Physics-Informed Deep-Learning For Elasticity: Forward, Inverse, and Mixed Problems.

Elastography is a medical imaging technique used to measure the elasticity of tissues by comparing ultrasound signals before and after a light compression. The lateral resolution of ultrasound is much inferior to the axial resolution. Current elastography methods generally require both axial and lateral displacement components, making them less effective for clinical applications. Additionally, these methods often rely on the assumption of material incompressibility, which can lead to inaccurate elasticity reconstruction as no materials are truly incompressible. To address these challenges, a new physics-informed deep-learning method for elastography is proposed. This new method integrates a displacement network and an elasticity network to reconstruct the Young's modulus field of a heterogeneous object based on only a measured axial displacement field. It also allows for the removal of the assumption of material incompressibility, enabling the reconstruction of both Young's modulus and Poisson's ratio fields simultaneously. The authors demonstrate that using multiple measurements can mitigate the potential error introduced by the "eggshell" effect, in which the presence of stiff material prevents the generation of strain in soft material. These improvements make this new method a valuable tool for a wide range of applications in medical imaging, materials characterization, and beyond.

Mechanically and electrically biocompatible hydrogel ionotronic fibers for fabricating structurally stable implants and enabling noncontact physioelectrical modulation.

Narrowing the mechanical and electrical mismatch between tissue and implantable microelectronics is essential for reducing immune responses and modulating physioelectrical signals. Nevertheless, the design of such implantable microelectronics remains a challenge due to the limited availability of suitable materials. Here, the fabrication of an electrically and mechanically biocompatible alginate hydrogel ionotronic fiber (AHIF) is reported, which is constructed by combing ionic chelation-assisted wet-spinning and mechanical training. The synergistic effects of these two processes allow the alginate to form a highly-oriented nanofibril and molecular network, with a hierarchical structure highly similar to that of natural fibers. These favourable structural features endow AHIF with tissue-mimicking mechanical characteristics, such as self-stiffening and soft tissue-like mechanical properties. In addition, tissue-like chemical components, i.e., biomacromolecules, Ca2+ ions, and water, endow AHIF with properties including biocompatibility and tissue-matching conductivity. These advantages bring light to the application of AHIFs in electrically-conductive implantable devices. As a prototype, an AHIF is designed to perform physioelectrical modulation through noncontact electromagnetic induction. Through experimental and machine learning optimizations, physioelectrical-like signals generated by the AHIF are used to identify the geometry and tension state of the implanted device in the body. Such an intelligent AHIF system has promising application prospects in bioelectronics, IntelliSense, and human-machine interactions.

Learning hidden elasticity with deep neural networks.

Elastography is an imaging technique to reconstruct elasticity distributions of heterogeneous objects. Since cancerous tissues are stiffer than healthy ones, for decades, elastography has been applied to medical imaging for noninvasive cancer diagnosis. Although the conventional strain-based elastography has been deployed on ultrasound diagnostic-imaging devices, the results are prone to inaccuracies. Model-based elastography, which reconstructs elasticity distributions by solving an inverse problem in elasticity, may provide more accurate results but is often unreliable in practice due to the ill-posed nature of the inverse problem. We introduce ElastNet, a de novo elastography method combining the theory of elasticity with a deep-learning approach. With prior knowledge from the laws of physics, ElastNet can escape the performance ceiling imposed by labeled data. ElastNet uses backpropagation to learn the hidden elasticity of objects, resulting in rapid and accurate predictions. We show that ElastNet is robust when dealing with noisy or missing measurements. Moreover, it can learn probable elasticity distributions for areas even without measurements and generate elasticity images of arbitrary resolution. When both strain and elasticity distributions are given, the hidden physics in elasticity-the conditions for equilibrium-can be learned by ElastNet.

Mechanical Training-Driven Structural Remodeling: A Rational Route for Outstanding Highly Hydrated Silk Materials.

Highly hydrated silk materials (HHSMs) have been the focus of extensive research due to their usefulness in tissue engineering, regenerative medicine, and soft devices, among other fields. However, HHSMs have weak mechanical properties that limit their practical applications. Inspired by the mechanical training-driven structural remodeling strategy (MTDSRS) in biological tissues, herein, engineered MTDSRS is developed for self-reinforcement of HHSMs to improve their inherent mechanical properties and broaden potential utility. The MTDSRS consists of repetitive mechanical training and solvent-induced conformation transitions. Solvent-induced conformation transition enables the formation of ß-sheet physical crosslinks among the proteins, while the repetitive mechanical loading allows the rearrangement of physically crosslinked proteins along the loading direction. Such synergistic effects produce strong and stiff mechanically trained-HHSMs (MT-HHSMs). The fracture strength and Young's modulus of the resultant MT-HHSMs (water content of 43 ± 4%) reach 4.7 ± 0.9 and 21.3 ± 2.1 MPa, respectively, which are 8-fold stronger and 13-fold stiffer than those of the as-prepared HHSMs, as well as superior to most previously reported HHSMs with comparable water content. In addition, the animal silk-like highly oriented molecular crosslinking network structure also provides MT-HHSMs with fascinating physical and functional features, such as stress-birefringence responsibility, humidity-induced actuation, and repeatable self-folding deformation.

