A numerical model for investigating the mechanics of calcaneal fat pad region

The present paper pertains to the definition of a numerical model of the calcaneal fat pad region, considering a structure composed of adipose and connective tissues organized in fibrous septae and adipose chambers. The mechanical response is strongly influenced by the structural conformation, as the dimension of adipose chambers, the thickness of connective septae walls and the mechanical properties of the different soft tissues. In order to define the constitutive formulation of adipose tissues, experimental data from pig specimens are considered, according to the functional similarity, while the mechanical response of connective tissue septae is assumed with regard to the mechanical behaviour that characterize ligaments. Different numerical models are provided accounting for the variation of chambers dimensions, septae wall thickness and tissues characteristics. The spiral angles of collagen fibres within the septae influence the capability of the structure to withstand the bulging of chambers. The analysis considers different orientation of the fibres. The response of calcaneal fat pad region is evaluated in comparison with experimental data from unconfined compression tests. The present work provides a preliminary approach to enhance the correlation between the structural conformation and tissues mechanical properties towards the biomechanical response of overall heel pad region.     

Constitutive formulation and analysis of heel pad tissues mechanics

This paper presents a visco-hyperelastic constitutive model developed to describe the biomechanical response of heel pad tissues. The model takes into account the typical features of the mechanical response such as large displacement, strain phenomena, and non-linear elasticity together with time-dependent effects. The constitutive model was formulated, starting from the analysis of the complex structural and micro-structural configuration of the tissues, to evaluate the relationship between tissue histology and mechanical properties. To define the constitutive model, experimental data from mechanical tests were analyzed. To obtain information about the mechanical response of the tissue so that the constitutive parameters could be established, data from both in vitro and in vivo tests were investigated. Specifically, the first evaluation of the constitutive parameters was performed by a coupled deterministic and stochastic optimization method, accounting for data from in vitro tests. The comparison of constitutive model results and experimental data confirmed the model's capability to describe the compression behaviour of the heel pad tissues, regarding both constant strain rate and stress relaxation tests. Based on the data from additional experimental tests, some of the constitutive parameters were modified in order to interpret the in vivo mechanical response of the heel pad tissues. This approach made it possible to interpret the actual mechanical function of the tissues.     

小动脉三维力学性质的实验研究

小动脉三维力学特性的检测，对于血管外科疾病的研究和临床诊断以及对于治疗效果的评价是十分重要的。为了定量描述动脉血管的工作性能，本文以血管的各向异性和非线性研究结果为基础，运用生物力学理论，建立了动脉血管三维本构方程。经过一系列力学分析、检测和统计，确定了小动脉数据的准确性和可靠性，为建立参数力学模型提供重要依据。     

Automated Estimation of Collagen Fibre Dispersion in the Dermis and its Contribution to the Anisotropic Behaviour of Skin

Collagen fibres play an important role in the mechanical behaviour of many soft tissues. Modelling of such tissues now often incorporates a collagen fibre distribution. However, the availability of accurate structural data has so far lagged behind the progress of anisotropic constitutive modelling. Here, an automated process is developed to identify the orientation of collagen fibres using inexpensive and relatively simple techniques. The method uses established histological techniques and an algorithm implemented in the MATLAB image processing toolbox. It takes an average of 15 s to evaluate one image, compared to several hours if assessed visually. The technique was applied to histological sections of human skin with different Langer line orientations and a definite correlation between the orientation of Langer lines and the preferred orientation of collagen fibres in the dermis (p < 0.001, R(2) = 0.95) was observed. The structural parameters of the Gasser-Ogden-Holzapfel (GOH) model were all successfully evaluated. The mean dispersion factor for the dermis was κ = 0.1404±0.0028. The constitutive parameters μ, k(1) and k(2) were evaluated through physically-based, least squares curve-fitting of experimental test data. The values found for μ, k(1) and k(2) were 0.2014 MPa, 243.6 and 0.1327, respectively. Finally, the above model was implemented in ABAQUS/Standard and a finite element (FE) computation was performed of uniaxial extension tests on human skin. It is expected that the results of this study will assist those wishing to model skin, and that the algorithm described will be of benefit to those who wish to evaluate the collagen dispersion of other soft tissues.     

Constitutive modelling of inelastic behaviour of cortical bone

A visco-elasto-plastic constitutive model is formulated for investigating the mechanics of cortical bone tissue, accounting for an anisotropic configuration and post-elastic and time-dependent phenomena. The constitutive model is developed with reference to experimental data obtained from literature on the behaviour of cortical bone taken from multiple samples. Regarding the constitutive model, a specific procedure based on a coupled deterministic and stochastic method is applied in order to determine the values of the constitutive parameters with regard to human samples. The procedure entails processing of data deduced from mechanical tests to achieve relationships between permanent and total strain, elastic modulus and strain rate, and creep elastic modulus and time. Numerical results obtained by using a finite element model are compared with tensile experimental data on cortical bone including the post-elastic range and creep phenomena. The model shows an excellent capability to describe the tensile behaviour of the cortical bone for the specific mechanical condition analysed.     

