Microstructural analysis of skeletal muscle force generation during aging.

Human aging results in a progressive decline in the active force generation capability of skeletal muscle. While many factors related to the changes of morphological and structural properties in muscle fibers and the extracellular matrix (ECM) have been considered as possible reasons for causing age-related force reduction, it is still not fully understood why the decrease in force generation under eccentric contraction (lengthening) is much less than that under concentric contraction (shortening). Biomechanically, it was observed that connective tissues (endomysium) stiffen as ages, and the volume ratio of connective tissues exhibits an age-related increase. However, limited skeletal muscle models take into account the microstructural characteristics as well as the volume fraction of tissue material. This study aims to provide a numerical investigation in which the muscle fibers and the ECM are explicitly represented to allow quantitative assessment of the age-related force reduction mechanism. To this end, a fiber-level honeycomb-like microstructure is constructed and modeled by a pixel-based Reproducing Kernel Particle Method (RKPM), which allows modeling of smooth transition in biomaterial properties across material interfaces. The numerical investigation reveals that the increased stiffness of the passive materials of muscle tissue reduces the force generation capability under concentric contraction while maintains the force generation capability under eccentric contraction. The proposed RKPM microscopic model provides effective means for the cellular-scale numerical investigation of skeletal muscle physiology. NOVELTY STATEMENT: A cellular-scale honeycomb-like microstructural muscle model constructed from a histological cross-sectional image of muscle is employed to study the causal relations between age-associated microstructural changes and age-related force loss using Reproducing Kernel Particle Method (RKPM). The employed RKPM offers an effective means for modeling biological materials based on pixel points in the medical images and allow modeling of smooth transition in the material properties across interfaces. The proposed microstructure-informed muscle model enables quantitative evaluation on how cellular-scale compositions contribute to muscle functionality and explain differences in age-related force changes during concentric, isometric and eccentric contractions

Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues.

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological tissues, and model classification

Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for non-crystalline materials, it may still be used as a first order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to 2-D cellular-scale models by assessing the mechanical behaviour of model biological tissues, including crystalline (honeycomb) and non-crystalline reference states. The numerical procedure consists in precribing an affine deformation on the boundary cells and computing the position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For centre-based models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete/continuous modelling, adaptation of atom-to-continuum (AtC) techniques to biological tissues and model classification

Bio-Inspired Active Skins for Surface Morphing.

Mechanical metamaterials that leverage precise geometrical designs and imperfections to induce unique material behavior have garnered significant attention. This study proposes a Bio-Inspired Active Skin (BIAS) as a new class of instability-induced morphable structures, where selective out-of-plane material deformations can be pre-programmed during design and activated by in-plane strains. The deformation mechanism of a unit cell geometrical design is analyzed to identify how the introduction of hinge-like notches or instabilities, versus their pristine counterparts, can pave way for controlling bulk BIAS behavior. Two-dimensional arrays of repeating unit cells were fabricated, with notches implemented at key locations throughout the structure, to harvest the instability-induced surface features for applications such as camouflage, surface morphing, and soft robotic grippers

Auxetic material in biomedical applications: a systematic review

This study reviews and analyzes the different auxetic materials that have been developed in recent years. The search for research articles was carried out through one of the largest databases such as ScienceDirect, where 845 articles were collected, of which several filters were carried out to have a base of 386 articles. There are a variety of materials depending on their structure, composition, and industrial application, highlighting biomedical applications from tissue engineering, cell proliferation, skeletal muscle regeneration, transportation, bio-prosthesis to biomaterial. The present paper provides an overview of auxetic materials and its applications, providing a guide for designers and manufacturers of devices and accessories in any industry

