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This paper aims to develop a numerical methodology to investigate the penetration process of nanoneedles into cells and the corresponding force and indentation length. The finite element approach via the explicit dynamic method handles convergence difficulties in the nonlinear phenomenon. The cell is modeled as an isotropic elastic hemiellipsoidal shell with a thickness of 200 nm, which represents the lipid membrane and actin cortex, encapsulating cytoplasm that is regarded as an Eulerian body because of its fluid‐type behavior. Nanoneedles with diameters 400, 200, and 50 nm are considered for model development based on available experimental data. The Von Mises strain failure criterion is used for rupture detection. A parameter study using 1, 2.5, 5, 7.5, and 10 kPa shows that Young's modulus of the HeLa cell membrane is about 5 kPa. Moreover, a failure strain of 1.2 chosen among 0.2, 0.4, 0.6, 0.8, 1, and 1.2 matches best the experimental data. In addition, a diameter study shows that the relations between force‐diameter and indentation length‐diameter are linear and polynomial, respectively. Furthermore, regarding the experimental data and by using contour of minimum principal stress around needle and an analytical equation for calculation of buckling force of a woven fabric, we proposed that for a given cell, membrane structural stability—a function of the coupled effect of Young's modulus and actin meshwork size—contributes directly to needle insertion success rate for that type of cell. [ABSTRACT FROM AUTHOR]

Healing of tibia demonstrates a complex mechanobiological process as it is stimulated by the major factor of strains applied by body weight. The effect of screw heads and bodies as well as their pressure distribution is often overlooked. Hence, effective mechanical conditions of the healing process of tibia can be categorized into the material of the plate and screws, post‐operation loadings, and screw type and pressure. In this paper, a mathematical biodegradation model was used to simulate the PGF/PLA plate‐screw device over 8 weeks. The effect of different post‐operation loading patterns was studied for both locking and non‐locking screws. The aim was to reach the best configuration for the most achievable healing using FEA by computing the healing pattern, trend, and efficiency with the mechano‐regulation theory based on deviatoric strain. The biodegradation process of the plate and screws resulted in 82% molecular weight loss and 1.05 GPa decrease in Young's modulus during 8 weeks. The healing efficiency of the cases ranged from 4.72% to 14.75% in the first week and 18.64% to 63.05% in the eighth week. Finally, an optimal case was achieved by considering the prevention of muscle erosion, bone density reduction, and nonunion, according to the obtained results. [ABSTRACT FROM AUTHOR]

The electromagnetic middle‐ear implant (MEI) is a new type of hearing device for addressing sensorineural and mixed hearing loss. The hearing compensation effect of the MEI varies depending on the transducer stimulation sites. This paper investigates the impact of transducer stimulation sites on MEI performance by analyzing stapes spatial motion. Firstly, we constructed a human‐ear finite element model based on micro‐CT scanning and inverse molding techniques. This model was validated by comparing its predictions of stapes spatial motion and cochlear response with experimental data. Then, stimulation force was applied at four common sites: umbo, incus body, incus long process and stapes to simulate the electromagnetic transducer. Results show that at low and middle frequencies, stapes‐stimulating and incus‐long‐process‐stimulating produce similar spatial motion to normal hearing; at high frequencies, incus‐body‐stimulating produces similar results to normal hearing. The equivalent sound pressure level generated by the stapes piston motion is less sensitive to the stimulation direction than that deduced by the stapes rocking motion. [ABSTRACT FROM AUTHOR]

Finite Element modeling has been an extended methodology to build numerical model to simulate the behavior of the hearing system. Due to the complexity of the system and the difficulties to reduce the uncertainties of the geometric data, they result in computationally expensive models, sometimes generic, representative of average geometries. It makes it difficult to validate the model with direct experimental data from the same specimen or to establish a patient‐oriented modeling strategy. In the present paper, a first attempt to automatize the process of model building is made. The source information is geometrical information obtained from CT of the different elements that compose the system. Importing that data, we have designed the complete procedure to build a model including tympanic membrane, ossicular chain and cavities. The methodology includes the proper coupling of all the elements and the generation of the corresponding finite element model. The whole automatic procedure is not complete, as we need to make some human‐assisted decisions; however, the model development time is reduced from 4 weeks to approximately 3 days. The goal of the modeling algorithm is to build a Finite Element Model with a limited computational cost. Several tasks as contour identification or model decimation are designed and integrated in order to follow a semi‐automated process that allows generating a patient‐oriented model. [ABSTRACT FROM AUTHOR]

Glioblastoma is the most aggressive and infiltrative glioma, classified as Grade IV, with the poorest survival rate among patients. Accurate and rigorously tested mechanistic in silico modeling offers great value to understand and quantify the progression of primary brain tumors. This paper presents a continuum‐based finite element framework that is built on high performance computing, open‐source libraries to simulate glioblastoma progression. We adopt the established proliferation invasion hypoxia necrosis angiogenesis model in our framework to realize scalable simulations of cancer, and has demonstrated to produce accurate and efficient solutions in both two‐ and three‐dimensional brain models. The in silico solver can successfully implement arbitrary order discretization schemes and adaptive remeshing algorithms. A model sensitivity analysis is conducted to test the impact of vascular density, cancer cell invasiveness and aggressiveness, the phenotypic transition potential, including that of necrosis, and the effect of tumor‐induced angiogenesis in the evolution of glioblastoma. Additionally, individualized simulations of brain cancer progression are carried out using pertinent magnetic resonance imaging data, where the in silico model is used to investigate the complex dynamics of the disease. We conclude by arguing how the proposed framework can deliver patient‐specific simulations of cancer prognosis and how it could bridge clinical imaging with modeling. [ABSTRACT FROM AUTHOR]

