Modelling midline shift and ventricle collapse in cerebral oedema following acute ischaemic stroke.

In ischaemic stroke, a large reduction in blood supply can lead to the breakdown of the blood-brain barrier and to cerebral oedema after reperfusion therapy. The resulting fluid accumulation in the brain may contribute to a significant rise in intracranial pressure (ICP) and tissue deformation. Changes in the level of ICP are essential for clinical decision-making and therapeutic strategies. However, the measurement of ICP is constrained by clinical techniques and obtaining the exact values of the ICP has proven challenging. In this study, we propose the first computational model for the simulation of cerebral oedema following acute ischaemic stroke for the investigation of ICP and midline shift (MLS) relationship. The model consists of three components for the simulation of healthy blood flow, occluded blood flow and oedema, respectively. The healthy and occluded blood flow components are utilized to obtain oedema core geometry and then imported into the oedema model for the simulation of oedema growth. The simulation results of the model are compared with clinical data from 97 traumatic brain injury patients for the validation of major model parameters. Midline shift has been widely used for the diagnosis, clinical decision-making, and prognosis of oedema patients. Therefore, we focus on quantifying the relationship between ICP and midline shift (MLS) and identify the factors that can affect the ICP-MLS relationship. Three major factors are investigated, including the brain geometry, blood-brain barrier damage severity and the types of oedema (including rare types of oedema). Meanwhile, the two major types (stress and tension/compression) of mechanical brain damage are also presented and the differences in the stress, tension, and compression between the intraparenchymal and periventricular regions are discussed. This work helps to predict ICP precisely and therefore provides improved clinical guidance for the treatment of brain oedema.

Modelling Drug Delivery to the Small Airways: Optimization Using Response Surface Methodology.

AIM: The aim of this in silico study was to investigate the effect of particle size, flow rate, and tidal volume on drug targeting to small airways in patients with mild COPD. METHOD: Design of Experiments (DoE) was used with an in silico whole lung particle deposition model for bolus administration to investigate whether controlling inhalation can improve drug delivery to the small conducting airways. The range of particle aerodynamic diameters studied was 0.4 - 10 µm for flow rates between 100 - 2000 mL/s (i.e., low to very high), and tidal volumes between 40 - 1500 mL. RESULTS: The model accurately predicted the relationship between independent variables and lung deposition, as confirmed by comparison with published experimental data. It was found that large particles (~ 5 µm) require very low flow rate (~ 100 mL/s) and very small tidal volume (~ 110 mL) to target small conducting airways, whereas fine particles (~ 2 µm) achieve drug targeting in the region at a relatively higher flow rate (~ 500 mL/s) and similar tidal volume (~ 110 mL). CONCLUSION: The simulation results indicated that controlling tidal volume and flow rate can achieve targeted delivery to the small airways (i.e., > 50% of emitted dose was predicted to deposit in the small airways), and the optimal parameters depend on the particle size. It is hoped that this finding could provide a means of improving drug targeting to the small conducting airways and improve prognosis in COPD management.

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.

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.

Poroelastic modelling of brain tissue swelling and decompressive craniectomy treatment in ischaemic stroke.

Brain oedema or tissue swelling that develops after ischaemic stroke can cause detrimental effects, including brain herniation and increased intracranial pressure (ICP). These effects can be reduced by performing a decompressive craniectomy (DC) operation, in which a portion of the skull is removed to allow swollen brain tissue to expand outside the skull. In this study, a poroelastic model is used to investigate the effect of brain ischaemic infarct size and location on the severity of brain tissue swelling. Furthermore, the model will also be used to evaluate the effectiveness of DC surgery as a treatment for brain tissue swelling after ischaemia. The poroelastic model consists of two equations: one describing the elasticity of the brain tissue and the other describing the changes in the interstitial tissue pressure. The model is applied on an idealized brain geometry, and it is found that infarcts with radius larger than approximately 14 mm and located near the lateral ventricle produce worse brain midline shift, measured through lateral ventricle compression. Furthermore, the model is also able to show the positive effect of DC treatment in reducing the brain midline shift by allowing part of the brain tissue to expand through the skull opening. However, the model does not show a decrease in the interstitial pressure during DC treatment. Further improvement and validation could enhance the capability of the proposed poroelastic model in predicting the occurrence of brain tissue swelling and DC treatment post ischaemia.

Quantifying heterogeneity in an animal model of acute respiratory distress syndrome, a comparison of inspired sinewave technique to computed tomography.

