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.

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.

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.

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.

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.

Modelling the impact of clot fragmentation on the microcirculation after thrombectomy.

Many ischaemic stroke patients who have a mechanical removal of their clot (thrombectomy) do not get reperfusion of tissue despite the thrombus being removed. One hypothesis for this 'no-reperfusion' phenomenon is micro-emboli fragmenting off the large clot during thrombectomy and occluding smaller blood vessels downstream of the clot location. This is impossible to observe in-vivo and so we here develop an in-silico model based on in-vitro experiments to model the effect of micro-emboli on brain tissue. Through in-vitro experiments we obtain, under a variety of clot consistencies and thrombectomy techniques, micro-emboli distributions post-thrombectomy. Blood flow through the microcirculation is modelled for statistically accurate voxels of brain microvasculature including penetrating arterioles and capillary beds. A novel micro-emboli algorithm, informed by the experimental data, is used to simulate the impact of micro-emboli successively entering the penetrating arterioles and the capillary bed. Scaled-up blood flow parameters-permeability and coupling coefficients-are calculated under various conditions. We find that capillary beds are more susceptible to occlusions than the penetrating arterioles with a 4x greater drop in permeability per volume of vessel occluded. Individual microvascular geometries determine robustness to micro-emboli. Hard clot fragmentation leads to larger micro-emboli and larger drops in blood flow for a given number of micro-emboli. Thrombectomy technique has a large impact on clot fragmentation and hence occlusions in the microvasculature. As such, in-silico modelling of mechanical thrombectomy predicts that clot specific factors, interventional technique, and microvascular geometry strongly influence reperfusion of the brain. Micro-emboli are likely contributory to the phenomenon of no-reperfusion following successful removal of a major clot.

Mathematical modelling of haemorrhagic transformation after ischaemic stroke.

With an increasingly elderly population globally, the impacts of cerebrovascular diseases, such as stroke and dementia, become increasingly significant. Haemorrhagic transformation (HT) is one of the most common complications of ischaemic stroke that is caused by dysfunction of endothelial cells in the blood-brain barrier (BBB) and that can be exacerbated by thrombolytic therapy. Recent studies also suggest that HT can lead to an increase in intracranial pressure (ICP) and result in capillary compression. The aim of this study is to develop a mathematical model that can be used to simulate the consequence of HT over a range of vasculature length scales. We use a 2D vasculature model to investigate the severity of HT with different vascular geometry. The resulting model shows that the haematoma radius is approximately constant across different length scales (100-1000µm) and in good agreement with the available experimental data. In addition, this study identified that the effects of capillary compression do appear to have a significant impact on the leakage fraction of blood and hence act to restrain the development of a haematoma.

Thrombus growth modelling and stenosis prediction in the cerebral microvasculature.

Cerebral microvascular occlusions cause restriction of blood supply to the brain, thus potentially severely impacting cognitive abilities. Thus, accurate prediction of thrombus growth in realistic geometries is important. Thrombi growth in an existing 13-generation cerebral microvasculature network is simulated here to study the haemodynamic effects of single and multiple blockages on the occlusion of the network. Compared to a single vessel, in a network, the occlusion probability is found to be different. It is the downstream/smaller arterioles (i.e. the 3rd, 4th, 5th, 6th generation arterioles in this study) that tend to reach occlusion first in a network and thus are the critical vessels. Simulations of simultaneous growth of two independent thrombi in the network (referred to here as the two-block case) show a close coupling between the locations of the various blocks in the network, each influencing the other's growth. The presence of the lead block (LB) slows the growth of the trailing block (TB). In some cases, it stops the TB's growth thereby preventing it from occluding the vessel. Findings in this work thus indicate that, to prevent ischaemia, blocks in the smaller arterioles need to be identified and treated first, and that this is more critical if the number of simultaneous blocks is higher.

Investigating the effects of a penetrating vessel occlusion with a multi-scale microvasculature model of the human cerebral cortex.

The effect of the microvasculature on observed clinical parameters, such as cerebral blood flow, is poorly understood. This is partly due to the gap between the vessels that can be individually imaged in humans and the microvasculature, meaning that mathematical models are required to understand the role of the microvasculature. As a result, a multi-scale model based on morphological data was developed here that is able to model large regions of the human microvasculature. From this model, a clear layering of flow (and 1-dimensional depth profiles) was observed within a voxel, with the flow in the microvasculature being driven predominantly by the geometry of the penetrating vessels. It also appears that the pressure and flow are decoupled, both in healthy vasculatures and in those where occlusions have occurred, again due to the topology of the penetrating vessels shunting flow between them. Occlusion of a penetrating arteriole resulted in a very high degree of overlap of blood pressure drop with experimentally observed cell death. However, drops in blood flow were far more widespread, providing additional support for the theory that pericyte controlled regulation on the capillary scale likely plays a large part in the perfusion of tissue post-occlusion.

