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Soft tissue modeling is a challenging issue in tissue engineering. Tissue is a complex environment. It is assumed to represent viscoelastic behavior. Therefore, a complicated process is required to model its stress-strain relationship. In this paper, a non-integer order model is considered for the tissue’s mechanical behavior. The order indicates the amount that the tissue tends to behave as a pure viscous or pure elastic material. The main goal of the paper and the main contribution is to interpret the order as a function of the state of the material. To this aim, an experimental estimated model is used in which the order is considered as a function of time. Stress and strain signals are also available as functions of time. Then, an identification process is used to obtain the direct functionality of the order with respect to the state of the material (i.e. the momentary stress and strain). Data are gathered through an experimental setup. The stress signal calculated using a force sensor is highly noisy. Hence, de-noising is necessary. However, noise elimination may cause losing meaningful data. Also, a slight amount of noise enhances the generalization of the trained network in the identification process. Accordingly, a multi-level noise reduction method is used. The method is based on Empirical Mode Decomposition (EMD). To obtain the optimal noise reduction level, the noise reduction process is performed level by level and the best levels in train and test stages are chosen. Results show that supposing an explicit functionality between the order (as the amount of viscoelasticity) and the state of the tissue is reasonable. Also, it is verified that multi-level de-noising significantly improves the identification process. [ABSTRACT FROM AUTHOR]

This article presents a general solution scheme for finite horizon optimal control of variable order Caputo dynamic systems with specified initial and final conditions. The main approach of the article is using variable order calculus of variations. After deriving the necessary optimality conditions, as the main contribution of the article, a change of variable is used to rearrange the set of conditions as a set of coupled variable order differential equations. Then, a numerical method is introduced to solve the corresponding equations. Finally, a case study shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]