Bio-Inspired Sutures: Simulating the Role of Suture Placement in the Mechanical Response of Interlocking Structures.

The hardest anatomical components of many animals are connected at thin seams known as sutures, which allow for growth and compliance required for respiration and movement and serve as a defense mechanism by absorbing energy during impacts. We take a bio-inspired approach and parameterize suture geometries to utilize geometric connections, rather than new engineering materials, to absorb high-impact loads. This study builds upon our work that investigated the effects of the dovetail suture contact angle, tangent length, and tab radius on the stiffness and toughness of an archway structure using finite element analysis. We explore how increasing the archway segmentation affects the mechanical response of the overall structure and investigate the effects of displacement when induced between sutures. First, when keeping displacement along a suture but increasing the number of archway pieces from two to four, we observed that stiffness and toughness were reduced substantially, although the overall trends stayed the same. Second, when the displacement was induced along an archway edge rather than upon a suture (in a three-piece archway), we observed that archway stiffness and toughness were much less sensitive to the changes in the suture parameters, but unlike the archway indented along the suture line, they tended to lose stiffness and toughness as the tangent length increased. This study is a step forward in the development of bio-inspired impact-resistant helmets.

Bio-Inspired Sutures: Using Finite Element Analysis to Parameterize the Mechanical Response of Dovetail Sutures in Simulated Bending of a Curved Structure.

Many animals have protective anatomical structures that allow for growth and flexibility; these structures contain thin seams called sutures that help the structure to absorb impacts. In this study, we parameterized the stiffness and toughness of a curved archway structure based on three geometric properties of a suture through finite element, quasi-static, three-point bending simulations. Each archway consisted of two symmetric pieces linked by a dovetail suture tab design. The three parameters included suture tab radii (1-5 mm), tangent lengths (0-20 mm), and contact angles (0-40°). In the simulations, a steel indenter was displaced 6.5 mm to induce progressive tab disengagement. Sutures with large contact angles and large tangent lengths generally led to stiffer and tougher structures. Sutures with a small tab radius exhibited the most sensitivity to the input parameters, and the smallest tab radius led to the stiffest and toughest archways. Results suggested that it was a combination of the largest number of tab repeats with the largest possible contact surface area that improved the mechanical response of the archway. The study revealed several suture geometries that hold significant promise, which can aid in the development of hemispherical 3D structures for dynamic impact applications.

A Mechanistic End-to-End Concussion Model That Translates Head Kinematics to Neurologic Injury.

Past concussion studies have focused on understanding the injury processes occurring on discrete length scales (e.g., tissue-level stresses and strains, cell-level stresses and strains, or injury-induced cellular pathology). A comprehensive approach that connects all length scales and relates measurable macroscopic parameters to neurological outcomes is the first step toward rationally unraveling the complexity of this multi-scale system, for better guidance of future research. This paper describes the development of the first quantitative end-to-end (E2E) multi-scale model that links gross head motion to neurological injury by integrating fundamental elements of tissue and cellular mechanical response with axonal dysfunction. The model quantifies axonal stretch (i.e., tension) injury in the corpus callosum, with axonal functionality parameterized in terms of axonal signaling. An internal injury correlate is obtained by calculating a neurological injury measure (the average reduction in the axonal signal amplitude) over the corpus callosum. By using a neurologically based quantity rather than externally measured head kinematics, the E2E model is able to unify concussion data across a range of exposure conditions and species with greater sensitivity and specificity than correlates based on external measures. In addition, this model quantitatively links injury of the corpus callosum to observed specific neurobehavioral outcomes that reflect clinical measures of mild traumatic brain injury. This comprehensive modeling framework provides a basis for the systematic improvement and expansion of this mechanistic-based understanding, including widening the range of neurological injury estimation, improving concussion risk correlates, guiding the design of protective equipment, and setting safety standards.

Computational mechanics of viral capsids.

