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Concept: Partial differential equation


A combined stress-vibration sensor was developed to measure stress and vibration simultaneously based on fiber Bragg grating (FBG) technology. The sensor is composed of two FBGs and a stainless steel plate with a special design. The two FBGs sense vibration and stress and the sensor can realize temperature compensation by itself. The stainless steel plate can significantly increase sensitivity of vibration measurement. Theoretical analysis and Finite Element Method (FEM) were used to analyze the sensor’s working mechanism. As demonstrated with analysis, the obtained sensor has working range of 0-6000 Hz for vibration sensing and 0-100 MPa for stress sensing, respectively. The corresponding sensitivity for vibration is 0.46 pm/g and the resulted stress sensitivity is 5.94 pm/MPa, while the nonlinearity error for vibration and stress measurement is 0.77% and 1.02%, respectively. Compared to general FBGs, the vibration sensitivity of this sensor is 26.2 times higher. Therefore, the developed sensor can be used to concurrently detect vibration and stress. As this sensor has height of 1 mm and weight of 1.15 g, it is beneficial for minimization and integration.

Concepts: Finite element method, Hilbert space, Bragg diffraction, Steel, Partial differential equation, Stainless steel, Bragg's law, Fiber Bragg grating


To improve understanding of the internal structure of the proximal phalanx (P1), response of the bone to load and possible relation to the pathogenesis of fractures in P1.

Concepts: Finite element method, Hilbert space, Set theory, Partial differential equation, Finite element method in structural mechanics, Discrete mathematics


This paper presents a novel reaction-diffusion (RD) method for implicit active contours that is completely free of the costly reinitialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in an RD-LSE equation, from which a piecewise constant solution can be derived. In order to obtain a stable numerical solution from the RD-based LSE, we propose a two-step splitting method to iteratively solve the RD-LSE equation, where we first iterate the LSE equation, then solve the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly reinitialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and partial differential equation-based level set method. The RD-LSE method shows very good performance on boundary antileakage. The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.

Concepts: Mathematics, Level set, Partial differential equation, Numerical analysis, Level set method, Finite difference, Finite difference method, Finite differences


Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace’s equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite’s membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Concepts: Mathematics, Cell membrane, Maxwell's equations, Action potential, Differential equation, Partial differential equation, Normal mode, Ordinary differential equation


Far field RF powering is an attractive solution to the challenge of remotely powering devices implanted in living tissue. The purpose of this study is to characterize the peak obtainable power levels in a wireless myoelectric sensor implanted in a patient while maintaining safe local temperature and RF powering conditions. This can serve as a guide for the design of onboard electronics in related medical implants and provide motivation for more efficient power management strategies for implantable integrated circuits (ICs). Safe powering conditions and peak received power levels are established using a simplified theoretical analysis and FCC (Federal Communications Commission)-established limits for radiating antennas. These conditions are subsequently affirmed and improved upon using the finite element method (FEM) and temperature modeling in bovine muscle.

Concepts: Implantable cardioverter-defibrillator, Engineering, Finite element method, Partial differential equation, Finite element method in structural mechanics, Federal Communications Commission


Abstract Objective. This study evaluated the influence of framework material and vertical misfit on stress created in an implant-supported partial prosthesis under load application. Materials and methods. The posterior part of a severely reabsorbed jaw with a fixed partial prosthesis above two osseointegrated titanium implants at the place of the second premolar and second molar was modeled using SolidWorks 2010 software. Finite element models were obtained by importing the solid model into an ANSYS Workbench 11 simulation. The models were divided into 15 groups according to their prosthetic framework material (type IV gold alloy, silver-palladium alloy, commercially pure titanium, cobalt-chromium alloy or zirconia) and vertical misfit level (10 µm, 50 µm and 100 µm). After settlement of the prosthesis with the closure of the misfit, simultaneous loads of 110 N vertical and 15 N horizontal were applied on the occlusal and lingual faces of each tooth, respectively. The data was evaluated using Maximum Principal Stress (framework, porcelain veneer and bone tissue) and a von Mises Stress (retention screw) provided by the software. Results. As a result, stiffer frameworks presented higher stress concentrations; however, these frameworks led to lower stresses in the porcelain veneer, the retention screw (faced to 10 µm and 50 µm of the misfit) and the peri-implant bone tissues. Conclusion. The increase in the vertical misfit resulted in stress values increasing in all of the prosthetic structures and peri-implant bone tissues. The framework material and vertical misfit level presented a relevant influence on the stresses for all of the structures evaluated.

Concepts: Bone, Finite element method, Materials science, Osseous tissue, Partial differential equation, Finite element method in structural mechanics, Canine tooth, Yield surface


BACKGROUND: This study aims to clarify the effect of various designs of reverse shoulder prosthesis (RSP) on stress variation of its glenoid component using 2-dimensional (2D) finite element analysis (FEA). This FEA study provides future reference for the optimal design of glenoid component of RSP. MATERIALS AND METHODS: In this study, a 2D finite element (FE) model of human shoulder with implementation of RSP was developed by commercial FE software. The proper material properties were adopted in our model. Various design factors were simulated and all the mechanical profile data were investigated by FEA. RESULTS: Both distal placement and increased lateral offset of glenosphere induce higher stress over glenoid-baseplate junction. Increased thickness of graft, inferiorly tilting of the baseplate, and adoption of BIO-RSA (bony increased-offset reverse shoulder arthroplasty) incur higher stresses over glenoid screws. The inferior screw attains more stress than superior screw. Maximum stress occurs at the base of inferior screw. CONCLUSION: Increased eccentric offset and lateral offset of glenosphere, although being able to reduce notching, may pay the penalty of significant stress concentration over glenoid and its subsequent loosening. Maximum stress occurs at the base of inferior screw elucidate the direct contact failure mode at the middle of inferior screw. This study provides an alternative tool for the optimal design of glenoid component of RSP in the future.

Concepts: Engineering, Finite element method, Hilbert space, Shoulder, Partial differential equation, Finite element method in structural mechanics, Structural analysis


To validate torsional analysis, based on finite elements, of WaveOne instruments against in vitro tests and to model the effects of different nickel titanium materials METHODOLOGY: WaveOne reciprocating instruments (Small, Primary and Large, n=8 each, M-Wire) were tested under torsion according to standard ISO 3630-1. Torsional profiles including torque and angle at fracture were determined. Test conditions were reproduced through Finite Element Analysis (FEA) simulations based on micro CT scans at 10μm resolution; results were compared to experimental data using analysis of variance and two-sided one sample t-tests. The same simulation was performed on virtual instruments with identical geometry and load condition, based on M-Wire or conventional NiTi alloy.

Concepts: Engineering, Finite element method, Hilbert space, Normal distribution, Analysis of variance, Standard, Partial differential equation, Torsion



The steady boundary layer flow and heat transfer of a nanofluid past a nonlinearly permeable stretching/shrinking sheet is numerically studied. The governing partial differential equations are reduced into a system of ordinary differential equations using a similarity transformation, which are then solved numerically using a shooting method. The local Nusselt number and the local Sherwood number and some samples of velocity, temperature and nanoparticle concentration profiles are graphically presented and discussed. Effects of the suction parameter, thermophoresis parameter, Brownian motion parameter and the stretching/shrinking parameter on the flow, concentration and heat transfer characteristics are thoroughly investigated. Dual solutions are found to exist in a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. Results indicate that suction widens the range of the stretching/shrinking parameter for which the solution exists.

Concepts: Temperature, Thermodynamics, Derivative, Differential equation, Heat transfer, Partial differential equation, Ordinary differential equation, Sherwood number