Nanomechanics of Hierarchical Cellular Solids

Materials Science and Engineering, a young and vibrant discipline with its inception in the 1950s, has expanded into three directions: metals, polymers, and ceramics (and their mixtures, composites). Beyond the traditional scope, biological materials have drawn much attention since 1990s due to their optimal structures, which rise from hundreds of million years of evolution. Generally, biological materials are complex composites and possess varieties of hierarchical structures, multifunctionality, self-organization and self-assembly. From the point of view of mechanics, mechanical properties of natural (or biological) materials are outstanding, although their constituent materials are weak. This is because the necessary mechanical support is in great need due to their surrounding environment. Therefore, their efficiency provides us with useful indications as to how to synthesize new materials inspired by natural ones, and thus drives scientists and engineers to reveal the mechanisms behind the observed phenomena of interest. In this regard, the tendency in the design of novel materials apparently holds a promising future in new Material Science. To date, it is widely accepted that the research on biological materials is a multidisciplinary field including chemistry, physics, and biology etc. Although some progress has been already made, there is still a long way to go to mass fabricate bio-inspired materials. In this thesis, employing a "bottom-up" approach, we have devised three hierarchical models (2-D hierarchical woven, 2-D hierarchical honeycomb and 3-D hierarchical foam) inspired by structures found in natural materials and investigated their mechanical properties. The common characteristic of these structures is their being quasi-self-similar. Regarding the derivation of their mechanical properties, we consider the (n-1)th level structure to be a continuous medium and from it we calculate the mechanical properties of the nth level structure. In the first chapter, we introduce the motivation for this work. By reviewing the literature on both well-studied and less familiar natural materials, we summarize their structural characteristics and biomechanical mechanisms. Chapter 2 deals with our first model—1-D or 2-D hierarchical woven tissue, and the elastic anisotropy of the structure is derived, based on the well-known stiffness averaging method by volumes. In order to verify the theory, an experiment on leaves, which are modeled as one-dimensional hierarchical woven structures, is performed. Also, a comparison between theoretical predictions and experimental data on tendons from the literature is made. The considered structure could be used as a scaffold, which can provide the mechanical support and optimize tissue regeneration at each hierarchical level. Chapters 3-5 discuss our second model—2-D hierarchical honeycomb. Incorporating the surface effect, the in-plane linear-elastic properties, elastic buckling properties, fracture strength and toughness are derived. Chapter 3 examines the linear elastic properties and the stiffness efficiency thanks to the minimum-weight analysis, and the parametric analysis shows that the structure can be optimized. Chapter 4 discusses elastic buckling by employing the Euler buckling formula; besides local buckling, progressive buckling is also investigated. The progressive failure behavior is found to be similar to that of balsa wood. Strength efficiency is also illustrated. Employing "Quantized Fracture Mechanics" (Pugno, 2002; Pugno and Ruoff, 2004), Chapter 5 modifies the classical strength formulas of the conventional honeycomb and investigates the defective hierarchical honeycomb; the fracture toughness of the perfect and defective hierarchical honeycomb are both derived. In general, hierarchical honeycombs can be used as energy-absorbing materials and bioscaffolds for directional tissue regeneration. Chapter 6 models our third hierarchical structure—3-D hierarchical foam. The Young's modulus and plastic strength are derived based on structural analysis. When the characteristic size of the lowest level is very small (less than 10nm), surface effects play an important role in determining the mechanical properties of the structure. The hierarchical foam could be used as nano-porous gold. Chapter 7 provides conclusions and an outlook for future wor

Passive Hydro-actuated Unfolding of Ice Plant Seed Capsules as a Concept Generator for Autonomously Deforming Devices

