Design of Adjustable Frame-Type Prosthetic Socket for Lower Limb

ObjectivesProsthetic socket is the contact interface between the stump and the prosthesis, and also the interface component that transmits forces from the stump to the prosthesis distal. The current prosthetic socket fit is a major factor affecting rehabilitation, especially with the stump volume fluctuations. The main goal of this article is to design an adjustable frame-type prosthetic socket with constant force to adapt to the stump volume fluctuations.Materials and methodsIn this paper, an adjustable frame-type prosthetic socket with constant force is designed. The constant force device is designed based on the superelasticity of the shape memory alloy for maintaining constant stump-socket interface stress and automatically adapting to certain volume fluctuations. The constant force extrusion performance of this prosthetic socket was verified and optimized by finite element analysis.ResultsThe results suggest that the constant force unit may maintain constant interface stress. According to the optimization results, the shape memory alloy dimensional parameters could be selected according to different requirements.ConclusionThe adjustable frame-type prosthetic socket allows the user to adjust the socket volume through the cable system and has a large heat dissipation area. The constant force unit maintains constant interface stress and automatically adapts to stump volume fluctuations.     

Modelling and simulation of substrate elasticity sensing in stem cells

Recently, we have developed a multiscale soft matter cell model aiming at improving the understanding of mechanotransduction mechanism of stem cells, which is responsible for information exchange between cells and their extracellular environment. In this paper, we report the preliminary results of our research on multiscale modelling and simulation of soft contact and adhesion of stem cells. The proposed multiscale soft matter cell model may be used to model soft contact and adhesion between cells and their extracellular substrates. To the authors' best knowledge, this may be the first time that a soft matter model has been developed for cell contact and adhesion. Moreover, we have developed and implemented a Lagrange-type meshfree Galerkin formulation and related computational algorithms for the proposed cell model. Comparison study with experimental data has been conducted to validate the parameters of the cell model. By using the soft matter cell model, we have simulated the soft adhesive contact process between cells and extracellular substrates. The simulation shows that the cell can sense substrate elasticity by responding it in different manners from cell spreading to cell contact configuration and molecular conformation changes.     

Efficient isogeometric thin shell formulations for soft biological materials

This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff–Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model soft biological materials, are examined for the three proposed constitutive approaches. Following an isogeometric approach, NURBS-based finite elements are used for the discretization of the shell surface. Several numerical examples are investigated to demonstrate the capabilities of the formulation. Those include the contact simulation during balloon angioplasty.     

Experimental-numerical analysis of minipig's multi-rooted teeth

The paper pertains to the analysis of the biomechanical behaviour of the periodontal ligament (PDL) by using a combined experimental and numerical approach. Experimental analysis provides information about a two-rooted pig premolar tooth in its socket with regard to morphological configuration and deformational response. The numerical analysis developed for the present investigation adopts a specific anisotropic hyperelastic formulation, accounting for tissue structural arrangement. The parameters to be adopted for the PDL constitutive model are evaluated with reference to data deducted from experimental in vitro tests on different specimens taken from literature. According to morphometric data relieved, solid models are provided as basis for the development of numerical models that adopt the constitutive formulation proposed. A reciprocal validation of experimental and numerical data allows for the evaluation of reliability of results obtained. The work is intended as preliminary investigation to study the correlation between mechanical status of PDL and induction to cellular activity in orthodontic treatments.     

Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear

Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.     

Network Reconstruction Based on Proteomic Data and Prior Knowledge of Protein Connectivity Using Graph Theory

Modeling of signal transduction pathways is instrumental for understanding cells’ function. People have been tackling modeling of signaling pathways in order to accurately represent the signaling events inside cells’ biochemical microenvironment in a way meaningful for scientists in a biological field. In this article, we propose a method to interrogate such pathways in order to produce cell-specific signaling models. We integrate available prior knowledge of protein connectivity, in a form of a Prior Knowledge Network (PKN) with phosphoproteomic data to construct predictive models of the protein connectivity of the interrogated cell type. Several computational methodologies focusing on pathways’ logic modeling using optimization formulations or machine learning algorithms have been published on this front over the past few years. Here, we introduce a light and fast approach that uses a breadth-first traversal of the graph to identify the shortest pathways and score proteins in the PKN, fitting the dependencies extracted from the experimental design. The pathways are then combined through a heuristic formulation to produce a final topology handling inconsistencies between the PKN and the experimental scenarios. Our results show that the algorithm we developed is efficient and accurate for the construction of medium and large scale signaling networks. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGF/TNFA stimulation against made up experimental data. To avoid the possibility of erroneous predictions, we performed a cross-validation analysis. Finally, we validate that the introduced approach generates predictive topologies, comparable to the ILP formulation. Overall, an efficient approach based on graph theory is presented herein to interrogate protein–protein interaction networks and to provide meaningful biological insights.     

