Zero-thickness interface models are developed to describe the encapsulation of microbubble contrast agents. Two different rheological models of the interface, Newtonian (viscous) and viscoelastic, with rheological parameters such as surface tension, surface dilatational viscosity, and surface dilatational elasticity are presented to characterize the encapsulation. The models are applied to characterize a widely used microbubble based ultrasound contrast agent. Attenuation of ultrasound passing through a solution of contrast agent is measured. The model parameters for the contrast agent are determined by matching the linearized model dynamics with measured attenuation data. The models are investigated for its ability to match with other experiments. Specifically, model predictions are compared with scattered fundamental and subharmonic responses. Experiments and model prediction results are discussed along with those obtained using an existing model [Church, J. Acoust. Soc. Am. 97, 1510 (1995) and Hoff et al., J. Acoust. Soc. Am. 107, 2272 (2000)] of contrast agents.

Four dimensional (4D) printing is an emerging technology with great capacity for fabricating complex, stimuli-responsive 3D structures, providing great potential for tissue and organ engineering applications. Although the 4D concept was first highlighted in 2013, extensive research has rapidly developed, along with more-in-depth understanding and assertions regarding the definition of 4D. In this review, we begin by establishing the criteria of 4D printing, followed by an extensive summary of state-of-the-art technological advances in the field. Both transformation-preprogrammed 4D printing and 4D printing of shape memory polymers are intensively surveyed. Afterwards we will explore and discuss the applications of 4D printing in tissue and organ regeneration, such as developing synthetic tissues and implantable scaffolds, as well as future perspectives and conclusions.

Gas diffusion from an encapsulated microbubble is modeled using an explicit linear relation for gas permeation through the encapsulation. Both the cases of single gas (air) and multiple gases (perfluorocarbon inside the bubble and air dissolved in surrounding liquid) are considered. An analytical expression for the dissolution time for an encapsulated air bubble is obtained; it showed that for small permeability the dissolution time increases linearly with decreasing permeability. A perfluorocarbon-filled contrast microbubble such as Definity was predicted to experience a transient growth due to air infusion before it dissolves in conformity with previous experimental findings. The growth phase occurs only for bubbles with a critical value of initial partial mole fraction of perfluorocarbon relative to air. With empirically obtained property values, the dissolution time of a 2.5 micron diameter (same as that of Definity) lipid coated octafluoropropane bubble with surface tension 25 mN/m predicts a lifetime of 42 minutes in an air saturated medium. The properties such as shell permeability, surface tension, relative mole fraction of octafluoropropane are varied to investigate their effects on the time scales of bubble growth and dissolution including their asymptotic scalings where appropriate. The dissolution dynamics scales with permeability, in that when the time is nondimensioanlized with permeability, curves for different permeabilities collapse on a single curve. Investigation of bubbles filled with other gases (non-octafluoropropane perfluorocarbon and sulfur hexafluoride) indicates longer dissolution time due to lower solubility and lower diffusivity for larger gas molecules. For such micron size encapsulated bubbles, lifetime of hours is possible only at extremely low surface tension (<1mN/m) or at extreme oversaturation.

4D printing represents one of the most advanced fabrication techniques for prospective applications in tissue engineering, biomedical devices, and soft robotics, among others. In this study, a novel multiresponsive architecture is developed through stereolithography-based 4D printing, where a universal concept of stress-induced shape transformation is applied to achieve the 4D reprogramming. The light-induced graded internal stress followed by a subsequent solvent-induced relaxation, driving an autonomous and reversible change of the programmed configuration after printing, is employed and investigated in depth and details. Moreover, the fabricated construct possesses shape memory property, offering a characteristic of multiple shape change. Using this novel multiple responsive 4D technique, a proof-of-concept smart nerve guidance conduit is demonstrated on a graphene hybrid 4D construct providing outstanding multifunctional characteristics for nerve regeneration including physical guidance, chemical cues, dynamic self-entubulation, and seamless integration. By employing this fabrication technique, creating multiresponsive smart architectures, as well as demonstrating application potential, this work paves the way for truly initiation of 4D printing in various high-value research fields.

Two nonlinear interfacial elasticity models-interfacial elasticity decreasing linearly and exponentially with area fraction-are developed for the encapsulation of contrast microbubbles. The strain softening ͑decreasing elasticity͒ results from the decreasing association between the constitutive molecules of the encapsulation. The models are used to find the characteristic properties ͑surface tension, interfacial elasticity, interfacial viscosity and nonlinear elasticity parameters͒ for a commercial contrast agent. Properties are found using the ultrasound attenuation measured through a suspension of contrast agent. Dynamics of the resulting models are simulated, compared with other existing models and discussed. Imposing non-negativity on the effective surface tension ͑the encapsulation experiences no net compressive stress͒ shows "compression-only" behavior. The exponential and the quadratic ͑linearly varying elasticity͒ models result in similar behaviors. The validity of the models is investigated by comparing their predictions of the scattered nonlinear response for the contrast agent at higher excitations against experimental measurement. All models predict well the scattered fundamental response. The nonlinear strain softening included in the proposed elastic models of the encapsulation improves their ability to predict subharmonic response. They predict the threshold excitation for the initiation of subharmonic response and its subsequent saturation.