Abstraction and operator characterization of fractal ladder viscoelastic hyper-cell for ligaments and tendons

This study investigates the viscoelastic behavior of soft bio-fibres in association with their fractal structures. A spring-dashpot fractal network with the self-similar topology, named the -type fractal ladder hyper-cell (FLHC), is abstracted from the micro/nano-structure of ligaments and tendons (LTs). Its constitutive operator is derived by the Heaviside operational calculus, which is of intrinsic fractional order. In terms of this operator, the long-term viscoelastic relaxation of bio-fibres arising from the fractal ladder topology is expounded. In addition, the fractional-order viscoelastic constitutive equation is obtained based on the FLHC of LTs, and its results are consistent with those of available human knee and spinal LT relaxation experiments. Results on the constitutive equation of FLHCs are formulated into two propositions. The multidisciplinary invariance and implications from the fractal ladder pattern of bio-fibres are also discussed.

A forward-inverse dynamics modeling framework for human musculoskeletal multibody system

Multibody musculoskeletal modeling of human gait has been proved helpful in investigating the pathology of musculoskeletal disorders.However,conventional inverse dynamics methods rely on external force sensors and cannot capture the nonlinear muscle behaviors.Meanwhile,the forward dynamics approach is computationally demanding and only suited for relatively simple tasks.This study proposed an integrated simulation methodology to fulfill the requirements of estimating foot-ground reaction force,tendon elasticity,and muscle recruitment optimization.A hybrid motion capture system,which combines the marker-based infrared device and markerless tracking through deep convolutional neural networks,was developed to track lower limb movements.The foot-ground reaction forces were determined by a contact model for soft materials,and its parameters were estimated using a two-step optimization method.The muscle recruitment problem was first resolved via a static optimization algorithm,and the obtained muscle activations were used as initial values for further simulation.A torque tracking procedure was then performed by minimizing the errors of joint torques calculated by musculotendon equilibrium equations and inverse dynamics.The proposed approach was validated against the electromyography measurements of a healthy subject during gait.The simulation framework provides a robust way of predicting joint torques,musculotendon forces,and muscle activations,which can be beneficial for understanding the biomechanics of normal and pathological gait.