Nano-topology optimization for materials design with atom-by-atom control.

Atoms are the building blocks of matter that make up the world. To create new materials to meet some of civilization's greatest needs, it is crucial to develop a technology to design materials on the atomic and molecular scales. However, there is currently no computational approach capable of designing materials atom-by-atom. In this study, we consider the possibility of direct manipulation of individual atoms to design materials at the nanoscale using a proposed method coined "Nano-Topology Optimization". Here, we apply the proposed method to design nanostructured materials to maximize elastic properties. Results show that the performance of our optimized designs not only surpasses that of the gyroid and other triply periodic minimal surface structures, but also exceeds the theoretical maximum (Hashin-Shtrikman upper bound). The significance of the proposed method lies in a platform that allows computers to design novel materials atom-by-atom without the need of a predetermined design.

Generative Deep Neural Networks for Inverse Materials Design Using Backpropagation and Active Learning.

In recent years, machine learning (ML) techniques are seen to be promising tools to discover and design novel materials. However, the lack of robust inverse design approaches to identify promising candidate materials without exploring the entire design space causes a fundamental bottleneck. A general-purpose inverse design approach is presented using generative inverse design networks. This ML-based inverse design approach uses backpropagation to calculate the analytical gradients of an objective function with respect to design variables. This inverse design approach is capable of overcoming local minima traps by using backpropagation to provide rapid calculations of gradient information and running millions of optimizations with different initial values. Furthermore, an active learning strategy is adopted in the inverse design approach to improve the performance of candidate materials and reduce the amount of training data needed to do so. Compared to passive learning, the active learning strategy is capable of generating better designs and reducing the amount of training data by at least an order-of-magnitude in the case study on composite materials. The inverse design approach is compared with conventional gradient-based topology optimization and gradient-free genetic algorithms and the pros and cons of each method are discussed when applied to materials discovery and design problems.

Dynamic pigmentary and structural coloration within cephalopod chromatophore organs.

Chromatophore organs in cephalopod skin are known to produce ultra-fast changes in appearance for camouflage and communication. Light-scattering pigment granules within chromatocytes have been presumed to be the sole source of coloration in these complex organs. We report the discovery of structural coloration emanating in precise register with expanded pigmented chromatocytes. Concurrently, using an annotated squid chromatophore proteome together with microscopy, we identify a likely biochemical component of this reflective coloration as reflectin proteins distributed in sheath cells that envelop each chromatocyte. Additionally, within the chromatocytes, where the pigment resides in nanostructured granules, we find the lens protein Ω- crystallin interfacing tightly with pigment molecules. These findings offer fresh perspectives on the intricate biophotonic interplay between pigmentary and structural coloration elements tightly co-located within the same dynamic flexible organ - a feature that may help inspire the development of new classes of engineered materials that change color and pattern.

Polydopamine and eumelanin models in various oxidation states.

We report a comprehensive ab initio structural investigation of more than 43 000 probable molecular structures of polydopamine (PDA) and eumelanin in various oxidation states. With the aid of a computational approach including a brute-force algorithmic generation of chemical isomers and density functional theory, all probable oxidized 5,6-dihydroxyindole (DHI) oligomers, ranging from dimers to tetramers, have been systematically generated and evaluated. We identify a set of the most stable molecular structures of PDA and eumelanin which represent the chemically diverse nature of these materials. Results show that more planar molecular structures have a tendency to be more stable. We also observe that, in some cases, forming cyclic molecular structures could reduce the energy of a DHI tetramer and make it more stable. This finding supports the hypothesis that cyclic molecules could exist in eumelanin-like materials. Additionally, the cyclic molecular models proposed in this work are energetically more favorable than the popular porphyrin-like models in this field.

Ultrathin thermoresponsive self-folding 3D graphene.

Graphene and other two-dimensional materials have unique physical and chemical properties of broad relevance. It has been suggested that the transformation of these atomically planar materials to three-dimensional (3D) geometries by bending, wrinkling, or folding could significantly alter their properties and lead to novel structures and devices with compact form factors, but strategies to enable this shape change remain limited. We report a benign thermally responsive method to fold and unfold monolayer graphene into predesigned, ordered 3D structures. The methodology involves the surface functionalization of monolayer graphene using ultrathin noncovalently bonded mussel-inspired polydopamine and thermoresponsive poly(N-isopropylacrylamide) brushes. The functionalized graphene is micropatterned and self-folds into ordered 3D structures with reversible deformation under a full control by temperature. The structures are characterized using spectroscopy and microscopy, and self-folding is rationalized using a multiscale molecular dynamics model. Our work demonstrates the potential to design and fabricate ordered 3D graphene structures with predictable shape and dynamics. We highlight applicability by encapsulating live cells and creating nonlinear resistor and creased transistor devices.