The Finite Element Method (FEM) is a numerical technique that is well‐established in the field of engineering. However, in biological sciences, it is just taking its first steps. Bone tissue is an example of biological material which is exposed to high loads in its natural environment. Practically every movement of the body results in changing stress levels in the bone. Nature copes with this very well but when human intervention is necessary (e.g., endoprostheses implants) bone strength has to be determined based on experience since bone tissue has a very heterogeneous structure. The goal of this paper is to demonstrate how standard FEM calculations may be readily modified to provide for variable material properties of such materials as, for example, bone or wood. [ABSTRACT FROM AUTHOR]

Cell's ability to proliferate constitutes one of the most defining features of life. The proliferation occurs through a succession of events; the cell cycle, whereby the cell grows and divides. In this paper, focus is made on the growth step and we deal specifically with Saccharomyces cerevisiae yeast that reproduces by budding. For this, we develop a theoretical model to predict the growth powered by the turgor pressure. This cell is herein considered as a thin‐walled structure with almost axisymmetrical shape. Due to its soft nature, the large deformation range is a priori assumed through a finite growth modeling framework. The used kinematics is based on the multiplicative decomposition of the deformation gradient into an elastically reversible part and a growth part. Constitutive equations are proposed where use is made of hyperelasticity together with a local evolution equation, this latter to describe the way growth takes place. In particular, two essential parameters are involved: a stress‐like threshold, and a characteristic time. The developed model is extended to a shell approach as well. In a finite element context, representative numerical simulations examining stress‐dependent growth are given and a parametric study is conducted to show the sensitivity with respect to the above mentioned parameters. Finally, a suggestion for natural contractile ring modeling closes this study. [ABSTRACT FROM AUTHOR]

Numerical simulations of pulsatile blood flow in an aortic coarctation require the use of turbulence modeling. This paper considers three models from the class of large eddy simulation (LES) models (Smagorinsky, Vreman, σ‐model) and one model from the class of variational multiscale models (residual‐based) within a finite element framework. The influence of these models on the estimation of clinically relevant biomarkers used to assess the degree of severity of the pathological condition (pressure difference, secondary flow degree, normalized flow displacement, wall shear stress) is investigated in detail. The simulations show that most methods are consistent in terms of severity indicators such as pressure difference and stenotic velocity. Moreover, using second‐order velocity finite elements, different turbulence models might lead to considerably different results concerning other clinically relevant quantities such as wall shear stresses. These differences may be attributed to differences in numerical dissipation introduced by the turbulence models. [ABSTRACT FROM AUTHOR]

Unlocking the biomechanical effects of cervical spine positioning rotation manipulation in the treatment of patients with neck pain. In this paper, the safety of the cervical positioning rotation manipulation is analyzed by experimentally obtaining head kinematic data, importing them into a finite element model that has been developed and validated, and calculating and analyzing the angular displacements, disc pressures, and articular surface contact forces in the normal and pathological models. The results show that the cervical spine positioning rotation technique is more effective in adjusting the position and applying force to the cervical spine C5–C6 "tendon out of the groove and bone misalignment" pathological model. Also, the cervical positioning rotation manipulation is applied with less variation in disc nucleus pulposus pressure than in the non‐positioning situation. Thus, in patients with disc degeneration, cervical positioning rotational manipulation has a more direct mechanical effect and is safer than non‐positioning rotational manipulation. The cervical spine positioning rotation manipulation is a safe method that can effectively treat patients with neck pain. It has been well demonstrated in the computational analysis of the pathological model. [ABSTRACT FROM AUTHOR]

Most researchers have performed finite element (FE) analysis of the human forearm fracture by exploring the strength and load transmission of the bones. However, few studies concentrated a complete simulation of the whole forearm complex including ligaments. This paper aims to investigate the load transmission through the bones, contact stress at the joints and strain in the ligaments by using an elaborate FE model, further validating the fracture condition for human forearm. The interosseous ligament was separated into three regions based on the distance to the proximal and distal ends. The FE simulation results were slightly more or less than a previous experimental data in the literature, but generally provided a close approximation of the bone and ligament behaviors. Compared with the experiment results under different loading conditions, maximum contact stress at the proximal radio ulnar joint (PRUJ) and distal radio ulnar joint (DRUJ) of the simulations was higher with an average of 13.4%, and peak strain in the interosseous ligament (IOL) was lower with an average of 11.0%. Under 10 kg load, the maximum stress in the radius (2.25 MPa) was less than double the value in the ulna (1.43 MPa). Finally, the FE model has been validated with the onset and location of the Colles' fracture in the literature. This study will provide a great benefit in terms of surgical and medical applications related to forearm fracture that require an extensive knowledge of the behavior of the bones and ligaments under various loading conditions. [ABSTRACT FROM AUTHOR]

