Mahmood Jabareen

Relation between mechanical properties and microstructure of human fetal membranes: An attempt towards a quantitative analysis

OBJECTIVE We sought to measure the mechanical baseline behavior of fetal membranes in order to determine constitutive mechanical model parameters for fetal membranes, and to examine their relation to molecular correlates for mechanical function, i.e. collagen and elastin. STUDY DESIGN The uniaxial stress-strain response of nine human term fetal membranes was measured. Methods of nonlinear continuum mechanics were applied for the analysis of the stress-strain curves. Thickness of amnion and chorion were determined from histologic sections for each fetal membrane sample. Complementary biochemical analysis was performed to quantify the soluble collagen and soluble elastin components for each sample. RESULTS We report a straightforward histologic modality for measurements of amnion and chorion thickness. Average thickness of the amnion and chorion layers were 111+/-78 microm, and 431+/-113 microm, respectively, which are about twice larger than previously reported. The average content of acid-soluble elastin was 2.1% of wet weight and the one of pepsin/acetic acid-soluble collagen was 10.5% of dry weight. Our data show an inverse proportionality between soluble elastin and soluble collagen content. The low strain elastic modulus ranged between 10 and 25 kPa. Correlations were found between biochemical data and mechanical parameters: there is clearly a direct proportionality between small strain elastic modulus and elastin content. Further, a (less pronounced) direct correlation was observed also between soluble collagen content and the parameter governing the increase in stiffness at larger strains in the nonlinear mechanical model. The mechanical tests revealed a relatively low variability for samples from the same membrane but a large variation between donors. The proposed nonlinear model provides a good fit of the experimental data, with a coefficient of determination, R(2), typically in the range of 0.94. Membranes failure originated at the clamping points thus impairing the quantification of ultimate stress and strain. Thus, no correlation was found between maximum stress and collagen or elastin content. CONCLUSIONS This study provides a starting point for comprehensive quantitative analysis of the relationship between fetal membranes microstructure and their nonlinear deformation behavior. These insights could become useful in identifying potential medical interventions to prevent membranes rupture.

Experimental and numerical study on the mechanical behavior of the superficial layers of the face

Background/purpose: This paper reports a study on the quasi‐static mechanical response of the superficial soft tissue of the face, in particular the skin and the superficial muscoloaponeurotic system (SMAS) plus the superficial fat. The mechanical characterization of soft tissues represents one of the main uncertainties of previously developed numerical models for face simulation.

Postbuckling of Laminated Cylindrical Shells in Different Formulations

The sensitivity of laminated cylindrical shells to imperfection is investigated throughout their entire nonlinear behavior. The study has two objectives: 1) comparison of the simplest formulation, using the Airy stress function (called the WF formulation), with the more accurate one, using the three displacement components (called the UVW formulation), and 2) examining the correlation between the sensitivity to imperfection according to this nonlinear analysis and that of Koiters process for the initial postbuckling behavior. For laminated cylindrical shells-in contrast to isotropic shells-significant differences are observed between the two formulations (WF and UVW) and Koiters theory does not always represent the actual sensitivity behavior. A general symbolic code (using MAPLE) was programmed to create the differential operators. Then the code used the Galerkin procedure, the Newton-Raphson procedure, and a finite difference scheme for automatic development of an efficient FORTRAN code, which was used for the parametric study.

Suction based mechanical characterization of superficial facial soft tissues

The present study is aimed at a combined experimental and numerical investigation of the mechanical response of superficial facial tissues. Suction based experiments provide the location, time, and history dependent behavior of skin and SMAS (superficial musculoaponeurotic system) by means of Cutometer and Aspiration measurements. The suction method is particularly suitable for in vivo, multi-axial testing of soft biological tissue including a high repeatability in subsequent tests. The campaign comprises three measurement sites in the face, i.e. jaw, parotid, and forehead, using two different loading profiles (instantaneous loading and a linearly increasing and decreasing loading curve), multiple loading magnitudes, and cyclic loading cases to quantify history dependent behavior. In an inverse finite element analysis based on anatomically detailed models an optimized set of material parameters for the implementation of an elastic-viscoplastic material model was determined, yielding an initial shear modulus of 2.32kPa for skin and 0.05kPa for SMAS, respectively. Apex displacements at maximum instantaneous and linear loading showed significant location specificity with variations of up to 18% with respect to the facial average response while observing variations in repeated measurements in the same location of less than 12%. In summary, the proposed parameter sets for skin and SMAS are shown to provide remarkable agreement between the experimentally observed and numerically predicted tissue response under all loading conditions considered in the present study, including cyclic tests.

