Revealing the mechanisms underlying embolic stroke using computational modelling

Three-dimensional simulations of embolic stroke and an equation for sizing emboli from imaging

Stroke simulations are needed to run in-silico trials, develop hypotheses for clinical studies and to interpret ultrasound monitoring and radiological imaging. We describe proof-of-concept three-dimensional stroke simulations, carrying out in silico trials to relate lesion volume to embolus diameter and calculate probabilistic lesion overlap maps, building on our previous Monte Carlo method. Simulated emboli were released into an in silico vasculature to simulate 1000 s of strokes. Infarct volume distributions and probabilistic lesion overlap maps were determined. Computer-generated lesions were assessed by clinicians and compared with radiological images. The key result of this study is development of a three-dimensional simulation for embolic stroke and its application to an in silico clinical trial. Probabilistic lesion overlap maps showed that the lesions from small emboli are homogeneously distributed throughout the cerebral vasculature. Mid-sized emboli were preferentially found in posterior cerebral artery (PCA) and posterior region of the middle cerebral artery (MCA) territories. For large emboli, MCA, PCA and anterior cerebral artery (ACA) lesions were comparable to clinical observations, with MCA, PCA then ACA territories identified as the most to least probable regions for lesions to occur. A power law relationship between lesion volume and embolus diameter was found. In conclusion, this article showed proof-of-concept for large in silico trials of embolic stroke including 3D information, identifying that embolus diameter could be determined from infarct volume and that embolus size is critically important to the resting place of emboli. We anticipate this work will form the basis of clinical applications including intraoperative monitoring, determining stroke origins, and in silico trials for complex situations such as multiple embolisation.

Micromechanical Force Measurement of Clotted Blood Particle Cohesion: Understanding Thromboembolic Aggregation Mechanisms

PURPOSE

Arterial shear forces may promote the embolization of clotted blood from the surface of thrombi, displacing particles that may occlude vasculature, with increased risk of physiological complications and mortality. Thromboemboli may also collide in vivo to form metastable aggregates that increase vessel occlusion likelihood.

METHODS

A micromechanical force (MMF) apparatus was modified for aqueous applications to study clot-liquid interfacial phenomena between clotted porcine blood particles suspended in modified continuous phases. The MMF measurement is based on visual observation of particle-particle separation, where Hooke's Law is applied to calculate separation force. This technique has previously been deployed to study solid-fluid interfacial phenomena in oil and gas pipelines, providing fundamental insight to cohesive and adhesive properties between solids in multiphase flow systems.

RESULTS

This manuscript introduces distributed inter-particle separation force properties as a function of governing physio-chemical parameters; pre-load (contact) force, contact time, and bulk phase chemical modification. In each experimental campaign, the hysteresis and distributed force properties were analysed, to derive insight as to the governing mechanism of cohesion between particles. Porcine serum, porcine albumin and pharmaceutical agents (alteplase, tranexamic acid and hydrolysed aspirin) reduced the measurement by an order of magnitude from the baseline measurement-the apparatus provides a platform to study how surface-active chemistries impact the solid-fluid interface.

CONCLUSION

These results provide new insight to potential mechanisms of macroscopic thromboembolic aggregation via particles cohering in the vascular system-data that can be directly applied to computational simulations to predict particle fate, better informing the mechanistic developments of embolic occlusion.

Simulated annealing approach to vascular structure with application to the coronary arteries

Do the complex processes of angiogenesis during organism development ultimately lead to a near optimal coronary vasculature in the organs of adult mammals? We examine this hypothesis using a powerful and universal method, built on physical and physiological principles, for the determination of globally energetically optimal arterial trees. The method is based on simulated annealing, and can be used to examine arteries in hollow organs with arbitrary tissue geometries. We demonstrate that the approach can generate in silico vasculatures which closely match porcine anatomical data for the coronary arteries on all length scales, and that the optimized arterial trees improve systematically as computational time increases. The method presented here is general, and could in principle be used to examine the arteries of other organs. Potential applications include improvement of medical imaging analysis and the design of vascular trees for artificial organs.

Size distribution of air bubbles entering the brain during cardiac surgery

Background

Thousands of air bubbles enter the cerebral circulation during cardiac surgery, but whether high numbers of bubbles explain post-operative cognitive decline is currently controversial. This study estimates the size distribution of air bubbles and volume of air entering the cerebral arteries intra-operatively based on analysis of transcranial Doppler ultrasound data.

Methods

Transcranial Doppler ultrasound recordings from ten patients undergoing heart surgery were analysed for the presence of embolic signals. The backscattered intensity of each embolic signal was modelled based on ultrasound scattering theory to provide an estimate of bubble diameter. The impact of showers of bubbles on cerebral blood-flow was then investigated using patient-specific Monte-Carlo simulations to model the accumulation and clearance of bubbles within a model vasculature.

