the end of maximal voluntary apnoea (P<0.05), suggesting that dynamic cerebral autoregulation had weakened by the apnoea breakpoint. The magnitude of impairment in dynamic cerebral autoregulation was strongly, and positively related to the rise in PETCO₂ observed during maximal breath holding (R² = 0.67, P<0.05). Interestingly, the impairment in dynamic cerebral autoregulation was not related to the fall in PETO₂ induced by apnoea (R² = 0.01, P = 0.75).

Conclusions

This study is the first to report that dynamic cerebral autoregulation is acutely impaired in trained divers performing maximal voluntary apnoea. Furthermore, our data suggest that the impaired autoregulatory response is related to the change in PETCO₂, but not PETO₂, during maximal apnoea in trained divers.

Spaceflight-induced alterations in cerebral artery vasoconstrictor, mechanical, and structural properties: implications for elevated cerebral perfusion and intracranial pressure

Evidence indicates that cerebral blood flow is both increased and diminished in astronauts on return to Earth. Data from ground-based animal models simulating the effects of microgravity have shown that decrements in cerebral perfusion are associated with enhanced vasoconstriction and structural remodeling of cerebral arteries. Based on these results, the purpose of this study was to test the hypothesis that 13 d of spaceflight [Space Transportation System (STS)-135 shuttle mission] enhances myogenic vasoconstriction, increases medial wall thickness, and elicits no change in the mechanical properties of mouse cerebral arteries. Basilar and posterior communicating arteries (PCAs) were isolated from 9-wk-old female C57BL/6 mice for in vitro vascular and mechanical testing. Contrary to that hypothesized, myogenic vasoconstrictor responses were lower and vascular distensibility greater in arteries from spaceflight group (SF) mice (n=7) relative to ground-based control group (GC) mice (n=12). Basilar artery maximal diameter was greater in SF mice (SF: 236±9 μm and GC: 215±5 μm) with no difference in medial wall thickness (SF: 12.4±1.6 μm; GC: 12.2±1.2 μm). Stiffness of the PCA, as characterized via nanoindentation, was lower in SF mice (SF: 3.4±0.3 N/m; GC: 5.4±0.8 N/m). Collectively, spaceflight-induced reductions in myogenic vasoconstriction and stiffness and increases in maximal diameter of cerebral arteries signify that elevations in brain blood flow may occur during spaceflight. Such changes in cerebral vascular control of perfusion could contribute to increases in intracranial pressure and an associated impairment of visual acuity in astronauts during spaceflight.

Ocular hemodynamics and glaucoma: the role of mathematical modeling

PURPOSE

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma.

METHODS

We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation.

RESULTS

Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression.

CONCLUSION

Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

A lumped parameter model of cerebral blood flow control combining cerebral autoregulation and neurovascular coupling

Cerebral blood flow regulation is based on a variety of different mechanisms, of which the relative regulatory role remains largely unknown. The cerebral regulatory system expresses two regulatory properties: cerebral autoregulation and neurovascular coupling. Since partly the same mechanisms play a role in cerebral autoregulation and neurovascular coupling, this study aimed to develop a physiologically based mathematical model of cerebral blood flow regulation combining these properties. A lumped parameter model of the P2 segment of the posterior cerebral artery and its distal vessels was constructed. Blood flow regulation is exerted at the arteriolar level by vascular smooth muscle and implements myogenic, shear stress based, neurogenic, and metabolic mechanisms. In eight healthy subjects, cerebral autoregulation and neurovascular coupling were challenged by squat-stand maneuvers and visual stimulation using a checkerboard pattern, respectively. Cerebral blood flow velocity was measured using transcranial Doppler, whereas blood pressure was measured by finger volume clamping. In seven subjects, the model proposed fits autoregulation and neurovascular coupling measurement data well. Myogenic regulation is found to dominate the autoregulatory response. Neurogenic regulation, although only implemented as a first-order mechanism, describes neurovascular coupling responses to a great extent. It is concluded that our single, integrated model of cerebral blood flow control may be used to identify the main mechanisms affecting cerebral blood flow regulation in individual subjects.

