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

Dynamic cerebral autoregulation is governed by two time constants: Arterial transit time and feedback time constant

Dynamic cerebral autoregulation (dCA) is the mechanism that describes how the brain maintains cerebral blood flow approximately constant in response to short-term changes in arterial blood pressure. This is known to be impaired in many different pathological conditions, including ischaemic and haemorrhagic stroke, dementia and traumatic brain injury. Many different approaches have thus been used both to analyse and to quantify this mechanism in a range of healthy and diseased subjects, including data-driven models (in both the time and the frequency domain) and biophysical models. However, despite the substantial body of work on both biophysical models and data-driven models of dCA, there remains little work that links the two together. One of the reasons for this is proposed to be the discrepancies between the time constants that govern dCA in models and in experimental data. In this study, the processes that govern dCA are examined and it is proposed that the application of biophysical models remains limited due to a lack of understanding about the physical processes that are being modelled, partly due to the specific model formulation that has been most widely used (the equivalent electrical circuit). Based on the analysis presented here, it is proposed that the two most important time constants are arterial transit time and feedback time constant. It is therefore time to revisit equivalent electrical circuit models of dCA and to develop a more physiologically realistic alternative, one that can more easily be related to experimental data. KEY POINTS: Dynamic cerebral autoregulation is governed by two time constants. The first time constant is the arterial transit time, rather than the traditional 'RC' time constant widely used in previous models. This arterial transit time is approximately 1 s in the brain. The second time constant is the feedback time constant, which is less accurately known, although it is somewhat larger than the arterial transit time. The equivalent electrical circuit model of dynamic cerebral autoregulation should be replaced with a more physiologically representative model.

Deep-learning-based real-time individualization for reduce-order haemodynamic model

The reduced-order lumped parameter model (LPM) has great computational efficiency in real-time numerical simulations of haemodynamics but is limited by the accuracy of patient-specific computation. This study proposed a method to achieve the individual LPM modeling with high accuracy to improve the practical clinical applicability of LPM. Clinical data was collected from two medical centres comprising haemodynamic indicators from 323 individuals, including brachial artery pressure waveforms, cardiac output data, and internal carotid artery flow waveforms. The data were expanded to 5000 synthesised cases that all fell within the physiological range of each indicator. LPM of the human blood circulation system was established. A double-path neural network (DPNN) was designed to input the waveforms of each haemodynamic indicator and their key features and then output the individual parameters of the LPM, which was labelled using a conventional optimization algorithm. Clinically collected data from the other 100 cases were used as the test set to verify the accuracy of the individual LPM parameters predicted by DPNN. The results show that DPNN provided good convergence in the training process. In the test set, compared with clinical measurements, the mean differences between each haemodynamic indicator and the estimate calculated by the individual LPM based on the DPNN were about 10 %. Furthermore, DPNN prediction only takes 4 s for 100 cases. The DPNN proposed in this study permits real-time and accurate individualization of LPM's. When facing medical issues involving haemodynamics, it lays the foundation for patient-specific numerical simulation, which may be beneficial for potential clinical application.

Neurovascular coupling is optimized to compensate for the increase in proton production from nonoxidative glycolysis and glycogenolysis during brain activation and maintain homeostasis of pH, pCO2, and pO2

During transient brain activation cerebral blood flow (CBF) increases substantially more than cerebral metabolic rate of oxygen consumption (CMRO2) resulting in blood hyperoxygenation, the basis of BOLD-fMRI contrast. Explanations for the high CBF versus CMRO2 slope, termed neurovascular coupling (NVC) constant, focused on maintenance of tissue oxygenation to support mitochondrial ATP production. However, paradoxically the brain has a 3-fold lower oxygen extraction fraction (OEF) than other organs with high energy requirements, like heart and muscle during exercise. Here, we hypothesize that the NVC constant and the capillary oxygen mass transfer coefficient (which in combination determine OEF) are co-regulated during activation to maintain simultaneous homeostasis of pH and partial pressure of CO2 and O2 (pCO2 and pO2). To test our hypothesis, we developed an arteriovenous flux balance model for calculating blood and brain pH, pCO2, and pO2 as a function of baseline OEF (OEF0), CBF, CMRO2, and proton production by nonoxidative metabolism coupled to ATP hydrolysis. Our model was validated against published brain arteriovenous difference studies and then used to calculate pH, pCO2, and pO2 in activated human cortex from published calibrated fMRI and PET measurements. In agreement with our hypothesis, calculated pH, pCO2, and pO2 remained close to constant independently of CMRO2 in correspondence to experimental measurements of NVC and OEF0. We also found that the optimum values of the NVC constant and OEF0 that ensure simultaneous homeostasis of pH, pCO2, and pO2 were remarkably similar to their experimental values. Thus, the high NVC constant is overall determined by proton removal by CBF due to increases in nonoxidative glycolysis and glycogenolysis. These findings resolve the paradox of the brain's high CBF yet low OEF during activation, and may contribute to explaining the vulnerability of brain function to reductions in blood flow and capillary density with aging and neurovascular disease.