The inspired sinewave technique (IST) is a non-invasive method to measure lung heterogeneity indices (including both uneven ventilation and perfusion or heterogeneity), which reveal multiple conditions of the lung and lung injury. To evaluate the reproducibility and predicted clinical outcomes of IST heterogeneity values, a comparison with a quantitative lung computed tomography (CT) scan is performed. Six anaesthetised pigs were studied after surfactant depletion by saline-lavage. Paired measurements of lung heterogeneity were then taken with both the IST and CT. Lung heterogeneity measured by the IST was calculated by (a) the ratio of tracer gas outputs measured at oscillation periods of 180 s and 60 s, and (b) by the standard deviation of the modelled log-normal distribution of ventilations and perfusions in the simulation lung. In the CT images, lungs were manually segmented and divided into different regions according to voxel density. A quantitative CT method to calculate the heterogeneity (the Cressoni method) was applied. The IST and CT show good Pearson correlation coefficients in lung heterogeneity measurements (ventilation: 0.71, and perfusion, 0.60, p < 0.001). Within individual animals, the coefficients of determination average ventilation (R2 = 0.53) and perfusion (R2 = 0.68) heterogeneity. Strong concordance rates of 98% in ventilation and 89% when the heterogeneity changes were reported in pairs measured by CT scanning and IST methods. This quantitative method to identify heterogeneity has the potential to replicate CT lung heterogeneity, and to aid individualised care in ARDS.

Static autoregulation in humans.

The process by which cerebral blood flow (CBF) remains approximately constant in response to short-term variations in arterial blood pressure (ABP) is known as cerebral autoregulation. This classic view, that it remains constant over a wide range of ABP, has however been challenged by a growing number of studies. To provide an updated understanding of the static cerebral pressure-flow relationship and to characterise the autoregulation curve more rigorously, we conducted a comprehensive literature research. Results were based on 143 studies in healthy individuals aged 18 to 65 years. The mean sensitivities of CBF to changes in ABP were found to be 1.47 ± 0.71%/% for decreased ABP and 0.37 ± 0.38%/% for increased ABP. The significant difference in CBF directional sensitivity suggests that cerebral autoregulation appears to be more effective in buffering increases in ABP than decreases in ABP. Regression analysis of absolute CBF and ABP identified an autoregulatory plateau of approximately 20 mmHg (ABP between 80 and 100 mmHg), which is much smaller than the widely accepted classical view. Age and sex were found to have no effect on autoregulation strength. This data-driven approach provides a quantitative method of analysing static autoregulation that can be easily updated as more experimental data become available.

Applying systems thinking to unravel the mechanisms underlying orthostatic hypotension related fall risk.

Orthostatic hypotension (OH) is an established and common cardiovascular risk factor for falls. An in-depth understanding of the various interacting pathophysiological pathways contributing to OH-related falls is essential to guide improvements in diagnostic and treatment opportunities. We applied systems thinking to multidisciplinary map out causal mechanisms and risk factors. For this, we used group model building (GMB) to develop a causal loop diagram (CLD). The GMB was based on the input of experts from multiple domains related to OH and falls and all proposed mechanisms were supported by scientific literature. Our CLD is a conceptual representation of factors involved in OH-related falls, and their interrelatedness. Network analysis and feedback loops were applied to analyze and interpret the CLD, and quantitatively summarize the function and relative importance of the variables. Our CLD contains 50 variables distributed over three intrinsic domains (cerebral, cardiovascular, and musculoskeletal), and an extrinsic domain (e.g., medications). Between the variables, 181 connections and 65 feedback loops were identified. Decreased cerebral blood flow, low blood pressure, impaired baroreflex activity, and physical inactivity were identified as key factors involved in OH-related falls, based on their high centralities. Our CLD reflects the multifactorial pathophysiology of OH-related falls. It enables us to identify key elements, suggesting their potential for new diagnostic and treatment approaches in fall prevention. The interactive online CLD renders it suitable for both research and educational purposes and this CLD is the first step in the development of a computational model for simulating the effects of risk factors on falls.

Investigating spatial variations in dynamic cerebral autoregulation through a computational model of stenosis.