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics. Even though the theory of continuum elasticity is most commonly used to study deformable bodies at larger macroscopic length scales, it has been shown that this very rich theoretical field can still offer useful insights into the mechanics of viral structures at the nanometer scale. Here we show the construction of viral capsid continuum mechanics models starting from different forms of experimental data. We will discuss the kinematics assumptions, the issue of the reference configuration, the material constitutive laws, and the numerical discretization necessary to construct a complete Finite Element capsid mechanical model. Some examples in the second part of the chapter will show the predictive capabilities of the constructed models and underline useful practical aspects related to efficiency and accuracy. We conclude each example by collecting several key findings discovered by simulating AFM indentation experiments using the constructed numerical models.

Finite element modeling of blast lung injury in sheep.

A detailed 3D finite element model (FEM) of the sheep thorax was developed to predict heterogeneous and volumetric lung injury due to blast. A shared node mesh of the sheep thorax was constructed from a computed tomography (CT) scan of a sheep cadaver, and while most material properties were taken from literature, an elastic-plastic material model was used for the ribs based on three-point bending experiments performed on sheep rib specimens. Anesthetized sheep were blasted in an enclosure, and blast overpressure data were collected using the blast test device (BTD), while surface lung injury was quantified during necropsy. Matching blasts were simulated using the sheep thorax FEM. Surface lung injury in the FEM was matched to pathology reports by setting a threshold value of the scalar output termed the strain product (maximum value of the dot product of strain and strain-rate vectors over all simulation time) in the surface elements. Volumetric lung injury was quantified by applying the threshold value to all elements in the model lungs, and a correlation was found between predicted volumetric injury and measured postblast lung weights. All predictions are made for the left and right lungs separately. This work represents a significant step toward the prediction of localized and heterogeneous blast lung injury, as well as volumetric injury, which was not recorded during field testing for sheep.

Diffusion-dependent mechanisms of receptor engagement and viral entry.

Enveloped viruses attach to host cells by binding to receptors on the cell surface. For many viruses, entry occurs via membrane fusion after a sufficient number of receptors have engaged ligand proteins on the virion. Under conditions where the cell surface receptor densities are low, recruitment of receptors may be limited by diffusion rather than by receptor-ligand interactions. We present a receptor-binding model that includes the effects of receptor availability at the viral binding site. The receptor binding and unbinding kinetics are coupled to receptor diffusion across the cell membrane. We find numerical solutions to our model and analyze the viral entry probabilities and the mean times to entry as functions of receptor concentration, receptor diffusivity, receptor binding stoichiometry, receptor detachment rates, and virus degradation/detachment rates. We also show how entry probabilities and times differ when receptors bind randomly or sequentially to the binding sites on the viral glycoprotein spikes. Our results provide general insight into the biophysical transport mechanisms that may arise in viral attachment and entry.

Influence of nonuniform geometry on nanoindentation of viral capsids.

A series of recent nanoindentation experiments on the protein shells (capsids) of viruses has established atomic force microscopy (AFM) as a useful framework for probing the mechanics of large protein assemblies. Specifically these experiments provide an opportunity to study the coupling of the global assembly response to local conformational changes. AFM experiments on cowpea chlorotic mottle virus, known to undergo a pH-controlled swelling conformational change, have revealed a pH-dependent mechanical response. Previous theoretical studies have shown that homogeneous changes in shell geometry can play a significant role in the mechanical response. This article develops a method for accurately capturing the heterogeneous geometry of a viral capsid and explores its effect on mechanical response with a nonlinear continuum elasticity model. Models of both native and swollen cowpea chlorotic mottle virus capsids are generated from x-ray crystal structures, and are used in finite element simulations of AFM indentation along two-, three-, and fivefold icosahedral symmetry orientations. The force response of the swollen capsid model is observed to be softer by roughly a factor of two, significantly more nonlinear, and more orientation-dependent than that of a native capsid with equivalent elastic moduli, demonstrating that capsid geometric heterogeneity can have significant effects on the global structural response.

Nonlinear finite-element analysis of nanoindentation of viral capsids.

Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage phi29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young's moduli of approximately 280-360 MPa for CCMV and approximately 4.5 GPa for phi29 .