Development of a model to aid NIRS data interpretation: results from a hypercapnia study in healthy adults

The use of a mathematical model of cerebral physiology and metabolism may aid the interpretation of experimentally measured data. In this study, model outputs of tissue oxygen saturation (TOS) and velocity of blood in the middle cerebral artery (Vmca) were compared with experimentally measured signals (TOS using near infrared spectroscopy and Vmca using transcranial Doppler) acquired during hypercapnia in healthy volunteers. Initially, some systematic discrepancies between predicted and measured values of these variables were identified. The model was optimised to best fit the measured data by adjusting model parameters. To improve the fit, three additional model mechanisms were considered. These were: an extracerebral contribution to TOS, a change in venous volume with CO₂ levels, and a change in oxygen consumption with CO₂ levels. Each mechanism, when used alone, improved the fit of the model to the data, although significant parameter changes were necessary. It is likely that a combination of these mechanisms will improve the success of modelling of TOS and Vmca changes during hypercapnia.

Modelling noninvasively measured cerebral signals during a hypoxemia challenge: steps towards individualised modelling

Noninvasive approaches to measuring cerebral circulation and metabolism are crucial to furthering our understanding of brain function. These approaches also have considerable potential for clinical use “at the bedside”. However, a highly nontrivial task and precondition if such methods are to be used routinely is the robust physiological interpretation of the data. In this paper, we explore the ability of a previously developed model of brain circulation and metabolism to explain and predict quantitatively the responses of physiological signals. The five signals all noninvasively-measured during hypoxemia in healthy volunteers include four signals measured using near-infrared spectroscopy along with middle cerebral artery blood flow measured using transcranial Doppler flowmetry. We show that optimising the model using partial data from an individual can increase its predictive power thus aiding the interpretation of NIRS signals in individuals. At the same time such optimisation can also help refine model parametrisation and provide confidence intervals on model parameters. Discrepancies between model and data which persist despite model optimisation are used to flag up important questions concerning the underlying physiology, and the reliability and physiological meaning of the signals.

Computational modelling of the piglet brain to simulate near-infrared spectroscopy and magnetic resonance spectroscopy data collected during oxygen deprivation

We describe a computational model to simulate measurements from near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS) in the piglet brain. Piglets are often subjected to anoxic, hypoxic and ischaemic insults, as experimental models for human neonates. The model aims to help interpret measurements and increase understanding of physiological processes occurring during such insults. It is an extension of a previous model of circulation and mitochondrial metabolism. This was developed to predict NIRS measurements in the brains of healthy adults i.e. concentration changes of oxyhaemoglobin and deoxyhaemoglobin and redox state changes of cytochrome c oxidase (CCO). We altered and enhanced the model to apply to the anaesthetized piglet brain. It now includes metabolites measured by ³¹P-MRS, namely phosphocreatine, inorganic phosphate and adenosine triphosphate (ATP). It also includes simple descriptions of glycolysis, lactate dynamics and the tricarboxylic acid (TCA) cycle. The model is described, and its simulations compared with existing measurements from piglets during anoxia. The NIRS and MRS measurements are predicted well, although this requires a reduction in blood pressure autoregulation. Predictions of the cerebral metabolic rate of oxygen consumption (CMRO₂) and lactate concentration, which were not measured, are given. Finally, the model is used to investigate hypotheses regarding changes in CCO redox state during anoxia.

The cerebrovascular response to carbon dioxide in humans

Carbon dioxide (CO2) increases cerebral blood flow and arterial blood pressure. Cerebral blood flow increases not only due to the vasodilating effect of CO2 but also because of the increased perfusion pressure after autoregulation is exhausted. Our objective was to measure the responses of both middle cerebral artery velocity (MCAv) and mean arterial blood pressure (MAP) to CO2 in human subjects using Duffin-type isoxic rebreathing tests. Comparisons of isoxic hyperoxic with isoxic hypoxic tests enabled the effect of oxygen tension to be determined. During rebreathing the MCAv response to CO2 was sigmoidal below a discernible threshold CO2 tension, increasing from a hypocapnic minimum to a hypercapnic maximum. In most subjects this threshold corresponded with the CO2 tension at which MAP began to increase. Above this threshold both MCAv and MAP increased linearly with CO2 tension. The sigmoidal MCAv response was centred at a CO2 tension close to normal resting values (overall mean 36 mmHg). While hypoxia increased the hypercapnic maximum percentage increase in MCAv with CO2 (overall means from76.5 to 108%) it did not affect other sigmoid parameters. Hypoxia also did not alter the supra-threshold MCAv and MAP responses to CO2 (overall mean slopes 5.5% mmHg⁻¹ and 2.1 mmHg mmHg⁻¹, respectively), but did reduce the threshold (overall means from 51.5 to 46.8 mmHg). We concluded that in the MCAv response range below the threshold for the increase of MAP with CO2, the MCAv measurement reflects vascular reactivity to CO2 alone at a constant MAP.

