Finite element analysis after rod fracture of the spinal hybrid elastic rod system.

BACKGROUND: The spinal hybrid elastic (SHE) rod dynamic stabilization system can provide sufficient spine support and less adjacent segment stress. This study aimed to investigate the biomechanical effects after the internal fracture of SHE rods using finite element analysis. METHODS: A three-dimensional nonlinear finite element model was developed. The SHE rod comprises an inner nitinol stick (NS) and an outer polycarbonate urethane (PCU) shell (PS). The fracture was set at the caudal third portion of the NS, where the maximum stress occurred. The resultant intervertebral range of motion (ROM), intervertebral disc stress, facet joint contact force, screw stress, NS stress, and PCU stress were analyzed. RESULTS: When compared with the intact spine model, the overall trend was that the ROM, intervertebral disc stress, and facet joint force decreased in the implanted level and increased in the adjacent level. When compared with the Ns-I, the trend in the Ns-F decreased and remained nearly half effect. Except for torsion, the PS stress of the Ns-F increased because of the sharing of NS stress after the NS fracture. CONCLUSIONS: The study concluded the biomechanical effects still afford nearly sufficient spine support and gentle adjacent segment stress after rod fracture in a worst-case scenario of the thinnest PS of the SHE rod system.

Double Tubular Contractile Structure of the Type VI Secretion System Displays Striking Flexibility and Elasticity.

Antimicrobial treatment can induce many bacterial pathogens to enter a cell wall-deficient state that contributes to persistent infections. The effect of this physiological state on the assembly of transenvelope-anchored organelles is not well understood. The type VI secretion system (T6SS) is a widespread molecular weapon for interspecies interactions and virulence, comprising a long double tubular structure and a transenvelope/baseplate complex. Here, we report that cell wall-deficient spheroplasts assembled highly flexible and elastic T6SS structures forming U, O, or S shapes. Upon contacting the inner membrane, the T6SS tubes did not contract but rather continued to grow along the membrane. Such deformation likely results from continual addition of sheath/tube subunits at the distal end. Induction of TagA repressed curved sheath formation. Curved sheaths could also contract and deliver T6SS substrates and were readily disassembled by the ClpV ATPase after contraction. Our data highlight the dramatic effect of cell wall deficiency on the shape of the T6SS structures and reveal the elastic nature of this double tubular contractile injection nanomachine.IMPORTANCE The cell wall is a physical scaffold that all transenvelope complexes have to cross for assembly. However, the cell wall-deficient state has been described as a common condition found in both Gram-negative and Gram-positive pathogens during persistent infections. Loss of cell wall is known to have pleiotropic physiological effects, but how membrane-anchored large cellular organelles adapt to this unique state is less completely understood. Our study examined the assembly of the T6SS in cell wall-deficient spheroplast cells. We report the elastic nature of contractile T6SS tubules under such conditions, providing key insights for understanding how large intracellular structures such as the T6SS accommodate the multifaceted changes in cell wall-deficient cells.

Patterns of Carbon Nanotubes by Flow-Directed Deposition on Substrates with Architectured Topographies.

We develop and perform continuum mechanics simulations of carbon nanotube (CNT) deployment directed by a combination of surface topography and rarefied gas flow. We employ the discrete elastic rods method to model the deposition of CNT as a slender elastic rod that evolves in time under two external forces, namely, van der Waals (vdW) and aerodynamic drag. Our results confirm that this self-assembly process is analogous to a previously studied macroscopic system, the "elastic sewing machine", where an elastic rod deployed onto a moving substrate forms nonlinear patterns. In the case of CNTs, the complex patterns observed on the substrate, such as coils and serpentines, result from an intricate interplay between van der Waals attraction, rarefied aerodynamics, and elastic bending. We systematically sweep through the multidimensional parameter space to quantify the pattern morphology as a function of the relevant material, flow, and geometric parameters. Our findings are in good agreement with available experimental data. Scaling analysis involving the relevant forces helps rationalize our observations.

Colonoscopy procedure simulation: virtual reality training based on a real time computational approach.

