Cerebral hemodynamics during arterial and CO(2) pressure changes: in vivo prediction by 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.

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.

A deformation model of pulsating brain tissue for neurosurgery simulation

BACKGROUND AND OBJECTIVES

For neurological simulation, an accurate deformation model of brain tissue is of key importance for faithful visual feedback. Existing models, however, do not take into account intracranial pulsation, which degrades significantly the realism of visual feedback.

METHODS

In this paper, a finite element model incorporating intracranial pressure is proposed for simulating brain tissue deformation with pulsation. An implicit Euler method is developed to calculate the deformation of brain tissue. A circuit model of intracranial pressure dynamics is established based on cerebral blood and cerebrospinal fluid circulations. The intracranial pulsation of pressure is introduced into the deformation model, so that the simulated brain tissues pulsate with a rhythm in accord with the changes of intracranial pressure, which resembles real-life neurosurgery.

RESULTS AND CONCLUSIONS

The experimental implementation of the proposed deformation model and the calculation method shows that it provides realistic simulation of brain tissue pulsation and real-time performance is achieved on an ordinary computer for certain procedures of neurosurgery.

Modelling physiology of haemodynamic adaptation in short-term microgravity exposure and orthostatic stress on Earth

Cardiovascular haemodynamics alters during posture changes and exposure to microgravity. Vascular auto-remodelling observed in subjects living in space environment causes them orthostatic intolerance when they return on Earth. In this study we modelled the human haemodynamics with focus on head and neck exposed to different hydrostatic pressures in supine, upright (head-up tilt), head-down tilt position, and microgravity environment by using a well-developed 1D-0D haemodynamic model. The model consists of two parts that simulates the arterial (1D) and brain-venous (0D) vascular tree. The cardiovascular system is built as a network of hydraulic resistances and capacitances to properly model physiological parameters like total peripheral resistance, and to calculate vascular pressure and the related flow rate at any branch of the tree. The model calculated 30.0 mmHg (30%), 7.1 mmHg (78%), 1.7 mmHg (38%) reduction in mean blood pressure, intracranial pressure and central venous pressure after posture change from supine to upright, respectively. The modelled brain drainage outflow percentage from internal jugular veins is 67% and 26% for supine and upright posture, while for head-down tilt and microgravity is 65% and 72%, respectively. The model confirmed the role of peripheral veins in regional blood redistribution during posture change from supine to upright and microgravity environment as hypothesized in literature. The model is able to reproduce the known haemodynamic effects of hydraulic pressure change and weightlessness. It also provides a virtual laboratory to examine the consequence of a wide range of orthostatic stresses on human haemodynamics.

Rude mechanicals in brain haemodynamics: non-neural actors that influence blood flow

Fluctuations in blood oxygenation and flow are widely used to infer brain activity during resting-state functional magnetic resonance imaging (fMRI). However, there are strong systemic and vascular contributions to resting-state signals that are unrelated to ongoing neural activity. Importantly, these non-neural contributions to haemodynamic signals (or 'rude mechanicals') can be as large as or larger than the neurally evoked components. Here, we review the two broad classes of drivers of these signals. One is systemic and is tied to fluctuations in external drivers such as heart rate and breathing, and the robust autoregulatory mechanisms that try to maintain a constant milieu in the brain. The other class comprises local, active fluctuations that appear to be intrinsic to vascular tissue and are likely similar to active local fluctuations seen in vasculature all over the body. In this review, we describe these non-neural fluctuations and some of the tools developed to correct for them when interpreting fMRI recordings. However, we also emphasize the links between these vascular fluctuations and brain physiology and point to ways in which fMRI measurements can be used to exploit such links to gain valuable information about neurovascular health and about internal brain states. This article is part of the theme issue 'Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity'.

Paediatric haemodynamic modelling: development and experimental validation using quantitative flow MRI

Background

Congenital vascular disease is one of the leading causes of death in paediatric age. Despite the importance of paediatric haemodynamics, large investigations have been devoted to the evaluation of circulation in adults. The novelty of this study consists in the development of a well calibrated mathematical model of cardiovascular circulation in paediatric subjects. To reach the purpose, a model for adult circulation was modified and recalibrated with experimental data and literature from children to be able to calculate the flow rates and pressures in the brain and neck.