A cerebrovascular response model for functional neuroimaging including dynamic cerebral autoregulation

Functional neuroimaging techniques such as functional magnetic resonance imaging (fMRI) and near-infrared spectroscopy (NIRS) can be used to isolate an evoked response to a stimulus from significant background physiological fluctuations. Data analysis approaches typically use averaging or linear regression to remove this physiological baseline with varying degrees of success. Biophysical model-based analysis of the functional hemodynamic response has also been advanced previously with the Balloon and Windkessel models. In the present work, a biophysical model of systemic and cerebral circulation and gas exchange is applied to resting state NIRS neuroimaging data from 10 human subjects. The model further includes dynamic cerebral autoregulation, which modulates the cerebral arteriole compliance to control cerebral blood flow. This biophysical model allows for prediction, from noninvasive blood pressure measurements, of the background hemodynamic fluctuations in the systemic and cerebral circulations. Significantly higher correlations with the NIRS data were found using the biophysical model predictions compared to blood pressure regression and compared to transfer function analysis (multifactor ANOVA, p<0.0001). This finding supports the further development and use of biophysical models for removing baseline activity in functional neuroimaging analysis. Future extensions of this work could model changes in cerebrovascular physiology that occur during development, aging, and disease.

Cerebral blood flow autoregulation during intracranial hypertension: a simple, purely hydraulic mechanism?

OBJECTIVE

In this paper, we re-propose the role of a hydraulic mechanism, acting where the bridging veins enter the dural sinuses in cerebral blood flow (CBF) autoregulation.

MATERIALS AND METHODS

We carried out an intraventricular infusion in ten albino rabbits and increased intracranial pressure (ICP) up to arterial blood pressure (ABP) levels. We measured CBF velocity by an ultrasound probe applied to a by-pass inserted in a carotid artery and recorded ICP by an intraventricular needle. Diastolic and pulsatile ICP and ABP values were analyzed from basal conditions up to brain tamponade and vice versa.

CONCLUSIONS

A biphasic pattern of pulsatile intracranial pressure (pICP) was observed in all trials. Initially, until the CBF velocity remained constant, pICP increased (from 1.2 to 5.4 mmHg) following a rise in diastolic intracranial pressure (dICP); thereafter, in spite of a further rise in dICP, pICP decreased (2.87 mmHg) following CBF velocity reduction until intracranial circulation arrest (pICP=1.2 mmHg). A specular pattern was observed when the intraventricular infusion was stopped and CBF velocity returned to basal levels. These findings can be interpreted as indicating a hydraulic mechanism. Initially, when CBF is still constant, pICP rise is due to an increase in venous outflow resistance; subsequently, when CBF decreases following a further increase in venous outflow resistance, the vascular engorgement produces an arteriolar vasodilation. This vasodilation determines an increase in vascular wall stiffness, thus reducing pulse transmission to surrounding subarachnoid spaces.

A model of brain circulation and metabolism: NIRS signal changes during physiological challenges

We construct a model of brain circulation and energy metabolism. The model is designed to explain experimental data and predict the response of the circulation and metabolism to a variety of stimuli, in particular, changes in arterial blood pressure, CO(2) levels, O(2) levels, and functional activation. Significant model outputs are predictions about blood flow, metabolic rate, and quantities measurable noninvasively using near-infrared spectroscopy (NIRS), including cerebral blood volume and oxygenation and the redox state of the Cu(A) centre in cytochrome c oxidase. These quantities are now frequently measured in clinical settings; however the relationship between the measurements and the underlying physiological events is in general complex. We anticipate that the model will play an important role in helping to understand the NIRS signals, in particular, the cytochrome signal, which has been hard to interpret. A range of model simulations are presented, and model outputs are compared to published data obtained from both in vivo and in vitro settings. The comparisons are encouraging, showing that the model is able to reproduce observed behaviour in response to various stimuli.