In this paper, we develop an algorithm to simulate blood flows in aneurysmal arteries and focus on the construction of robust and efficient multilevel preconditioners to speed up the convergence of both linear and nonlinear solvers. The work is motivated by the observation that in the local aneurysmal region, the flow is often quite complicated with one or more vortices, but in the healthy section of the artery, the principal component of blood flows along the centerline of the artery. Based on this observation, we introduce a novel two‐level additive Schwarz method with a mixed‐dimensional coarse preconditioner. The key components of the preconditioner include (1) a three‐dimensional coarse preconditioner covering the aneurysm; (2) a one‐dimensional coarse preconditioner covering the central line of the healthy section of the artery; (3) a collection of three‐dimensional overlapping subdomain preconditioners covering the fine meshes of the entire artery; (4) extension/restriction operators constructed by radial basis functions. The blood flow is modeled by the unsteady incompressible Navier–Stokes equations with resistance outflow boundary conditions discretized by a stabilized finite element method on fully unstructured meshes and the second‐order backward differentiation formula in time. The resulting large nonlinear algebraic systems are solved by a Newton‐Krylov algorithm accelerated by the new preconditioner in two ways: (1) the initial guess of Newton is obtained by solving a linear system defined by the coarse preconditioner; (2) the Krylov solver of the Jacobian system is preconditioned by the new preconditioner. Numerical experiments indicate that the proposed preconditioner is highly effective and robust for complex flows in a patient‐specific artery with aneurysm, and it significantly reduces the numbers of linear and nonlinear iterations. [ABSTRACT FROM AUTHOR]

This paper presents a patient-sensitive simulation strategy capable of using the most efficient way the high-performance computational resources. The proposed strategy directly involves three different players: Computational Mechanics Scientists (CMS), Image Processing Scientists and Cardiologists, each one mastering its own expertise area within the project. This paper describes the general integrative scheme but focusing on the CMS side presents a massively parallel implementation of computational electrophysiology applied to cardiac tissue simulation. The paper covers different angles of the computational problem: equations, numerical issues, the algorithm and parallel implementation. The proposed methodology is illustrated with numerical simulations testing all the different possibilities, ranging from small domains up to very large ones. A key issue is the almost ideal scalability not only for large and complex problems but also for medium-size meshes. The explicit formulation is particularly well suited for solving this highly transient problems, with very short time-scale. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

One difficulty in solving the Poisson–Nernst–Planck (PNP) equations used for studying the ion transport in channel proteins is the possible convection‐dominant problem in the Nernst–Planck equations. In this paper, to overcome this issue, considering the general mixed boundary conditions of concentration functions on the interface, a novel stabilized finite volume element method based on the standard weak formulation to solve the steady‐state PNP equations is proposed and analyzed. Numerical tests on four ion‐channel proteins served as benchmark with varying boundary conditions in a certain range show that the new stabilized technique not only improves the robustness of the new PNP solver, but also makes the computed (especially the maximal) concentration values much more reasonable. A new stabilized technique for the mixed boundary condition on the interface is proposed and analyzed.The new stabilized PNP solver is fulfilled in Fortran and Python, and well validated using the test models.The effectiveness of the new stabilized technique as well as the robustness of the new PNP solver is demonstrated. [ABSTRACT FROM AUTHOR]

We construct an idealized computational model of the left human heart for the study of the blood flow dynamics in the left atrium and ventricle. We solve the Navier‐Stokes equations in the ALE formulation and we prescribe the left heart wall displacement based on physiological data; moreover, we consider the presence of both the mitral and aortic valves through the resistive method. We simulate the left heart hemodynamics by means of the finite element method and we consider the variational multiscale large eddy simulation (LES) formulation to account for the transitional and nearly turbulent regimes of the blood flow in physiological conditions. The main contribution of this paper is the characterization of the blood flow in an idealized configuration of the left heart aiming at reproducing function in normal conditions. Our assessment is based on the analysis of instantaneous and phase averaged velocity fields, blood pressure, and other clinically meaningful fluid dynamics indicators. Finally, we show that our idealized computational model can be suitably used to study and critically discuss pathological scenarios like that of a regurgitant mitral valve. [ABSTRACT FROM AUTHOR]

Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty—from uncertain input parameters to uncertain output quantities—in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon standard Monte Carlo (MC) methods, but their applicability and performance in biomedical applications is underexplored. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convection‐diffusion model of tracer transport within the brain. We show that QMC outperforms standard MC simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard MC methods and should therefore be preferred for brain transport models. [ABSTRACT FROM AUTHOR]