Methods

The haemodynamic model simulates the 76 main arteries, together with the main veins in brain and neck. A proper magnetic resonance imaging (MRI) dataset of 29 volunteers aged 12 ± 5 years (mean ± standard deviation) was used to extract age-dependent physiological and clinical parameters such as heart rate, flow rate, vessel cross section area, and blood pressure. The computational model was calibrated using such experimental data. The paediatric and adult model results were compared.

Results

Increase of the vessels stiffness due to aging contributes to a flow rate decrease while blood pressure increases. In accordance, our simulation results show about 16% decrease in mean pressure of internal jugular vein in paediatric rather than adult subjects. The model outcomes indicated about 88% correlation with MRI data.

Conclusions

The mathematical model simulates the paediatric head and neck blood circulation. The model provides detailed information of human haemodynamics including arterial and venous network to study both paediatric and adult blood circulation.

Quantification of dynamic cerebral autoregulation and CO2 dynamic vasomotor reactivity impairment in essential hypertension

The study of dynamic cerebral autoregulation (DCA) in essential hypertension has received considerable attention because of its clinical importance. Several studies have examined the dynamic relationship between spontaneous beat-to-beat arterial blood pressure data and contemporaneous cerebral blood flow velocity measurements (obtained via transcranial Doppler at the middle cerebral arteries) in the form of a linear input-output model using transfer function analysis. This analysis is more reliable when the contemporaneous effects of changes in blood CO₂ tension are also taken into account, because of the significant effects of CO₂ dynamic vasomotor reactivity (DVR) upon cerebral flow. In this article, we extract such input-output predictive models from spontaneous time series hemodynamic data of 24 patients with essential hypertension and 20 normotensive control subjects under resting conditions, using the novel methodology of principal dynamic modes (PDMs) that achieves improved estimation accuracy over previous methods for relatively short and noisy data. The obtained data-based models are subsequently used to compute indexes and markers that quantify DCA and DVR in each subject or patient and therefore can be used to assess the effects of essential hypertension. These model-based DCA and DVR indexes were properly defined to capture the observed effects of DCA and VR and found to be significantly different (P < 0.05) in the hypertensive patients. We also found significant differences between patients and control subjects in the relative contribution of three PDMs to the model output prediction, a finding that offers the prospect of identifying the physiological mechanisms affected by essential hypertension when the PDMs are interpreted in terms of specific physiological mechanisms.NEW & NOTEWORTHY This article presents novel model-based methodology for obtaining diagnostic indexes of dynamic cerebral autoregulation and dynamic vasomotor reactivity in hypertension.

System dynamics of active and passive postural changes: Insights from principal dynamic modes analysis of baroreflex loop

The baroreflex being a key modulator of cardiovascular control ensures adequate blood pressure regulation under orthostatic stress which otherwise may cause severe hypotension. Contrary to conventional baroreflex sensitivity indices derived across a-priori traditional frequency bands, the present study is aimed at proposing new indices for the assessment of baroreflex drive which follows active (supine to stand-up) and passive (supine to head-up tilt) postural changes. To achieve this, a novel system identification approach of principal dynamic modes (PDM) was utilized to extract data-adaptive frequency components of closed-loop interactions between beat-to-beat interval and systolic blood pressure recorded from 10 healthy humans. We observed that the gain of low-pass global PDM of cardiac arm (:feedback reflex loop, mediated by pressure sensors to adjust heart rate in response to arterial blood pressure), and 0.2 Hz global PDM of mechanical arm (:feed-forward pathways, originating changes in arterial blood pressure in response to heart rate variations) may function as potential markers to distinguish active and passive orthostatic tests in healthy subjects.