In der Natur und ihren biologischen Systemen existieren zahlreiche Beispiele für gerichtete Bewegung durch spezifische Reaktion auf externe Stimuli. Diese potentiellen Quellen der Inspiration dienen oft als Vorbilder für energieeffiziente "Smart" Technologien. Vom Wasser getriebenen schnellen Zuschnappen der Venusfliegenfalle bis zum einfacheren ebenso hydroresponsiven Biegen der Weizengrannen, viele Pflanzen haben im Laufe der Evolution verschiedene Mechanismen entwickelt, um Wasser als Triebkraft ihrer Aktoren-Gewebe zu nutzen, die für spezifische und gerichtete Bewegung sowie die gewünschte Verformung sorgen. Das ist diesen Pflanzen möglich durch die Organisation ihrer Gewebe in ausgereiften, komplexen und hierarchisch organisierten Architekturen auf verschiedensten Skalen. Einige Arten der Familie Aizoaceae, auch bekannt als Mittagsblumen oder Ice plant, zeigen ein geniales Beispiel für solche passiven Betätigungssysteme, da sie einen "intelligenten" Mechanismus entwickelt haben, um ihre Schutzsamenkapseln öffnen zu lassen und die Samen nur in Anwesenheit von flüssigem Wasser (Regen) freizugeben. Schwerpunkt der ersten Phase dieser Arbeit war die Untersuchung der zu Grunde liegenden Mechanismen und der strukturellen und kompositorischen Basis von Wasser-getriebenen Bewegungen der Samenkapseln von Ice plant (Delosperma nakurense) auf ihren verschiedenen hierarchischen Ebenen. Fünf hygroskopische Kiele erwiesen sich als aktive "Muskeln", die zu einer reversiblen origamiartigen Entfaltung der Samenkapsel führen, wenn diese mit Wasser benetzt wird. Jeder Kiel besteht aus zwei wabenartigen Geweben, die aus hochgradig schwellfähigen und elliptisch-sechseckig geformten Zellen zusammengesetzt sind, die entlang einem inerten Träger organisiert sind. Als Hauptmotor der Aktuation wurde die signifikante Schwellung von hochgradig schwellfähigen zellulosereichen Innenschichten (CIL) im Lumen der Zellen identifiziert. Die Morphologie der CIL und deren physikochemische Reaktion auf Wasser wurde unter Verwendung einer Vielzahl von Techniken untersucht und damit gezeigt, dass der Entropiegewinn während der Wasserabsorption die Hauptantriebskraft für die Schwellung der Zellen ist. Die Umsetzung dieser relativ kleinen Energiebeiträge in eine konzertierte und komplexe makroskopische Bewegung, wurde durch ein optimiertes Design auf den verschiedenen Ebenen der hierarchischen Organisation des Systems erläutert. Das kooperative anisotropische Anschwellen der Zellen des hygroskopischen Gewebes führt durch das Timoschenko Doppelschicht-Biegeprinzip zu einer Umsetzung in eine Biegebewegung der Strukturen und letztlich zur Entfaltung der Samenkapseln. Inspiriert von den zugrunde liegenden Mechanismen in Ice plants, wurden zwei unterschiedliche Strategien entwickelt, um durch kleine Dehnungen im mikroskopischen Bereich eine vorprogrammierte Makro-Bewegung einer Wabenstruktur zu ermöglichen. Durch eine geschickte Anwendung dieses einfachen Prinzips, kann eine Mimik des biologischen Vorbilds im weiteren technischen Sinne zu zahlreichen Anwendungsbeispielen führen, wie als passive Schalter und Aktoren in der Biomedizin, Landschaftsgestaltung oder der Architektur.Numerous examples of actuated-movements with specific responses of the structure to external stimuli can be found in biological systems, which can be a potential source of inspiration for the design of energy-efficient "smart" devices. From the hydro-driven rapid snapping of the Venus fly trap leaves to simple hydro-responsive bending of wheat awns, various plants have evolved different mechanisms to utilize water as an actuator to undergo a desired deformation via sophisticated architecture at different hierarchical levels of their systems. Some species of the family Aizoaceae, also known as ice plants, show an ingenious example of such passive actuation systems, as they evolved a smart mechanism to open their protective seed capsules and release their seeds only in the presence of liquid water (rain). The scope of the first phase of the thesis was to investigate the underlying mechanism and the structural and compositional basis of the hydro-actuated movement of the ice plant seed capsules (Delosperma nakurense) at several hierarchical levels. Five hygroscopic keels were found to be the active muscles responsible for the reversible origami-like unfolding of the seed capsule upon wetting. Each keel consists of two honeycomb-like tissues made up of highly swellable hexagonal/elliptical shape cells running along an inert backing tissue. The significant swelling of a highly swellable cellulosic inner layer (CIL) inside the lumen of these cells was found to be the main engine of the actuation. The morphology and physicochemical response of the CIL to water was studied using a variety of techniques and it was shown that the entropic changes during water absorption were the main driving force for swelling of the cells. The translation of such relatively small available energy to the complex movement at a macro scale was explained by an optimized design at different hierarchical levels of the system. The cooperative anisotropic swelling of the cells in the hygroscopic tissue is translated into a flexing movement of the structure via simple Timoshenko’s bilayer bending principle, which then results in an unfolding of the seed capsules. Inspired by the underlying mechanism in ice plant, two different strategies were developed to translate small strains at micro scale into a pre-programmed macro movement of a honeycomb structure. Through a clever application of the same simple concepts, one can "mimic" the biological model system in a broader engineering sense, with potential applications of such passive switches in biomedicine, agricultural engineering or architectural design

Strain-controlled criticality governs the nonlinear mechanics of fibre networks

Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable (Maxwell, J. C., Philosophical Magazine 27, 294 (1864)). Upon increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even sub-isostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modeling of fibre networks and experiments on networks of type I collagen fibers, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical properties consistent with our model, including the predicted critical exponents. We show that the nonlinear mechanics of collagen networks can be quantitatively captured by the predictions of scaling theory for the strain-controlled critical behavior over a wide range of network concentrations and strains up to failure of the material