Theoretical model of blood flow autoregulation: roles of myogenic, shear-dependent, and metabolic responses

The autoregulation of blood flow, the maintenance of almost constant blood flow in the face of variations in arterial pressure, is characteristic of many tissue types. Here, contributions to the autoregulation of pressure-dependent, shear stress-dependent, and metabolic vasoactive responses are analyzed using a theoretical model. Seven segments, connected in series, represent classes of vessels: arteries, large arterioles, small arterioles, capillaries, small venules, large venules, and veins. The large and small arterioles respond actively to local changes in pressure and wall shear stress and to the downstream metabolic state communicated via conducted responses. All other segments are considered fixed resistances. The myogenic, shear-dependent, and metabolic responses of the arteriolar segments are represented by a theoretical model based on experimental data from isolated vessels. To assess autoregulation, the predicted flow at an arterial pressure of 130 mmHg is compared with that at 80 mmHg. If the degree of vascular smooth muscle activation is held constant at 0.5, there is a fivefold increase in blood flow. When myogenic variation of tone is included, flow increases by a factor of 1.66 over the same pressure range, indicating weak autoregulation. The inclusion of both myogenic and shear-dependent responses results in an increase in flow by a factor of 2.43. A further addition of the metabolic response produces strong autoregulation with flow increasing by a factor of 1.18 and gives results consistent with experimental observation. The model results indicate that the combined effects of myogenic and metabolic regulation overcome the vasodilatory effect of the shear response and lead to the autoregulation of blood flow.

Impaired autoregulation in preterm infants identified by using spatially resolved spectroscopy

OBJECTIVE

The absence of cerebral autoregulation in preterm infants has been associated with adverse outcome, but its bedside assessment in the immature brain is problematic. We used spatially resolved spectroscopy to continuously measure cerebral oxygen saturation (expressed as a tissue-oxygenation index) and used the correlation of tissue-oxygenation index with spontaneous fluctuations in mean arterial blood pressure to assess cerebral autoregulation.

PATIENTS AND METHODS

The tissue-oxygenation index and mean arterial blood pressure were continuously measured in very premature infants (n = 24) of mean (+/-SD) gestational age of 26 (+/-2.3) weeks at a mean postnatal age of 28 (+/-22) hours. The correlation between mean arterial blood pressure and tissue-oxygenation index in the frequency domain was assessed by using cross-spectral analysis techniques (coherence and transfer-function gain). Values of coherence reflect the strength of linear correlation, whereas transfer-function gain reflects the amplitude of tissue-oxygenation index changes relative to mean arterial blood pressure changes.

RESULTS

High coherence (coherence > or = 0.5) values were found in 9 infants who were of lower gestational age, lower birth weight, and lower mean arterial blood pressure than infants with coherence of < 0.5; high-coherence infants also had higher median Clinical Risk Index for Babies scores and a higher rate of neonatal deaths. Coherence of > or = 0.5 predicted mortality with a positive predictive value of 67% and negative predictive value of 100%. In multifactorial analysis, coherence alone was the best predictor of mortality and Clinical Risk Index for Babies score alone was the best predictor of coherence.

CONCLUSIONS

High coherence between mean arterial blood pressure and tissue-oxygenation index indicates impaired cerebral autoregulation in clinically sick preterm infants and is strongly associated with subsequent mortality. Cross-spectral analysis of mean arterial blood pressure and tissue-oxygenation index has the potential to provide continuous bedside assessment of cerebral autoregulation and to guide therapeutic interventions.

Mathematical models of cerebral hemodynamics for detection of vasospasm in major cerebral arteries

BACKGROUND

Vasospasm is a common complication of aneurismal subarachnoid hemorrhage (SAH) that may lead to cerebral ischemia and death. The standard method for detection of vasospasm is conventional cerebral angiography, which is invasive and does not allow continuous monitoring of arterial radius. Monitoring of vasospasm is typically performed by measuring Cerebral Blood Flow Velocity (CBFV) in the major cerebral arteries and calculating the Lindegaard ratio. We describe an alternative approach to estimate intracranial arterial radius, which is based on modeling and state-estimation techniques. The objective is to obtain a better estimation than that offered by the Lindegaard ratio, that might allow for continuous monitoring and possibly vasospam prediction without the need for angiography.

METHODS

We propose two new models of cerebral hemodynamics. Model 1 is a more general version of Ursino's 1991 model that includes the effects of vasospasm, and Model 2 is a simplified version of Model 1. We use Model 1 to generate Intracranial Pressure (ICP) and CBFV signals for different vasospasm conditions, where CBFV is measured at the middle cerebral artery (MCA). Then we use Model 2 to estimate the arterial radii from these signals.

FINDINGS

Simulations show that Model 2 is capable of providing good estimates for the radius of the MCA, allowing the detection of the vasospasm. These changes in arterial radius are being estimated from measurements of CBFV, and CBF is never being measured directly. This is the main advantage of the model-based approach where several interrelations between CBFV, ABP and ICP are taken into account by the differential equations of the model.

CONCLUSIONS

Our results indicate that arterial radius may be estimated using measurements of ABP, ICP and CBFV, allowing the detection of vasospasm.