Identifying the myogenic and metabolic components of cerebral autoregulation

Cerebral autoregulation is the term used to describe a number of mechanisms that act together to maintain a near constant cerebral blood flow in response to changes in arterial blood pressure. These mechanisms are complex and known to be affected in a range of cerebrovascular diseases. However, it can be difficult to assign an alteration in cerebral autoregulation to one of the underlying physiological mechanisms without the use of a complex mathematical model. In this paper, we thus set out a new approach that enables these mechanisms to be related to the autoregulation behaviour and hence inferred from experimental measurements. We show that the arteriolar response is a function of just three parameters, which we term the elastic, the myogenic and the metabolic sensitivity coefficients, and that the full vascular response is dependent upon only seven parameters. The ratio of the strengths of the myogenic and the metabolic responses is found to be in the range 2.5 to 5 over a wide range of pressure, indicating that the balance between the two appears to lie within this range. We validate the model with existing experimental data both at the level of an individual vessel and across the whole vasculature, and show that the results are consistent with findings from the literature. We then conduct a sensitivity analysis of the model to demonstrate which parameters are most important in determining the strength of static autoregulation, showing that autoregulation strength is predominantly set by the arteriolar sensitivity coefficients. This new approach could be used in future studies to help to interpret the components of the autoregulation response and how they are affected under different conditions, providing a greater insight into the fundamental processes that govern autoregulation.

Increased blood pressure variability upon standing up improves reproducibility of cerebral autoregulation indices

Dynamic cerebral autoregulation, that is the transient response of cerebral blood flow to changes in arterial blood pressure, is currently assessed using a variety of different time series methods and data collection protocols. In the continuing absence of a gold standard for the study of cerebral autoregulation it is unclear to what extent does the assessment depend on the choice of a computational method and protocol. We use continuous measurements of blood pressure and cerebral blood flow velocity in the middle cerebral artery from the cohorts of 18 normotensive subjects performing sit-to-stand manoeuvre. We estimate cerebral autoregulation using a wide variety of black-box approaches (including the following six autoregulation indices ARI, Mx, Sx, Dx, FIR and ARX) and compare them in the context of reproducibility and variability. For all autoregulation indices, considered here, the intra-class correlation was greater during the standing protocol, however, it was significantly greater (Fisher's Z-test) for Mx (p < 0.03), Sx (p < 0.003) and Dx (p < 0.03). In the specific case of the sit-to-stand manoeuvre, measurements taken immediately after standing up greatly improve the reproducibility of the autoregulation coefficients. This is generally coupled with an increase of the within-group spread of the estimates.

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.

Physiome approach for the analysis of vascular flow reserve in the heart and brain

This work reviews the key aspects of coronary and neurovascular flow reserves with an emphasis on physiomic modeling characteristics by the use of a variety of numerical approaches. First, we explain the definition of fractional flow reserve (FFR) in coronary artery and introduce its clinical significance. Then, computational researches for obtaining FFR are reviewed, and their clinical outcomes are compared. In the case of cerebrovascular reserve (CVR), in spite of substantial progress in the simulation of cerebral hemodynamics, only a few computational studies exist. Thus, we discuss the limitations of CVR simulation study and suggest the challenging issue to overcome these. Also, the future direction of physiomic researches for the flow reserves in coronary arteries and cerebral arteries is described. Also, we introduce a machine learning algorithm trained by the existing physiomic simulation data of flow reserve and suggest a prospective research direction related to this.

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 simulation model to study the role of the extracranial venous drainage pathways in intracranial hemodynamics

Alterations in the extracranial venous circulation due to posture changes, and/or extracranial venous obstructions in patients with vascular diseases, can have important implications on cerebral hemodynamics. A hemodynamic model for the study of cerebral venous outflow was developed to investigate the correlations between extracranial blood redistributions and changes in the intracranial environment. Flow data obtained with both magnetic resonance (MR) and Echo-Color Doppler (ECD) technique are used to validate the model. The very good agreement between simulated supine and upright flows and experimental results means that the model can correctly reproduce the main factors affecting the extracranial venous circulation.

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.

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.

