A theoretical model of cerebral hemodynamics: application to the study of arteriovenous malformations

Challenges in Modeling Hemodynamics in Cerebral Aneurysms Related to Arteriovenous Malformations

PURPOSE

The significantly higher incidence of aneurysms in patients with arteriovenous malformations (AVMs) suggests a strong hemodynamic relationship between these lesions. The presence of an AVM alters hemodynamics in proximal vessels by drastically changing the distal resistance, thus affecting intra-aneurysmal flow. This study discusses the challenges associated with patient-specific modeling of aneurysms in the presence of AVMs.

METHODS

We explore how the presence of a generic distal AVM affects upstream aneurysms by examining the relationship between distal resistance and aneurysmal wall shear stress using physiologically realistic estimates for the influence of the AVM on hemodynamics. Using image-based computational models of aneurysms and surrounding vasculature, aneurysmal wall-shear stress is calculated for a range of distal resistances corresponding to the presence of AVMs of various sizes and compared with a control case representing the absence of an AVM.

RESULTS

In the patient cases considered, the alteration in aneurysmal wall shear stress due to the presence of an AVM is considerable, as much as 19 times the base case wall shear stress. Furthermore, the relationship between aneurysmal wall shear stress and distal resistance is shown to be highly geometry-dependent and nonlinear. In most cases, the range of physiologically realistic possibilities for AVM-related distal resistance are so large that patient-specific flow measurements are necessary for meaningful predictions of wall shear stress.

CONCLUSIONS

The presented work offers insight on the impact of distal AVMs on aneurysmal wall shear stress using physiologically realistic computational models. Patient-specific modeling of hemodynamics in aneurysms and associated AVMs has great potential for understanding lesion pathogenesis, surgical planning, and assessing the effect of treatment of one lesion relative to another. However, we show that modeling approaches cannot usually meaningfully quantify the impact of AVMs if based solely on imaging data from CT and X-ray angiography, currently used in clinical practice. Based on recent studies, it appears that 4D flow MRI is one promising approach to obtaining meaningful patient-specific flow boundary conditions that improve modeling fidelity.

Angiotensin II type 1 receptor is involved in flow-induced vasomotor responses of isolated middle cerebral arteries: role of oxidative stress

This study aimed to determine the mechanosensing role of angiotensin II type 1 receptor (AT1R) in flow-induced dilation (FID) and oxidative stress production in middle cerebral arteries (MCA) of Sprague-Dawley rats. Eleven-week old, healthy male Sprague-Dawley rats on a standard diet were given the AT1R blocker losartan (1 mg/mL) in drinking water (losartan group) or tap water (control group) ad libitum for 7 days. Blockade of AT1R attenuated FID and acetylcholine-induced dilation was compared with control group. Nitric oxide (NO) synthase inhibitor Nω-nitro-l-arginine methyl ester (l-NAME) and cyclooxygenase inhibitor indomethacin (Indo) significantly reduced FID in control group. The attenuated FID in losartan group was further reduced by Indo only at Δ100 mmHg, whereas l-NAME had no effect. In losartan group, Tempol (a superoxide scavenger) restored dilatation, whereas Tempol + l-NAME together significantly reduced FID compared with restored dilatation with Tempol alone. Direct fluorescence measurements of NO and reactive oxygen species (ROS) production in MCA, in no-flow conditions revealed significantly reduced vascular NO levels with AT1R blockade compared with control group, whereas in flow condition increased the NO and ROS production in losartan group and had no effect in the control group. In losartan group, Tempol decreased ROS production in both no-flow and flow conditions. AT1R blockade elicited increased serum concentrations of ANG II, 8-iso-PGF2α, and TBARS, and decreased antioxidant enzyme activity (SOD and CAT). These results suggest that in small isolated cerebral arteries: 1) AT1 receptor maintains dilations in physiological conditions; 2) AT1R blockade leads to increased vascular and systemic oxidative stress, which underlies impaired FID.NEW & NOTEWORTHY The AT1R blockade impaired the endothelium-dependent, both flow- and acetylcholine-induced dilations of MCA by decreasing vascular NO production and increasing the level of vascular and systemic oxidative stress, whereas it mildly influenced the vascular wall inflammatory phenotype, but had no effect on the systemic inflammatory response. Our data provide functional and molecular evidence for an important role of AT1 receptor activation in physiological conditions, suggesting that AT1 receptors have multiple biological functions.