Objective. Dynamic cerebral autoregulation (dCA) is a well-established mechanism that acts to maintain cerebral blood flow (CBF) reasonably constant in response to short-term fluctuations in blood pressure. It is known to be impaired in many clinical conditions, including stenosis, which is also a major risk factor for ischaemic stroke. However, it is not yet well understood whether impairment in dCA in one brain region is independent or not on dCA impairment in other brain regions, for example, whether there are spatial effects of stenosis on dCA. This is due to the complex blood flow environment and the lack of physiological experiments.Approach. We thus establish and apply a novel computational stenosis model including the circle of Willis to investigate and to quantify the degree of dCA impairment and CBF patterns as a function of stenosis fraction, measured in different configurations of the cerebral vasculature.Main results. We find some evidence for dependence between dCA in different brain regions, although this is very preliminary and much more experimental data will be required to answer this question fully.Significance.Our study has provided a first attempt to consider the effect of stenosis in various arteries on cerebral autoregulation to investigate spatial variations in dCA. This has potential applications in the treatment of cerebrovascular diseases where the control of cerebral perfusion is critical but where measurements are scarce.

Regional Cerebral Blood Flow Changes in Healthy Ageing and Alzheimer's Disease: A Narrative Review.

BACKGROUND: Cerebral blood flow is known to decline with increasing age and is a potential biomarker to distinguish between healthy and unhealthy ageing, where healthy ageing is defined as an absence of comorbidities in senescence. This review aims to synthesize evidence of cerebral blood flow changes over multiple brain regions, for use as a clinical reference or for in silico modelling. SUMMARY: The search identified 1,087 studies, of which 33 met the inclusion criteria to map the difference in cerebral blood flow reduction between healthy ageing and Alzheimer's disease. Analysis was also performed on the effect of imaging modality and brain region functionality as potential confounding factors. KEY MESSAGES: No significant difference was found between the specific functionality of a brain region and cerebral blood flow in healthy ageing (p = 0.65) or Alzheimer's disease (p = 0.42). Arterial spin labelling MRI imaging was shown to measure statistically larger decreases in flow in both healthy ageing (p = 0.0001) and Alzheimer's disease (p = 0.0465). Cerebral blood flow was shown to decrease 0.3-0.5% per year in healthy ageing, which increased to a decline of 2-5% per year in Alzheimer's disease. There was large variability both between and within individual brain regions, and this variability increased greatly in Alzheimer's disease. Future studies would add value by taking more cerebral blood flow measurements during Alzheimer's disease progression and by investigating ageing with comorbidities such as hypertension.

Transfer function analysis of dynamic cerebral autoregulation: A CARNet white paper 2022 update.

Cerebral autoregulation (CA) refers to the control of cerebral tissue blood flow (CBF) in response to changes in perfusion pressure. Due to the challenges of measuring intracranial pressure, CA is often described as the relationship between mean arterial pressure (MAP) and CBF. Dynamic CA (dCA) can be assessed using multiple techniques, with transfer function analysis (TFA) being the most common. A 2016 white paper by members of an international Cerebrovascular Research Network (CARNet) that is focused on CA strove to improve TFA standardization by way of introducing data acquisition, analysis, and reporting guidelines. Since then, additional evidence has allowed for the improvement and refinement of the original recommendations, as well as for the inclusion of new guidelines to reflect recent advances in the field. This second edition of the white paper contains more robust, evidence-based recommendations, which have been expanded to address current streams of inquiry, including optimizing MAP variability, acquiring CBF estimates from alternative methods, estimating alternative dCA metrics, and incorporating dCA quantification into clinical trials. Implementation of these new and revised recommendations is important to improve the reliability and reproducibility of dCA studies, and to facilitate inter-institutional collaboration and the comparison of results between studies.

Computational modelling of cerebral oedema and osmotherapy following ischaemic stroke.

In ischaemic stroke, a large reduction in blood supply can lead to the breakdown of the blood brain barrier and to cerebral oedema after reperfusion therapy. Cerebral oedema is marked by elevated intracranial pressure (ICP), tissue herniation and reduced cerebral perfusion pressure. In clinical settings, osmotherapy has been a common practice to decrease ICP. However, there are no guidelines on the choice of administration protocol parameters such as injection doses, infusion time and retention time. Most importantly, the effects of osmotherapy have been proven controversial since the infusion of osmotic agents can lead to a range of side effects. Here, a new Finite Element model of brain oedema and osmotherapy is thus proposed to predict treatment outcome. The model consists of three components that simulate blood perfusion, oedema, and osmotherapy, respectively. In the perfusion model (comprising arteriolar, venous, and capillary blood compartments), an anatomically accurate brain geometry is used to identify regions with a perfusion reduction and potential oedema occurrence in stroke. The oedema model is then used to predict ICP using a porous circulation model with four fluid compartments (arteriolar blood, venular blood, capillary blood, and interstitial fluid). In the osmotherapy model, the osmotic pressure is varied and the changes in ICP during different osmotherapy episodes are quantified. The simulation results of the model show excellent agreement with available clinical data and the model is employed to study osmotherapy under various parameters. Consequently, it is demonstrated how therapeutic strategies can be proposed for patients with different pathological parameters based on simulations.