A new hemodynamic model for the study of cerebral venous outflow

We developed a mathematical model of the cerebral venous outflow for the simulation of the average blood flows and pressures in the main drainage vessels of the brain. The main features of the model are that it includes a validated model for the simulation of the intracranial circulation and it accounts for the dependence of the hydraulic properties of the jugular veins with respect to the gravity field, which makes it an useful tool for the study of the correlations between extracranial blood redistributions and changes in the intracranial environment. The model is able to simulate the average pressures and flows in different points of the jugular ducts, taking into account the amount of blood coming from the anastomotic connections; simulate how the blood redistribution due to change of posture affects flows and pressures in specific points of the system; and simulate redistributions due to stenotic patterns. Sensitivity analysis to check the robustness of the model was performed. The model reproduces average physiologic behavior of the jugular, vertebral, and cerebral ducts in terms of pressures and flows. In fact, jugular flow drops from ∼11.7 to ∼1.4 ml/s in the passage from supine to standing. At the same time, vertebral flow increases from 0.8 to 3.4 ml/s, while cerebral blood flow, venous sinuses pressure, and intracranial pressure are constant around the average value of 12.5 ml/s, 6 mmHg, and 10 mmHg, respectively. All these values are in agreement with literature data.

Microgravity-induced fluid shift and ophthalmic changes

Although changes to visual acuity in spaceflight have been observed in some astronauts since the early days of the space program, the impact to the crew was considered minor. Since that time, missions to the International Space Station have extended the typical duration of time spent in microgravity from a few days or weeks to many months. This has been accompanied by the emergence of a variety of ophthalmic pathologies in a significant proportion of long-duration crewmembers, including globe flattening, choroidal folding, optic disc edema, and optic nerve kinking, among others. The clinical findings of affected astronauts are reminiscent of terrestrial pathologies such as idiopathic intracranial hypertension that are characterized by high intracranial pressure. As a result, NASA has placed an emphasis on determining the relevant factors and their interactions that are responsible for detrimental ophthalmic response to space. This article will describe the Visual Impairment and Intracranial Pressure syndrome, link it to key factors in physiological adaptation to the microgravity environment, particularly a cephalad shifting of bodily fluids, and discuss the implications for ocular biomechanics and physiological function in long-duration spaceflight.

Impedance boundary conditions for general transient hemodynamics

We discuss the implementation and calibration of a new generalized structured tree boundary condition for hemodynamics. The main idea is to approximate the impedance corresponding to the vessels downstream from a specific outlet. Unlike previous impedance conditions, the one considered here is applicable to general transient flows as opposed to periodic ones only. The physiological character of the approach significantly simplifies calibration. We also describe a novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost. The strength of the approach is illustrated and validated on several examples through comparison with clinical data.

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.

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.

A coupled hydrodynamic model of the cardiovascular and cerebrospinal fluid system

Coupling of the cardiovascular and cerebrospinal fluid (CSF) system is considered to be important to understand the pathophysiology of cerebrovascular and craniospinal disease and intrathecal drug delivery. A coupled cardiovascular and CSF system model was designed to examine the relation of spinal cord (SC) blood flow (SCBF) and CSF pulsations along the spinal subarachnoid space (SSS). A one-dimensional (1-D) cardiovascular tree model was constructed including a simplified SC arterial network. Connection between the cardiovascular and CSF system was accomplished by a transfer function based on in vivo measurements of CSF and cerebral blood flow. A 1-D tube model of the SSS was constructed based on in vivo measurements in the literature. Pressure and flow throughout the cardiovascular and CSF system were determined for different values of craniospinal compliance. SCBF results indicated that the cervical, thoracic, and lumbar SC each had a signature waveform shape. The cerebral blood flow to CSF transfer function reproduced an in vivo-like CSF flow waveform. The 1-D tube model of the SSS resulted in a distribution of CSF pressure and flow and a wave speed that were similar to those in vivo. The SCBF to CSF pulse delay was found to vary a great degree along the spine depending on craniospinal compliance and vascular anatomy. The properties and anatomy of the SC arterial network and SSS were found to have an important impact on pressure and flow and perivascular fluid movement to the SC. Overall, the coupled model provides predictions about the flow and pressure environment in the SC and SSS. More detailed measurements are needed to fully validate the model.