Patient-Specific Blood Flow Analysis for Cerebral Arteriovenous Malformation Based on Digital Subtraction Angiography Images

Real-time digital subtraction angiography (DSA) is capable of revealing the cerebral vascular morphology and blood flow perfusion patterns of arterial venous malformations (AVMs). In this study, we analyze the DSA images of a subject-specific left posterior AVM case and customize a generic electric analog model for cerebral circulation accordingly. The generic model consists of electronic components representing 49 major cerebral arteries and veins, and yields their blood pressure and flow rate profiles. The model was adapted by incorporating the supplying and draining patterns of the AVM to simulate some typical AVM features such as the blood "steal" syndrome, where the flow rate in the left posterior artery increases by almost three times (∼300 ml/min vs 100 ml/min) compared with the healthy case. Meanwhile, the flow rate to the right posterior artery is reduced to ∼30 ml/min from 100 ml/min despite the presence of an autoregulation mechanism in the model. In addition, the blood pressure in the draining veins is increased from 9 to 22 mmHg, and the blood pressure in the feeding arteries is reduced from 85 to 30 mmHg due to the fistula effects of the AVM. In summary, a first DSA-based AVM model has been developed. More subject-specific AVM cases are required to apply the presented in silico model, and in vivo data are used to validate the simulation results.

Hemodynamics Associated With Intracerebral Arteriovenous Malformations: The Effects of Treatment Modalities

The understanding of the physiology of cerebral arteriovenous malformations (AVMs) continues to expand. Knowledge of the hemodynamics of blood flow associated with AVMs is also progressing as imaging and treatment modalities advance. The authors present a comprehensive literature review that reveals the physical hemodynamics of AVMs, and the effect that various treatment modalities have on AVM hemodynamics and the surrounding cortex and vasculature. The authors discuss feeding arteries, flow through the nidus, venous outflow, and the relative effects of radiosurgical monotherapy, endovascular embolization alone, and combined microsurgical treatments. The hemodynamics associated with intracranial AVMs is complex and likely changes over time with changes in the physical morphology and angioarchitecture of the lesions. Hemodynamic change may be even more of a factor as it pertains to the vast array of single and multimodal treatment options available. An understanding of AVM hemodynamics associated with differing treatment modalities can affect treatment strategies and should be considered for optimal clinical outcomes.

Effective Surgical Management of Competitive Venous Outflow Restriction After Radiosurgery for Cerebral AVMs: Report of 2 Cases

BACKGROUND

Intracranial arteriovenous malformations (AVMs) are complex pathologies. For patients who do not present with hemorrhage, treatment strategies are often predicated on reducing the risk of hemorrhage and minimizing morbidity. Outcomes vary according to the efficacy of treatment selected. Radiosurgical treatment of certain AVMs can result in incomplete obliteration and may also have only a minimal effect on the presenting nonhemorrhagic symptoms.

CASE DESCRIPTIONS

We present 2 cases of patients with AVMs who were initially treated with radiosurgery. Both patients' primary clinical symptoms were headaches, which persisted after radiosurgical treatment but abated after subsequent microsurgical resection with or without endovascular embolization.

CONCLUSION

Venous outflow obstruction is likely a sizable contributive factor in occipital AVMs among patients who present with headaches and symptoms of intracranial hypertension. Because these high-flow lesions may be suboptimally responsive to stereotactic radiosurgery, microsurgical resection, with or without adjunctive endovascular embolization, should be considered as an initial and definitive treatment strategy. Optimal outcomes may be achieved in patients with a visual deficit that is anatomically correlated to their AVMs.

