Numerical simulation and pattern characterization of nonlinear spatiotemporal dynamics on fractal surfaces for the whole-heart modeling applications

Engineered and natural systems often involve irregular and self-similar geometric forms, which is called fractal geometry. For instance, precision machining produces a visually flat surface, while which looks like a rough mountain in the nanometer scale under the microscope. Human heart consists of...

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Veröffentlicht in:The European physical journal. B, Condensed matter physics Jg. 89; H. 8; S. 1 - 16
Hauptverfasser: Chen, Yun, Yang, Hui
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2016
Springer
Springer Nature B.V
Schlagworte:
Cardiology
Complex Systems
Condensed Matter Physics
Electric properties
Electrical conduction
Euclidean geometry
Fluid- and Aerodynamics
Fractal geometry
Initial conditions
Modelling
Nonlinear dynamics
Numerical analysis
Pattern recognition
Physics
Physics and Astronomy
Precision machining
Regular Article
Self-similarity
Solid State Physics
Statistical and Nonlinear Physics
ISSN:1434-6028, 1434-6036
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Zusammenfassung:Engineered and natural systems often involve irregular and self-similar geometric forms, which is called fractal geometry. For instance, precision machining produces a visually flat surface, while which looks like a rough mountain in the nanometer scale under the microscope. Human heart consists of a fractal network of muscle cells, Purkinje fibers, arteries and veins. Cardiac electrical activity exhibits highly nonlinear and fractal behaviors. Although space-time dynamics occur on the fractal geometry, e.g., chemical etching on the surface of machined parts and electrical conduction in the heart, most of existing works modeled space-time dynamics (e.g., reaction, diffusion and propagation) on the Euclidean geometry (e.g., flat planes and rectangular volumes). This brings inaccurate approximation of real-world dynamics, due to sensitive dependence of nonlinear dynamical systems on initial conditions. In this paper, we developed novel methods and tools for the numerical simulation and pattern recognition of spatiotemporal dynamics on fractal surfaces of complex systems, which include (1) characterization and modeling of fractal geometry, (2) fractal-based simulation and modeling of spatiotemporal dynamics, (3) recognizing and quantifying spatiotemporal patterns. Experimental results show that the proposed methods outperform traditional modeling approaches based on the Euclidean geometry, and provide effective tools to model and characterize space-time dynamics on fractal surfaces of complex systems.
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ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2016-60960-6