Simulation of existing and future electromechanical shunt valves in combination with a model for brain fluid dynamics

Several models are available to simulate raised intracranial pressure (ICP) in hydrocephalus. However, the hydrodynamic effect of an implanted shunt has seldom been examined. In this study, the simple model of Ursino and Lodi [14]is extended to include (1) the effect of a typical ball-in-cone valve, (2) the effect of the size of the diameter of the connecting tube from valve to abdomen, and (3) the concept of a controlled electromechanical shunt valve in overall cerebrospinal fluid dynamics.By means of simulation, it is shown how a shunt can lower ICP. Simulation results indicate that P and B waves still exist but at a lower ICP level and that, due to the exponential pressure-volume curve, their amplitude is also considerably lowered. A waves only develop if the valve is partially blocked. The resulting ICP is above the opening pressure of the valve, depending on the drain and resistance of the shunt.The concept of a new electromechanical shunt was more successful than the traditional mechanical valves in keeping ICP at a desired level. The influence of the patient's movements or coughing on ICP as well as the body position affecting the reference ICP, which can be measured, has not yet been modeled and should be addressed in future using suitable algorithms.

Changes of circulatory-metabolic indices and skull biomechanics with brain activity during aging

The cerebral blood flow values used in experimental and clinical investigations as the informative criteria for brain blood supply are often misleading. The correlation between the cerebral blood supply and brain function is not proven in all cases. An increase of brain activity is known to be accompanied by a rise of blood flow in activated regions, while a decreased activity results in a decreased blood flow. This demonstrates the close correlation between the brain blood supply and its activity. Such a correlation had not been noted in the age-dependent decrease of cerebral blood flow, suggesting the existence of special age-related mechanisms that develop with age to maintain brain metabolism. The biomechanical properties are of special significance as predicted in the early 20th century. Only recently were they validated by the simultaneous recording of Transcranial Dopplerogram and Rheoencephalogram with in-depth analysis focused on single cardiac cycles. Functioning of the intracranial blood and cerebrospinal fluid dynamics was integrated with a special physiological test "Prognosis-2" to measure brain cognitive function. Correlation was demonstrated with the circulatory-metabolic state of brain activity, especially in people with changing cognitive function. The data supports a conceptual model of adequate circulatory-metabolic supply of brain activity, showing the functional unity, which follows from integration of the mentioned systems.

Review of zero-D and 1-D models of blood flow in the cardiovascular system

Background

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.

Method and Results

The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities.

Conclusion

Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

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.

Relationship between myogenic reaction and autoregulation of cerebral circulation

Dilatation of rat pial arterioles at constant arteriolar wall strain during autoregulation of cerebral circulation was shown by the method of biomicroscopy. Wavelet-analysis of cerebral blood flow oscillations during this period revealed increased oscillation amplitude in the endothelial and neurogenic frequency ranges and unchanged amplitude at myogenic frequency range. These findings probably attest to the leading role of myogenic reaction in the autoregulation.

Continuous estimates of dynamic cerebral autoregulation during transient hypocapnia and hypercapnia

Dynamic cerebral autoregulation (CA) is the transient response of cerebral blood flow (CBF) to rapid blood pressure changes: it improves in hypocapnia and becomes impaired during hypercapnia. Batch-processing techniques have mostly been used to measure CA, providing a single estimate for an entire recording. A new approach to increase the temporal resolution of dynamic CA parameters was applied to transient hypercapnia and hypocapnia to describe the time-varying properties of dynamic CA during these conditions. Thirty healthy subjects (mean +/- SD: 25 +/- 6 yr, 9 men) were recruited. CBF velocity was recorded in both middle cerebral arteries (MCAs) with transcranial Doppler ultrasound. Arterial blood pressure (Finapres), end-tidal CO(2) (ET(CO(2)); infrared capnograph), and a three-lead ECG were also measured at rest and during repeated breath hold and hyperventilation. A moving window autoregressive moving average model provided continuous values of the dynamic CA index [autoregulation index (ARI)] and unconstrained gain. Breath hold led to significant increase in ET(CO(2)) (+5.4 +/- 6.1 mmHg), with concomitant increase in CBF velocity in both MCAs. Continuous dynamic CA parameters showed highly significant changes (P < 0.001), with a temporal pattern reflecting a delayed dynamic response of CA to changes in arterial Pco(2) and a maximal reduction in ARI of -5.1 +/- 2.4 and -5.1 +/- 2.3 for the right and left MCA, respectively. Hyperventilation led to a marked decrease in ET(CO(2)) (-7.2 +/- 4.1 mmHg, P < 0.001). Unexpectedly, CA efficiency dropped significantly with the inception of the metronome-controlled hyperventilation, but, after approximately 30 s, the ARI increased gradually to show a maximum change of 5.7 +/- 2.9 and 5.3 +/- 3.0 for the right and left MCA, respectively (P < 0.001). These results confirm the potential of continuous estimates of dynamic CA to improve our understanding of human cerebrovascular physiology and represent a promising new approach to improve the sensitivity of clinical applications of dynamic CA modeling.