A thermoelastic deformation model of tissue contraction during thermal ablation.

PURPOSE: Thermal ablation is an energy-based ablation technique widely used during minimally invasive cancer treatment. Simulations are used to predict the dead tissue post therapy. However, one difficulty with the simulations is accurately predicting the ablation zone in post-procedural images due to the contraction of tissue as a result of exposure to elevated temperatures. MATERIALS AND METHODS: A mathematical model of the thermoelastic deformation for an elastic isotropic material was coupled with a three state thermal denaturation model to determine the contraction of tissue during thermal ablation. A finite difference method was considered to quantify the tissue contraction for a typical temperature distribution during thermal ablation. RESULTS: The simulations show that tissue displacement during thermal ablation was not bound to the tissue heated regions only. Both tissue expansion and contraction were observed at the different stages of the heating process. Tissue contraction of up to 42% was obtained with an applicator temperature of 90 °C. A recovery of around 2% was observed with heating removed as a result of unfolded state proteins returning back to its native state. Poisson's ratio and the applicator temperature have both been shown to affect the tissue displacement significantly. The maximum tissue contraction was found to increase with both increasing Poisson's ratio and temperature. CONCLUSIONS: The model presented here will allow predictions of thermal ablation to be corrected for tissue contraction, which is an important effect, during comparison with post-procedural images, thus improving the accuracy of mathematical simulations for treatment planning.

The influence of multiple trials and computer-mediated communication on collaborative and individual semantic recall.

Collaborative inhibition is a phenomenon where collaborating groups experience a decrement in recall when interacting with others. Despite this, collaboration has been found to improve subsequent individual recall. We explore these effects in semantic recall, which is seldom studied in collaborative retrieval. We also examine "parallel CMC", a synchronous form of computer-mediated communication that has previously been found to improve collaborative recall [Hinds, J. M., & Payne, S. J. (2016). Collaborative inhibition and semantic recall: Improving collaboration through computer-mediated communication. Applied Cognitive Psychology, 30(4), 554-565]. Sixty three triads completed a semantic recall task, which involved generating words beginning with "PO" or "HE" across three recall trials, in one of three retrieval conditions: Individual-Individual-Individual (III), Face-to-face-Face-to-Face-Individual (FFI) and Parallel-Parallel-Individual (PPI). Collaborative inhibition was present across both collaborative conditions. Individual recall in Recall 3 was higher when participants had previously collaborated in comparison to recalling three times individually. There was no difference between face-to-face and parallel CMC recall, however subsidiary analyses of instance repetitions and subjective organisation highlighted differences in group members' approaches to recall in terms of organisation and attention to others' contributions. We discuss the implications of these findings in relation to retrieval strategy disruption.

Autoregulating Cerebral Tissue Selfishly Exploits Collateral Flow Routes Through the Circle of Willis.

OBJECTIVE: Ischemic stroke is a leading cause of death and disability. Autoregulation and collateral blood flow through the circle of Willis both play a role in preventing tissue infarction. A steady-state model of the cerebral arterial network was used to investigate the interaction of these mechanisms when autoregulation is impaired ipsilateral to an occluded artery. MATERIALS AND METHODS: Twelve structural variants of the circle of Willis were modelled with left internal carotid artery occlusion and coupled with (1) a passive model of the cerebral vascular bed, (2) a steady-state model of an autoregulating cerebral vascular bed, and (3) a model in which the contralateral hemisphere autoregulates and the ipsilateral hemisphere does not. RESULTS: Results showed that if the autoregulatory response is impaired ipsilaterally, then, in the autoregulating hemisphere, cerebral flows are preserved at the expense of those on the ipsilateral side. CONCLUSIONS: Thus, although autoregulation is an essential facilitator of collateral flow through the circle of Willis, contralateral autoregulation can exacerbate flow reductions if not balanced by the same response in the vascular beds on the ipsilateral side. The status of the autoregulatory response in both hemispheres can strongly influence cerebral blood flows and tissue survival and should, therefore, be monitored in stroke.

A mathematical model of cellular swelling in Neuromyelitis optica.