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.

A real-time patient-specific treatment strategy for enhanced external counterpulsation

Diastolic/systolic blood pressure ratio (D/S) ≥ 1.2 is the gold standard of enhanced external counterpulsation (EECP) treatment, but it does not show a clear clinical correspondence with the configuration of the EECP mode. As such, a single target results in different treatment effects in different individuals. The local haemodynamic effect (wall shear stress, WSS) of EECP on vascular endothelial cells is conducive to promote the growth of collateral circulation vessels and restore the blood supply distal to the stenosis lesion. Considering the haemodynamic effects of WSS on human arteries, this study developed a real-time patient-specific treatment strategy of EECP for patients with cardio-cerebrovascular diseases. Based on patient-specific haemodynamic data from 113 individuals, an optimization algorithm was developed to achieve the individualization of a 0D lumped-parameter model of the human circulatory system, thereby simulating the patient-specific global haemodynamic effects. 0D/3D coupled cardio-cerebrovascular models of two subjects were established to simulate the local WSS. We then established statistical models to evaluate clinically unmeasurable WSS based on measurable global haemodynamic indicators. With the aim of attaining appropriate area- and time-averaged WSS (ATAWSS, 4-7 Pa), as evaluated by global haemodynamic indicators, a closed-loop feedback tuning method was developed to provide patient-specific EECP treatment strategies. Results showed that for clinical data collected from 113 individuals, the individualized 0D model can accurately simulate patient-specific global haemodynamic effects (average error <5%). Based on two subjects, the statistical models can be used to evaluate local ATAWSS (error <6%) for coronary arteries and for cerebral arteries. An EECP mode planned by the patient-specific treatment strategy can promote an appropriate ATAWSS within a 16 s calculation time. The real-time patient-specific treatment strategy of EECP is expected to improve the long-term outcome for each patient and have potential clinical significance.

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.

Hemodynamics of vascular shunts: trends, challenges, and prospects

Vascular bypass surgery takes a significant place in the treatment of vascular disease. According to various assessments, this type of surgery is associated with almost 20 % of all vascular surgery episodes (up to 23 % according to the Federal Neurosurgical Center of Novosibirsk). Even though the problem of using of vascular grafts is obvious and natural, many problems associated with them are not still elucidated. From the mechanics' point of view, a vascular bypass is a converging or diverging tee, and the functioning of such structures still does not have strict mathematical formulations and proofs in the general case, which forces many researchers to solve specific engineering problems associated with shunting. Mathematical modeling, which is the gold standard for virtual simulations of industrial and medical problems, faces great difficulties and limitations in solving problems for vascular bypasses. Complications in the treatment of the vascular disease may follow the difficulties in mathematical modeling, and the price can be a cardiac arrest or a stroke. This work is devoted to the main aspects of the medical application of vascular bypasses and their functioning as a mechanical system, as well the mathematical aspects of their possible setup.

Cerebral multi-autoregulation model based enhanced external counterpulsation treatment planning for cerebral ischemic stroke

Enhanced external counterpulsation (EECP) treatment for cerebral ischemic stroke patients with differing severity of stenosis, is subject to uncertainties due to the varying effects of the cerebral autoregulation mechanism on haemodynamics. The current study reports the development of a cerebral multi-autoregulation (MR) mathematical model, based on cerebral arteriole regulation of neurogenic, vascular smooth muscle reflex and shear stress mechanisms which takes into account the severity of stenosis. The model was evaluated by comparison to authentic clinical measurements of cerebral autoregulatory efficiency. Then it was applied to a 0D/3D geometric multi-scale haemodynamic model of a cerebral artery. Haemodynamic indicators were calculated under different pressurization durations of EECP to evaluate the efficacy for different stenosis lesions. Moderate stenosis of 50% to 60% produced excessive time-averaged wall shear stress in the distal area of the stenosis (>7 Pa) during prolonged pressurization and may result in damage to vascular endothelial cells. However, prolonged pressurization did not result in haemodynamic risk for severe stenosis of 70% to 80%, indicating that the duration of pressurization may be extended with increasing severity of stenosis. The current MR model accurately simulated cerebral blood flow and has relevance to the simulation of cerebral haemodynamics in a clinical setting.