The existence of vegetation in unsaturated soil can change the moisture content of its nearby soil, especially in drought condition. This moisture content reduction produces matric suction in the soil. When the vegetation is capable of extracting significant amount of water and hence, producing large matric suction values, the study of the phenomenon becomes crucial. However, unfortunately, this phenomenon has always been neglected by geotechnical engineers. In this paper the authors have suggested a set of mathematical formulas, which sets the stage to study the effect of root water uptake in unsaturated soils. The root water uptake relationship has been written in the integral form of θ-STOCK formulation, a fully coupled formulation of unsaturated porous media proposed by Gatmiri at CERMES-ENPC. It is shown that the results of finite element simulations of the model for case studies, which are presented in this paper, are in good agreement with the results of other works and field measurements. Finally, the settlement of a strip footing near a row of trees is studied. It is shown that how vegetation water uptake can impose settlement to residential municipalities. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Homotopy perturbation method (HPM) for solving the Fokker–Planck equation and some similar equations. This method is a powerful tool for solving various kinds of problems. Employing this technique, it is possible to find the exact solution or an approximate solution of the problem. The results show applicability, accuracy and efficiency of HPM in solving nonlinear differential equations. It is predicted that HPM can be widely applied in science and engineering problems. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a stabilizing finite element method using a new bubble element for the unsteady fluid flow expressed by the compressible Euler equations to save efficient computational memory for computers. The formulation is based on the mixed interpolation for a transient term. The main idea of the present paper is to use the mixed interpolation for the transient term with bubble function as the weighting function and with linear function as the interpolation function. The nodal values at the bubble node can be eliminated even in the transient formulation. The stabilizing effect of the bubble function is effectively used. The formulation leads to the stabilizing effect, which is efficient to the unsteady fluid flow problems. The efficiency is verified based on the numerical studies, in which a rotating cone problem, a shock tube problem and a problem of flow around an airfoil are calculated. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Thermoelectric generators (TEG) convert the thermal energy into electrical energy and are under investigation as a power supply for medical implants. To improve the performance of TEG, the design optimization process through finite element model simulation is preferred by biomedical engineers. This paper aims to provide an efficient method of speeding up the design optimization process of TEG. A three‐dimensional realistic human torso model incorporating the TEG is investigated, where the internal heat transfer in human tissue is characterized by Pennes bioheat equation. In addition, convection, radiation, and evaporation effects at the skin surface are applied to identify the heat transfer effects between the human body and the environment. To speed up finite element simulation of the large‐scale human torso model, projection‐based model order reduction (MOR) is applied for generation of a compact but highly accurate model. Parametric MOR (pMOR) further enables generating a parameter‐independent compact model. For an efficient design optimization of TEG, this compact human torso model is applied within a thermal submodeling approach. Its temperature distribution results are back‐projected and used as boundary conditions for the TEG submodel. The achieved speed‐up in simulation time, demonstrated in this work, clearly indicates that the design optimization process of TEG is more efficient with the combination of MOR and submodeling techniques. [ABSTRACT FROM AUTHOR]

SUMMARY Modeling behavior of broadband (30-1000 MHz) frequency modulated near infrared photons through a multilayer phantom is of interest to optical bio-imaging research. Photon dynamics in phantom are predicted using three-dimension (3D) finite element numerical simulation and are related to the measured insertion loss and phase for a given human head geometry in this paper based on three layers of phantom each with distinct optical parameter properties. Simulation and experimental results are achieved for single, two, and three layers solid phantoms using COMSOL (COMSOL AB, Tegnérgatan 23, SE-111 40, Stockholm, Sweden) (for FEM) simulation and custom-designed broadband free space optical transmitter (Tx) and receiver (Rx) modules that are developed for photon migration at wavelengths of 680, 795, and 850 nm. Standard error is used to compute error between two-dimension and 3D FE modeling along with experimental results by fitting experimental data to the functional form of [ABSTRACT FROM AUTHOR]