Quantifying Cartilage Biomechanical Properties Using a Linearized Frequency-Domain Method

Articular cartilage function relies on its unique mechanical behavior. Cartilage mechanics have been described by several analytic models, whose parameters are usually estimated by fitting their constitutive equations to stress-relaxation data. This procedure can be long and is prone to experimental and fitting errors. Τhis study describes a novel methodology for estimating the biomechanical properties of cartilage samples based on their linearized frequency response, derived by applying a series of small-amplitude harmonic displacements superimposed to a bias strain. The proposed methodology, denoted as linearized frequency-domain method (LFM), was demonstrated by quantifying the effects of collagenase and hyaluronidase on cartilage, where it provided robust cartilage parameter estimates that overall agreed well with estimates obtained by stress-relaxation analysis. LFM was also applied to unveil the strain-dependent nature of porcine cartilage biomechanical parameters. Results showed that increasing the bias strain from 5% to 15% caused a significant decrease in cartilage permeability but did not have significant effect on the compression modulus and the Poisson’s ratio. Apart from cartilage, LFM can potentially quantify the strain-dependent nature of tissues and biomaterials, thereby enhance tissue-level understanding on organ physiology and pathology, lead to better computational tissue models, and guide tissue engineering research.     

A constitutive model of the posterior cruciate ligament

Further to our previous work on the development of a general constitutive framework for transversely isotropic viscohyperelasticity (Limbert, G, Middleton, J. A transversely isotropic viscohyperelastic material. Application to the modelling of biological soft connective tissues. Int J Solids Struct 2004;41(15):4237-60.), we propose a phenomenological constitutive law to describe the anisotropic viscohyperelastic behaviour of the human posterior cruciate ligament (PCL) at high strain rates. The mechanical formulation is based on the definition of a Helmholtz free energy function containing a hyperelastic and a viscous potential. The equations are valid for arbitrary kinematics and satisfy elemental thermodynamic principles. Identification of the constitutive model with experimental data obtained from human PCL specimens was performed and showed the ability of the model to capture accurately the mechanical characteristics of the PCL at various strain rates. Influence of the isotropic and directional viscous stress responses on the global mechanical response are discussed in connection with the modelling hypotheses. This work was motivated by the need to provide an accurate constitutive model of the PCL to be used in finite element analyses of human occupants in car crash simulations. Besides uniaxial tests along the natural fibre orientation of the PCL, additional tests such as equibiaxial, strip biaxial compression-tension and shear tests were also performed in order to assess the physical response of the model in different loading situations. It was found that the model performed as well in these conditions.     

骨组织的多层次生物力学特性及本构关系

骨组织是人体主要的承重器官,其承载能力与自身生物力学特性密切相关。作为一种复杂的多层次生物材料,骨组织的生物力学特性由其自身结构和生物学特性等因素共同决定。在不同程度的力学载荷下,骨组织表现出不同的生物力学特性。因此,深入研究骨组织不同层次的生物力学特性,构建能够反映骨组织生物学特性的本构关系,量化骨组织对力学载荷的响应,实现从骨组织生物力学特性到力学生物学特性的研究,为临床治疗提供精确的理论依据,一直以来都是研究者关注的重点。基于骨组织多层次生物力学特性,对近年来骨组织本构方程的相关研究进行归纳总结。     

Constitutive modeling of ascending thoracic aortic aneurysms using microstructural parameters

Ascending thoracic aortic aneurysm (ATAA) has been associated with diminished biomechanical strength and disruption in the collagen fiber microarchitecture. Additionally, the congenital bicuspid aortic valve (BAV) leads to a distinct extracellular matrix structure that may be related to ATAA development at an earlier age than degenerative aneurysms arising in patients with the morphological normal tricuspid aortic valve (TAV). The purpose of this study was to model the fiber-reinforced mechanical response of ATAA specimens from patients with either BAV or TAV. This was achieved by combining image-analysis derived parameters of collagen fiber dispersion and alignment with tensile testing data. Then, numerical simulations were performed to assess the role of anisotropic constitutive formulation on the wall stress distribution of aneurysmal aorta. Results indicate that both BAV ATAA and TAV ATAA have altered collagen fiber architecture in the medial plane of experimentally-dissected aortic tissues when compared to normal ascending aortic specimens. The study findings highlight that differences in the collagen fiber distribution mostly influences the resulting wall stress distribution rather than the peak stress. We conclude that fiber-reinforced constitutive modeling that takes into account the collagen fiber defect inherent to the aneurysmal ascending aorta is paramount for accurate finite element predictions and ultimately for biomechanical-based indicators to reliably distinguish the more from the less ‘malignant’ ATAAs.     