A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics

Combining musculoskeletal simulations with anatomical joint models capable of predicting cartilage contact mechanics would provide a valuable tool for studying the relationships between muscle force and cartilage loading. As a step towards producing multibody musculoskeletal models that include representation of cartilage tissue mechanics, this research developed a subject-specific multibody knee model that represented the tibia plateau cartilage as discrete rigid bodies that interacted with the femur through deformable contacts. Parameters for the compliant contact law were derived using three methods: (1) simplified Hertzian contact theory, (2) simplified elastic foundation contact theory and (3) parameter optimisation from a finite element (FE) solution. The contact parameters and contact friction were evaluated during a simulated walk in a virtual dynamic knee simulator, and the resulting kinematics were compared with measured in vitro kinematics. The effects on predicted contact pressures and cartilage–bone interface shear forces during the simulated walk were also evaluated. The compliant contact stiffness parameters had a statistically significant effect on predicted contact pressures as well as all tibio-femoral motions except flexion–extension. The contact friction was not statistically significant to contact pressures, but was statistically significant to medial–lateral translation and all rotations except flexion–extension. The magnitude of kinematic differences between model formulations was relatively small, but contact pressure predictions were sensitive to model formulation. The developed multibody knee model was computationally efficient and had a computation time 283 times faster than a FE simulation using the same geometries and boundary conditions.     

Load transfer mechanics between trans-tibial prosthetic socket and residual limb--dynamic effects

The effects of inertial loads on the interface stresses between trans-tibial residual limb and prosthetic socket were investigated. The motion of the limb and prosthesis was monitored using a Vicon motion analysis system and the ground reaction force was measured by a force platform. Equivalent loads at the knee joint during walking were calculated in two cases with and without consideration of the material inertia. A 3D nonlinear finite element (FE) model based on the actual geometry of residual limb, internal bones and socket liner was developed to study the mechanical interaction between socket and residual limb during walking. To simulate the friction/slip boundary conditions between the skin and liner, automated surface-to-surface contact was used. The prediction results indicated that interface pressure and shear stress had the similar double-peaked waveform shape in stance phase. The average difference in interface stresses between the two cases with and without consideration of inertial forces was 8.4% in stance phase and 20.1% in swing phase. The maximum difference during stance phase is up to 19%. This suggests that it is preferable to consider the material inertia effect in a fully dynamic FE model.     

Computational study of cell adhesion and rolling in flow channel by meshfree method

Tethering and rolling of circulating leukocytes on the surface of endothelium are critical steps during an inflammatory response. A soft solid cell model was proposed to study monocytes tethering and rolling behaviors on substrate surface in shear flow. The interactions between monocytes and micro-channel surface were modeled by a coarse-grained molecular adhesive potential. The computational model was implemented in a Lagrange-type meshfree Galerkin formulation to investigate the monocyte tethering and rolling process with different flow rates. From the simulation results, it was found that the flow rate has profound effects on the rolling velocity, contact area and effective stress of monocytes. As the flow rate increased, the rolling velocity would increase linearly, whereas the contact area and average effective stress in monocyte showed nonlinear increase.     

Design and analysis of orthogonally compliant features for local contact pressure relief in transtibial prostheses

A very attractive advantage of manufacturing prosthetic sockets using solid freeform fabrication is the freedom to introduce design solutions that would be difficult to implement using traditional manufacturing techniques. Such is the case with compliant features embedded in amputee prosthetic sockets to relieve contact pressure at the residual limb-socket interface. The purpose of this study was to present a framework for designing compliant features to be incorporated into transtibial sockets and manufacturing prototypes using selective laser sintering (SLS) and Duraform material. The design process included identifying optimal compliant features using topology optimization algorithms and integrating these features within the geometry of the socket model. Using this process, a compliant feature consisting of spiral beams and a supporting external structure was identified. To assess its effectiveness in reducing residual limb-socket interface pressure, a case study was conducted using SLS manufactured prototypes to quantify the difference in interface pressure while a patient walked at his self-selected pace with one noncompliant and two different compliant sockets. The pressure measurements were performed using thin pressure transducers located at the distal tibia and fibula head. The measurements revealed that the socket with the greatest compliance reduced the average and peak pressure by 22% and 45% at the anterior side distal tibia, respectively, and 19% and 23% at the lateral side of the fibula head, respectively. These results indicate that the integration of compliant features within the socket structure is an effective way to reduce potentially harmful contact pressure and increase patient comfort.     