An anatomically detailed arterial network model for one-dimensional computational hemodynamics

Simulation platforms are increasingly becoming complementary tools for cutting-edge cardiovascular research. The interplay among structural properties of the arterial wall, morphometry, anatomy, wave propagation phenomena, and ultimately, cardiovascular diseases continues to be poorly understood. Accurate models are powerful tools to shed light on these open problems. We developed an anatomically detailed computational model of the arterial vasculature to conduct 1-D blood flow simulations to serve as simulation infrastructure to aid cardiovascular research. An average arterial vasculature of a man was outlined in 3-D space to serve as geometrical substrate for the mathematical model. The architecture of this model comprises almost every arterial vessel acknowledged in the medical/anatomical literature, with a resolution down to the luminal area of perforator arteries. Over 2000 arterial vessels compose the model. Anatomical, physiological, and mechanical considerations were employed for the set up of model parameters and to determine criteria for blood flow distribution. Computational fluid dynamics was used to simulate blood flow and wave propagation phenomena in such arterial network. A sensitivity analysis was developed to unveil the contributions of model parameters to the conformation of the pressure waveforms. In addition, parameters were modified to target model to a patient-specific scenario. On the light of the knowledge domain, we conclude that the present model features excellent descriptive and predictive capabilities in both patient-generic and patient-specific cases, presenting a new step toward integrating an unprecedented anatomical description, morphometric, and simulations data to help in understanding complex arterial blood flow phenomena and related cardiovascular diseases.

An approach to the symbolic representation of brain arteriovenous malformations for management and treatment planning

INTRODUCTION

There is currently no standardised approach to arteriovenous malformation (AVM) reporting. Existing AVM classification systems focuses on angioarchitectural features and omit haemodynamic, anatomical and topological parameters intuitively used by therapists.

METHODS

We introduce a symbolic vocabulary to represent the state of an AVM of the brain at different stages of treatment. The vocabulary encompasses the main anatomic and haemodynamic features of interest in treatment planning and provides shorthand symbols to represent the interventions themselves in a schematic representation.

RESULTS

The method was presented to 50 neuroradiologists from 14 countries during a workshop and graded 7.34 ± 1.92 out of ten for its usefulness as means of standardising and facilitating communication between clinicians and allowing comparisons between AVM cases. Feedback from the survey was used to revise the method and improve its completeness. For an AVM test case, participants were asked to produce a conventional written report and subsequently a diagrammatic report. The two required, on average, 6.19 ± 2.05 and 5.09 ± 3.01 min, respectively. Eighteen participants said that producing the diagram changed the way they thought about the AVM test case.

CONCLUSION

Introduced into routine practice, the diagrams would represent a step towards a standardised approach to AVM reporting with consequent benefits for comparative analysis and communication as well as for identifying best treatment strategies.

Observations on the flow characteristics of blood flow in arteriovenous fistulae (experimental)

Hemodynamic play a very significant role in the pathophysiology of intracranial arteriovenous malformation. The surgical decisions are based on the understanding of the complexities of the flow. Quantification of the abnormal flow is difficult. The mathematical models provide limited information due to the simplicity of the design of these models. Flow of fluid in a tube is very sensitive to small changes in the diameter. We studied the flow characteristics of a fistula by introducing accurately machined acrylic fistulae between the femoral arteries and veins of dogs. The influences of systemic arterial pressure, diameter of the arterial feeders, volume of blood flow, velocity of flow and the diameter of the shunt on the flow of blood across the shunt were studied. Our experiments suggest that the flow characteristics of an arteriovenous fistulae are complex and are influenced by small changes in the diameters of the fistula and the feeding artery. Our model demonstrates the occurrence of the anomalous flow reduction in the fistula and steal phenomenon and is therefore a more realistic representation of the clinical situation. The design of a mathematical model should include the diameter of the fistula if it is intended to replicate the hemodynamic characteristics of an arteriovenous malformation more faithfully.

Development of a cerebral microvascular dysplasia model in rodents

Normal vasculature development of the central nervous system is extremely important because patients with vascular malformations are at life-threatening risk for intracranial hemorrhage or cerebral ischemia. The etiology and pathogenesis of abnormal vasculature development in the central nervous system are unknown, and progress is hampered by the lack of animal models for human cerebrovascular diseases. Here, we report our current study on cerebral microvascular dysplasia (CMVD) development. Using vascular endothelial growth factor hyper-stimulation, we demonstrated that aberrant microvessels could be developed in the rodent brain under certain conditions (such as genetic deficient background, local cytokine and chemokine release, or exogenous vessel dilating stimulation) that may speed up focal angiogenesis and lead to cerebral vascular dysplasia.

Analysis of the hemodynamic characteristics of brain arteriovenous malformations using electrical models: baseline settings, surgical extirpation, endovascular embolization, and surgical bypass

OBJECTIVE

The goal of this report is to analyze the hemodynamic characteristics of low- and high-flow arteriovenous malformations (AVM) using computerized electrical models.

