Modeling perfusion in the cerebral vasculature

Incomplete circle of Willis variants and stroke outcome

BACKGROUND

There is considerable variation in circle of Willis morphology among the general population, and these variations have been correlated with risk of aneurysms, cerebral ischemia, and other clinical events.

PURPOSE

To investigate the relationship between circle of Willis variants and stroke outcome.

MATERIALS AND METHODS

We performed a retrospective study involving 297 patients from our institution's acute stroke academic registry. All received MRA examinations of the head upon admission for acute strokes. All imaging was reviewed to assess for circle of Willis variants (particularly A1 and P1 aplasia or hypoplasia) along with vertebral artery aplasia or hypoplasia. Stroke outcome was defined as good (walking independently at the time of discharge) or poor (inability to walk at discharge, assistance needed to walk at discharge, or death). Severity of stroke was assessed using the National Institute of Health Stroke Scale.

RESULTS

An incomplete circle of Willis was seen in 34% of subjects. There was no significant association between age, gender, hypertension, or presence of arterial stenosis and circle of Willis completeness. Using logistic regression, we found that the presence of an incomplete circle of Willis decreased the odds of a stroke patient having a good outcome by 47% (p = 0.046, OR 0.53, 95% CI 0.281-0.988), after adjusting for age and severity of stroke at admission.

CONCLUSION

This study suggests that an incomplete circle of Willis may be associated with a poorer prognosis for stroke patients.

Association Between Incomplete Circle of Willis and Carotid Vulnerable Atherosclerotic Plaques

Objective—

Carotid high-risk plaque, characterized by intraplaque hemorrhage, fibrous cap rupture, and large lipid-rich necrotic core, is associated with cerebrovascular events. This study sought to investigate the relationship between high-risk carotid plaque and an incomplete circle of Willis (COW).

Approach and Results—

Patients were recruited from a multicenter study, Chinese Atherosclerosis Risk Evaluation (CARE-II) and underwent 3-dimensional time-of-flight magnetic resonance angiography for intracranial arteries and 2-dimensional multicontrast magnetic resonance vessel wall imaging for carotid arteries on a 3.0T magnetic resonance scanner. The integrity of the COW in anterior and posterior portions was evaluated. Characteristics of carotid plaques were assessed. Correlation between incomplete COW and carotid plaque features was determined. Of 482 eligible patients, patients with carotid intraplaque hemorrhage showed significantly higher prevalence of an incomplete anterior COW (52.7% versus 38.5%; P =0.022) compared with those without. An incomplete anterior COW was associated with intraplaque hemorrhage before (odds ratio, 1.781; 95% CI, 1.083–2.931; P =0.023) and after adjusted for clinical risk factors (odds ratio, 1.945; 95% CI, 1.139–3.321; P =0.015). The unilateral carotid artery stenosis showed no correlation with incomplete anterior COW and posterior COW (all P >0.025). No significant associations were found between other plaque features and any type of incomplete COW (all P >0.025).

Conclusions—

An incomplete COW is independently associated with intraplaque hemorrhage of carotid atherosclerotic plaques.

Clinical Trial Registration—

URL: http://www.clinicaltrials.gov . Unique identifier: NCT02017756.

Fluid-structure interaction of patient-specific Circle of Willis with aneurysm: Investigation of hemodynamic parameters

BACKGROUND

Circle of Willis (COW) is a network of cerebral artery which continually supplies the brain with blood. Any disturbance in this supply will result in trauma or even death. One of these damages is known as brain Aneurysm. Clinical methods for diagnosing aneurysm can only measure blood velocity; while, in order to understand the causes of these occurrences it is necessary to have information about the amount of pressure and wall shear stress, which is possible through computational models.

OBJECTIVE

In this study purpose is achieving exact information of hemodynamic blood flow in COW with an aneurysm and investigation of effective factors on growth and rupture of aneurysm.

METHODS

Here, realistic three-dimensional models have been produced from angiography images. Considering fluid-structure interaction have been simulated by the ANSYS.CFX software.

RESULTS

Hemodynamic Studying of the COW and intra-aneurysm showed that the WSS and wall tension in the neck of aneurysms for case A are 129.5 Pa, and 12.2 kPa and for case B they are 53.3 Pa and 56.2 kPa, and more than their fundus, thus neck of aneurysm is prone to rupture.

CONCLUSION

This study showed that the distribution of parameters was dependent on the geometry of the COW, and maximum values are seen in areas prone to aneurysm formation.

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

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

Mathematical and computational models of the retina in health, development and disease

The retina confers upon us the gift of vision, enabling us to perceive the world in a manner unparalleled by any other tissue. Experimental and clinical studies have provided great insight into the physiology and biochemistry of the retina; however, there are questions which cannot be answered using these methods alone. Mathematical and computational techniques can provide complementary insight into this inherently complex and nonlinear system. They allow us to characterise and predict the behaviour of the retina, as well as to test hypotheses which are experimentally intractable. In this review, we survey some of the key theoretical models of the retina in the healthy, developmental and diseased states. The main insights derived from each of these modelling studies are highlighted, as are model predictions which have yet to be tested, and data which need to be gathered to inform future modelling work. Possible directions for future research are also discussed. Whilst the present modelling studies have achieved great success in unravelling the workings of the retina, they have yet to achieve their full potential. For this to happen, greater involvement with the modelling community is required, and stronger collaborations forged between experimentalists, clinicians and theoreticians. It is hoped that, in addition to bringing the fruits of current modelling studies to the attention of the ophthalmological community, this review will encourage many such future collaborations.