Computer-aided design and manufacture of an above-knee amputee socket

This paper describes the initial test results obtained from a newly developed computer-aided socket design (CASD) and manufacturing (CASM) process for above-knee amputees. Anthropometric measures taken from an amputee provided input information to a CASD system. Using these measurements, data from a reference shape library stored in the computer were selected and modified to create a unique socket shape reflecting the particular characteristics of the amputation stump. The resultant shape was produced as a ‘primitive’ test socket by a CASM process. Numerical shape data were then transferred to a CNC milling machine to construct a negative cast, from which the primitive socket was produced by a vacuum-forming procedure. The resultant primitive socket shape was fitted and the amputee was able to load the socket without discomfort. Some shape discrepancies were identified and the shape data were modified interactively by the CASD system to create a final socket shape. The final socket shape was manufactured and worn by the amputee during a 35 min walking trial. Subjective evaluation was that the socket provided comfort and control comparable with that of the conventional socket, and proved to be acceptable to the amputee. This was followed by a 2-month home trial which was also successful. The CASD socket shapes were compared numerically in area, shape and volume with data taken from the original socket worn by the amputee, a new socket made by conventional methods and a topographic model of the amputation stump. The final CASD socket shape compared favourably with that of a socket manufactured by conventional methods. Results indicated that by the use of the CASD/CASM process, it was possible to produce an above-knee prosthetic socket which provided comfort and control for the amputee.     

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain ${D(\kappa)}$ , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.     

Investigation of Critical Core Formulation and Process Parameters for Osmotic Pump Oral Drug Delivery

Push–pull osmotic pump (PPOP) tablets of a practically insoluble model drug were developed and the effect of various formulation and process parameters on tablet performance was evaluated in order to identify critical factors. The formulation factors such as the viscosity grade of polyethylene oxide as the primary polymer as well as the level and location of osmogen within the bilayer tablets led to a difference in performance of osmotic tablets and hence should be critically evaluated in the design of such dosage forms. Modification of granulation process, i.e., the granulating liquid composition or drying method of granules, did not impact the drug release from the osmotic tablets at the evaluated scale of this study. The influence of varying dose and aqueous solubility of other model drugs (i.e., theophylline, acetaminophen, and verapamil HCl) on the developed PPOP template was also investigated. Results showed that irrespective of the perceived complexity of development and manufacturing of osmotic pumps, the osmotic tablets in this study demonstrated a robust and yet flexible platform in accommodating different types of drug candidates, regardless of solubility, for the dose levels below 25% w/w of the pull layer formulation.     

Scheduling unrelated parallel machines in semiconductor manufacturing by problem reduction and local search heuristics

We investigate a difficult scheduling problem in a semiconductor manufacturing process that seeks to minimize the number of tardy jobs and makespan with sequence-dependent setup time, release time, due dates and tool constraints. We propose a mixed integer programming (MIP) formulation which treats tardy jobs as soft constraints so that our objective seeks the minimum weighted sum of makespan and heavily penalized tardy jobs. Although our polynomial-sized MIP formulation can correctly model this scheduling problem, it is so difficult that even a feasible solution can not be calculated efficiently for small-scale problems. We then propose a technique to estimate the upper bound for the number of jobs processed by a machine, and use it to effectively reduce the size of the MIP formulation. In order to handle real-world large-scale scheduling problems, we propose an efficient dispatching rule that assigns a job of the earliest due date to a machine with least recipe changeover (EDDLC) and try to re-optimize the solution by local search heuristics which involves interchange, translocation and transposition between assigned jobs. Our computational experiments indicate that EDDLC and our proposed reoptimization techniques are very efficient and effective. In particular, our method usually gives solutions very close to the exact optimum for smaller scheduling problems, and calculates good solutions for scheduling up to 200 jobs on 40 machines within 10 min.     

