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

An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations

Constitutive models are important to biomechanics for two key reasons. First, constitutive modelling is an essential component of characterizing tissues' mechanical properties for informing theoretical and computational models of biomechanical systems. Second, constitutive models can be used as a theoretical framework for extracting and comparing key quantities of interest from material characterization experiments. Over the past five decades, the Ogden model has emerged as a popular constitutive model in soft tissue biomechanics with relevance to both informing theoretical and computational models and to comparing material characterization experiments. The goal of this short review is threefold. First, we will discuss the broad relevance of the Ogden model to soft tissue biomechanics and the general characteristics of soft tissues that are suitable for approximating with the Ogden model. Second, we will highlight exemplary uses of the Ogden model in brain tissue, blood clot and other tissues. Finally, we offer a tutorial on fitting the one-term Ogden model to pure shear experimental data via both an analytical approximation of homogeneous deformation and a finite-element model of the tissue domain. Overall, we anticipate that this short review will serve as a practical introduction to the use of the Ogden model in biomechanics. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations

Constitutive models are important to biomechanics for two key reasons. First, constitutive modelling is an essential component of characterizing tissues' mechanical properties for informing theoretical and computational models of biomechanical systems. Second, constitutive models can be used as a theoretical framework for extracting and comparing key quantities of interest from material characterization experiments. Over the past five decades, the Ogden model has emerged as a popular constitutive model in soft tissue biomechanics with relevance to both informing theoretical and computational models and to comparing material characterization experiments. The goal of this short review is threefold. First, we will discuss the broad relevance of the Ogden model to soft tissue biomechanics and the general characteristics of soft tissues that are suitable for approximating with the Ogden model. Second, we will highlight exemplary uses of the Ogden model in brain tissue, blood clot and other tissues. Finally, we offer a tutorial on fitting the one-term Ogden model to pure shear experimental data via both an analytical approximation of homogeneous deformation and a finite-element model of the tissue domain. Overall, we anticipate that this short review will serve as a practical introduction to the use of the Ogden model in biomechanics. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

On the Reliability of Suction Measurements for Skin Characterization

in vivo skin characterization methods were shown to be useful in the detection of microstructural alterations of the dermis due to skin diseases. Specifically, the diagnostic potential of skin suction has been widely explored, yet measurement uncertainties prevented so far its application in clinical assessment. In this work, we analyze specific factors influencing the reliability of suction measurements. We recently proposed a novel suction device, called Nimble, addressing the limitations of existing instruments, and applied it in clinical trials quantifying mechanical differences between healthy skin and scars. Measurements were performed with the commercial device Cutometer and with the new device. A set of new suction measurements was carried out on scar tissue and healthy skin, and FE-based inverse analysis was applied to determine corresponding parameters of a hyperelastic-viscoelastic material model. FE simulations were used to rationalize differences between suction protocols and to analyze specific factors influencing the measurement procedure. Tissue stiffness obtained from Cutometer measurements was significantly higher compared to the one from Nimble measurements, which was shown to be associated with the higher deformation levels in the Cutometer and the nonlinear mechanical response of skin. The effect of the contact force exerted on skin during suction measurements was quantified, along with an analysis of the effectiveness of a corresponding correction procedure. Parametric studies demonstrated the inherently higher sensitivity of displacement- over load-controlled suction measurements, thus rationalizing the superior ability of the Nimble to distinguish between tissues.

How cosmetic tightening products modulate the biomechanics and morphology of human skin

The active and passive mechanical behavior of a cosmetic tightening product for skin anti-aging is investigated based on a wide range of in vivo and in vitro measurements. The experimental data are used to inform a numerical model of the attained cosmetic effect, which is then implemented in a commercial finite-element framework and used to analyze the mechanisms that regulate the biomechanical interaction between the native tissue and the tightening film. Such a film reduces wrinkles and enhances skin consistency by increasing its stiffness by 48-107% and reducing inelastic, non-recoverable deformations (-47%). The substrate deformability influences both the extent of tightening and the reduction of wrinkle amplitude. The present findings allow, for the first time, to rationalize the mechanisms of action of cosmetic products with a tightening action and provide quantitative evidence for further optimization of this fascinating class of biomaterials.

Activin-mediated alterations of the fibroblast transcriptome and matrisome control the biomechanical properties of skin wounds

Matrix deposition is essential for wound repair, but when excessive, leads to hypertrophic scars and fibrosis. The factors that control matrix deposition in skin wounds have only partially been identified and the consequences of matrix alterations for the mechanical properties of wounds are largely unknown. Here, we report how a single diffusible factor, activin A, affects the healing process across scales. Bioinformatics analysis of wound fibroblast transcriptome data combined with biochemical and histopathological analyses of wounds and functional in vitro studies identify that activin promotes pro-fibrotic gene expression signatures and processes, including glycoprotein and proteoglycan biosynthesis, collagen deposition, and altered collagen cross-linking. As a consequence, activin strongly reduces the wound and scar deformability, as identified by a non-invasive in vivo method for biomechanical analysis. These results provide mechanistic insight into the roles of activin in wound repair and fibrosis and identify the functional consequences of alterations in the wound matrisome at the biomechanical level.