Mechanical and histological characterization of the abdominal muscle. A previous step to modelling hernia surgery

The aims of this study are to experimentally characterize the passive elastic behaviour of the rabbit abdominal wall and to develop a mechanical constitutive law which accurately reproduces the obtained experimental results. For this purpose, tissue samples from New Zealand White rabbits 2150±50?(g) were mechanically tested in vitro. Mechanical tests, consisting of uniaxial loading on tissue samples oriented along the craneo-caudal and the perpendicular directions, respectively, revealed the anisotropic non-linear mechanical behaviour of the abdominal tissues. Experiments were performed considering the composite muscle (including external oblique-EO, internal oblique-IO and transverse abdominis-TA muscle layers), as well as separated muscle layers (i.e.,?external oblique, and the bilayer formed by internal oblique and transverse abdominis). Both the EO muscle layer and the IO-TA bilayer demonstrated a stiffer behaviour along the transversal direction to muscle fibres than along the longitudinal one. The fibre arrangement was measured by means of a histological study which confirmed that collagen fibres are mainly responsible for the passive mechanical strength and stiffness. Furthermore, the degree of anisotropy of the abdominal composite muscle turned out to be less pronounced than those obtained while studying the EO and IO-TA separately. Moreover, a phenomenological constitutive law was used to capture the measured experimental curves. A Levenberg-Marquardt optimization algorithm was used to fit the model constants to reproduce the experimental curves.     

Non-linear elastic properties of the lingual and facial tissues assessed by indentation technique. Application to the biomechanics of speech production

This paper aims at characterizing the mechanical behavior of two human anatomical structures, namely the tongue and the cheek. For this, an indentation experiment was provided, by measuring the mechanical response of tongue and cheek tissues removed from the fresh cadaver of a 74 year old woman. Non-linear relationships were observed between the force applied to the tissues and the corresponding displacements. To infer the mechanical constitutive laws from these measurements, a finite element (FE) analysis was provided. This analysis aimed at simulating the indentation experiment. An optimization process was used to determine the FE constitutive laws that provided the non-linear force/displacements observed during the indentation experiments. The tongue constitutive law was used for simulations provided by a 3D FE biomechanical model of the human tongue. This dynamical model was designed to study speech production. Given a set of tongue muscular commands, which levels correspond to the force classically measured during speech production, the FE model successfully simulated the main tongue movements observed during speech data.     

Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery

A preoperative simulation of soft tissue deformations during plastic and reconstructive surgery is desirable to support the surgeon’s planning and to improve surgical outcomes. The current development of constitutive adipose tissue models, for the implementation in multilayer computational frameworks for the simulation of human soft tissue deformations, has proved difficult because knowledge of the required mechanical parameters of fat tissue is limited. Therefore, for the first time, human abdominal adipose tissues were mechanically investigated by biaxial tensile and triaxial shear tests. The results of this study suggest that human abdominal adipose tissues under quasi-static and dynamic multiaxial loadings can be characterized as a nonlinear, anisotropic and viscoelastic soft biological material. The nonlinear and anisotropic features are consequences of the material’s collagenous microstructure. The aligned collagenous septa observed in histological investigations causes the anisotropy of the tissue. A hyperelastic model used in this study was appropriate to represent the quasi-static multiaxial mechanical behavior of fat tissue. The constitutive parameters are intended to serve as a basis for soft tissue simulations using the finite element method, which is an apparent method for obtaining promising results in the field of plastic and reconstructive surgery.     

Design and analysis of tissue engineering scaffolds that mimic soft tissue mechanical anisotropy

Tissue engineered constructs must exhibit tissue-like functional properties, including mechanical behavior comparable to the native tissues they are intended to replace. Moreover, the ability to reversibly undergo large strains can help to promote and guide tissue growth. Electrospun poly (ester urethane) ureas (ES-PEUU) are elastomeric and allow for the control of fiber diameter, porosity, and degradation rate. ES-PEUU scaffolds can be fabricated to have a well-aligned fiber network, which is important for applications involving mechanically anisotropic soft tissues. We have developed ES-PEUU scaffolds under variable speed conditions and modeled the effects of fiber orientation on the macro-mechanical properties of the scaffold. To illustrate the ability to simulate native tissue mechanical behavior, we demonstrated that the high velocity spun scaffolds exhibited highly anisotropic mechanical properties closely resembling the native pulmonary heart valve leaflet. Moreover, use of the present fiber-level structural constitutive model allows for the determination of electrospinning conditions to tailor ES-PEUU scaffolds for specific soft tissue applications. The results of this study will help to provide the basis for rationally designed mechanically anisotropic soft tissue engineered implants.     