METHODS

Two electrical models of brain AVMs were created. These models consist of electrical resistors that simulate AVM vessels. In both models, a low-flow AVM and a high-flow AVM, the flow of electrons simulates the flow of blood.

RESULTS

Using the models, it was possible to analyze the pressure and flow patterns in the nidus of the small, low-flow AVM and in the nidus of the large, high-flow AVM. Baseline hemodynamic "physiological" conditions of the two AVMs were studied. With the models, it was also possible to assess the AVM hemodynamic changes (in the feeding arteries, in the various parts of the nidus, and in the draining veins) after surgery, after embolization, and after surgical bypass of the malformation. The role of autoregulation in the three treatment modalities was also assessed.

CONCLUSION

These electrical models seem to be useful in simulating and studying the behavior of flow and pressure in the different parts of the AVM nidus (arterial, arteriolar, arteriolar-venular, venular, venous) before and after treatment. The models can also be used to devise and simulate new treatment strategies that might lead to improved treatment of these highly complex vascular malformations of the brain.

A review of physiological simulation models of intracranial pressure dynamics

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

A hypothesis of cerebral venous system regulation based on a study of the junction between the cortical bridging veins and the superior sagittal sinus

Object

The cerebral venous regulation involved in various physiological and pathological processes has received little attention. Here the authors describe the anatomy of the junction between the cortical vein and the superior sagittal sinus (SSS) and propose a new theory of cerebral venous regulation.

Methods

Ten adult human cadaveric heads (20 sides), including five specimens into which stained latex had been injected, were used for anatomical study. Formalin-fixed cadaver heads were dissected to demonstrate the cortical veins along the SSS. The characteristics of the cortical bridging veins and their openings into the SSS were established by anatomical, histological, immunohistochemical, and ultrastructural study of the junction.

Results

After their subarachnoid course, the cortical bridging veins penetrated the SSS at different points in the dura mater depending on their rostrocaudal position. The venous endothelium stretched beyond the sinus endothelium. The orientation of the collagen fibers changed at the level of the venous openings, with the luminal diameter becoming narrow and oval-shaped. The major finding was the organization of the smooth-muscle cells at the end of each cortical vein. At this site and particularly in the frontoparietal region, the vessel resembled a myoendothelial “sphincter.” The authors hypothesize that this organization is involved in cerebral venous system regulation.

Conclusions

The point of convergence between the cortical veins and the SSS is a key area. The authors also hypothesize that the myoendothelial junction acts as a smooth sphincter and that it plays a role in cerebral venous hemodynamics and pathological conditions.

Experimental cerebral arteriovenous fistulas

OBJECTIVE

The aim of this paper is to analyse and summarize the main advances in experimental research on cerebral arteriovenous fistulas.

METHODS

A detailed analysis of the literature and my own research experience were employed to outline the methodology whereby experimental cerebral arteriovenous fistulas are created and further studied.

RESULTS

The analysis and quantification of the anatomical and functional variables in different experimental cerebral arteriovenous fistula models make it possible to develop more appropriate and individual ways of treatment in affected patients.

CONCLUSION

Experimental research on cerebral arteriovenous fistulas helps physicians to understand and predict more accurately the future evolution of arteriovenous malformations in humans.

Endovascular Pressure Measurements: Validation with a Pulsatile Flow Model and Haemodynamic Assessment of Brain AVMs

SUMMARY

Intravascular pressure measurements for several types of endovascular catheters were obtained in an in vitro model to validate the pressure readings obtained during the interventional procedures of brain AVM embolization. An experimental model was used where the beat rate, flow and pressures were as close as possible to the average human values of interest. It is shown that the corrections increase with the decreasing inner diameter of the catheter used and with increasing vascular pressure. We have also shown that there were no differences between measurements made with the catheter in the direction of flow or against it. An average pressure reading corrections for the various microcatheters to compensate the readings obtained during in vivo monitoring is presented. The haemodynamic assessment of 81 brain AVMs was performed using the endovascular measurement of arterial pressure in 389 feeding arteries during embolization. Mostly, the feeders' arterial median pressure was half the systemic arterial pressure but there was a wide variability of AV shunts in brain AVMs not only from one brain AVM to another but also within the same brain AVM. Measurement of arterial feeder pressure is an inexpensive, quick and accurate tool to evaluate the type of AV shunts within brain AVM.