SUMMARY The complexity and heterogeneity of bone tissue require a multiscale modeling to understand its mechanical behavior and its remodeling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based on hybrid neural network (NN) computation and homogenization equations was developed to link nanoscopic and macroscopic scales to estimate the elastic properties of human cortical bone. The multiscale model is divided into three main phases: (i) in step 0, the elastic constants of collagen-water and mineral-water composites are calculated by averaging the upper and lower Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril are computed using a trained NN simulation. Finite element calculation is performed at nanoscopic levels to provide a database to train an in-house NN program; and (iii) in steps 2-10 from fibril to continuum cortical bone tissue, homogenization equations are used to perform the computation at the higher scales. The NN outputs (elastic properties of the microfibril) are used as inputs for the homogenization computation to determine the properties of mineralized collagen fibril. The mechanical and geometrical properties of bone constituents (mineral, collagen, and cross-links) as well as the porosity were taken in consideration. This paper aims to predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, ranging from the nanostructural to mesostructural levels. Our findings of the lowest scale's output were well integrated with the other higher levels and serve as inputs for the next higher scale modeling. Good agreement was obtained between our predicted results and literature data. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Chronic scapholunate ligament (SL) injury is a common disorder affecting the wrist. Despite advances in surgical techniques used to treat this injury, SL gap re-emergence may occur postoperatively. This paper presents an investigation into the performance of the Corella, schapolunate axis (SLAM), and modified Brunelli tenodesis (MBT) surgical reconstruction techniques used to treat scapholunate instability. Finite element (FE) models were used to undertake virtual surgery, and the resulting scapholunate (SL) gap and angle obtained using the 3 techniques were compared. The Corella technique was found to achieve the SL gap and angle closest to the intact (ligament) wrist, restoring SL gap and angle to within 5.6% and 0.6%, respectively. The MBT method resulted in an SL gap least close to the intact. The results of our study indicate that the contribution of volar scapholunate interosseous ligament to scapholunate stability could be important. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a highly parallel coupled electromechanical model of the heart is presented and assessed. The parallel-coupled model is thoroughly discussed, with scalability proven up to hundreds of cores. This work focuses on the mechanical part, including the constitutive model (proposing some modifications to pre-existent models), the numerical scheme and the coupling strategy. The model is next assessed through two examples. First, the simulation of a small piece of cardiac tissue is used to introduce the main features of the coupled model and calibrate its parameters against experimental evidence. Then, a more realistic problem is solved using those parameters, with a mesh of the Oxford ventricular rabbit model. The results of both examples demonstrate the capability of the model to run efficiently in hundreds of processors and to reproduce some basic characteristic of cardiac deformation. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a stabilization scheme for the discrete gradient method proposed by the authors ( Int. J. Numer. Methods Eng. 2009; :505-527). The discrete method is an extension of the nodal average strain triangle element to arbitrary polygon meshes. The method outperforms the low-order finite elements in many aspects; however, it is susceptible to spurious zero-energy or low-energy modes arising from cancelation of strains during strain averaging. In this paper, stabilization is achieved by a penalty scheme that penalizes the difference between the nodal strain and the subcell strains. Several examples, including an analytical dispersion analysis, are presented to demonstrate the stabilization effect. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Dynamic relaxation is an explicit method that can be used for computing the steady-state solution for a discretized continuum mechanics problem. The convergence speed of the method depends on the accurate estimation of the parameters involved, which is especially difficult for nonlinear problems. In this paper, we propose a completely adaptive dynamic relaxation method in which the parameters are updated during the iteration process, converging to their optimal values. We use the proposed method for computing intra-operative organ deformations using non-linear finite element models involving large deformations, non-linear materials and contacts. The simulation results prove the accuracy and the computational efficiency of the method. The proposed method is also very well suited for GPU implementation. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A major difficulty when applying the kinematic theorem in limit analysis is the derivation of expressions of the dissipation functions and the set of plastically admissible strains. At present, no standard methodology exists. Here, it is shown that they can be readily obtained, provided that the yield restriction can be rewritten as an intersection of cones, and that the expression defining the dual cones is available. This is always possible for the case of self-dual cones and some other classes, and covers many of the well-known criteria. Therefore, a difficult obstacle with respect to the use of the kinematic theorem in conjunction with any numerical method can be overcome. The methodology is illustrated by giving the expressions of the dissipation functions for various conic yield restrictions. A special emphasis is given on upper bound finite element limit analysis. Taking advantage of duality in conic programming, we can obtain the dual problem, where knowledge of the dual cone is not necessary. Therefore, this formulation is feasible for any cone. Finally, it is interesting that the form of the dual problem, for varying yield strength within the finite element, differs from that presented in other papers. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In stress analysis procedures using the finite element method, where the results are generated through approximations using interpolation functions, there is a need to establish optimal points in a typical element that correspond to the exact values of stresses and strains. Conventionally, Gauss' points and Barlow's points are used as optimal points for stress recovery. In this paper it is shown that the justification for the existence of optimal strain/stress recovery points, referred to as Prathap points in an element, is a consequence of the best-fit paradigm, originally proposed by Prathap through the stress correspondence principle. Through the analysis of a statically indeterminate structure like a simple bar of linearly varying elastic rigidity with fixed ends, the existence of Prathap's points has been demonstrated through the best-fit paradigm that remains valid even for statically indeterminate problems in a subtle manner. The present paper reconciles the prima facie, yet misleading, violation of the best-fit rule with the fundamental theory of the finite element method, and effectively restores the validity of the best-fit paradigm even for statically indeterminate problems in a deeper sense. Furthermore, consistent modified definitions of the global and local errors from the strain point of view are prescribed here. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new approach for approximating energy flux of temperature diffusion equation on unstructured meshes is presented, which is based on different formulae of the finite point method with different accuracies. In addition, a new numerical formula for computing cell nodal temperature is given. Numerical experiments show the good performance and accuracy of our methods. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The human shoulder is a complicated musculoskeletal structure and is a perfect compromise between mobility and stability. The objective of this paper is to provide a thorough review of previous finite element (FE) studies in biomechanics of the human shoulder complex. Those FE studies to investigate shoulder biomechanics have been reviewed according to the physiological and clinical problems addressed: glenohumeral joint stability, rotator cuff tears, joint capsular and labral defects and shoulder arthroplasty. The major findings, limitations, potential clinical applications and modelling techniques of those FE studies are critically discussed. The main challenges faced in order to accurately represent the realistic physiological functions of the shoulder mechanism in FE simulations involve (1) subject-specific representation of the anisotropic nonhomogeneous material properties of the shoulder tissues in both healthy and pathological conditions; (2) definition of boundary and loading conditions based on individualised physiological data; (3) more comprehensive modelling describing the whole shoulder complex including appropriate three-dimensional (3D) representation of all major shoulder hard tissues and soft tissues and their delicate interactions; (4) rigorous in vivo experimental validation of FE simulation results. Fully validated shoulder FE models would greatly enhance our understanding of the aetiology of shoulder disorders, and hence facilitate the development of more efficient clinical diagnoses, non-surgical and surgical treatments, as well as shoulder orthotics and prosthetics. © 2016 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd. [ABSTRACT FROM AUTHOR]