Cerebral blood flow predicts multiple demand network activity and fluid intelligence across the adult lifespan

The preservation of cognitive function in old age is a public health priority. Cerebral hypoperfusion is a hallmark of dementia but its impact on maintaining cognitive ability across the lifespan is less clear. We investigated the relationship between baseline cerebral blood flow (CBF) and blood oxygenation level-dependent (BOLD) response during a fluid reasoning task in a population-based adult lifespan cohort. As age differences in CBF could lead to non-neuronal contributions to the BOLD signal, we introduced commonality analysis to neuroimaging to dissociate performance-related CBF effects from the physiological confounding effects of CBF on the BOLD response. Accounting for CBF, we confirmed that performance- and age-related differences in BOLD responses in the multiple-demand network were implicated in fluid reasoning. Age differences in CBF explained not only performance-related BOLD responses but also performance-independent BOLD responses. Our results suggest that CBF is important for maintaining cognitive function, while its non-neuronal contributions to BOLD signals reflect an age-related confound. Maintaining perfusion into old age may serve to support brain function and preserve cognitive performance.

Multiple blood flow surges during intermittent pneumatic compression: The origins and their implications

Intermittent pneumatic compression (IPC) therapy has been used to enhance peripheral blood flow for prevention and rehabilitation of ischemic-related vascular diseases. A novel phenomenon has been reported that multiple blood flow surges appeared in the skin blood flow signal during each compression, but its mechanism has not been fully revealed. This study aimed to gain insights into the origins of these blood flow surges through experiment and biomechanical modeling methods. Foot skin blood flow (SBF) signals of 13 healthy adults (23.8 ± 0.5 yr old, 7 males) and air cuff pressure signals were recorded during IPC. Lumped parameter modeling and wavelet analysis were adopted to investigate the multiple blood flow surges (named as Peak₁, Peak₂ and Peak₃). The results of the simulated Peak₁ and Peak₂ were in good agreements with the experiment results, suggesting that IPC could enhance foot SBF not only by deflation, but also by inflation. Statistical analysis demonstrated that high frequency compression with more frequent occurrence of Peak₁ and Peak₂ lead to significantly higher (Friedman test, p < 0.001) time-averaged SBF enhancement than the traditional mode. In addition, wavelet analysis showed that the major frequency component of the Peak₃ (0.059 Hz) was within the range of the vascular myogenic activity, suggesting a vascular regulation process triggered by intravascular pressure changes. Our study provide new insights into the mechanism of how IPC enhance foot SBF.

Changes in neurovascular coupling with cerebral perfusion pressure indicate a link to cerebral autoregulation

Cerebral autoregulation ensures a stable average blood supply to brain tissue across steady state cerebral perfusion pressure (CPP) levels. Neurovascular coupling, in turn, relies on sufficient blood flow to meet neuronal demands during activation. These mechanisms break down in pathologies where extreme levels of CPP can cause dysregulation in cerebral blood flow. Here, we experimentally tested the influence of changes in CPP on neurovascular coupling in a hydrocephalus-type non-human primate model (n = 3). We recorded local neural and vascular evoked responses to a checkerboard visual stimulus, non-invasively, using electroencephalography and near-infrared spectroscopy respectively. The evoked signals showed changes in various waveform features in the visual evoked potentials and the hemodynamic responses, with CPP. We further used these signals to fit for a hemodynamic response function (HRF) to describe neurovascular coupling. We estimated n = 26 distinct HRFs at a subset of CPP values ranging from 40-120 mmHg across all subjects. The HRFs, when compared to a subject dependent healthy baseline (CPP 70-90 mmHg) HRF, showed significant changes in shape with increasing CPP (ρ_CPP = -0.55, p-value_CPP = 0.0049). Our study provides preliminary experimental evidence on the relationship between neurovascular coupling and CPP changes, especially when beyond the limits of static autoregulation.

Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory

A mathematical model of cerebral blood flow in the form of a dynamical system is studied. The cerebral blood flow autoregulation modeling problem is treated as a nonlinear control problem and the potential and applicability of the nonlinear control theory techniques are analyzed in this respect. It is shown that the cerebral hemodynamics model in question is differentially flat. Then, the integrator backstepping approach combined with barrier Lyapunov functions is applied to construct the control laws that recover the cerebral autoregulation performance of a healthy human. Simulation results confirm the good performance and flexibility of the suggested cerebral blood flow autoregulation design. The conducted research should enrich our understanding of the mathematics behind the cerebral blood flow autoregulation mechanisms and medical treatments to compensate for impaired cerebral autoregulation, e.g., in preterm infants.

Variations of human cerebral and ocular blood flow during exposure to multi-axial accelerations : A mathematical modeling study

Human hemodynamic responses during exposure to multi-axial acceleration was a relatively new topic in the fields of acceleration physiology. This study aimed to focus on these responses, especially variations of blood perfusion to brain and eyes, through mathematical modeling. A mathematical model was established using lumped parameter methods, containing compartments of four heart chambers, systemic arteries and veins, circulation of typical systemic organs, and some compartments for pulmonary circulation, together with autonomic regulation considered. This model was firstly validated by using experimental data from experiment of posture change and centrifuge tests of +Gz accelerations, and then applied to analyze human hemodynamic responses to typical multi-axial accelerations. Validation results demonstrated the mathematical model could generate reasonable responses of human cardiovascular system during posture change and exposure to +Gz accelerations. Simulation results of hemodynamic responses to multi-axial accelerations depicted Gy induced significant differences of blood flow to the left and right eyes. And some contour maps were generated based on these results, which provided a quick way to estimate blood flow variations in brain and eyes during exposure to different accelerations. Graphical Abstract This study aimed to focus on variations of blood perfusion to brain and eyes during exposure to typical multi-axial accelerations through mathematical modeling. This model was firstly validated by using experimental data from experiment of posture change and centrifuge tests of +Gz accelerations, and then applied to analyze human hemodynamic responses to typical multi-axial accelerations. Simulation results of hemodynamic responses to multi-axial accelerations depicted Gy induced significant differences of blood flow to the left and right eyes. And contour maps that generated based on these results provided a quick way to estimate blood flow variations in brain and eyes during exposure to different accelerations.

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

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

Superior fitting of arterial resistance and compliance parameters with genetic algorithms in models of dynamic cerebral autoregulation

OBJECTIVE

The capacity of discriminating between normal and impaired dynamic cerebral autoregulation (dCA), based on spontaneous fluctuations in arterial blood pressure (ABP) and cerebral blood flow (CBF), has considerable clinical relevance. This study aimed to quantify the separate contributions of vascular resistance and compliance as parameters that could reflect myogenic and metabolic mechanisms to dCA.

METHODS

Forty-five subjects were studied under normo and hypercapnic conditions induced by breathing a mixture of 5% carbon dioxide in air. Dynamic cerebrovascular resistance and compliance models with ABP as input and CBFV as output were fitted using Genetic Algorithms to identify parameter values for each subject, and respiratory condition.

RESULTS

The efficiency of dCA was assessed from the models generated CBFV response to an ABP step change, corresponding to an autoregulation index of 5.561.57 in normocapnia and 2.381.73 in hypercapnia, with an area under the ROC curve (AUC) of 0.9 between both conditions. Vascular compliance increased from 0.750.7 ml/mmHg in normocapnia to 5.8212.0 ml/mmHg during hypercapnia, with an AUC of 0.88.

CONCLUSION

we demonstrated that Genetic Algorithms are a powerful tool to provide accurate identification of model parameters expressing the performance of human CA Significance: Further work is needed to validate this approach in clinical applications where individualised model parameters could provide relevant diagnostic and prognostic information about dCA impairment Index Terms arterial compliance, autoregulation impairment, cerebral blood flow, Genetic Algorithms, hypercapnia.

Neurovascular-modulation: A review of primary vascular responses to transcranial electrical stimulation as a mechanism of action

BACKGROUND

The ubiquitous vascular response to transcranial electrical stimulation (tES) has been attributed to the secondary effect of neuronal activity forming the classic neurovascular coupling. However, the current density delivered transcranially concentrates in: A) the cerebrospinal fluid of subarachnoid space where cerebral vasculature resides after reaching the dural and pial surfaces and B) across the blood-brain-barrier after reaching the brain parenchyma. Therefore, it is anticipated that tES has a primary vascular influence.