[Diffusion, perfusion and activation functional MRI studies of brain arteriovenous malformations]

The management of Brain Arteriovenous Malformations continues to be challenged by a lack of understanding and control of pathophysiological processes implied in the clinical symptoms. New data from functional MRI with diffusion-weighted, perfusion-weighted and neuronal activation highlight abnormal brain areas near or remote to the AVM nidus. Moreover, these techniques are able to show hemodynamic and neuronal adaptative phenomena involved in brain plasticity. They reflect the instantaneous hemodynamic brain conditions that may help to correlate the clinical symptoms with the anatomical and functional substratum and to influence any invasive therapy.

MR perfusion imaging in proliferative angiopathy

Seizures, which may be the main expression of cerebral arteriovenous malformations (CAVM) can be difficult to control medically. Our goal was to use perfusion-weighted imaging (PWI) in correlation with clinical data to detect abnormal areas of the cerebrum related to a particular type of CAVM (proliferative angiopathy) and to study the pathophysiology. We use PWI, with a bolus injection of contrast medium, to investigate seven patients with proliferative angiopathy and fits producing language disturbance. Perfusion parameters were calculated using the first-pass moment theory. Five patients had perimalformative and/or contralateral abnormal areas with relative hyperperfusion (cerebral blood volume +20.7+/-16.2%, blood flow 92.5+/-68.8 ml/min/100 g). Areas of hypoperfusion and venous congestion were detected in two patients. One patient who underwent MRI after a severe focal deficit had no significant haemodynamic abnormality.

Parameter fitting of digital models of pulsatile hemodynamics based on intravascular measurements in the rabbit aorta

The objective was to describe and evaluate methods of in vivo intravascular assessment of pressure and flow within the systemic arterial tree for further digital processing and individualized simulation. In rabbits intra-aortic pressure and flow were measured by insertion of microcatheters and/or a Doppler probe, which were moved to different angiographically documented sites. Various catheters and sheaths were evaluated prior to digitized processing of the obtained data, which was based on electrotechnical analoga for description of elastic vascular segments. Fourier transformation and filtering provided signal data for further identification of the investigated parameters. Catheters with an inner diameter > or = 0.9 mm produced reliable pressure signals. Simultaneous measurement of pressure and flow reduced the reliability of the absolute values by reduction of the cross-sectional diameter of the investigated vascular segments. Numerical optimization methods were used to identify parameters in the proposed models from the measured data sets. Characterization of hemodynamics by intravascular measurements of pressure and flow proved feasible. Pressure recordings should be judged critically if the cross-sectional area of the catheter covers a significant fraction of the vessel. Post-processing of such data sets may assist in future treatment planning and simulation of concomitant changes of intravascular pressure and flow.

Adaptation of cerebral circulation to brain arteriovenous malformations increases feeding artery pressure and decreases regional hypotension

PURPOSE

To determine how the adaptation of extranidal cerebral vessels affects feeding artery pressure, draining vein pressure, and regional hypotension due to the presence of brain arteriovenous malformations (BAVMs).

CONCEPT

BAVMs cause high flows in feeding arteries and draining veins and can induce profound hypotension in the neighboring vasculature. Despite the large difference in flow, endothelial shear stress (tau) observed in vessels ipsilateral to the BAVM is similar to tau in vessels contralateral to the BAVM, suggesting that the conductance vessels successfully adapt to keep tau constant. However, because BAVMs are discovered only after they are well developed, the natural history of the adaptation process in extranidal vessels is unknown.

RATIONALE

Currently, no way exists to determine experimentally the effects of adaptation of extranidal vessels in human patients. Therefore, a mathematical model of the cerebral vasculature is used to study adaptation in response to BAVMs. By comparing pressures and flows calculated before and after adaptation, the effect of adaptation of the conductance vessels on regional hemodynamics can be evaluated.

DISCUSSION

Structural adaptation of the extranidal circulation seems not only to reset tau, but also to ameliorate regional hypotension induced by BAVMs. However, this compensatory mechanism also increases feeding artery pressure and thus may increase the risk of hemorrhagic stroke.

