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.

The role of vascular complexity on optimal junction exponents.

We examine the role of complexity on arterial tree structures, determining globally optimal vessel arrangements using the Simulated AnneaLing Vascular Optimization algorithm, a computational method which we have previously used to reproduce features of cardiac and cerebral vasculatures. In order to progress computational methods for growing arterial networks, deeper understanding of the stability of computational arterial growth algorithms to complexity, variations in physiological parameters (such as metabolic costs for maintaining and pumping blood), and underlying assumptions regarding the value of junction exponents is needed. We determine the globally optimal structure of two-dimensional arterial trees; analysing how physiological parameters affect tree morphology and optimal bifurcation exponent. We find that considering the full complexity of arterial trees is essential for determining the fundamental properties of vasculatures. We conclude that optimisation-based arterial growth algorithms are stable against uncertainties in physiological parameters, while optimal bifurcation exponents (a key parameter for many arterial growth algorithms) are affected by the complexity of vascular networks and the boundary conditions dictated by organs.

Development of a globally optimised model of the cerebral arteries.

The cerebral arteries are difficult to reproduce from first principles, featuring interwoven territories, and intricate layers of grey and white matter with differing metabolic demand. The aim of this study was to identify the ideal configuration of arteries required to sustain an entire brain hemisphere based on minimisation of the energy required to supply the tissue. The 3D distribution of grey and white matter within a healthy human brain was first segmented from magnetic resonance images. A novel simulated annealing algorithm was then applied to determine the optimal configuration of arteries required to supply brain tissue. The model was validated through comparison of this ideal, entirely optimised, brain vasculature with the structure and properties of real arteries. This analysis established that the human cerebral vasculature is highly optimised; closely resembling the most energy efficient arrangement of vessels. In addition to local adherence to fluid dynamical optimisation principles, the optimised vasculature reproduced expected brain perfusion territories, featuring well-defined boundaries between anterior, middle and posterior regions. This validated brain vascular model and algorithm can be used for patient-specific modelling of stroke and cerebral haemodynamics, identification of sub-optimal conditions associated with vascular disease, and optimising vascular structures for tissue engineering applications and artificial organ design.

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.