Constitutive modeling of crimped collagen fibrils in soft tissues

A microstructurally oriented constitutive formulation for the hyperelastic response of crimped collagen fibrils existing in soft connective tissues is proposed. The model is based on observations that collagen fibrils embedded in a soft matrix crimp into a smooth three-dimensional pattern when unloaded. Following ideas presented by Beskos and Jenkins [Beskos, D., Jenkins, J., 1975. A mechanical model for mammalian tendon. ASME Journal of Applied Mechanics 42, 755–758] and Freed and Doehring [Freed, A., Doehring, T., 2005. Elastic model for crimped collagen fibrils. Journal of Biomechanical Engineering 127, 587–593] the collagen fibril crimp is approximated by a cylindrical helix to represent the constitutive behavior of the hierarchical organized substructure of biological tissues at the fibrillar level. The model is derived from the nonlinear axial force–stretch relationship of an extensible helical spring, including the full extension of the spring as a limit case. The geometrically nonlinear solution of the extensible helical spring is carried out by an iterative procedure. The model only requires one material parameter and two geometrical parameters to be determined from experiments. The ability of the proposed model to reproduce the biomechanical response of fibrous tissues is demonstrated for fascicles from rat tail tendons, for porcine cornea strips, and for bovine Achilles tendons.     

Transversely isotropic properties of porcine liver tissue: experiments and constitutive modelling

Knowledge of the biomechanical properties of soft tissue, such as liver, is important in modelling computer aided surgical procedures. Liver tissue does not bear mechanical loads, and, in numerical simulation research, is typically assumed to be isotropic. Nevertheless, a typical biological soft tissue is anisotropic. In vitro uniaxial tension and compression experiments were conducted on porcine cylindrical and cubical liver tissue samples respectively assuming a simplistic architecture of liver tissue with its constituent lobule and connective tissues components. With the primary axis perpendicular to the cross sectional surface of samples, the tissue is stiffer with tensile or compressive force in the axial direction compared to that of the transverse direction. At 20% strain, about twice as much force is required to elongate a longitudinal tissue sample than that of a transverse sample. Results of the study suggest that liver tissue is transversely isotropic. A combined strain energy based constitutive equation for transversely isotropic material is proposed. The improved capability of this equation to model the experimental data compared to its previously disclosed isotropic version suggests that the assumption on the fourth invariant in the constitutive equation is probably correct and that anisotropy properties of liver tissue should be considered in surgical simulation.     

Implementation and validation of constitutive relations for human dermis mechanical response

Finite element models in conjunction with adequate constitutive relations are pivotal in several physiological and medical applications related to both native and engineered tissues, allowing to predict the tissue response under various loading states. In order to get reliable results, however, the validation of the constitutive models is crucial. Therefore, the main purpose of this work is to provide an experimental-computational approach to the biomechanical investigation of soft tissues such as the dermis. This is accomplished by implementing and validating three widely adopted hyperelastic constitutive models (the Ogden, the Holzapfel, and the Gasser-Ogden-Holzapfel laws) supposed to be adequate to reproduce human reticular dermis mechanical behavior. Biaxial experimental data have represented the basis for the determination of the respective material parameters identified thanks to the definition of a cost function accounting for the discrepancy between experimental and predicted data. Afterwards, the experimental tests have been reproduced through finite element simulations. Hence, the constitutive laws have been validated comparing experimental and numerical outcomes in terms of displacements of four reference points and stress-strain relations. Hence, an experimental-numerical framework is proposed for the investigation of collagenous tissues, which could become more accurate with larger and independent experimental datasets.

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An elastomeric material for facial prostheses: synthesis, experimental and numerical testing aspects

Current materials used for maxillofacial prostheses are far from ideal and there is a need for new improved materials which better simulate the tissues they are replacing. This study was based on a mixed experimental/analytical/numerical approach. A new polymeric material was developed to provide a better alternative to the materials currently used in maxillofacial prosthetics. A series of experimental tensile tests were performed in order to characterise the tensile properties of the material. A Mooney-Rivlin type hyperelastic formulation was chosen to describe the constitutive behaviour of the polymer which operates at the finite strain regime. The material parameters (two) of the constitutive law were identified with the experimental data. The Mooney-Rivlin material was found to be suitable to represent accurately the mechanical behaviour of the polymer up to 50% strain as shown by the excellent agreement between analytical and experimental results. An FE model reproducing all the characteristics of the experimental tensile tests was built and a series of three FE analyses were conducted and has proven the proper finite element implementation of the material model. This preliminary study will serve as a basis to introduce more complex features such as viscoelasticity and wrinkling of the soft polymeric structure in order to optimise the performances of the final prosthetic material.