Modelling collateral flow and thrombus permeability during acute ischaemic stroke.

The presence of collaterals and high thrombus permeability are associated with good functional outcomes after an acute ischaemic stroke. We aim to understand the combined effect of the collaterals and thrombus permeability on cerebral blood flow during an acute ischaemic stroke. A cerebral blood flow model including the leptomeningeal collateral circulation is used to simulate cerebral blood flow during an acute ischaemic stroke. The collateral circulation is varied to capture the collateral scores: absent, poor, moderate and good. Measurements of the transit time, void fraction and thrombus length in acute ischaemic stroke patients are used to estimate thrombus permeability. Estimated thrombus permeability ranges between 10-7 and 10-4 mm2. Measured flow rates through the thrombus are small and the effect of a permeable thrombus on brain perfusion during stroke is small compared with the effect of collaterals. Our simulations suggest that the collaterals are a dominant factor in the resulting infarct volume after a stroke.

Point/counterpoint: We should not take the direction of blood pressure change into consideration for dynamic cerebral autoregulation quantification.

Over the past years, a wide range of studies have provided evidence of asymmetry in the response of static and dynamic cerebral autoregulation (CA) during increasing and decreasing pressure challenges. The main message is that CA is stronger during transient increases of arterial blood pressure rather than decreases. Here we do not argue against the presence of CA asymmetry but we seek to raise questions regarding the measurement of the effect and whether this effect needs to be taken into account, especially in clinical settings.

Quantification of hypoxic regions distant from occlusions in cerebral penetrating arteriole trees.

The microvasculature plays a key role in oxygen transport in the mammalian brain. Despite the close coupling between cerebral vascular geometry and local oxygen demand, recent experiments have reported that microvascular occlusions can lead to unexpected distant tissue hypoxia and infarction. To better understand the spatial correlation between the hypoxic regions and the occlusion sites, we used both in vivo experiments and in silico simulations to investigate the effects of occlusions in cerebral penetrating arteriole trees on tissue hypoxia. In a rat model of microembolisation, 25 µm microspheres were injected through the carotid artery to occlude penetrating arterioles. In representative models of human cortical columns, the penetrating arterioles were occluded by simulating the transport of microspheres of the same size and the oxygen transport was simulated using a Green's function method. The locations of microspheres and hypoxic regions were segmented, and two novel distance analyses were implemented to study their spatial correlation. The distant hypoxic regions were found to be present in both experiments and simulations, and mainly due to the hypoperfusion in the region downstream of the occlusion site. Furthermore, a reasonable agreement for the spatial correlation between hypoxic regions and occlusion sites is shown between experiments and simulations, which indicates the good applicability of in silico models in understanding the response of cerebral blood flow and oxygen transport to microemboli.

Mathematical modelling of haemorrhagic transformation within a multiscale microvasculature network.

Objective.Haemorrhagic transformation (HT) is one of the most common complications after ischaemic stroke, caused by damage to the blood-brain barrier (BBB) that could be the result of stroke progression or a complication of stroke treatment with reperfusion therapy. The aim of this study is to develop further a previous simple HT mathematical model into an enlarged multiscale microvasculature model in order to investigate the effects of HT on the surrounding tissue and vasculature. In addition, this study investigates the relationship between tissue displacement and vascular geometry.Approach.By modelling tissue displacement, capillary compression, hydraulic conductivity in tissue and vascular permeability, we establish a mathematical model to describe the change of intracranial pressure (ICP) surrounding the damaged vascular bed after HT onset, applied to a 3D multiscale microvasculature. The use of a voxel-scale model then enables us to compare our HT simulation with available clinical imaging data for perfusion and cerebral blood volume (CBV) in the multiscale microvasculature network.Main results. We showed that the haematoma diameter and the maximum tissue displacement are approximately proportional to the diameter of the breakdown vessel. Based on the voxel-scale model, we found that perfusion reduces by approximately13-17%andCBVreduces by around20-25%after HT onset due to the effect of capillary compression caused by increased interstitial pressure. The results are in good agreement with the limited experimental data.Significance. This model, by enabling us to bridge the gap between the microvascular scale and clinically measurable parameters, providing a foundation for more detailed validation and understanding of HT in patients.