Polydopamine and eumelanin molecular structures investigated with ab initio calculations.

A set of computational methods that contains a brute-force algorithmic generation of chemical isomers, molecular dynamics (MD) simulations, and density functional theory (DFT) calculations is reported and applied to investigate nearly 3000 probable molecular structures of polydopamine (PDA) and eumelanin. All probable early-polymerized 5,6-dihydroxyindole (DHI) oligomers, ranging from dimers to tetramers, have been systematically analyzed to find the most stable geometry connections as well as to propose a set of molecular models that represents the chemically diverse nature of PDA and eumelanin. Our results indicate that more planar oligomers have a tendency to be more stable. This finding is in good agreement with recent experimental observations, which suggested that PDA and eumelanin are composed of nearly planar oligomers that appear to be stacked together via π-π interactions to form graphite-like layered aggregates. We also show that there is a group of tetramers notably more stable than the others, implying that even though there is an inherent chemical diversity in PDA and eumelanin, the molecular structures of the majority of the species are quite repetitive. Our results also suggest that larger oligomers are less likely to form. This observation is also consistent with experimental measurements, supporting the existence of small oligomers instead of large polymers as main components of PDA and eumelanin. In summary, this work brings an insight into the controversial structure of PDA and eumelanin, explaining some of the most important structural features, and providing a set of molecular models for more accurate modeling of eumelanin-like materials.

Polydopamine and eumelanin: from structure-property relationships to a unified tailoring strategy.

CONSPECTUS: Polydopamine (PDA), a black insoluble biopolymer produced by autoxidation of the catecholamine neurotransmitter dopamine (DA), and synthetic eumelanin polymers modeled to the black functional pigments of human skin, hair, and eyes have burst into the scene of materials science as versatile bioinspired functional systems for a very broad range of applications. PDA is characterized by extraordinary adhesion properties providing efficient and universal surface coating for diverse settings that include drug delivery, microfluidic systems, and water-treatment devices. Synthetic eumelanins from dopa or 5,6-dihydroxyindoles are the focus of increasing interest as UV-absorbing agents, antioxidants, free radical scavengers, and water-dependent hybrid electronic-ionic semiconductors. Because of their peculiar physicochemical properties, eumelanins and PDA hold considerable promise in nanomedicine and bioelectronics, as they are biocompatible, biodegradable, and exhibit suitable mechanical properties for integration with biological tissues. Despite considerable similarities, very few attempts have so far been made to provide an integrated unifying perspective of these two fields of technology-oriented chemical research, and progress toward application has been based more on empirical approaches than on a solid conceptual framework of structure-property relationships. The present Account is an attempt to fill this gap. Following a vis-à-vis of PDA and eumelanin chemistries, it provides an overall view of the various levels of chemical disorder in both systems and draws simple correlations with physicochemical properties based on experimental and computational approaches. The potential of large-scale simulations to capture the macroproperties of eumelanin-like materials and their hierarchical structures, to predict the physicochemical properties of new melanin-inspired materials, to understand the structure-property-function relationships of these materials from the bottom up, and to design and optimize materials to achieve desired properties is illustrated. The impact of synthetic conditions on melanin structure and physicochemical properties is systematically discussed for the first time. Rational tailoring strategies directed to critical control points of the synthetic pathways, such as dopaquinone, DAquinone, and dopachrome, are then proposed, with a view to translating basic chemical knowledge into practical guidelines for material manipulation and tailoring. This key concept is exemplified by the recent demonstration that varying DA concentration, or using Tris instead of phosphate as the buffer, results in PDA materials with quite different structural properties. Realizing that PDA and synthetic eumelanins belong to the same family of functional materials may foster unprecedented synergisms between research fields that have so far been apart in the pursuit of tailorable and marketable materials for energy, biomedical, and environmental applications.

Excitonic effects from geometric order and disorder explain broadband optical absorption in eumelanin.

