179Mathematical perspectives on biomechanical signal processing

Le résumé fourni par la source

The fields of biomedical engineering and healthcare have been significantly incorporating biomechanical signals and measurements. Biomechanical signals from the cardiovascular, musculoskeletal, and neural systems neural systems represent some of the most complex dynamics that can be modelled using mathematical approaches. This is often done by utilizing linear differential equations linear differential equation used to formulate mathematical models representing the time evolution of what is experimentally measured and quantified in terms of biomechanical fields, forces, and flows. However, these linear models were incapable of describing the actual complexity observed in biological tissues. As a result of these limitiations, researchers now have started studying the thought of applying fractional calculus. This will simulate the dynamics in tissues much more effectively. The viscoelastic and memory-dependent properties of biological materials will be explained better by models based on fractional calculus. This helps to improve the characterization of biomechanical signals. Conducting involving numerical processing, such as velocity and acceleration signal acquisition from position/angular measurements, brings measurement uncertainties that can be handled much better with approaches based on fractional calculus. Comparative filtering methods have been proposed to optimize the dynamic biomechanical measurement process and minimize the contribution of uncertainty from the processing method. This could vary from injury to remodeling bone, to tissue engineering, and also to cases of traumatic blast injuries of the brain. They work on bringing together the biomechanical and biological mechanisms. While models of biomechanical signals and processes have been analyzed through mathematical and computational means, other aspects of analysis with regards to biomechanical data have used the approaches in question. For instance, analysis of variance models with smoothing spline analysis can be applied to compare noisy biomechanical signals from several locations and experimental conditions. Therefore, these statistical models are very suitable for robust biomechanical quantification between experimental conditions and/or subject populations. Other applications include the biomechanical modeling in fields such as bone remodeling, electromechanical platform dynamics, and inverse muscle modeling. Such applications show the flexibility of the mathematical and computational methods in attempting to understand and analyze complex biomechanical systems.

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