Treatment of anterior vaginal prolapse (AVP), suffered by over 500,000 women in the USA, is a challenge in urogynecology because of the poorly understood mechanics of AVP. Recently, computational modeling combined with finite element method has been used to model AVP through the study of pelvic floor muscle and connective tissue impairments on the anterior vaginal wall (AVW). Also, the effects of pelvic organ displacements on the AVW were studied numerically. In our current work, an MRI-based full-scale biofidelic computational model of the female pelvic system composed of the urinary bladder, vaginal canal, and the uterus was developed, and a novel finite element method framework was employed to simulate vaginal tissue stiffening and also bladder filling due to expansion for the first time. A mesh convergence study was conducted to choose a computationally efficient mesh, and a non-linear hyperelastic Yeoh's material model was adopted for the study. The AVW displacements, mechanical stresses, and strains were estimated at varying degrees of bladder fills and vaginal tissue stiffening. Both bladder filling and vaginal stiffening were found to increase the stress concentration on the AVW with varying trends, which have been discussed in detail in the paper. To our knowledge, this study is the first to estimate the individual and combined effects of bladder filling and vaginal tissue stiffening due to prolapse on the AVW. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In a number of human diseases such as diabetes mellitus and sickle cell anemia, variations in mechanical properties of red blood cells (RBCs) occur and cause reduced deformability. Investigating the behavior of such abnormal, hardened RBCs in microcapillary flow is of prime importance because of their effects on oxygen transport process. In the present paper, dynamic response of a RBC to a microcapillary flow is numerically studied at steady and transient conditions, considering the effect of essential parameters including RBC deformability, its initial orientation, velocity, and flow pressure gradient. Simulations are performed using a three-dimensional hybrid method, combining lattice Boltzmann method for plasma flow, finite element method for RBC membrane analysis, and immersed boundary method for their interaction. Quantitative and qualitative validations with the experimental data for different RBC velocities verify the accuracy of applied numerical method. Apart from the initial orientation, RBC experiences a complex shape deformation in which the biconcave discoid shape changes to a parachute-like shape. While deformation index of RBC does not change considerably with RBC deformability at steady state condition, it plays an important role in its shape evolution under transient condition. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm that optimizes the ventricular fiber structure of the human heart. A number of histological studies and diffusion tensor magnetic resonance imaging analyses have revealed that the myocardial fiber forms a right-handed helix at the endocardium. However, the fiber formation changes its orientation as a function of transmural depth, becoming a left-handed helix at the epicardium. To determine how nature can construct such a structure, which obtains surprising pumping performance, we introduce macroscopic modeling of the branching structure of cardiac myocytes in our finite element ventricular model and utilize this in an optimization process. We put a set of multidirectional fibers around a central fiber orientation at each point of the ventricle walls and simulate heartbeats by generating contraction forces along each of these directions. We examine two optimization processes using the workloads or impulses measured in these directions to update the central fiber orientation. Both processes improve the pumping performance towards an optimal value within several tens of heartbeats, starting from an almost-flat fiber orientation. However, compared with the workload optimization, the impulse optimization produces better agreement with experimental studies on transmural changes of fiber helix angle, streamline patterns of characteristic helical structures, and temporal changes in strain. Furthermore, the impulse optimization is robust under geometrical changes of the heart and tends to homogenize various mechanical factors such as the stretch and stretch rate along the fiber orientation, the contraction force, and energy consumption. [ABSTRACT FROM AUTHOR]

SUMMARY Longitudinal tensile and simple shear stress-strain curves of human medial collateral ligaments (MCL) were fitted by six frequently used constitutive relations of ligaments using two different fitting methods for determining which was the best fitting method and the most preferable constitutive model for describing the ligament properties. According to the results of fitting goodness, two typical constitutive models were further analyzed by FEM to investigate the effect of the variation in MCL constitutive models under some physiological loads (i.e., 4.5 Nm external tibial and 10 Nm valgus tibial torques). It was found that different fitting methods induced great variations in describing the simple shear behavior whereas no obvious difference in the longitudinal tensile behavior. The most accurate description of both the longitudinal tensile and simple shear behaviors was obtained from the constitutive model with ground substance defined by an exponential function when the parameters were fitted by the two test data, respectively. Although the distributions of maximal principal stress were almost the same, the variation in MCL constitutive models affected the highest value of the stress greatly when MCL was under the complex physiological loads. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, a computational modeling for biomechanical analysis of primary blast injuries is presented. The responses of the brain in terms of mechanical parameters under different blast spaces including open, semi-confined, and confined environments are studied. In the study, the effect of direct and indirect blast waves from the neighboring walls in the confined environments will be taken into consideration. A 50th percentile finite element head model is exposed to blast waves of different intensities. In the open space, the head experiences a sudden intracranial pressure (ICP) change, which vanishes in a matter of a few milliseconds. The situation is similar in semi-confined space, but in the confined space, the reflections from the walls will create a number of subsequent peaks in ICP with a longer duration. The analysis procedure is based on a simultaneous interaction simulation of the deformable head and its components with the blast wave propagations. It is concluded that compared with the open and semi-confined space settings, the walls in the confined space scenario enhance the risk of primary blast injuries considerably because of indirect blast waves transferring a larger amount of damaging energy to the head. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Craniosynostosis is a skull malformation because of premature fusing of one or more cranial sutures. The most common types of craniosynostosis are scaphocephaly (with the sagittal suture fused) and trigonocephaly (with the metopic suture fused). In this paper we describe and discuss how finite element analysis and three-dimensional modeling can be used for preoperative planning of the correction of craniosynostosis and for the postoperative evaluation of the treatment results. We used the engineering software MIMICS MATERIALISE to obtain three-dimensional geometry from computed tomography scans, and applied finite element method for the sake of biomechanical analysis. These simulations help to improve the surgical treatment, making it more accurate, safer, and faster. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities of the forward problem and replace the finite element solution of the incompressible Navier-Stokes equations by a computationally less-expensive reduced-basis approximation. This greatly reduces the cost of simulating the forward problem. We then consider the solution of inverse problems both in the deterministic sense, by solving a least-squares problem, and in the statistical sense, by using a Bayesian framework for quantifying uncertainty. Two inverse problems arising in hemodynamics modeling are considered: (i) a simplified fluid-structure interaction model problem in a portion of a stenosed artery for quantifying the risk of atherosclerosis by identifying the material parameters of the arterial wall on the basis of pressure measurements; (ii) a simplified femoral bypass graft model for robust shape design under uncertain residual flow in the main arterial branch identified from pressure measurements. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Arterial walls in the healthy physiological regime are characterized by quasi-incompressible, anisotropic, hyperelastic material behavior. Polyconvex material functions representing such materials typically incorporate a penalty function to account for the incompressibility. Unfortunately, the penalty will affect the conditioning of the stiffness matrices. For high penalty parameters, the performance of iterative solvers will degrade, and when direct solvers are used, the quality of the solutions will deteriorate. In this paper, an augmented Lagrange approach is used to cope with the quasi-incompressibility condition. Here, the penalty parameter can be chosen much smaller, and as a consequence, the arising linear systems of equations have better properties. An improved convergence is then observed for the finite element tearing and interconnecting-dual primal domain decomposition method, which is used as an iterative solver. Numerical results for an arterial geometry obtained from ultrasound imaging are presented. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A correct estimation of the material parameters from a planar biaxial test is crucial since they will affect the outcome of the finite element model in which they are used. In a virtual planar biaxial experiment, a difference can be noticed in the stress calculated from the force measured experimentally at the rakes and the actual stress at the center of the sample. As a consequence, a classic parameter fitting does not result in a correct estimation of the material parameters. This difference is caused by the boundary conditions of the set‐up and is among others dependent on the sample material. To overcome this problem, a new parameter fitting procedure is proposed that takes this difference into account by calculating a finite element–based correction vector. This paper describes the methodology to apply this new parameter fitting procedure on real experimental data from a planar biaxial test using rakes. To this end, image processing is used to extract the experiment characteristics. This information is used to construct a finite element model. Two variations of the new parameter fitting procedure are investigated using two human aortic samples: a basic approach and an image‐based approach. The performance of the method is assessed by the difference between the force measured at the rakes during the experiment and the force at the rakes obtained from the finite element simulation. Both approaches of the new parameter fitting procedure lead to an improved estimation of the sample behavior compared with the classic approach. This paper presents a new parameter fitting method for a rake‐based planar biaxial test that takes the boundary conditions of the experiment into account. To this end, an image‐based finite element model of the experiment is created to calculate a correction factor that can be applied to the experimental data. The new method results in a significant improvement of the parameter fitting results compared with the classic approach. [ABSTRACT FROM AUTHOR]