The relationship between histopathology, gene expression, and biochemical and mechanical properties of wounds is largely unknown. Here, the authors show that activin A alters wound healing at multiple levels by promoting pro-fibrotic gene expression and matrix deposition, thereby affecting biomechanical properties of skin wounds.

Mechanical characterization of disordered and anisotropic cellular monolayers

We consider a cellular monolayer, described using a vertex-based model, for which cells form a spatially disordered array of convex polygons that tile the plane. Equilibrium cell configurations are assumed to minimize a global energy defined in terms of cell areas and perimeters; energy is dissipated via dynamic area and length changes, as well as cell neighbor exchanges. The model captures our observations of an epithelium from a Xenopus embryo showing that uniaxial stretching induces spatial ordering, with cells under net tension (compression) tending to align with (against) the direction of stretch, but with the stress remaining heterogeneous at the single-cell level. We use the vertex model to derive the linearized relation between tissue-level stress, strain, and strain rate about a deformed base state, which can be used to characterize the tissue’s anisotropic mechanical properties; expressions for viscoelastic tissue moduli are given as direct sums over cells. When the base state is isotropic, the model predicts that tissue properties can be tuned to a regime with high elastic shear resistance but low resistance to area changes, or vice versa.

A novel ultra-light suction device for mechanical characterization of skin

Suction experiments have been extensively applied for skin characterization. In these tests the deformation behavior of superficial tissue layers determines the elevation of the skin surface observed when a predefined negative (suction) pressure history is applied. The ability of such measurements to differentiate between skin conditions is limited by the variability of the elevation response observed in repeated experiments. The scatter was shown to be associated with the force exerted by the observer when holding the instrument against the skin. We have developed a novel suction device and a measurement procedure aiming at a tighter control of mechanical boundary conditions during the experiments. The new device weighs only 3.5 g and thus allows to minimize the force applied on the skin during the test. In this way, it is possible to reliably characterize the mechanical response of skin, also in case of low values of suction pressure and deformation. The influence of the contact force is analyzed through experiments on skin and synthetic materials, and rationalized based on corresponding finite element calculations. A comparative study, involving measurements on four body locations in two subjects by three observers, showed the good performance of the new procedure, specific advantages, and limitations with respect to the Cutometer^®, i.e. the suction device most widely applied for skin characterization. As a byproduct of the present investigation, a correction procedure is proposed for the Cutometer measurements, which allows to partially compensate for the influence of the contact force. The characteristics of the new suction method are discussed in view of future applications for diagnostic purposes.

Location-specific mechanical response and morphology of facial soft tissues

The facial tissue of 9 healthy volunteers (m/f; age: 23-60y) is characterized at three different locations using a procedure combining suction measurements and 18MHz ultrasound imaging. The time-dependent and multilayered nature of skin is accounted for by adopting multiple loading protocols which differ with respect to suction probe opening size and rate of tissue deformation. Over 700 suction measurements were conducted and analyzed according to location-specific mechanical and morphological characteristics. All corresponding data are reported and made available for facial tissue analysis and biomechanical modeling. Higher skin stiffness is measured at the forehead in comparison to jaw and parotid; these two regions are further characterized by lower creep deformation. Thicker tissue regions display a tendency towards a more compliant and less dissipative response. Comparison of superficial layer thickness and corresponding mechanical measurements suggests that connective tissue density determines the resistance to deformation in suction experiments.

Mathematical and computational modelling of skin biophysics: a review

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

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.

Simulating uterine contraction by using an electro-chemo-mechanical model

Contractions of uterine smooth muscle cells consist of a chain of physiological processes. These contractions provide the required force to expel the fetus from the uterus. The inclusion of these physiological processes is, therefore, imperative when studying uterine contractions. In this study, an electro-chemo-mechanical model to replicate the excitation, activation, and contraction of uterine smooth muscle cells is developed. The presented modeling strategy enables efficient integration of knowledge about physiological processes at the cellular level to the organ level. The model is implemented in a three-dimensional finite element setting to simulate uterus contraction during labor in response to electrical discharges generated by pacemaker cells and propagated within the myometrium via gap junctions. Important clinical factors, such as uterine electrical activity and intrauterine pressure, are predicted using this simulation. The predictions are in agreement with clinically measured data reported in the literature. A parameter study is also carried out to investigate the impact of physiologically related parameters on the uterine contractility.