Microplane constitutive model and computational framework for blood vessel tissue

This paper presents a nonlinearly elastic anisotropic microplane formulation in 3D for computational constitutive modeling of arterial soft tissue in the passive regime. The constitutive modeling of arterial (and other biological) soft tissue is crucial for accurate finite element calculations, which in turn are essential for design of implants, surgical procedures, bioartificial tissue, as well as determination of effect of progressive diseases on tissues and implants. The model presented is defined at a lower scale (mesoscale) than the conventional macroscale and it incorporates the effect of all the (collagen) fibers which are anisotropic structural components distributed in all directions within the tissue material in addition to that of isotropic bulk tissue. It is shown that the proposed model not only reproduces Holzapfel's recent model but also improves on it by accounting for the actual three-dimensional distribution of fiber orientation in the arterial wall, which endows the model with advanced capabilities in simulation of remodeling of soft tissue. The formulation is flexible so that its parameters could be adjusted to represent the arterial wall either as a single material or a material composed of several layers in finite element analyses of arteries. Explicit algorithms for both the material subroutine and the explicit integration with dynamic relaxation of equations of motion using finite element method are given. To circumvent the slow convergence of the standard dynamic relaxation and small time steps dictated by the stability of the explicit integrator, an adaptive dynamic relaxation technique that ensures stability and fastest possible convergence rates is developed. Incompressibility is enforced using penalty method with an updated penalty parameter. The model is used to simulate experimental data from the literature demonstrating that the model response is in excellent agreement with the data. An experimental procedure to determine the distribution of fiber directions in 3D for biological soft tissue is suggested in accordance with the microplane concept. It is also argued that this microplane formulation could be modified or extended to model many other phenomena of interest in biomechanics.     

Towards accurate residue-residue hydrophobic contact prediction for alpha helical proteins via integer linear optimization

A new optimization-based method is presented to predict the hydrophobic residue contacts in alpha-helical proteins. The proposed approach uses a high resolution distance dependent force field to calculate the interaction energy between different residues of a protein. The formulation predicts the hydrophobic contacts by minimizing the sum of these contact energies. These residue contacts are highly useful in narrowing down the conformational space searched by protein structure prediction algorithms. The proposed algorithm also offers the algorithmic advantage of producing a rank ordered list of the best contact sets. This model was tested on four independent alpha-helical protein test sets and was found to perform very well. The average accuracy of the predictions (separated by at least six residues) obtained using the presented method was approximately 66% for single domain proteins. The average true positive and false positive distances were also calculated for each protein test set and they are 8.87 and 14.67 A, respectively.     

Using numerical plant models and phenotypic correlation space to design achievable ideotypes

Numerical plant models can predict the outcome of plant traits modifications resulting from genetic variations, on plant performance, by simulating physiological processes and their interaction with the environment. Optimization methods complement those models to design ideotypes, that is, ideal values of a set of plant traits, resulting in optimal adaptation for given combinations of environment and management, mainly through the maximization of performance criteria (e.g. yield and light interception). As use of simulation models gains momentum in plant breeding, numerical experiments must be carefully engineered to provide accurate and attainable results, rooting them in biological reality. Here, we propose a multi‐objective optimization formulation that includes a metric of performance, returned by the numerical model, and a metric of feasibility, accounting for correlations between traits based on field observations. We applied this approach to two contrasting models: a process‐based crop model of sunflower and a functional–structural plant model of apple trees. In both cases, the method successfully characterized key plant traits and identified a continuum of optimal solutions, ranging from the most feasible to the most efficient. The present study thus provides successful proof of concept for this enhanced modelling approach, which identified paths for desirable trait modification, including direction and intensity.     

Experimental evaluation of an elastic foundation model to predict contact pressures in knee replacements

Computational wear prediction is an attractive concept for evaluating new total knee replacement designs prior to physical testing and implementation. An important hurdle to such technology is the lack of in vivo contact pressure predictions. To address this issue, this study evaluates a computationally efficient simulation approach that combines the advantages of rigid and deformable body modeling. The hybrid method uses rigid body dynamics to predict body positions and orientations and elastic foundation theory to predict contact pressures between general three-dimensional surfaces. To evaluate the method, we performed static pressure experiments with a commercial knee implant in neutral alignment using flexion angles of 0, 30, 60, and 90 degrees and loads of 750, 1500, 2250, and 3000N. Using manufacturer CAD geometry for the same implant, an elastic foundation model with linear or nonlinear polyethylene material properties was implemented within a commercial multibody dynamics software program. The model's ability to predict experimental peak and average contact pressures simultaneously was evaluated by performing dynamic simulations to find the static configuration. Both the linear and nonlinear material models predicted the average contact pressure data well, while only the linear material model could simultaneously predict the trends in the peak contact pressure data. This novel modeling approach is sufficiently fast and accurate to be used in design sensitivity and optimization studies of knee implant mechanics and ultimately wear.