Blood Pressure Complexity Discriminates Pathological Beat-to-Beat Variability as a Marker of Vascular Aging.

Background Beat-to-beat blood pressure variability (BPV) is associated with an increased risk of stroke but can be driven by both healthy physiological processes and failure of compensatory mechanisms. Blood pressure (BP) complexity measures structured, organized variations in BP, as opposed to random fluctuations, and its reduction may therefore identify pathological beat-to-beat BPV. Methods and Results In the prospective, population-based OXVASC (Oxford Vascular Study) Phenotyped Cohort with transient ischemic attack or minor stroke, patients underwent at least 5 minutes of noninvasive beat-to-beat monitoring of BP (Finometer) and ECG to derive the following: BPV (coefficient of variation) and complexity (modified multiscale entropy) of systolic BP and diastolic BP, heart rate variability (SD of R-R intervals), and baroreflex sensitivity (BRS; Welch's method), in low- (0.04-0.15 Hz) and high-frequency (0.15-0.4 Hz) bands. Associations between BPV or BP complexity with autonomic indexes and arterial stiffness were determined (linear regression), unadjusted, and adjusted for age, sex, and cardiovascular risk factors. In 908 consecutive, consenting patients, BP complexity was inversely correlated with BPV coefficient of variation (P<0.001) and was similarly reduced in patients with hypertension or diabetes (P<0.001). However, although BPV coefficient of variation had a U-shaped relationship with age, BP complexity fell systematically across age quintiles (quintile 1: 15.1 [14.0-16.1] versus quintile 5: 13.8 [12.4-15.1]) and was correlated with markers of autonomic dysfunction (heart rate variability SD of R-R intervals: r = 0.20; BRS low frequency: 0.19; BRS high frequency: 0.26) and arterial stiffness (pulse wave velocity: -0.21; all P<0.001), even after adjustment for clinical variables (heart rate variability SD of R-R intervals: 0.12; BRS low frequency and BRS high frequency: 0.13 and 0.17; and pulse wave velocity: -0.07; all P<0.05). Conclusions Loss of BP complexity discriminates BPV because of pathological failure of compensatory mechanisms and may represent a less confounded and potentially modifiable risk factor for stroke.

The INfoMATAS project: Methods for assessing cerebral autoregulation in stroke.

Cerebral autoregulation refers to the physiological mechanism that aims to maintain blood flow to the brain approximately constant when blood pressure changes. Impairment of this protective mechanism has been linked to a number of serious clinical conditions, including carotid stenosis, head trauma, subarachnoid haemorrhage and stroke. While the concept and experimental evidence is well established, methods for the assessment of autoregulation in individual patients remains an open challenge, with no gold-standard having emerged. In the current review paper, we will outline some of the basic concepts of autoregulation, as a foundation for experimental protocols and signal analysis methods used to extract indexes of cerebral autoregulation. Measurement methods for blood flow and pressure are discussed, followed by an outline of signal pre-processing steps. An outline of the data analysis methods is then provided, linking the different approaches through their underlying principles and rationale. The methods cover correlation based approaches (e.g. Mx) through Transfer Function Analysis to non-linear, multivariate and time-variant approaches. Challenges in choosing which method may be 'best' and some directions for ongoing and future research conclude this work.

Lung simulation to support non-invasive pulmonary blood flow measurement in Acute Respiratory Distress Syndrome in animals.

Patients undergoing mechanical lung ventilation are at risk of lung injury. A noninvasive bedside lung monitor may benefit these patients. The Inspired Sinewave Test (IST) can measure cardio-pulmonary parameters noninvasively. We propose a lung simulation to improve the measurement of pulmonary blood flow using IST. The new method was applied to 12 pigs' data before lung injury (control) and after lung injury (ARDS model). Results using the lung simulation shown improvements in correlation in both simulated data (R2 increased from 0.98 to 1) and pigs' data (R2 increased from <0.001 to 0.26). Paired blood flow measurements were performed by both the IST (noninvasive) and thermodilution (invasive). In the control group, the bias of the two methods was negligible (0.02L/min), and the limit of agreement was from -1.20 to 1.18 L/min. The bias was -0.68 L/min in the ARDS group and with a broader limit of agreement (-2.49 to 1.13 L/min).Clinical Relevance- the inspired sinewave test can be used to measure cardiac output noninvasively in mechanically ventilated subjects with and without acute respiratory distress syndrome.