OBJECTIVES

Focused review of studies that demonstrated the direct vascular response to electrical stimulation and studies demonstrating evidence for tES-induced vascular effect in coupled neurovascular systems.

RESULTS

tES induces both primary and secondary vascular phenomena originating from four cellular elements; the first two mediating a primary vascular phenomenon mainly in the form of an immediate vasodilatory response and the latter two leading to secondary vascular effects and as parts of classic neurovascular coupling: 1) The perivascular nerves of more superficially located dural and pial arteries and medium-sized arterioles with multilayered smooth muscle cells; and 2) The endothelial lining of all vessels including microvasculature of blood-brain barrier; 3) Astrocytes; and 4) Neurons of neurovascular units.

CONCLUSION

A primary vascular effect of tES is highly suggested based on various preclinical and clinical studies. We explain how the nature of vascular response can depend on vessel anatomy (size) and physiology and be controlled by stimulation waveform. Further studies are warranted to investigate the mechanisms underlying the vascular response and its contribution to neural activity in both healthy brain and pathological conditions - recognizing many brain diseases are associated with alteration of cerebral hemodynamics and decoupling of neurovascular units.

Vascular and haemodynamic issues of brain ageing

The population is ageing worldwide, thus increasing the burden of common age-related disorders to the individual, society and economy. Cerebrovascular diseases (stroke, dementia) contribute a significant proportion of this burden and are associated with high morbidity and mortality. Thus, understanding and promoting healthy vascular brain ageing are becoming an increasing priority for healthcare systems. In this review, we consider the effects of normal ageing on two major physiological processes responsible for vascular brain function: Cerebral autoregulation (CA) and neurovascular coupling (NVC). CA is the process by which the brain regulates cerebral blood flow (CBF) and protects against falls and surges in cerebral perfusion pressure, which risk hypoxic brain injury and pressure damage, respectively. In contrast, NVC is the process by which CBF is matched to cerebral metabolic activity, ensuring adequate local oxygenation and nutrient delivery for increased neuronal activity. Healthy ageing is associated with a number of key physiological adaptations in these processes to mitigate age-related functional and structural declines. Through multiple different paradigms assessing CA in healthy younger and older humans, generating conflicting findings, carbon dioxide studies in CA have provided the greatest understanding of intrinsic vascular anatomical factors that may mediate healthy ageing responses. In NVC, studies have found mixed results, with reduced, equivalent and increased activation of vascular responses to cognitive stimulation. In summary, vascular and haemodynamic changes occur in response to ageing and are important in distinguishing “normal” ageing from disease states and may help to develop effective therapeutic strategies to promote healthy brain ageing.

A patient-specific modelling method of blood circulatory system for the numerical simulation of enhanced external counterpulsation

Lumped parameter model (LPM) is a common numerical model for hemodynamic simulation of human's blood circulatory system. The numerical simulation of enhanced external counterpulsation (EECP) is a typical biomechanical simulation process based on the LPM of blood circulatory system. In order to simulate patient-specific hemodynamic effects of EECP and develop best treatment strategy for each individual, this study developed an optimization algorithm to individualize LPM elements. Physiological data from 30 volunteers including approximate aortic pressure, cardiac output, ankle pressure and carotid artery flow were clinically collected as optimization objectives. A closed-loop LPM was established for the simulation of blood circulatory system. Aiming at clinical data, a sensitivity analysis for each element was conducted to identify the significant ones. We improved the traditional simulated annealing algorithm to iteratively optimize the sensitive elements. To verify the accuracy of the patient-specific model, 30 samples of simulated data were compared with clinical measurements. In addition, an EECP experiment was conducted on a volunteer to verify the applicability of the optimized model for the simulation of EECP. For these 30 samples, the optimization results show a slight difference between clinical data and simulated data. The average relative root mean square error is lower than 5%. For the subject of EECP experiment, the relative error of hemodynamic responses during EECP is lower than 10%. This slight error demonstrated a good state of optimization. The optimized modeling algorithm can effectively individualize the LPM for blood circulatory system, which is significant to the numerical simulation of patient-specific hemodynamics.