BACKGROUND: Colonoscopy plays an important role in the clinical screening and management of colorectal cancer. The traditional 'see one, do one, teach one' training style for such invasive procedure is resource intensive and ineffective. Given that colonoscopy is difficult, and time-consuming to master, the use of virtual reality simulators to train gastroenterologists in colonoscopy operations offers a promising alternative. METHODS: In this paper, a realistic and real-time interactive simulator for training colonoscopy procedure is presented, which can even include polypectomy simulation. Our approach models the colonoscopy as thick flexible elastic rods with different resolutions which are dynamically adaptive to the curvature of the colon. More material characteristics of this deformable material are integrated into our discrete model to realistically simulate the behavior of the colonoscope. CONCLUSION: We present a simulator for training colonoscopy procedure. In addition, we propose a set of key aspects of our simulator that give fast, high fidelity feedback to trainees. We also conducted an initial validation of this colonoscopic simulator to determine its clinical utility and efficacy.

Knot soliton in DNA and geometric structure of its free-energy density.

In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.

Whisker Sensing by Force and Moment Measurements at the Whisker Base.

We address the theoretical question which forces and moments measured at the base of a whisker (tactile sensor) allow for the prediction of the location in space of the point at which a whisker makes contact with an object. We deal with the general case of three-dimensional deformations as well as with the special case of planar configurations. All deformations are treated as quasi-static, and contact is assumed to be frictionless. We show that the minimum number of independent forces or moments required is three but that conserved quantities of the governing elastic equilibrium equations prevent certain triples from giving a unique solution in the case of contact at any point along the whisker except the tip. The existence of these conserved quantities depends on the material and geometrical properties of the whisker. For whiskers that are tapered and intrinsically curved, there is no obstruction to the prediction of the contact point. We show that the choice of coordinate system (Cartesian or cylindrical) affects the number of suitable triples. Tip and multiple point contact are also briefly discussed. Our results explain recent numerical observations in the literature and offer guidance for the design of robotic tactile sensory devices.

Treatment of Lumbar Degenerative Disease with a Novel Interlaminar Screw Elastic Spacer Technique: A Finite Element Analysis.

A novel interlaminar elastic screw spacer technique was designed to maintain lumbar mobility in treating lumbar degenerative diseases. A validated finite element model of L4/5 was used to establish an ISES-1/2 model and an ISES-1/3 model based on different insertion points, a unilateral fixation model and a bilateral fixed model based on different fixation methods, and a Coflex-F model based on different implants. The elastic rods were used to fix screws. Under the same mechanical conditions, we compared the biomechanical characteristics to investigate the optimal entry point for ISES technology, demonstrate the effectiveness of unilateral fixation, and validate the feasibility of the ISES technique. Compared to ISES-1/3, the ISES-1/2 model had lower intradiscal pressure, facet cartilage stress, and posterior structural stress. Compared to the ISES-BF model, the ISES-UF model had lower intervertebral pressure, larger mobility, and smaller stress on the posterior structures. The ISES model had a similar intervertebral pressure and limitation of extension as the Coflex-F model. The ISES model retained greater mobility and reduced the stress on the facet cartilage and posterior structure compared with the Coflex-F model. Our study suggests that the ISES technique is a promising treatment of lumbar degenerative diseases, especially those with osteoporosis.

Morphological peculiarities of a harbour seal (Phoca vitulina) whisker revealed by normal skeletonisation.

Of all mammalian vibrissae, those of certain species of pinnipeds are exceptional. Researchers believe that their curious undulating form evolved for hydrodynamic detection. Our understanding of how these whiskers work depends on a geometrical model that captures the crucial pertinent features of the natural vibrissae including its tapering and curvature. It should also account for the form of the whisker when it flexes under external loading. We introduce and study a normal skeleton of a two-dimensional projection of a harbour seal whisker. The normal skeleton is a complete shape descriptor that involves reduction to the centreline equipped with a thickness function of the orthogonal cross-section. The contours of the whisker shape are extracted from a 2D greyscale scan. Our analysis reveals correspondence between the undulations of the width and oscillations of the centreline curvature as functions of arc length. We discuss two possible explanations for that remarkable feature: one based on consideration of growth and the other of plastic deformation. For the latter we employ a mechanical model to demonstrate appearance of curvature oscillations caused by extensive deflection of the undulating whisker due to external loading.

Hydrophilic and opened canals in honey bee tongue rods endow elastic structures with multiple functions.