Effects of autoregulation and CO2 reactivity on cerebral oxygen transport

Both autoregulation and CO(2) reactivity are known to have significant effects on cerebral blood flow and thus on the transport of oxygen through the vasculature. In this paper, a previous model of the autoregulation of blood flow in the cerebral vasculature is expanded to include the dynamic behavior of oxygen transport through binding with hemoglobin. The model is used to predict the transfer functions for both oxyhemoglobin and deoxyhemoglobin in response to fluctuations in arterial blood pressure and arterial CO(2) concentration. It is shown that only six additional nondimensional groups are required in addition to the five that were previously found to characterize the cerebral blood flow response. A resonant frequency in the pressure-oxyhemoglobin transfer function is found to occur in the region of 0.1 Hz, which is a frequency of considerable physiological interest. The model predictions are compared with results from the published literature of phase angle at this frequency, showing that the effects of changes in breathing rate can significantly alter the inferred phase dynamics between blood pressure and hemoglobin. The question of whether dynamic cerebral autoregulation is affected under conditions of stenosis or stroke is then examined.

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.

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.

Modeling perfusion in the cerebral vasculature

The constant perfusion of a human organ with nutrients and oxygen demands a robust regulatory mechanisms in the face of normal day-to-day pressure variations in the vasculature. The brain, in a similar manner to the heart requires this mechanism to be extremely quick acting, relative to other ways of altering perfusion such as varying systemic blood pressure, since oxygen depravation in the tissues of the brain can be tolerated for only of the order of tens of seconds before significant damage can be done. In recent years computational models, and it must be noted computer architecture have evolved to an extent where mathematicians and engineers can play a large part in discovering how the brain functions physiologically as well as investigating pathological conditions. This review will look at a number of increasingly complex computational models of blood flow to the brain and how variations in arterial geometry can influence the perfusion in the cerebral vasculature. Although these models have provided an insight into complex mechanisms the research area is densely populated with important questions that perhaps only computer models can answer. The review will indicate possible areas of investigation.

A review of physiological simulation models of intracranial pressure dynamics

This paper reviews the literature regarding the development, testing, and application of physiology-based computer simulation models of intracranial pressure dynamics. Detailed comparative information is provided in tabular format about the model variables and logic, any data collected, model testing and validation methods, and model results. Several syntheses are given that summarize the research carried out by influential research teams and researchers, review important findings, and discuss the methods employed, limitations, and opportunities for further research.

Noninvasive monitoring of cerebral perfusion pressure in patients with acute liver failure using transcranial doppler ultrasonography