Mathematical Modelling of a Brain Tumour Initiation and Early Development: A Coupled Model of Glioblastoma Growth, Pre-Existing Vessel Co-Option, Angiogenesis and Blood Perfusion

We propose a coupled mathematical modelling system to investigate glioblastoma growth in response to dynamic changes in chemical and haemodynamic microenvironments caused by pre-existing vessel co-option, remodelling, collapse and angiogenesis. A typical tree-like architecture network with different orders for vessel diameter is designed to model pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated based on the haemodynamic environment which is obtained by coupled modelling of intravascular blood flow with interstitial fluid flow. The haemodynamic changes, including vessel diameter and permeability, are introduced to reflect a series of pathological characteristics of abnormal tumour vessels including vessel dilation, leakage, angiogenesis, regression and collapse. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. The simulation focuses on the avascular phase of tumour development and stops at an early phase of angiogenesis. The model is able to demonstrate the main features of glioblastoma growth in this phase such as the formation of pseudopalisades, cell migration along the host vessels, the pre-existing vasculature co-option, angiogenesis and remodelling. The model also enables us to examine the influence of initial conditions and local environment on the early phase of glioblastoma growth.

Mechanics of the brain: perspectives, challenges, and opportunities

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

Numerical Simulation of the blood flow behavior in the circle of Willis

Introduction: This paper represents the numerical simulation of blood flow in the circle of Willis (CoW). Circle of Willis is responsible for the oxygenated blood distribution into the cerebral mass. To investigate the blood behavior, two Newtonian and non-Newtonian viscosity models were considered and the results were compared under steady state conditions.

Methods: Methodologically, the arterial geometry was obtained using 3D magnetic resonance angiography (MRA) data. The blood flow through the cerebral vasculature was considered to be steady and laminar, and the Galerkin’s finite element method was applied to solve the systems of non-linear Navier-Stokes equations.

Results: Flow patterns including flow rates and shear rates were obtained through the simulation. The minimal magnitude of shear rates was much greater than 100 s^-1 through the larger arteries; thus, the non-Newtonian blood viscosity tended to approach the constant limit of infinite shear viscosity through the CoW. So, in larger arteries the non-Newtonian nature of blood was less dominant and it would be treated as a Newtonian fluid. The only exception was the anterior communicating artery (ACoA) in which the blood flow showed different behavior for the Newtonian and non-Newtonian cases.

Conclusion By comparing the results it was concluded that the Newtonian viscosity assumption of blood flow through the healthy, complete circle of Willis under the normal and steady conditions would be acceptably accurate.

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

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

Contribution of the hemodynamics of A1 dysplasia or hypoplasia to anterior communicating artery aneurysms: a 3-dimensional numerical simulation study

OBJECTIVE

To explore the association between the hemodynamics and formation, growth, and rupture of aneurysms in anterior communicating arteries (ACoA) with A1 dysplasia or hypoplasia.

METHODS

A series of 3-dimensional numerical simulation models of the anterior communicating artery complex (ACoAC) were designed geometrically. The diameter of A1 was fixed on one side and decreased gradually on the other side. Three groups of ACoA aneurysm model growth were constructed with different positions to the dominant bifurcation. Blood flow was modeled as an incompressible Newtonian fluid described by the unsteady Navier-Stokes equations. Vessel walls were assumed to be rigid; no slip boundary conditions were applied at the walls.

RESULTS

Wall shear stress (WSS), flow velocity, and pressure were influenced by the dynamic variations of A1 diameter. When the diameter of the nondominant A1 gradually decreased, WSS and flow velocity dynamically increased in the dominant bifurcation and pressure decreased. Wall shear stress differences were significant between the dominant and nondominant bifurcations (t = 6.543; P < 0.05). With aneurysm growth, WSS and flow velocity gradually decreased, and turbulence appeared. Wall shear stress was lower at the bifurcation than that 0.02 mm and 0.1 mm to the bifurcation, whereas flow velocity and turbulent flow were more obvious.

CONCLUSIONS

A1 dysplasia/hypoplasia is a potential risk factor in the formation of ACoA aneurysms. Wall shear stress increase may contribute to aneurysm formation. Wall shear stress decrease and turbulent flow may be responsible for the growth and rupture of ACoA aneurysms. The hemodynamic mechanism in the growth and rupture of aneurysms in different locations might be different.

Patient-specific computational modeling of upper extremity arteriovenous fistula creation: its feasibility to support clinical decision-making

Introduction

Inadequate flow enhancement on the one hand, and excessive flow enhancement on the other hand, remain frequent complications of arteriovenous fistula (AVF) creation, and hamper hemodialysis therapy in patients with end-stage renal disease. In an effort to reduce these, a patient-specific computational model, capable of predicting postoperative flow, has been developed. The purpose of this study was to determine the accuracy of the patient-specific model and to investigate its feasibility to support decision-making in AVF surgery.