Conservative and non‐conservative phase‐field models are considered for the numerical simulation of lateral phase separation and coarsening in biological membranes. An unfitted finite element method is proposed to allow for a flexible treatment of complex shapes in the absence of an explicit surface parametrization. For a set of biologically relevant shapes and parameter values, the paper compares the dynamic coarsening produced by conservative and non‐conservative numerical models, its dependence on certain geometric characteristics and convergence to the final equilibrium. Conservative and nonconservative phase‐field models are considered for the numerical simulation of lateral phase separation and coarsening in biological membranes. An unfitted finite element method is proposed to allow for a flexible treatment of complex shapes in the absence of an explicit surface parametrization. For a set of biologically relevant shapes and parameter values, the paper compares the dynamic coarsening produced by conservative and nonconservative numerical models, its dependence on certain geometric characteristics, and convergence to the final equilibrium. [ABSTRACT FROM AUTHOR]

SUMMARY A coupled computational model of the foot consisting of a three-dimensional soft tissue continuum and a one-dimensional (1D) transient blood flow network is presented in this article. The primary aim of the model is to investigate the blood flow in major arteries of the pathologic foot where the soft tissue stiffening occurs. It has been reported in the literature that there could be up to about five-fold increase in the mechanical stiffness of the plantar soft tissues in pathologic (e.g. diabetic) feet compared with healthy ones. The increased stiffness results in higher tissue hydrostatic pressure within the plantar area of the foot when loaded. The hydrostatic pressure acts on the external surface of blood vessels and tend to reduce the flow cross-section area and hence the blood supply. The soft tissue continuum model of the foot was modelled as a tricubic Hermite finite element mesh representing all the muscles, skin and fat of the foot and treated as incompressible with transversely isotropic properties. The details of the mechanical model of soft tissue are presented in the companion paper, Part 1. The deformed state of the soft tissue continuum because of the applied ground reaction force at three foot positions (heel-strike, midstance and toe-off) was obtained by solving the Cauchy equations based on the theory of finite elasticity using the Galerkin finite element method. The geometry of the main arterial network in the foot was represented using a 1D Hermite cubic finite element mesh. The flow model consists of 1D Navier-Stokes equations and a nonlinear constitutive equation to describe vessel radius-transmural pressure relation. The latter was defined as the difference between the fluid and soft tissue hydrostatic pressure. Transient flow governing equations were numerically solved using the two-step Lax-Wendroff finite difference method. The geometry of both the soft tissue continuum and arterial network is anatomically-based and was developed using the data derived from visible human images and magnetic resonance images of a healthy male volunteer. Simulation results reveal that a two-fold increase in tissue stiffness leads to about 28% reduction in blood flow to the affected region.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY A recent verification study compared 11 large-scale cardiac electrophysiology solvers on an unambiguously defined common problem. An unexpected amount of variation was observed between the codes, including significant error in conduction velocity in the majority of the codes at certain spatial resolutions. In particular, the results of the six finite element codes varied considerably despite each using the same order of interpolation. In this present study, we compare various algorithms for cardiac electrophysiological simulation, which allows us to fully explain the differences between the solvers. We identify the use of mass lumping as the fundamental cause of the largest variations, specifically the combination of the commonly used techniques of mass lumping and operator splitting, which results in a slightly different form of mass lumping to that supported by theory and leads to increased numerical error. Other variations are explained through the manner in which the ionic current is interpolated. We also investigate the effect of different forms of mass lumping in various types of simulation. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Thanks to advances in medical imaging technologies and numerical methods, patient-specific modelling is more and more used to improve diagnosis and to estimate the outcome of surgical interventions. It requires the extraction of the domain of interest from the medical scans of the patient, as well as the discretisation of this geometry. However, extracting smooth multi-material meshes that conform to the tissue boundaries described in the segmented image is still an active field of research. We propose to solve this issue by combining an implicit surface reconstruction method with a multi-region mesh extraction scheme. The surface reconstruction algorithm is based on multi-level partition of unity implicit surfaces, which we extended to the multi-material case. The mesh generation algorithm consists in a novel multi-domain version of the marching tetrahedra. It generates multi-region meshes as a set of triangular surface patches consistently joining each other at material junctions. This paper presents this original meshing strategy, starting from boundary points extraction from the segmented data to heterogeneous implicit surface definition, multi-region surface triangulation and mesh adaptation. Results indicate that the proposed approach produces smooth and high-quality triangular meshes with a reasonable geometric accuracy. Hence, the proposed method is well suited for subsequent volume mesh generation and finite element simulations. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper describes a novel approach for the simulation of surgery by a combined technique of model order reduction and extended finite element method (X-FEM) methods. Whereas model order reduction techniques employ globally supported (Ritz) shape functions, a combination with X-FEM methods on a locally superimposed patch is developed for cutting simulation without remeshing. This enables to obtain models with very few degrees of freedom that run under real-time constrains even for highly non-linear tissue constitutive equations. To show the performance of the technique, we studied an application to refractive surgery in the cornea. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, head-neck boundary conditions and modeling of the head are studied circumspectly. The neck is modeled using discrete elements and the head model is three-dimensional. In the study presented here, a viscoelastic foundation (i.e., foundation defined by both springs and dampers) concept is introduced to simulate the head-neck boundary conditions during the impact load to the head. Time histories of the brain response in finite element head models with a viscoelastic neck are compared with the corresponding solutions of finite element head models with an elastic neck, and without a neck. It is observed that the magnitude of peaks in the brain's response time histories, at a later stage (i.e., 6 to 15 ms) of the simulation, decreases when dampers are induced to the elastic neck. A parametric study is also conducted to examine the brain response while varying different damping coefficient values for the neck. The magnitude of peaks in the brain's response time histories for models with different neck damping coefficients is observed to maintain some form of proportionality. In other words, the magnitude of peaks in the brain's response time histories decreases with an increased damping coefficient of the neck at the later stage of the simulation (i.e., 6 to 15 ms). From the outcomes of this study, it can be determined that the head-neck boundary conditions during head impact loading are important for studying the brain's response at the later stages of the head impact. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which currently is only feasible at the expense of extremely high computational costs, coarser models can be used if the local morphology has been linked to the apparent mechanical behavior. The aim of this paper is to implement and validate such a constitutive law. This law is able to capture the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using an elastoplastic material model incorporating hardening. These features are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strain framework. This material model was implemented into metafor (LTAS-MNNL, University of Liège, Belgium), a non-linear FE software. The implementation was validated against experimental data of cylindrical samples subjected to compression. Three materials with bone-like microstructure were tested: aluminum foams of variable density (ERG, Oakland, CA, USA), polylactic acid foam (CERM, University of Liège, Liège, Belgium), and cancellous bone tissue of a deer antler (Faculty of Veterinary Medicine, University of Liège, Liège, Belgium). Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we develop a thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce. A time-stepping algorithm is then presented for this system, which is shown to be first order accurate and energy gradient stable. The results of an array of numerical experiments are presented, which demonstrate a wide range of solutions produced by various choices of model parameters.Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents a three-dimensional finite element model of the tongue and surrounding soft tissues with potential application to the study of sleep apnoea and of linguistics and speech therapy. The anatomical data was obtained from the Visible Human Project, and the underlying histological data was also extracted and incorporated into the model. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we try to settle the bases of a concise modelling of growth within the unified framework of continuum thermodynamics. Special emphasis is placed on the modelling of soft biological tissues at finite strains. For this, we adopt the nowadays well-known kinematic assumption of a multiplicative decomposition of the deformation gradient into an elastic part and a growth part. It is shown how continuum thermodynamics is crucial in setting convenient forms for the coupling between stress and growth in general. The particularization to isotropy simplifies considerably the growth modelling from both the theoretical and the numerical points of view. Simple growth constitutive equations are proposed and embedded into a finite element context. Finally, representative numerical examples examining stress-dependent growth and residual stress arising from growth and resorption close this study. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a discrete method for the dynamic analysis of biomechanical systems. The method works directly on a point-cloud representation of a material domain. An elastic body is represented by a set of interacting particles, and the dynamic behavior is described by Hamilton's equations. A first-order symplectic integrator, which also conserves the total linear and angular momentum, is utilized for numerical integration. The discrete formulation and integration method are presented in detail. Numerical examples are presented to show the numerical properties and demonstrate the method. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]