Neuromyelitis Optica (NMO) is a severe neuro-inflammatory disease of the central nervous system characterized by predominant damage to the optic nerve and of the spinal cord. The pathogenic antibody found in the majority of patients targets the AQP4 channels on astrocytic endfeet and causes the cells to swell. Although, the pathophysiology of the disease is broadly known, there are no specific targeted treatments for this process clinically available nor accurate prognostic markers both during attacks and for predicting long term neuronal damage. This lack is, in part, due to the rarity of the disease and its relatively recent pathogenic clarity. Hence, the ability to mathematically model the progress of the condition to test prospective therapies in silico would be a step forward. This paper combines state of the art models of cellular metabolism and cytotoxic oedema in neurons and astrocytes and augments it with a detailed characterization of water transport across the cellular membrane. In particular, we capture the process of perforation of the cell through the human complement cascade and resulting water and ionic fluxes. Simulating NMO by injecting its antibody and human complement into the extracellular space showed a 25% increase of the astrocytic volume after 12 h from onset. Most of the volume change occurred during the first 30 min of simulation with a peak volume change of 38%. The model was further adapted to simulate the therapeutic potential of CD59. It was found that there is a threshold of CD59 concentration that can prevent the swelling of astrocytes. Since the astrocyte volume changes mostly during the first hour, further experimental work should focus on this time scale to provide data for further model refinement and validation.

Mathematical model of the post-ablation enhancement zone as a tissue-level oedematic response.

PURPOSE: A hyperdense rim is commonly observed at the periphery of ablation zones during post-ablation imaging (e.g. ultrasound) in tumours. A mathematical model has been developed here to investigate the occurrence of this enhanced rim, caused by the ablated cells, giving an indication of the location of the final ablation region. MATERIALS AND METHODS: The enhanced rim has been assumed here to be due to a tissue-level oedematic response of viable cells, which necessitated coupling multiple modelling elements in a spatially distributed system: thermal cell death, tissue-state dependent ion concentration dynamics, ion transport in the extracellular space, and osmotic cell volume regulation. RESULTS: In response to the imposed temperature function, an ablation zone was predicted, distinguishing the tissue state between 'dead' and 'alive'. A disturbance in intracellular/extracellular ion concentrations was induced due to ion redistribution, which acted as an osmotic stress and contributed to significant cell swelling in a thin rim at the periphery of the ablation zone. It was also found that the rim size only changed slightly with varying lesion size, in response to different temperature profiles. CONCLUSIONS: The study presents a novel mathematical model to understand the enhanced rim surrounding the ablation zone by assuming tissue-level cell oedema as the primary potential cause. The model links the direct response to thermal injury to an observable secondary response, which could be of clinical value in that the location of this bright ring could potentially be used for more accurate determination of the extent of the ablation zone.

Doppler-based fetal heart rate analysis markers for the detection of early intrauterine growth restriction.

INTRODUCTION: One indicator for fetal risk of mortality is intrauterine growth restriction (IUGR). Whether markers reflecting the impact of growth restriction on the cardiovascular system, computed from a Doppler-derived heart rate signal, would be suitable for its detection antenatally was studied. MATERIAL AND METHODS: We used a cardiotocography archive of 1163 IUGR cases and 1163 healthy controls, matched for gestation and gender. We assessed the discriminative power of short-term variability and long-term variability of the fetal heart rate, computed over episodes of high and low variation aiming to separate growth-restricted fetuses from controls. Metrics characterizing the sleep state distribution within a trace were also considered for inclusion into an IUGR detection model. RESULTS: Significant differences in the risk markers comparing growth-restricted with healthy fetuses were found. When used in a logistic regression classifier, their performance for identifying IUGR was considerably superior before 34 weeks of gestation. Long-term variability in active sleep was superior to short-term variability [area under the receiver operator curve (AUC) of 72% compared with 71%]. Most predictive was the number of minutes in high variation per hour (AUC of 75%). A multivariate IUGR prediction model improved the AUC to 76%. CONCLUSION: We suggest that heart rate variability markers together with surrogate information on sleep states can contribute to the detection of early-onset IUGR.

A statistical model of the penetrating arterioles and venules in the human cerebral cortex.