Elevated intracranial pressure (ICP) leads to loss of cerebral perfusion, cerebral herniation, and irreversible brain damage in patients with acute liver failure (ALF). Conventional techniques for monitoring ICP can be complicated by hemorrhage and infection. Transcranial doppler ultrasonography (TCD) is a noninvasive device which can continuously measure cerebral blood flow velocity, producing a velocity-time waveform that indirectly monitors changes in cerebral hemodynamics, including ICP. The primary goal of this study was to determine whether TCD waveform features could be used to differentiate ALF patients with respect to ICP or, equally important, cerebral perfusion pressure (CPP) levels. A retrospective study of 16 ALF subjects with simultaneous TCD, ICP, and CPP measurements yielded a total of 209 coupled ICP-CPP-TCD observations. The TCD waveforms were digitally scanned and seven points corresponding to a simplified linear waveform were identified. TCD waveform features including velocity, pulsatility index, resistive index, fraction of the cycle in systole, slopes, and angles associated with changes in the slope in each region, were calculated from the simplified waveform data. Paired ICP-TCD observations were divided into three groups (ICP < 20 mmHg, n = 102; 20 < or = ICP < 30 mmHg, n = 74; and ICP > or = 30 mmHg, n = 33). Paired CPP-TCD observations were also divided into three groups (CPP > or = 80 mmHg, n = 42; 80 > CPP > or = 60 mmHg, n = 111; and CPP < 60 mmHg, n = 56). Stepwise linear discriminant analysis was used to identify TCD waveform features that discriminate between ICP groups and CPP groups. Four primary features were found to discriminate between ICP groups: the blood velocity at the start of the Windkessel effect, the slope of the Windkessel upstroke, the angle between the end systolic downstroke and start diastolic upstroke, and the fraction of time spent in systole. Likewise, 4 features were found to discriminate between the CPP groups: the slope of the Windkessel upstroke, the slope of the Windkessel downstroke, the slope of the diastolic downstroke, and the angle between the end systolic downstroke and start diastolic upstroke. The TCD waveform captures the cerebral hemodynamic state and can be used to predict dynamic changes in ICP or CPP in patients with ALF. The mean TCD waveforms for corresponding, correctly classified ICP and CPP groups are remarkably similar. However, this approach to predicting intracranial hypertension and CPP needs to be further refined and developed before clinical application is feasible.

Multivariate system identification for cerebral autoregulation

The effect of spontaneous beat-to-beat mean arterial blood pressure (ABP) fluctuations and breath-to-breath end-tidal carbon dioxide (PETCO2) and end-tidal oxygen (PETO2) fluctuations on beat-to-beat cerebral bloodflow velocity (CBFV) variations is studied using a multiple coherence function. Multiple coherence is a measure of the extent to which the output, CBFV, can be represented as a linear time invariant system of multiple input signals. Analysis of experimental measurements from 13 different healthy subjects reveal that, with additional inputs, PETCO2 and PETO2, the multiple coherence for frequencies <0.05 Hz is significantly higher than the corresponding values obtained for univariate coherence with a single input of ABP. The result illustrates that the low value of univariate coherence at small frequencies may be due to the effects of PETCO2 and PETO2 fluctuations on CBFV variability. Moreover, it is also found that the transfer function between ABP and CBFVtime series identified from previous univariate techniques at low frequencies can be modified by CO2 and O2 reactivity and no longer represents pressure autoregulation only. Multivariate system identification provides a technique of incorporating additional variability and recovering from this artifact. Finally, a physiologically based model and its linear transfer function are used as a simulation tool to investigate possible causes of low univariate coherence.

Cerebral autoregulation and gas exchange studied using a human cardiopulmonary model

The goal of this work is to study the cerebral autoregulation, brain gas exchange, and their interaction by means of a mathematical model. We have previously developed a model of the human cardiopulmonary (CP) system, which included the whole body circulatory system, lung and peripheral tissue gas exchange, and the central nervous system control of arterial pressure and ventilation. In this study, we added a more detailed description of cerebral circulation, cerebrospinal fluid (CSF) dynamics, brain gas exchange, and cerebral blood flow (CBF) autoregulation. Two CBF regulatory mechanisms are included: autoregulation and CO(2) reactivity. Central chemoreceptor control of ventilation is also included. We first established nominal operating conditions for the cerebral model in an open-loop configuration using data generated by the CP model as inputs. The cerebral model was then integrated into the larger CP model to form a new integrated CP model, which was subsequently used to study cerebral hemodynamic and gas exchange responses to test protocols commonly used in the assessment of CBF autoregulation (e.g., carotid artery compression and the thigh-cuff deflation test). The model can closely mimic the experimental findings and provide biophysically based insights into the dynamics of cerebral autoregulation and brain tissue gas exchange as well as the mechanisms of their interaction during test protocols, which are aimed at assessing the degree of autoregulation. With further refinement, our CP model may be used on measured data associated with the clinical evaluation of the cerebral autoregulation and brain oxygenation in patients.