Cerebrovascular Dynamics During Continuous Motor Task

We investigated the cerebral autoregulation (CA) dynamics parameter phase and gain change when exposed to a longlasting motor task. 25 healthy subjects (mean age ± SE, 38±2.6 years, 13 females) underwent simultaneous recordings of spontaneous fluctuations in blood pressure (BP), cerebral blood flow velocity (CBFV), and end-tidal CO(2) (ETCO(2)) over 5 min of rest followed by 5 min of left elbow flexion at a frequency of 1 Hz. Tansfer function gain and phase between BP and CBFV were assessed in the frequency ranges of very low frequencies (VLF, 0.02-0.07 Hz), low frequencies (LF, 0.07-0.15), and high frequencies (HF, >0.15). CBFV increased on both sides rapidly to maintain an elevated steady state until movement stopped. Cerebrovascular resistance fell on the right side (rest 1.35±0.06, movement 1.28±0.06, p<0.01), LF gain decreased from baseline (right side 0.97±0.07 %/mm Hg, left 1.01±0.09) to movement epoch (right 0.73±0.08, left 0.76±0.06, p</=0.01). VLF phase decreased from baseline (right 1.03±0.05 radians, left 1.10±0.06) to the movement epoch (right 0.81±0.07, left 0.82±0.10, p?0.05). CA regulates continuous motor efforts by changes in resistance, gain and phase.

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.

High salt diet impairs cerebral blood flow regulation via salt-induced angiotensin II suppression

OBJECTIVES

This study sought to determine whether salt-induced ANG II suppression contributes to impaired CBF autoregulation.

METHODS

Cerebral autoregulation was evaluated with LDF during graded reductions of blood pressure. Autoregulatory responses in rats fed HS (4% NaCl) diet vs LS (0.4% NaCl) diet were analyzed using linear regression analysis, model-free analysis, and a mechanistic theoretical model of blood flow through cerebral arterioles.

RESULTS

Autoregulation was intact in LS-fed animals as MAP was reduced via graded hemorrhage to approximately 50 mm Hg. Short-term (3 days) and chronic (4 weeks) HS diet impaired CBF autoregulation, as evidenced by progressive reductions of laser Doppler flux with arterial pressure reduction. Chronic low dose ANG II infusion (5 mg/kg/min, i.v.) restored CBF autoregulation between the pre-hemorrhage MAP and 50 mm Hg in rats fed short-term HS diet. Mechanistic-based model analysis showed a reduced myogenic response and reduced baseline VSM tone with short-term HS diet, which was restored by ANG II infusion.

CONCLUSIONS

Short-term and chronic HS diet lead to impaired autoregulation in the cerebral circulation, with salt-induced ANG II suppression as a major factor in the initiation of impaired CBF regulation.

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.

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.

A physiological model for interpretation of arterial spin labeling reactive hyperemia of calf muscles

To characterize and interpret arterial spin labeling (ASL) reactive hyperemia of calf muscles for a better understanding of the microcirculation in peripheral arterial disease (PAD), we present a physiological model incorporating oxygen transport, tissue metabolism, and vascular regulation mechanisms. The model demonstrated distinct effects between arterial stenoses and microvascular dysfunction on reactive hyperemia, and indicated a higher sensitivity of 2-minute thigh cuffing to microvascular dysfunction than 5-minute cuffing. The recorded perfusion responses in PAD patients (n = 9) were better differentiated from the normal subjects (n = 7) using the model-based analysis rather than characterization using the apparent peak and time-to-peak of the responses. The analysis results suggested different amounts of microvascular disease within the patient group. Overall, this work demonstrates a novel analysis method and facilitates understanding of the physiology involved in ASL reactive hyperemia. ASL reactive hyperemia with model-based analysis may be used as a noninvasive microvascular assessment in the presence of arterial stenoses, allowing us to look beyond the macrovascular disease in PAD. A subgroup who will have a poor prognosis after revascularization in the patients with critical limb ischemia may be associated with more severe microvascular diseases, which may potentially be identified using ASL reactive hyperemia.