The honey bee (Apis mellifera L.) tongue is a sophisticated and dexterous probing device that can bend and twist, adapting to various surfaces for liquid imbibition and/or gustatory sensing. The tongue exhibits remarkable extendibility, flexibility, and durability, which may be essentially ascribed to the internal elastic rod that supports the entire tongue. However, neither the material composition nor the structural features of the rod, especially a peculiar inner canal that facilitates feeding, have been studied in relation to their function. Herein, by combining a set of imaging techniques, including optical microscopy, high-speed videography, scanning electron microscopy, micro-computed tomography (micro-CT), and confocal laser scanning microscopy, we characterize the spatial morphology, surface wettability and material composition of honey bee tongue rods. By performing mechanical testing, including atomic force microscopy, fracture testing, and finite element analysis, we provide the first evidence that the internal canal of the rod may represent a specialized structure for water retention due to the specific chemistry of resilin, which is an elastomeric protein that dominates the entire rod and renders it highly elastic, compliant and robust. Numerical simulations also suggest that the opening of the canal may facilitate larger deformations in twisting, extending the flexibility of the rod. STATEMENT OF SIGNIFICANCE: The honey bee is one of the most important pollinators around the world and is capable of foraging a wide spectrum of liquid sources by dipping into them with a miniature hairy tongue. However, there are no direct muscles distributed inside the tongue, instead, there is a conspicuous elastic rod with a hollow core. The rod extends for its full length and, according to our study, structurally reinforces the entire tongue to achieve functional versatility, and suggests a water containing function of the rod canal for maintaining the elasticity of the protein (resilin) that constitutes the rod. Our results broaden understandings of the relationship among morphology, materials science, and function of a honey bee tongue.

Bending Properties of an Extensile Fluidic Artificial Muscle.

Low stiffness, large stroke, and axial force capabilities make Extensile Fluidic Artificial Muscles (EFAMs) a feasible soft actuator for continuum soft robots. EFAMs can be used to construct soft actuated structures that feature large deformation and enable soft robots to access large effective workspaces. Although FAM axial properties have been well studied, their bending behavior is not well characterized in the literature. Static and dynamic bending properties of a cantilevered EFAM specimen were investigated over a pressure range of 5-100 psi. The static properties were then estimated using an Euler-Bernoulli beam model and discrete elastic rod models. The experiments provided data for the determination of bending stiffness, damping ratio, and natural frequency of the tested specimen. The bending stiffness and the damping ratio were found to change fourfold over the pressure range. Experimentally validated bending properties of the EFAM presented insights into structural and control considerations of soft robots. Future work will utilize the data and models obtained in this study to predict the behavior of an EFAM-actuated continuum robot carrying payloads.

Modulating DNA configuration by interfacial traction: an elastic rod model to characterize DNA folding and unfolding.

As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in intracellular solution. The interfacial traction between the rod and the solution environment is derived in detail. Kirchhoff's theory of elastic rods is used to analyze the equilibrium configuration of a DNA segment under the action of the interfacial traction. The influences of the interfacial energy factor and bending stiffness on the toroidal spool formation of the DNA segment are discussed. The results show that the equilibrium configuration of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of the forces that drives DNA folding and unfolding.

The role of mechanics in the growth and homeostasis of the intestinal crypt.

We present a mechanical model of tissue homeostasis that is specialised to the intestinal crypt. Growth and deformation of the crypt, idealised as a line of cells on a substrate, are modelled using morphoelastic rod theory. Alternating between Lagrangian and Eulerian mechanical descriptions enables us to precisely characterise the dynamic nature of tissue homeostasis, whereby the proliferative structure and morphology are static in the Eulerian frame, but there is active migration of Lagrangian material points out of the crypt. Assuming mechanochemical growth, we identify the necessary conditions for homeostasis, reducing the full, time-dependent system to a static boundary value problem characterising a spatially heterogeneous "treadmilling" state. We extract essential features of crypt homeostasis, such as the morphology, the proliferative structure, the migration velocity, and the sloughing rate. We also derive closed-form solutions for growth and sloughing dynamics in homeostasis, and show that mechanochemical growth is sufficient to generate the observed proliferative structure of the crypt. Key to this is the concept of threshold-dependent mechanical feedback, that regulates an established Wnt signal for biochemical growth. Numerical solutions demonstrate the importance of crypt morphology on homeostatic growth, migration, and sloughing, and highlight the value of this framework as a foundation for studying the role of mechanics in homeostasis.

How different the scoliotic curves are?