Eumelanin is a ubiquitous biological pigment, and the origin of its broadband absorption spectrum has long been a topic of scientific debate. Here, we report a first-principles computational investigation to explain its broadband absorption feature. These computations are complemented by experimental results showing a broadening of the absorption spectra of dopamine solutions upon their oxidation. We consider a variety of eumelanin molecular structures supported by experiments or theoretical studies, and calculate the absorption spectra with proper account of the excitonic couplings based on the Frenkel exciton model. The interplay of geometric order and disorder of eumelanin aggregate structures broadens the absorption spectrum and gives rise to a relative enhancement of absorption intensity at the higher-energy end, proportional to the cube of absorption energy. These findings show that the geometric disorder model is as able as the chemical disorder model, and complements this model, to describe the optical properties of eumelanin.

Molecular mechanics of elastic and bendable caffeine co-crystals.

Complementing recent experimental results, here we report a computational study of remarkably flexible, elastically bendable caffeine cocrystals (cocrystal solvate 1), formed from caffeine (CAF), 4-chloro-3-nitrobenzoic acid (CNB), and methanol, and compare with its unsolvated brittle form, 1 (dry). We show that 1 is able to maintain stable cocrystal structures at temperatures between 100 K and 400 K. The tensile and compressive Young's modulus of 1 are close to ~10 GPa. The ultimate strength is more than 600 MPa in tensile and 400 MPa in compressive at temperature of 100 K. The simulation results of the structural and mechanical properties of 1 are in good agreement with our previous experimental work. Notably, before the ultimate tensile stress, the stress-to-strain curves of 1 show linear behavior, but 1 (dry) show nonlinear behavior. This study might explain the remarkable elasticity of 1 and is relevant to the design of high-performance organic materials with excellent self-healing or efficient stress dissipating properties.

Tuning heterogeneous poly(dopamine) structures and mechanics: in silico covalent cross-linking and thin film nanoindentation.

Mussel-inspired synthetic poly(dopamine) thin films from dihydroxyphenylalanine (DOPA) and lysine, structurally similar to natural melanin, have drawn extensive interest as a versatile surface functionalization and coating material for use in a broad range of applications. In order to gain a better understanding of its complex and heterogeneous polymeric structure and mechanical properties, we report a computational model of poly(dopamine) by mimicking the polymerization process of the intermediate oxidized product of dopamine, 5,6-dihydroxyindole (DHI), via controlled in silico covalent cross-linking under the two most possible reaction schemes proposed in experiments. To validate our results using experiment, we synthesize poly(dopamine) thin films and perform experimental nanoindentations on the film. We observe an overall linear behavior for Young's modulus as a function of the degree of cross-linking, demonstrating the possibility of enhancing the mechanical robustness of poly(dopamine) materials by increasing the extent of polymerization. At the highest degree of polymerization considered (70%), the model mimics the linear tetrameric model for poly(dopamine) and melanin. At this degree of polymerization, we find a Young's modulus of 4.1-4.4 GPa, in agreement with our nanoindentation results of 4.3-10.5 GPa, previous experiments for natural melanin, as well as simulation results for the cyclic tetrameric melanin model (Chen et al., ACS Nano, 2013). Our results suggest that the non-covalent DHI aggregate model might not be appropriate to represent the structure of poly(dopamine) and melanin-like materials, since it gives a much smaller Young's modulus than the experimental lower bound. Our model not only nicely complements the previous computational work, but also provides new computational tools to study the heterogeneous structural and physicochemical properties of poly(dopamine) and melanin, as well as their formation pathways.

Self-assembly of tetramers of 5,6-dihydroxyindole explains the primary physical properties of eumelanin: experiment, simulation, and design.

Eumelanin is a ubiquitous pigment in nature and has many intriguing physicochemical properties, such as broad-band and monotonous absorption spectrum, antioxidant and free radical scavenging behavior, and strong nonradiative relaxation of photoexcited electronic states. These properties are highly related to its structural and mechanical properties and make eumelanin a fascinating candidate for the design of multifunctional nanomaterials. Here we report joint experimental-computational investigation of the structural and mechanical properties of eumelanin assemblies produced from dopamine, revealing that the mass density of dry eumelanin is 1.55 g/cm³ and its Young's modulus is ≈5 GPa. We also find that wet eumelanin has a lower mass density and Young's modulus depending on the water-to-melanin ratio. Most importantly, our data show that eumelanin molecules tend to form secondary structures based on noncovalent π stacking in both dry and wet conditions, with an interlayer distance between eumelanin molecules of 3.3 Å. Corresponding transmission electron microscope images confirm the supramolecular organization predicted in our simulations. Our simulations show that eumelanin is an isotropic material at a larger scale when eumelanin molecules are randomly oriented to form secondary structures. These results are in good agreement with experimental observations, density functional theory calculations, and bridge the gap between earlier experimental and small-scale quantum mechanical studies of eumelanin. We use the knowledge acquired from the simulations to select a partner molecule, a cationic phthalocyanine, allowing us to produce layer-by-layer films containing eumelanin that display an electrical conductivity 5 orders of magnitudes higher than that of pure eumelanin films.