Dynamic cerebral autoregulation assessment using an ARX model: comparative study using step response and phase shift analysis

Middle cerebral arterial blood velocity (MCAv) response to spontaneous and manipulated changes of arterial blood pressure (ABP) was studied in eight subjects using a linear autoregressive with exogenous input (ARX) model. ABP and MCAv were measured non-invasively by photoplethysmograph and transcranial Doppler ultrasound, respectively. Data were recorded at rest (spontaneous changes in ABP) and during thigh cuff (step-wise changes) and lower body negative pressure (sinusoidal changes of 1/12 Hz) tests in both normocapnia and hypercapnia (5% CO2). Since autoregulation is modulated by CO2, respiratory CO2 was simultaneously monitored to allow comparison of cerebral autoregulation status with different CO2 levels. ABP and MCAv were fitted by ARX models and dynamic cerebral autoregulation was estimated by analysing both the step responses and phase shift at the 1/12 Hz of the corresponding ARX models. The ARX model consistently modelled the phase lead of MCAv to ABP and it showed that the phase shift at 1/12 Hz of ARX model is consistent with the real phase shift of the data (p=0.59). Strong linear relationships between pCO2 and gradient of the step response (r=-0.58, p<0.0001) and between pCO2 and phase shift (r=-0.76, p<0.0001) were observed, which suggests that cerebral autoregulation can be assessed by step response or phase shift analysis of the ARX model fitted to ABP and MCAv data with spontaneous changes.

Traumatic Cerebral Vascular Injury: The Effects of Concussive Brain Injury on the Cerebral Vasculature

In terms of human suffering, medical expenses, and lost productivity, head injury is one of the major health care problems in the United States, and inadequate cerebral blood flow is an important contributor to mortality and morbidity after traumatic brain injury. Despite the importance of cerebral vascular dysfunction in the pathophysiology of traumatic brain injury, the effects of trauma on the cerebral circulation have been less well studied than the effects of trauma on the brain. Recent research has led to a better understanding of the physiologic, cellular, and molecular components and causes of traumatic cerebral vascular injury. A more thorough understanding of the direct and indirect effects of trauma on the cerebral vasculature will lead to improvements in current treatments of brain trauma as well as to the development of novel and, hopefully, more effective therapeutic strategies.

Changes in intracranial pressure and cerebral autoregulation in patients with severe traumatic brain injury

BACKGROUND

Impaired cerebral autoregulation is frequent after severe traumatic head injury. This could result in intracranial pressure fluctuating passively with the mean arterial pressure.

OBJECTIVE

This study examines the influence of autoregulation on the amplitude and direction of changes in intracranial pressure in patients with severe head injuries during the management of cerebral perfusion pressure.

DESIGN

Prospective study.

SETTING

Neurosurgical intensive care unit

PATIENTS

A total of 42 patients with severe head injuries.

INTERVENTIONS

Continuous recording of cerebral blood flow velocity, intracranial pressure, and mean arterial pressure during the start or change of continuous norepinephrine infusion.

MEASUREMENTS AND MAIN RESULTS

Cerebrovascular resistance was calculated from the cerebral perfusion pressure and middle cerebral artery blood flow velocity. The strength of autoregulation index was calculated as the ratio of the percentage of change in cerebrovascular resistance by the percentage of change in cerebral perfusion pressure before and after 121 changes in mean arterial pressure at constant ventilation between day 1 and day 18 after trauma. The strength of autoregulation index varied widely, indicating either preserved or severely perturbed autoregulation during hypotensive or hypertensive challenge in patients with or without intracranial hypertension at the basal state (strength of autoregulation index, 0.51 +/- 0.32 to 0.71 +/- 0.25). The change in intracranial pressure varied linearly with the strength of autoregulation index. There was a clinically significant change in intracranial pressure (> or =5 mm Hg) in the same direction as the change in mean arterial pressure in five tracings of three patients. This was caused by the mean arterial pressure dropping below the identified lower limit of autoregulation in three tracings for two patients. It seemed to be caused by a loss of cerebral autoregulation in the remaining two tracings for one patient.

CONCLUSION

Cerebral perfusion pressure-oriented therapy can be a safe way to reduce intracranial pressure, whatever the status of autoregulation, in almost all patients with severe head injuries.