The pathomechanism of spinal deformity development in adolescent idiopathic scoliosis (AIS) has been related to the sagittal curvature of the spine. It is not known how the variations in the sagittal profile relates to the coronal deformity patterns in AIS. A total of 70 Lenke 1 and 50 Lenke 5 AIS patients were included retrospectively. A finite element (FE) model was developed for each spine where the sagittal spinal curvatures were modeled as 2D S shaped elastic rods. Transverse plane deformation patterns of these rods under physiological loading were determined and clustered based on their similarities. The patients' characteristics, including the Lenke type, and the spinal measurements in these deformation pattern clusters were statistically compared. Three different axial deformation patterns were determined from the FE simulations of the 120 sagittal curves. Two axial groups were looped shaped in opposing directions (Group I and III) and one was lemniscate shaped (Group II). 94% of the patients in Groups I and II were Lenke 1 and 100% of Group III was Lenke 5. The position of the sagittal inflection point moved downward from Group I-III resulting in significantly different ratio of the arc lengths above and below the sagittal inflection points for Groups I, II and III (0.49±0.59, 1.15±0.44, and 3.22±1.8). A classification of idiopathic scoliosis, based on the biomechanics of S-shaped flexible rods deformation could distinguish between different coronal curve types. The geometrical parameters of the sagittal profiles in the axial deformation pattern groups were significantly different.

Sagittal curvature of the spine as a predictor of the pediatric spinal deformity development.

BACKGROUND: The sagittal curvature of the spine is hypothesized to play an important role in induction of spinal deformities in adolescent idiopathic scoliosis. We previously showed an S shaped flexible rod, with the same curvature as the pediatric sagittal spinal curve, produces scoliotic-like deformities under physiologic loading. Yet, detailed characteristics of the pediatric sagittal spinal curves associated with higher risk of scoliosis are not well defined. METHODS: A total of 32 patients in a population with a high prevalence of idiopathic-like scoliosis, 22q11.2 deletion syndrome (22q), were included and followed up for at least two-years. We developed a reduced order finite element model (FEM) of the sagittal profile of these 32 patients where the spine was modeled as an S shaped elastic rod. We related the geometrical parameters of the sagittal curves and the deformed FEM of the corresponding S shaped rods to the risk of scoliosis development at two-year follow-up in this cohort. RESULTS: Variations in the sagittal curvature in the cohort of 22q patients resulted in five different deformity patterns shown by finite element analyses. Two sagittal plane deformity pattern groups had high rate of scoliosis development (86% and 100%) whereas the other 3 groups had less than 50% rate of scoliosis development (40%, 33%, and 0%). The pre-scoliotic position of the inflection point (where lordosis turns into kyphosis), the ratio of the spinal curvatures above and below the inflection point, and the length of the spinal curve above and below the inflection point were significantly different between the five deformity patterns groups, p < 0.05. CONCLUSION: Combination of geometrical parameters of the sagittal profile prior to onset of scoliosis can relate to the development of spinal deformity in pediatric population.

Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape.

Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modelling of thin flexible structures such as DNA, hair or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

Eulerian formulation of elastic rods.

In numerous biological, medical and engineering applications, elastic rods are constrained to deform inside or around tube-like surfaces. To solve efficiently this class of problems, the equations governing the deflection of elastic rods are reformulated within the Eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface. This reformulation hinges on describing the rod-deformed configuration by means of its relative position with respect to a reference curve, defined as the axis or spine curve of the constraint, and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve. Associated with a segmentation strategy, which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact (except for their extremities), this re-parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two-points boundary-value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment.

A robust and real-time vascular intervention simulation based on Kirchhoff elastic rod.

A virtual reality (VR) based vascular intervention simulation system is introduced in this paper, which helps trainees develop surgical skills and experience complications in safety remote from patients. The system simulates interventional radiology procedures, in which flexible tipped guidewires are employed to advance diagnostic or therapeutic catheters into vascular anatomy of a patient. A real-time physically-based modeling approach ground on Kirchhoff elastic rod is proposed to simulate complicated behaviors of guidewires and catheters. The slender body of guidewire and catheter is modeled using more efficient special case of naturally straight, isotropic Kirchhoff rods, and the shorter flexible tip composed of straight or angled design is modeled using more complex generalized Kirchhoff rods. The motion equations for guidewire and catheter were derived with continuous elastic energy, followed by a discretization using a linear implicit scheme that guarantees stability and robustness. In addition, we used a fast-projection method to enforce the inextensibility of guidewire and catheter. An adaptive sampling algorithm was also implemented to improve the simulation efficiency without decrease of accuracy. Experimental results revealed that our system is both robust and efficient in a real-time performance.