Non-linear modeling of active biohybrid materials

Recent advances in engineered muscle tissue attached to a synthetic substrate motivates the development of appropriate constitutive and numerical models. Applications of active materials can be expanded by using robust, non-mammalian muscle cells, such as those of Manduca sexta. In this study, we propose a model to assist in the analysis of biohybrid constructs by generalizing a recently proposed constitutive law for Manduca muscle tissue. The continuum model accounts (i) for the stimulation of muscle fibers by introducing multiple stress-free reference configurations for the active and passive states and (ii) for the hysteretic response by specifying a pseudo-elastic energy function. A simple example representing uniaxial loading-unloading is used to validate and verify the characteristics of the model. Then, based on experimental data of muscular thin films, a more complex case shows the qualitative potential of Manduca muscle tissue in active biohybrid constructs

Strain controlled biaxial stretch: An experimental characterization of natural rubber

In this paper we provide new experimental data showing the response of 40A natural rubber in uniaxial, pure shear and biaxial tension. Real-time biaxial strain control allows for independent and automatic variation of the velocity of extension and retraction of each actuator to maintain the pre-selected deformation rate within the gage area of the specimen. The remaining part of the paper focuses on the Valanis-Landel hypothesis that is used to verify and validate the consistency of the data. We use a three term Ogden model to derive stress-stretch relations to validate the experimental data. The material model parameters are determined using the primary loading path in uniaxial and equibiaxial tension. Excellent agreement is found when the model is used to predict the response in biaxial tension for different maximum in-plane stretches. The application of the Valanis-Landel hypothesis also results in excellent agreement with the theoretical prediction

A constitutive description of the anisotropic response of the fascia lata

In this paper we propose a constitutive model to analyze in-plane extension of goat fascia lata. We first perform a histological analysis of the fascia that shows a well-organized bi-layered arrangement of undulated collagen fascicles oriented along two well defined directions. To develop a model consistent with the tissue structure we identify the absolute and relative thickness of each layer and the orientation of the preferred directions. New data are presented showing the mechanical response in uniaxial and planar biaxial extension. The paper proposes a constitutive relation to describe the mechanical response. We provide a summary of the main ingredients of the nonlinear theory of elasticity and introduce a suitable strain-energy function to describe the anisotropic response of the fascia. We validate the model by showing good fit of the numerical results and the experimental data. Comments are included about differences and analogies between goat fascia lata and the human iliotibial band.Organismic and Evolutionary Biolog

Isolation and Maintenance-Free Culture of Contractile Myotubes from Manduca sexta Embryos

Skeletal muscle tissue engineering has the potential to treat tissue loss and degenerative diseases. However, these systems are also applicable for a variety of devices where actuation is needed, such as microelectromechanical systems (MEMS) and robotics. Most current efforts to generate muscle bioactuators are focused on using mammalian cells, which require exacting conditions for survival and function. In contrast, invertebrate cells are more environmentally robust, metabolically adaptable and relatively autonomous. Our hypothesis is that the use of invertebrate muscle cells will obviate many of the limitations encountered when mammalian cells are used for bioactuation. We focus on the tobacco hornworm, Manduca sexta, due to its easy availability, large size and well-characterized muscle contractile properties. Using isolated embryonic cells, we have developed culture conditions to grow and characterize contractile M. sexta muscles. The insect hormone 20-hydroxyecdysone was used to induce differentiation in the system, resulting in cells that stained positive for myosin, contract spontaneously for the duration of the culture, and do not require media changes over periods of more than a month. These cells proliferate under normal conditions, but the application of juvenile hormone induced further proliferation and inhibited differentiation. Cellular metabolism under normal and low glucose conditions was compared for C2C12 mouse and M. sexta myoblast cells. While differentiated C2C12 cells consumed glucose and produced lactate over one week as expected, M. sexta muscle did not consume significant glucose, and lactate production exceeded mammalian muscle production on a per cell basis. Contractile properties were evaluated using index of movement analysis, which demonstrated the potential of these cells to perform mechanical work. The ability of cultured M. sexta muscle to continuously function at ambient conditions without medium replenishment, combined with the interesting metabolic properties, suggests that this cell source is a promising candidate for further investigation toward bioactuator applications

Soft network composite materials with deterministic and bio-inspired designs

Hard and soft structural composites found in biology provide inspiration for the design of advanced synthetic materials. Many examples of bio-inspired hard materials can be found in the literature; far less attention has been devoted to soft systems. Here we introduce deterministic routes to low-modulus thin film materials with stress/strain responses that can be tailored precisely to match the non-linear properties of biological tissues, with application opportunities that range from soft biomedical devices to constructs for tissue engineering. The approach combines a low-modulus matrix with an open, stretchable network as a structural reinforcement that can yield classes of composites with a wide range of desired mechanical responses, including anisotropic, spatially heterogeneous, hierarchical and self-similar designs. Demonstrative application examples in thin, skin-mounted electrophysiological sensors with mechanics precisely matched to the human epidermis and in soft, hydrogel-based vehicles for triggered drug release suggest their broad potential uses in biomedical devices. © 2015 Macmillan Publishers Limited. All rights reservedopen7

Classical R-matrix theory for bi-Hamiltonian field systems

The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The theory is developed for (1+1)-dimensional case where the space variable belongs either to R or to various discrete sets. Then, the extension onto (2+1)-dimensional case is made, when the second space variable belongs to R. The formalism presented contains many proofs and important details to make it self-contained and complete. The general theory is applied to several infinite dimensional Lie algebras in order to construct both dispersionless and dispersive (soliton) integrable field systems.Comment: review article, 39 page

Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models

A unified variational theory is proposed for a general class of multiscale models based on the concept of Representative Volume Element. The entire theory lies on three fundamental principles: (1) kinematical admissibility, whereby the macro- and micro-scale kinematics are defined and linked in a physically meaningful way; (2) duality, through which the natures of the force- and stress-like quantities are uniquely identified as the duals (power-conjugates) of the adopted kinematical variables; and (3) the Principle of Multiscale Virtual Power, a generalization of the well-known Hill-Mandel Principle of Macrohomogeneity, from which equilibrium equations and homogenization relations for the force- and stress-like quantities are unequivocally obtained by straightforward variational arguments. The proposed theory provides a clear, logically-structured framework within which existing formulations can be rationally justified and new, more general multiscale models can be rigorously derived in well-defined steps. Its generality allows the treatment of problems involving phenomena as diverse as dynamics, higher order strain effects, material failure with kinematical discontinuities, fluid mechanics and coupled multi-physics. This is illustrated in a number of examples where a range of models is systematically derived by following the same steps. Due to the variational basis of the theory, the format in which derived models are presented is naturally well suited for discretization by finite element-based or related methods of numerical approximation. Numerical examples illustrate the use of resulting models, including a non-conventional failure-oriented model with discontinuous kinematics, in practical computations