A 1D pulse wave propagation model of the hemodynamics of calf muscle pump function

The calf muscle pump is a mechanism which increases venous return and thereby compensates for the fluid shift towards the lower body during standing. During a muscle contraction, the embedded deep veins collapse and venous return increases. In the subsequent relaxation phase, muscle perfusion increases due to increased perfusion pressure, as the proximal venous valves temporarily reduce the distal venous pressure (shielding). The superficial and deep veins are connected via perforators, which contain valves allowing flow in the superficial-to-deep direction. The aim of this study is to investigate and quantify the physiological mechanisms of the calf muscle pump, including the effect of venous valves, hydrostatic pressure, and the superficial venous system. Using a one-dimensional pulse wave propagation model, a muscle contraction is simulated by increasing the extravascular pressure in the deep venous segments. The hemodynamics are studied in three different configurations: a single artery-vein configuration with and without valves and a more detailed configuration including a superficial vein. Proximal venous valves increase effective venous return by 53% by preventing reflux. Furthermore, the proximal valves shielding function increases perfusion following contraction. Finally, the superficial system aids in maintaining the perfusion during the contraction phase and reduces the refilling time by 37%.

A stochastic delay differential model of cerebral autoregulation

Mathematical models of the cardiovascular system and of cerebral autoregulation (CAR) have been employed for several years in order to describe the time course of pressures and flows changes subsequent to postural changes. The assessment of the degree of efficiency of cerebral auto regulation has indeed importance in the prognosis of such conditions as cerebro-vascular accidents or Alzheimer. In the quest for a simple but realistic mathematical description of cardiovascular control, which may be fitted onto non-invasive experimental observations after postural changes, the present work proposes a first version of an empirical Stochastic Delay Differential Equations (SDDEs) model. The model consists of a total of four SDDEs and two ancillary algebraic equations, incorporates four distinct delayed controls from the brain onto different components of the circulation, and is able to accurately capture the time course of mean arterial pressure and cerebral blood flow velocity signals, reproducing observed auto-correlated error around the expected drift.

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.

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.

Mathematical modelling of cerebral blood circulation and cerebral autoregulation: towards preventing intracranial hemorrhages in preterm newborns

Impaired cerebral autoregulation leads to fluctuations in cerebral blood flow, which can be especially dangerous for immature brain of preterm newborns. In this paper, two mathematical models of cerebral autoregulation are discussed. The first one is an enhancement of a vascular model proposed by Piechnik et al. We extend this model by adding a polynomial dependence of the vascular radius on the arterial blood pressure and adjusting the polynomial coefficients to experimental data to gain the autoregulation behavior. Moreover, the inclusion of a Preisach hysteresis operator, simulating a hysteretic dependence of the cerebral blood flow on the arterial pressure, is tested. The second model couples the blood vessel system model by Piechnik et al. with an ordinary differential equation model of cerebral autoregulation by Ursino and Lodi. An optimal control setting is proposed for a simplified variant of this coupled model. The objective of the control is the maintenance of the autoregulatory function for a wider range of the arterial pressure. The control can be interpreted as the effect of a medicament changing the cerebral blood flow by, for example, dilation of blood vessels. Advanced numerical methods developed by the authors are applied for the numerical treatment of the control problem.

Influence of CO2 on neurovascular coupling: interaction with dynamic cerebral autoregulation and cerebrovascular reactivity

PaCO₂ affects cerebral blood flow (CBF) and its regulatory mechanisms, but the interaction between neurovascular coupling (NVC), cerebral autoregulation (CA), and cerebrovascular reactivity to CO₂ (CVR), in response to hypercapnia, is not known. Recordings of cerebral blood flow velocity (CBFv), blood pressure (BP), heart rate, and end‐tidal CO₂ (EtCO₂) were performed in 18 subjects during normocapnia and 5% CO₂ inhalation while performing a passive motor paradigm. Together with BP and EtCO₂, a gate signal to represent the effect of stimulation was used as input to a multivariate autoregressive‐moving average model to calculate their separate effects on CBFv. Hypercapnia led to a depression of dynamic CA at rest and during stimulation in both hemispheres (P <0.02) as well as impairment of the NVC response, particularly in the ipsilateral hemisphere (P <0.01). Neither hypercapnia nor the passive motor stimulation influenced CVR. Dynamic CA was not influenced by the motor paradigm during normocapnia. The CBFv step responses to each individual input (BP, EtCO₂, stimulation) allowed identification of the influences of hypercapnia and neuromotor stimulation on CA, CVR, and NVC, which have not been previously described, and also confirmed the depressing effects of hypercapnia on CA and NVC. The stability of CVR during these maneuvers and the lack of influence of stimulation on dynamic CA are novel findings which deserve further investigation. Dynamic multivariate modeling can identify the complex interplay between different CBF regulatory mechanisms and should be recommended for studies involving similar interactions, such as the effects of exercise or posture on cerebral hemodynamics.

