A Semi-Analytic Elastic Rod Model of Pediatric Spinal Deformity

The mechanism of the scoliotic curve development in healthy adolescents remains unknown in the field of orthopedic surgery. Variations in the sagittal curvature of the spine are believed to be a leading cause of scoliosis in this patient population. Here, we formulate the mechanics of S-shaped slender elastic rods as a model for pediatric spine under physiological loading. Second, applying inverse mechanics to clinical data of the subtypes of scoliotic spines, with characteristic 3D deformity, we determine the undeformed geometry of the spine before the induction of scoliosis. Our result successfully reproduces the clinical data of the deformed spine under varying loads, confirming that the prescoliotic sagittal curvature of the spine impacts the 3D loading that leads to scoliosis.

A semi-analytic elastic rod model of pediatric spinal deformity

The mechanism of the scoliotic curve development in healthy adolescents remains unknown in the field of orthopedic surgery. Variations in the sagittal curvature of the spine are believed to be a leading cause of scoliosis in this patient population. Here, we formulate the mechanics of S-shaped slender elastic rods as a model for pediatric spine under physiological loading. Secondarily, applying inverse mechanics to clinical data of the scoliotic spines, with characteristic 3D deformity, we determine the undeformed geometry of the spine before the induction of scoliosis. Our result successfully reproduces the clinical data of the deformed spine under varying loads confirming that the pre-scoliotic sagittal curvature of the spine impacts the 3D loading that leads to scoliosis.

KOBRA: a fluctuating elastic rod model for slender biological macromolecules

KOBRA is a coarse-grained algorithm for parameterising and simulating slender proteins using Kirchoff rods.

Distributed Control of a Planar Discrete Elastic Rod Model for Caterpillar-Inspired Locomotion

During crawling, a caterpillar body stretches and bends, and a wave repeatedly travels from the tail to the head. Recently, caterpillar locomotion has been modeled using the theory of planar discrete elastic rods (PDER). This work takes a similar modeling approach and introduces feedback control laws with communication between neighboring segments. Caterpillar locomotion is modeled first as a network of spring-mass-dampers connected through nearest neighbor interactions and then as a network of linked torsional springs. Feedback laws are designed to achieve consensus and traveling wave solutions. Simulation results show the displacement of each segment of a caterpillar during locomotion. These results show promise for the design of feedback control laws in a network model of soft robotic systems.

Follower Forces in Pre-Stressed Fixed-Fixed Rods to Mimic Oscillatory Beating of Active Filaments

Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a way to mimic oscillatory beating in synthetic settings. In the continuum limit, this spatiotemporal response is an emergent phenomenon resulting from the interplay between the structural elastic instability of the slender rods subjected to the non-conservative follower forces, geometric constraints that control the onset of this instability, and viscous dissipation due to fluid drag by ambient media. In this paper, we use an elastic rod model to characterize beating frequencies, the critical follower forces and the non-linear rod shapes, for pre-stressed, clamped rods subject to two types of fluid drag forces, namely, linear Stokes drag and non-linear Morrison drag. We find that the critical follower force depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies however, depend strongly on both the extent of pre-stress as well as the nature of the fluid drag.

Estimating Constitutive Law of a Filament From its Deformed Shapes Using Input Reconstruction

Twisting and bending dynamics of biological filaments such as DNA play a central role in their biological activity including gene expression. The elastic rod model is an efficient tool to simulate such deformations. However, the accuracy of elastic rod predictions depend strongly on the constitutive law, which follows from the atomistic structure of the DNA molecule and is known to be nonlinear and to vary along the length according to the base pair sequence of the DNA. Unfortunately, it is impractical to derive the constitutive law analytically from the atomistic structure. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we extend earlier work by employing techniques based on input reconstruction and state estimation filters to estimate the constitutive law using molecular dynamics data of deformations in bio-filaments.