Methods

Patient-specific pulse wave propagation models were created for 25 patients awaiting AVF creation. Model input parameters were obtained from clinical measurements and literature. For every patient, a radiocephalic AVF, a brachiocephalic AVF, and a brachiobasilic AVF configuration were simulated and analyzed for their postoperative flow. The most distal configuration with a predicted flow between 400 and 1500 ml/min was considered the preferred location for AVF surgery. The suggestion of the model was compared to the choice of an experienced vascular surgeon. Furthermore, predicted flows were compared to measured postoperative flows.

Results

Taken into account the confidence interval (25^th and 75^th percentile interval), overlap between predicted and measured postoperative flows was observed in 70% of the patients. Differentiation between upper and lower arm configuration was similar in 76% of the patients, whereas discrimination between two upper arm AVF configurations was more difficult. In 3 patients the surgeon created an upper arm AVF, while model based predictions allowed for lower arm AVF creation, thereby preserving proximal vessels. In one patient early thrombosis in a radiocephalic AVF was observed which might have been indicated by the low predicted postoperative flow.

Conclusions

Postoperative flow can be predicted relatively accurately for multiple AVF configurations by using computational modeling. This model may therefore be considered a valuable additional tool in the preoperative work-up of patients awaiting AVF creation.

Clinical Study Protocol for the ARCH Project Computational Modeling for Improvement of Outcome after Vascular Access Creation

Despite clinical guidelines and the possibility of diagnostic vascular imaging, creation and maintenance of a vascular access (VA) remains problematic: avoiding short- and long-term VA dysfunction is challenging. Although prognostic factors for VA dysfunction have been identified in previous studies, their potential interplay at a systemic level is disregarded. Consideration of multiple prognostic patient specific factors and their complex interaction using dedicated computational modeling tools might improve outcome after VA creation by enabling a better selection of VA configuration. These computational modeling tools are developed and validated in the ARCH project: a joint initiative of four medical centers and three industrial partners (FP7-ICT-224390). This paper reports the rationale behind computational modeling and presents the clinical study protocol designed for calibrating and validating these modeling tools. The clinical study is based on the pre-operative collection of structural and functional data at a vascular level, as well as a VA functional evaluation during the follow-up period. The strategy adopted to perform the study and for data collection is also described here.

The influence of contrast agent injection on physiological flow in the circle of Willis

X-ray videodensitometry allows in vivo flow measurements from gradients in contrast agent concentration. However, the injection of contrast agent alters the flow to be measured. Here, the temporal, spatial, and inter-patient variability of the response to injection are examined. To this purpose, an injection is prescribed in the internal carotid in a 1D wave propagation model of the arterial circulation. Although the resulting effect of injection is constant over a cardiac cycle, the response does vary with the location within the cerebral circulation and the geometry of the circle of Willis. At the injection site, the injection partly suppresses the incoming blood flow, such that the distal flow is increased by approximately 10%. This corresponds to approximately 20% of the injection rate added to the blood flow during injection, depending on the vascular geometry. In the communicating arteries, the flow direction is reversed during injection. Since the measured flow is not equal to the physiological blood flow, the effect of injection should be taken into account when deriving the flow from travelling contrast agent.

The role of biofluid mechanics in the assessment of clinical and pathological observations: sixth International Bio-Fluid Mechanics Symposium and Workshop, March 28-30, 2008 Pasadena, California

Biofluid mechanics is increasingly applied in support of diagnosis and decision-making for treatment of clinical pathologies. Exploring the relationship between blood flow phenomena and pathophysiological observations is enhanced by continuing advances in the imaging modalities, measurement techniques, and capabilities of computational models. When combined with underlying physiological models, a powerful set of tools becomes available to address unmet clinical needs, predominantly in the direction of enhanced diagnosis, as well as assessment and prediction of treatment outcomes. This position paper presents an overview of current approaches and future developments along this theme that were discussed at the 5th International Biofluid Symposium and Workshop held at the California Institute of Technology in 2008. The introduction of novel mechanical biomarkers in device design and optimization, and applications in the characterization of more specific and focal conditions such as aneurysms, are at the center of attention. Further advances in integrative modeling, incorporating multiscale and multiphysics techniques are also discussed.

Modeling cerebral blood flow and regulation

Cerebral autoregulation is a homeostatic mechanism which maintains blood flow despite changes in blood pressure in order to meet local metabolic demands. Several mechanisms play a role in cerebral autoregulation in order to adjust vascular tone and caliber of the cerebral vessels, but the exact etiology of the dynamics of these mechanism is not well understood. In this study, we discuss two patient specific models predicting cerebral blood flow velocity during postural change from sitting to standing. One model characterises cerebral autoregulation, the other describes the beat-to-beat distribution of blood flow to the major regions of the brain. Both models have been validated against experimental data from a healthy young subject.