Cerebral venous blood outflow: a theoretical model based on laboratory simulation

OBJECTIVE

The cerebrovascular bed and cerebrospinal fluid circulation have been modeled extensively except for the cerebral venous outflow, which is the object of this study.

METHODS

A hydraulic experiment was designed for perfusion of a collapsible tube in a pressurized chamber to simulate the venous outflow from the cranial cavity.

CONCEPT

The laboratory measurements demonstrate that the majority of change in venous flow can be attributed to either inflow pressure when the outflow is open, or the upstream transmural pressure when outflow is collapsed. On this basis, we propose a mathematical model for pressure distribution along the venous outflow pathway depending on cerebral blood flow and intracranial pressure. The model explains the physiological strong coupling between intracranial pressure and venous pressure in the bridging veins, and we discuss the limits of applicability of the Starling resistor formula to the venous flow rates. The model provides a complementary explanation for ventricular collapse and origin of subdural hematomas resulting from overshunting in hydrocephalus. The noncontinuous pressure flow characteristic of the venous outflow is pinpointed as a possible source of the spontaneous generation of intracranial slow waves.

CONCLUSION

A new conceptual mathematical model can be used to explain the relationship between pressures and flow at the venous outflow from the cranium.

Task-related signal decrease on functional magnetic resonance imaging

An atypical pattern of signal change was identified on functional magnetic resonance (fMR) imaging in pathologic patients. Three normal volunteers and 34 patients with pathologic lesions near the primary motor cortex underwent fMR imaging with echo-planar imaging while performing a hand motor task. Signal intensities were evaluated with the z-score method, and the time course and changes of the signal intensity were calculated. Nine of the 34 patients with pathologic lesions displayed a significant task-related signal reduction in motor-related areas. They also presented a conventional task-related signal increase in other motor-related areas. The time courses of the increase and decrease were the inverse of each other. There was no significant difference between rates of signal increase and decrease. Our findings suggest that this atypical signal decrease is clinically significant, and that impaired vascular reactivity and altered oxygen metabolism could contribute to the task-related signal reduction. Brain areas showing such task-related signal decrease should be preserved at surgery.

A model of the cerebral and cerebrospinal fluid circulations to examine asymmetry in cerebrovascular reactivity

The authors examined the steal phenomenon using a new mathematical model of cerebral blood flow and the cerebrospinal fluid circulation. In this model, the two hemispheres are connected through the circle of Willis by an anterior communicating artery (ACoA) of varying size. The right hemisphere has no cerebrovascular reactivity and the left is normally reactive. The authors studied the asymmetry of hemispheric blood flow in response to simulated changes in arterial blood pressure and carbon dioxide concentration. The hemispheric blood flow was dependent on the local regulatory capacity but not on the size of the ACoA. Flow through the ACoA and carotid artery was strongly dependent on the size of the communicating artery. A global interhemispheric "steal effect" was demonstrated to be unlikely to occur in subjects with nonstenosed carotid arteries. Vasoreactive effects on intracranial pressure had a major influence on the circulation in both hemispheres, provoking additional changes in blood flow on the nonregulating side. A method for the quantification of the crosscirculatory capacity has been proposed.

Hemodynamic role of the circle of Willis in stenoses of internal carotid arteries. An analytical solution of a linear model

A mathematical model of blood flow through the circle of Willis was developed, within a linear framework. Comprehensive analytical solutions, including a remarkably small number of parameters, were derived in the cases of obstructive lesions of extracranial carotid arteries. The influence of these lesions and the role of anterior and posterior communicating arteries on the blood pressure at the entry of the cerebral territories were quantified and analyzed emphasizing that the responses of the system of Willis to obstructive carotid lesions are extremely varied, depending on the communicating artery anatomy. Comparison with numerical results obtained by using a non-linear model showed no physiologically significant differences. Such a model might be an essential tool for an accurate assessment of the cerebral hemodynamics in carotid diseases.

Theoretical modelling of arteriovenous malformation rupture risk: a feasibility and validation study

PURPOSE

To explore the feasibility of using a theoretical computational model to simulate the risk of spontaneous arteriovenous malformation (AVM) haemorrhage.