The influence of hypercapnia on dynamic cerebral autoregulation (CA), CO₂ vasoreactivity (CVR), and neurovascular coupling (NVC) was described based on a single recording during motor stimulation coupled to a new multivariate modeling approach. Hypercapnia led to a depression of CA at rest and during stimulation in both hemispheres as well as impairment of the NVC response. Neither hypercapnia nor the passive motor stimulation influenced CVR. Dynamic CA was not influenced by the motor paradigm during normocapnia. The stability of CVR during these maneuvers and the lack of influence of stimulation on dynamic CA are novel findings which deserve further investigation.

Visually evoked blood flow responses and interaction with dynamic cerebral autoregulation: correction for blood pressure variation

Visually evoked flow responses recorded using transcranial Doppler ultrasonography are often quantified using a dynamic model of neurovascular coupling. The evoked flow response is seen as the model's response to a visual step input stimulus. However, the continuously active process of dynamic cerebral autoregulation (dCA) compensating cerebral blood flow for blood pressure fluctuations may induce changes of cerebral blood flow velocity (CBFV) as well. The effect of blood pressure variability on the flow response is evaluated by separately modeling the dCA-induced effects of beat-to-beat measured blood pressure related CBFV changes. Parameters of 71 subjects are estimated using an existing, well-known second order dynamic neurovascular coupling model proposed by Rosengarten et al., and a new model extending the existing model with a CBFV contributing component as the output of a dCA model driven by blood pressure as input. Both models were evaluated for mean and systolic CBFV responses. The model-to-data fit errors of mean and systolic blood pressure for the new model were significantly lower compared to the existing model: mean: 0.8%±0.6 vs. 2.4%±2.8, p<0.001; systolic: 1.5%±1.2 vs. 2.2%±2.6, p<0.001. The confidence bounds of all estimated neurovascular coupling model parameters were significantly (p<0.005) narrowed for the new model. In conclusion, blood pressure correction of visual evoked flow responses by including cerebral autoregulation in model fitting of averaged responses results in significantly lower fit errors and by that in more reliable model parameter estimation. Blood pressure correction is more effective when mean instead of systolic CBFV responses are used. Measurement and quantification of neurovascular coupling should include beat-to-beat blood pressure measurement.

Blood pressure regulation IX: cerebral autoregulation under blood pressure challenges

Cerebral autoregulation (CA) is integral to the delicate process of maintaining stable cerebral perfusion and brain tissue oxygenation against changes in arterial blood pressure. The last four decades has seen dramatic advances in understanding CA physiology, and the role that CA might play in the causation and progression of disease processes that affect the cerebral circulation such as stroke. However, the translation of these basic scientific advances into clinical practice has been limited by the maintenance of old constructs and because there are persistent gaps in our understanding of how this vital vascular mechanism should be quantified. In this review, we re-evaluate relevant studies that challenge established paradigms about how the cerebral perfusion pressure and blood flow are related. In the context of blood pressure being a major haemodynamic challenge to the cerebral circulation, we conclude that: (1) the physiological properties of CA remain inconclusive, (2) many extant methods for CA characterisation are based on simplistic assumptions that can give rise to misleading interpretations, and (3) robust evaluation of CA requires thorough consideration not only of active vasomotor function, but also the unique properties of the intracranial environment.

Blood pressure regulation IX: cerebral autoregulation under blood pressure challenges

Cerebral autoregulation (CA) is integral to the delicate process of maintaining stable cerebral perfusion and brain tissue oxygenation against changes in arterial blood pressure. The last four decades has seen dramatic advances in understanding CA physiology, and the role that CA might play in the causation and progression of disease processes that affect the cerebral circulation such as stroke. However, the translation of these basic scientific advances into clinical practice has been limited by the maintenance of old constructs and because there are persistent gaps in our understanding of how this vital vascular mechanism should be quantified. In this review, we re-evaluate relevant studies that challenge established paradigms about how the cerebral perfusion pressure and blood flow are related. In the context of blood pressure being a major haemodynamic challenge to the cerebral circulation, we conclude that: (1) the physiological properties of CA remain inconclusive, (2) many extant methods for CA characterisation are based on simplistic assumptions that can give rise to misleading interpretations, and (3) robust evaluation of CA requires thorough consideration not only of active vasomotor function, but also the unique properties of the intracranial environment.