Numerical simulation of a stroke: Computational problems and methodology

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.

Mathematical Models of Blast-Induced TBI: Current Status, Challenges, and Prospects

Blast-induced traumatic brain injury (TBI) has become a signature wound of recent military activities and is the leading cause of death and long-term disability among U.S. soldiers. The current limited understanding of brain injury mechanisms impedes the development of protection, diagnostic, and treatment strategies. We believe mathematical models of blast wave brain injury biomechanics and neurobiology, complemented with in vitro and in vivo experimental studies, will enable a better understanding of injury mechanisms and accelerate the development of both protective and treatment strategies. The goal of this paper is to review the current state of the art in mathematical and computational modeling of blast-induced TBI, identify research gaps, and recommend future developments. A brief overview of blast wave physics, injury biomechanics, and the neurobiology of brain injury is used as a foundation for a more detailed discussion of multiscale mathematical models of primary biomechanics and secondary injury and repair mechanisms. The paper also presents a discussion of model development strategies, experimental approaches to generate benchmark data for model validation, and potential applications of the model for prevention and protection against blast wave TBI.

Modelling methodology in physiopathology

Diseases are complex systems. Modelling them, i.e. systems physiopathology, is a quite demanding, complicated, multidimensional, multiscale process. As such, in order to achieve the goal of the model and further to optimise a rather-time and resource-consuming process, a relevant and easy to practice methodology is required. It includes guidance for validation. Also, the model development should be managed as a complicated process, along a strategy which has been elaborated in the beginning. It should be flexible enough to meet every case. A model is a representation of the available knowledge. All available knowledge does not have the same level of evidence and, further, there is a large variability of the values of all parameters (e.g. affinity constant or ionic current) across the literature. In addition, in a complex biological system there are always values lacking for a few or sometimes many parameters. All these three aspects are sources of uncertainty on the range of validity of the models and raise unsolved problems for designing a relevant model. Tools and techniques for integrating the parameter range of experimental values, level of evidence and missing data are needed.