OBJECTIVE: Models of the cerebral microvasculature are required at many different scales in order to understand the effects of microvascular topology on CBF. There are, however, no data-driven models at the arteriolar/venular scale. In this paper, we develop a data-driven algorithm based on available data to generate statistically accurate penetrating arterioles and venules. METHODS: A novel order-based density-filling algorithm is developed based on the statistical data including bifurcating angles, LDRs, and area ratios. Three thousand simulations are presented, and the results validated against morphological data. These are combined with a previous capillary network in order to calculate full vascular network parameters. RESULTS: Statistically accurate penetrating trees were successfully generated. All properties provided a good fit to experimental data. The k exponent had a median of 2.5 and an interquartile range of 1.75-3.7. CBF showed a standard deviation ranging from ±18% to ±34% of the mean, depending on the penetrating vessel diameter. CONCLUSIONS: Small CBF variations indicate that the topology of the penetrating vessels plays only a small part in the large regional variations of CBF seen in the brain. These results open up the possibility of efficient oxygen and blood flow simulations at MRI voxel scales which can be directly validated against MRI data.

Multi-scale homogenization of blood flow in 3-dimensional human cerebral microvascular networks.

The microvasculature plays a crucial role in the perfusion of blood through cerebral tissue. Current models of the cerebral microvasculature are discrete, and hence only able to model the perfusion over small voxel sizes before becoming computationally prohibitive. Larger models are required to provide comparisons and validation against imaging data. In this work, multi-scale homogenization methods were employed to develop continuum models of blood flow in a capillary network model of the human cortex. Homogenization of the local scale blood flow equations produced an averaged form of Darcy׳s law, with the permeability tensor encapsulating the capillary bed topology. A statistically accurate network model of the human cortex microvasculature was adapted to impose periodicity, and the elements of the permeability tensor calculated over a range of voxel sizes. The permeability tensor was found to converge to an effective permeability as voxel size increased. This converged permeability tensor was isotropic, reflecting the mesh-like structure of the cerebral microvasculature, with off-diagonal terms normally distributed about zero. A representative elementary volume of 375µm, with a standard deviation of 4.5% from the effective permeability, was determined. Using the converged permeability values, the cerebral blood flow was calculated to be around 55mLmin(-1)100g(-1), which is in very close agreement with experimental values. These results open up the possibility of future multi-scale modeling of the cerebral vascular network.

Cell death, perfusion and electrical parameters are critical in models of hepatic radiofrequency ablation.

PURPOSE: A sensitivity analysis has been performed on a mathematical model of radiofrequency ablation (RFA) in the liver. The purpose of this is to identify the most important parameters in the model, defined as those that produce the largest changes in the prediction. This is important in understanding the role of uncertainty and when comparing the model predictions to experimental data. MATERIALS AND METHODS: The Morris method was chosen to perform the sensitivity analysis because it is ideal for models with many parameters or that take a significant length of time to obtain solutions. A comprehensive literature review was performed to obtain ranges over which the model parameters are expected to vary, crucial input information. RESULTS: The most important parameters in predicting the ablation zone size in our model of RFA are those representing the blood perfusion, electrical conductivity and the cell death model. The size of the 50 °C isotherm is sensitive to the electrical properties of tissue while the heat source is active, and to the thermal parameters during cooling. CONCLUSIONS: The parameter ranges chosen for the sensitivity analysis are believed to represent all that is currently known about their values in combination. The Morris method is able to compute global parameter sensitivities taking into account the interaction of all parameters, something that has not been done before. Research is needed to better understand the uncertainties in the cell death, electrical conductivity and perfusion models, but the other parameters are only of second order, providing a significant simplification.

Modeling and correction of bolus dispersion effects in dynamic susceptibility contrast MRI.

PURPOSE: Bolus dispersion in DSC-MRI can lead to errors in cerebral blood flow (CBF) estimation by up to 70% when using singular value decomposition analysis. However, it might be possible to correct for dispersion using two alternative methods: the vascular model (VM) and control point interpolation (CPI). Additionally, these approaches potentially provide a means to quantify the microvascular residue function. METHODS: VM and CPI were extended to correct for dispersion by means of a vascular transport function. Simulations were performed at multiple dispersion levels and an in vivo analysis was performed on a healthy subject and two patients with carotid atherosclerotic disease. RESULTS: Simulations showed that methods that could not address dispersion tended to underestimate CBF (ratio in CBF estimation, CBFratio = 0.57-0.77) in the presence of dispersion; whereas modified CPI showed the best performance at low-to-medium dispersion; CBFratio = 0.99 and 0.81, respectively. The in vivo data showed trends in CBF estimation and residue function that were consistent with the predictions from simulations. CONCLUSION: In patients with atherosclerotic disease the estimated residue function showed considerable differences in the ipsilateral hemisphere. These differences could partly be attributed to dispersive effects arising from the stenosis when dispersion corrected CPI was used. It is thus beneficial to correct for dispersion in perfusion analysis using this method.