Elastic–viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.

Physically Based Finite Element Model of the Face

The proposed 3D finite element model of the face aims at a faithful representation of the anatomy, the mechanical interactions between different tissues, and the non linear force deformation characteristics of tissues. Bones and soft tissues were reconstructed from magnetic resonance images. Non linear constitutive equations are implemented in the numerical model. The corresponding model parameters were selected according to previous work with mechanical measurements on soft facial tissue. Model assumptions concerning tissues geometry, mechanical properties and boundary conditions were validated through comparison with measurements of the facial tissue response to gravity loads and to the application of a pressure inside the oral cavity. In particular, parametric studies were carried out in order to quantify the influence of constitutive model parameters of muscles. The model described in this paper might be used for simulation of plastic and reconstructive surgery and for investigation of the physiology and pathology of face deformation.

A physically motivated constitutive model for 3D numerical simulation of skeletal muscles.

A detailed numerical implementation within the FEM is presented for a physically motivated three-dimensional constitutive model describing the passive and active mechanical behaviors of the skeletal muscle. The derivations for the Cauchy stress tensor and the consistent material tangent are provided. For nearly incompressible skeletal muscle tissue, the strain energy function may be represented either by a coupling or a decoupling of the distortional and volumetric material response. In the present paper, both functionally different formulations are introduced allowing for a direct comparison between the coupled and decoupled isochoric-volumetric approach. The numerical validation of both implementations revealed significant limitations for the decoupled approach. For an extensive characterization of the model response to different muscle contraction modes, a benchmark model is introduced. Finally, the proposed implementation is shown to provide a reliable tool for the analysis of complex and highly nonlinear problems through the example of the human mastication system by studying bite force and three-dimensional muscle shape changes during mastication.

A general framework for the numerical implementation of anisotropic hyperelastic material models including non-local damage.

The highly nonlinear mechanical behaviour of soft tissues solicited within the physiological range usually involves degradation of the material properties. Mechanically, having these biostructures undergoing such stretch patterns may bring about pathological conditions related to the steady deterioration of both collagen fibres and material’s ground substance. Tissue and subject variability observed in the phenomenological mechanical characterisation of soft tissues often hinder the choice of the computational constitutive model. Therefore, this contribution brings forth a detailed overview of the constitutive implementation in a computational framework of anisotropic hyperelastic materials with damage. Surmounting the challenge posed by the mesh dependency pathology requires the incorporation of an integral-type non-local averaging, which seeks to include the effects of the microstructure in order to limit the localisation phenomena of the damage variables. By adopting this approach, one can make use of multiple developed material models available in the literature, a combination of those, or even propose new models within the same numerical framework. The numerical examples of three-dimensional displacement and force-driven boundary value problems highlight the possibility of using multiple material models within the same numerical framework. Particularities concerning the considered material models and the damage effect implications to represent the Mullins effect, induced anisotropy, hysteresis, and mesh dependency are discussed.

A Cosserat Point Element (CPE) for the Numerical Solution of Problems in Finite Elasticity

The theory of a Cosserat Point is a special continuum theory that characterizes the motion of a small material region which can be modeled as a point with finite volume. This theory has been used to develop a 3-D eight-noded brick Cosserat Point Element (CPE) to formulate the numerical solution of dynamical problems in finite elasticity. The kinematics of the CPE are characterized by eight director vectors which are functions of time only. Also, the kinetics of the CPE are characterized by balance laws which include: conservation of mass, balances of linear and angular momentum, as well as balances of director momentum. The main difference between the standard Bubnov–Galerkin and the Cosserat approaches is the way that they each develop constitutive equations. In the direct Cosserat approach, the kinetic quantities are given by derivatives of a strain energy function that models the CPE as a structure and that characterizes resistance to all models of deformation. A generalized strain energy function has been developed which yields a CPE that is truly a robust user friendly element for nonlinear elasticity that can be used with confidence for 3-D problems as well as for problems of thin shells and rods.

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

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