METHODS

Data from 12 patients were collected from a prospective databank which documented the angioarchitecture and morphological characteristics of the AVM and the feeding mean arterial pressure (FMAP) measured during initial superselective angiography prior to any treatment. Using the data, a computational model of the cerebral circulation and the AVM was constructed for each patient (patient-specific model). Two model risk (Risk(model)) calculations (haemodynamic- and structural-weighted estimates) were performed by using the patient-specific models. In our previously developed method of haemodynamic-weighted estimate, Risk(model) was calculated with the simulated intranidal pressures related to its maximal and minimal values. In the method of structural-weighted estimate developed and described in this paper, the vessel mechanical properties and probability calculation were considered in more detail than in the haemodynamic-weighted estimate. Risk(model) was then compared to experimentally determined risk which was calculated using a statistical method for determining the relative risk of having initially presented with AVM haemorrhage, termed Risk(exp).

RESULTS

The Risk(model) calculated by both haemodynamic- and structural-weighted estimates correlated with experimental risks with chi2 = 6.0 and 0.64, respectively. The risks of the structural-weighted estimate were more correlated to experimental risks.

CONCLUSIONS

Using two different approaches to the calculation of AVM haemorrhage risk, we found a general agreement with independent statistical estimates of haemorrhagic risk based on patient data. Computational approaches are feasible; future work can focus on specific pathomechanistic questions. Detailed patient-specific computational models can also be developed as an adjunct to individual patient risk assessment for risk-stratification purposes.

Mathematical considerations for modeling cerebral blood flow autoregulation to systemic arterial pressure

The shape of the autoregulation curve for cerebral blood flow (CBF) vs. pressure is depicted in a variety of ways to fit experimentally derived data. However, there is no general empirical description to reproduce CBF changes resulting from systemic arterial pressure variations that is consistent with the reported data. We analyzed previously reported experimental data used to construct autoregulation curves. To improve on existing portrayals of the fitting of the observed data, a compartmental model was developed for synthesis of the autoregulation curve. The resistive arterial and arteriolar network was simplified as an autoregulation device (ARD), which consists of four compartments in series controlling CBF. Each compartment consists of a group of identical vessels in parallel. The response of each vessel category to changes in perfusion pressure was simulated using reported experimental data. The CBF-pressure curve was calculated from the resistance of the ARD. The predicted autoregulation curve was consistent with reported experimental data. The lower and upper limits of autoregulation (LLA and ULA) were predicted as 69 and 153 mmHg, respectively. The average value of the slope of the CBF-pressure curve below LLA and beyond ULA was predicted as 1.3 and 3.3% change in CBF per mmHg, respectively. Our four-compartment ARD model, which simulated small arteries and arterioles, predicted an autoregulation function similar to experimental data with respect to the LLA, ULA, and average slopes of the autoregulation curve below LLA and above ULA.

Cerebral arteriovenous malformation feeding artery aneurysms: a theoretical model of intravascular pressure changes after treatment

OBJECTIVE

A quantitative model may be used to estimate the magnitude of expected pressure changes along the vascular tree with shunt ablation and may provide information to assess the hemodynamic risk of arteriovenous malformation (AVM) treatment.

METHODS

A computer model of the cerebral circulation was applied to estimate the changes in intravascular pressure, velocity, biomechanical stress, and shear stress that might be expected from either endovascular or surgical ablation of AVMs. Two AVM sizes and two feeding artery constellations were simulated. The effect of different shunt flows on vascular pressure was modeled. In each simulation, AVMs were occluded in a stepwise fashion. The effects of systemic hypertension and hypotension in various vascular zones were also simulated.

RESULTS

As large (1000 ml/min) AVMs were occluded, the mean feeding arterial pressure increased from 18 to 68 mm Hg; the percent-occlusion at half-maximal pressure increase was 92%. For medium (500 ml/min) AVMs, feeding arterial pressure increased from 37 to 66 mm Hg; the percent-occlusion at half-maximal pressure increase was 71%. During manipulation of systemic pressure, hemodynamic changes in the circulation close to the nidus were proportionally less than changes in systemic pressure; the degree of proportionality depended on the magnitude of AVM shunt flow.

CONCLUSION

In this simulation, shunt obliteration increased pressure in the nidus and feeding arteries with little effect on the proximal circulation. The shunt provided a "buffering" effect, i.e., higher flow fistulas were exposed to smaller variations in intravascular pressure in feeding artery and nidal pressures during manipulation of systemic pressure.