Results

Analysis of Doppler ultrasound recordings revealed a minimum of 371 and maximum of 6476 bubbles entering the middle cerebral artery territories during surgery. This was estimated to correspond to a total volume of air ranging between 0.003 and 0.12 mL. Based on analysis of a total of 18667 embolic signals, the median diameter of bubbles entering the cerebral arteries was 33 μm (IQR: 18 to 69 μm). Although bubble diameters ranged from ~5 μm to 3.5 mm, the majority (85%) were less than 100 μm. Numerous small bubbles detected during cardiopulmonary bypass were estimated by Monte-Carlo simulation to be benign. However, during weaning from bypass, showers containing large macro-bubbles were observed, which were estimated to transiently affect up to 2.2% of arterioles.

Conclusions

Detailed analysis of Doppler ultrasound data can be used to provide an estimate of bubble diameter, total volume of air, and the likely impact of embolic showers on cerebral blood flow. Although bubbles are alarmingly numerous during surgery, our simulations suggest that the majority of bubbles are too small to be harmful.

Modelling of impaired cerebral blood flow due to gaseous emboli

Bubbles introduced to the arterial circulation during invasive medical procedures can have devastating consequences for brain function but their effects are currently difficult to quantify. Here we present a Monte Carlo simulation investigating the impact of gas bubbles on cerebral blood flow. For the first time, this model includes realistic adhesion forces, bubble deformation, fluid dynamical considerations, and bubble dissolution. This allows investigation of the effects of buoyancy, solubility, and blood pressure on embolus clearance. Our results illustrate that blockages depend on several factors, including the number and size distribution of incident emboli, dissolution time and blood pressure. We found it essential to model the deformation of bubbles to avoid overestimation of arterial obstruction. Incorporation of buoyancy effects within our model slightly reduced the overall level of obstruction but did not decrease embolus clearance times. We found that higher blood pressures generate lower levels of obstruction and improve embolus clearance. Finally, we demonstrate the effects of gas solubility and discuss potential clinical applications of the model.

Sizing gaseous emboli using Doppler embolic signal intensity

Extension of transcranial Doppler embolus detection to estimation of bubble size has historically been hindered by difficulties in applying scattering theory to the interpretation of clinical data. This article presents a simplified approach to the sizing of air emboli based on analysis of Doppler embolic signal intensity, by using an approximation to the full scattering theory that can be solved to estimate embolus size. Tests using simulated emboli show that our algorithm is theoretically capable of sizing 90% of "emboli" to within 10% of their true radius. In vitro tests show that 69% of emboli can be sized to within 20% of their true value under ideal conditions, which reduces to 30% of emboli if the beam and vessel are severely misaligned. Our results demonstrate that estimation of bubble size during clinical monitoring could be used to distinguish benign microbubbles from potentially harmful macrobubbles during intraoperative clinical monitoring.

Embolus trajectory through a physical replica of the major cerebral arteries

BACKGROUND AND PURPOSE

The observed distribution of cerebral infarcts varies markedly from expectations based on blood-flow volume or Doppler embolus detection. In this study, we used an in vitro model of the cerebral arteries to test whether embolus microspheres encountering the circle of Willis are carried proportionally to volume flow or express a preferred trajectory related to arterial morphology or embolus size.

METHODS

Our model consisted of a patient-specific silicone replica of the cerebral macrocirculation featuring physiologically realistic pulsatile flow of a blood-mimicking fluid at approximately 1000 mL/min and an input pressure of approximately 150/70 mm Hg. Particles of 200, 500, and 1000 microm diameter with equivalent density to thrombus were introduced to the carotid arteries and counted on exiting the model outlets.

RESULTS

The middle cerebral arteries (MCAs) of the replica attracted a disproportionate number of emboli compared with the anterior cerebral arteries; 98%+/-3% of 1000 microm and 93%+/-2% of 500 microm emboli entered the MCA compared with 82%+/-5% of the flow. The observed distribution of large emboli was consistent with the ratio of MCA:anterior cerebral artery infarcts, approximately 95% of which occur in territories supplied by the MCA. With decreasing embolus size, the distribution of emboli approaches that of the flow (approximately 89% of 200 microm emboli took the MCA).

CONCLUSIONS

Embolus trajectory through the cerebral arteries is dependent on embolus size and strongly favors the MCA for large emboli. The 70:30 ratio of MCA:anterior cerebral artery emboli observed by Doppler ultrasound is consistent with the trajectories of small emboli that tend to be asymptomatic.

Statistical physics of cerebral embolization leading to stroke

We discuss the physics of embolic stroke using a minimal model of emboli moving through the cerebral arteries. Our model of the blood flow network consists of a bifurcating tree into which we introduce particles (emboli) that halt flow on reaching a node of similar size. Flow is weighted away from blocked arteries inducing an effective interaction between emboli. We justify the form of the flow weighting using a steady flow (Poiseuille) analysis and a more complicated nonlinear analysis. We discuss free flowing and heavily congested limits and examine the transition from free flow to congestion using numerics. The correlation time is found to increase significantly at a critical value and a finite-size scaling is carried out. An order parameter for nonequilibrium critical behavior is identified as the overlap of blockages' flow shadows. Our work shows embolic stroke to be a feature of the cerebral blood flow network on the verge of a phase transition.