The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

Soft Tissue Artifact Compensation Using Triangular Cosserat Point Elements (TCPEs)

Existing methods which compensate for the Soft Tissue Artifact (STA) in optoelectronic motion measurements estimate the rigid motion of a nearly rigid underlying body segment based on analysis of the motion of all fiducial markers. The objective of the proposed Triangular Cosserat Point Elements (TCPE) method is to estimate the motion of the underlying body segment even when the STA in the entire cluster of markers can be large. This is accomplished by characterizing the cluster of markers with TCPEs defined by triangles based on all combinations of three markers. Then, scalar deformation measures characterizing the magnitudes of strain and relative rotation of pairs of TCPEs are defined for each TCPE. These deformation measures are used to define a filtered group of TCPEs which best represents the motion of the underlying body segment. The method was tested using an experimental setup that consists of a rigid pendulum with a deformable 300ml silicone breast implant attached to it as a simulation of the soft tissue around a bony segment. The rotation angles extracted from markers on the deformable implant were compared with simultaneous measurements of the rigid pendulum using an optoelectronic system. Analysis of the experimental data shows that this filtering process substantially reduces the error due to the STA even though the data set includes large deformations. In particular, the analysis shows that the error reduction using the TCPE approach is larger than the reductions obtained using standard least-squares minimization methods.

Bone Orientation and Position Estimation Errors Using Cosserat Point Elements and Least Squares methods: Application to Gait

The aim of this study was to analyze the accuracy of bone pose estimation based on sub-clusters of three skin-markers characterized by triangular Cosserat point elements (TCPEs) and to evaluate the capability of four instantaneous physical parameters, which can be measured non-invasively in-vivo, to identify the most accurate TCPEs. Moreover, TCPE pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers, using rigid body (RBLS) and homogeneous deformation (HDLS) assumptions. Analysis was performed on previously collected in-vivo treadmill gait data composed of simultaneous measurements of the gold-standard bone pose by bi-plane fluoroscopy tracking the subjects' knee prosthesis and a stereophotogrammetric system tracking skin-markers affected by soft tissue artifact. Femur orientation and position errors estimated from skin-marker clusters were computed for 18 subjects using clusters of up to 35 markers. Results based on gold-standard data revealed that instantaneous subsets of TCPEs exist which estimate the femur pose with reasonable accuracy (median root mean square error during stance/swing: 1.4/2.8 deg for orientation, 1.5/4.2 mm for position). A non-invasive and instantaneous criteria to select accurate TCPEs for pose estimation (4.8/7.3 deg, 5.8/12.3 mm), was compared with RBLS (4.3/6.6 deg, 6.9/16.6 mm) and HDLS (4.6/7.6 deg, 6.7/12.5 mm). Accounting for homogeneous deformation, using HDLS or selected TCPEs, yielded more accurate position estimations than RBLS method, which, conversely, yielded more accurate orientation estimations. Further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy.

Bone Pose Estimation in the Presence of Soft Tissue Artifact Using Triangular Cosserat Point Elements

Accurate estimation of the position and orientation (pose) of a bone from a cluster of skin markers is limited mostly by the relative motion between the bone and the markers, which is known as the Soft Tissue Artifact (STA). This work presents a method, based on continuum mechanics, to describe the kinematics of a cluster affected by STA. The cluster is characterized by Triangular Cosserat Point Elements (TCPEs) defined by all combinations of three markers. The effects of the STA on the TCPEs are quantified using three parameters describing the strain in each TCPE and the relative rotation and translation between TCPEs. The method was evaluated using previously collected ex-vivo kinematic data. Femur pose was estimated from 12 skin markers on the thigh, while its reference pose was measured using bone pins. Analysis revealed that instantaneous subsets of TCPEs exist which estimate bone position and orientation more accurately than the Procrustes Superimposition applied to the cluster of all markers. It has been shown that some of these parameters correlate well with femur pose errors, which suggests that they can be used to select, at each instant, subsets of TCPEs leading an improved estimation of the underlying bone pose.

Chest Wall Kinematics Using Triangular Cosserat Point Elements in Healthy and Neuromuscular Subjects

Optoelectronic plethysmography (OEP) is a noninvasive method for assessing lung volume variations and the contributions of different anatomical compartments of the chest wall (CW) through measurements of the motion of markers attached to the CW surface. The present study proposes a new method for analyzing the local CW kinematics from OEP measurements based on the kinematics of triangular Cosserat point elements (TCPEs). 52 reflective markers were placed on the anterior CW to create a mesh of 78 triangles according to an anatomical model. Each triangle was characterized by a TCPE and its kinematics was described using four time-variant scalar TCPE parameters. The total CW volume ( VTCW) and the contributions of its six compartments were also estimated, using the same markers. The method was evaluated using measurements of ten healthy subjects, nine patients with Pompe disease, and ten patients with Duchenne muscular dystrophy (DMD), during spontaneous breathing (SB) and vital capacity maneuvers (VC) in the supine position. TCPE parameters and compartmental volumes were compared with VTCW by computing the phase angles θ (for SB) and the correlation r (for VC) between them. Analysis of θ and r of the outward translation parameter PT of each TCPE revealed that for healthy subjects it provided similar results to those obtained by compartmental volumes, whereas for the neuromuscular patients the TCPE method was capable of detecting local asynchronous and paradoxical movements also in cases where they were undistinguished by volumes. Therefore, the TCPE approach provides additional information to OEP that may enhance its clinical evaluation capabilities.