Mathematical and computational modelling of skin biophysics: a review

A machine learning approach to predict in vivo skin growth

Since their invention, tissue expanders, which are designed to trigger additional skin growth, have revolutionised many reconstructive surgeries. Currently, however, the sole quantitative method to assess skin growth requires skin excision. Thus, in the context of patient outcomes, a machine learning method which uses non-invasive measurements to predict in vivo skin growth and other skin properties, holds significant value. In this study, the finite element method was used to simulate a typical skin expansion protocol and to perform various simulated wave propagation experiments during the first few days of expansion on 1,000 individual virtual subjects. An artificial neural network trained on this dataset was shown to be capable of predicting the future skin growth at 7 days (avg. R2 = 0.9353) as well as the subject-specific shear modulus (R2 = 0.9801), growth rate (R2 = 0.8649), and natural pre-stretch (R2 = 0.9783) with a very high degree of accuracy. The method presented here has implications for the real-time prediction of patient-specific skin expansion outcomes and could facilitate the development of patient-specific protocols.

Rapid flapping and fibre-reinforced membrane wings are key to high-performance bat flight

Bats fly using significantly different wing motions from other fliers, stemming from the complex interplay of their membrane wings' motion and structural properties. Biological studies show that many bats fly at Strouhal numbers, the ratio of flapping to flight speed, 50-150% above the range typically associated with optimal locomotion. We use high-resolution fluid-structure interaction simulations of a bat wing to independently study the role of kinematics and material/structural properties in aerodynamic performance and show that peak propulsive and lift efficiencies for a bat-like wing motion require flapping 66% faster than for a symmetric motion, agreeing with the increased flapping frequency observed in zoological studies. In addition, we find that reduced membrane stiffness is associated with improved propulsive efficiency until the membrane flutters, but that incorporating microstructural anisotropy arising from biological fibre reinforcement enables a tenfold reduction of the flutter energy while maintaining high aerodynamic efficiency. Our results indicate that animals with specialized flapping motions may have correspondingly specialized flapping speeds, in contrast to arguments for a universally efficient Strouhal range. Additionally, our study demonstrates the significant role that the microstructural constitutive properties of the membrane wing of a bat can have in its propulsive performance.

Radial Expansion Favors the Burrowing Behavior of Urechis unicinctus

Urechis unicinctus can utilize the ability of large deformation to advance in sands by radial expansion, just using a small force. However, the large deformation of U. unicinctus skin and the discrete nature of the sands make it hard to analyze this process quantitatively. In this study, we aim to uncover the burrowing mechanism of U. unicinctus in granular sediments by combining discrete and finite elements. We observe that U. unicinctus will expand radially at the head, and then the head will shrink to move forward. The radial expansion will collapse the sands and let them flow, making it easy to advance. U. unicinctus mainly relies on the skin's large deformation and sufficient pressure to achieve radial expansion. Thus, we first establish the large deformation constitutive model of the skin. The stress-strain relationship can be expressed by the Yeoh model. Meanwhile, the pressure required for radial expansion is indirectly measured by the balloon experiment. To study the effect of radial expansion on the burrowing behavior, we use the finite element method-discrete element method (FEM-DEM) coupling model to simulate the expansion process of burrowing. The simulated pressure for radial expansion is very close to the experimental data, verifying the reliability of the simulation. The results show that the expansion can drastically reduce the pressure of sand particles on the head front face by 97.1% ± 0.6%, significantly decreasing the difficulty of burrowing. This unique underwater burrow method of U. unicinctus can provide new ideas for engineering burrowing devices in soft soil, especially for granular sediments.

Impact of Indenter Size and Microrelief Anisotropy on the Tribological Behavior of Human Skin

Everyday, we interact with screens, sensors, and many other devices through contact with the skin. Experimental efforts have increased our knowledge of skin tribology but are challenged by the fact that skin has a complex structure, undergoes finite deformations, has nonlinear material response, and has properties that vary with anatomical location, age, sex, and environmental conditions. Computational models are powerful tools to dissect the individual contribution of these variables to the overall frictional response. Here, we present a three-dimensional high-fidelity multilayer skin computational model including a detailed surface topography or skin microrelief. Four variables are explored: local coefficient of friction (COF), indenter size, mechanical properties of the stratum corneum, and displacement direction. The results indicate that the global COF depends nonlinearly on the local COF, implying a role for skin deformation on the friction response. The global COF is also influenced by the ratio of the indenter size to the microrelief features, with larger indenters smoothing out the role of skin topography. Changes in stiffness of the uppermost layer of skin associated with humidity have a substantial effect on both the contact area and the reaction forces, but the overall changes in the COF are small. Finally, for the microrelief tested, the response can be considered isotropic. We anticipate that this model and results will enable the design of materials and devices for a desired interaction against skin.

Developing failure criteria for laceration injury of dermal tissue

Despite its importance, there is a poor understanding of human injury tolerance to trauma generally, and more specifically understanding of the mechanics of skin penetration or laceration. The objective of this analysis is to determine the failure criteria that will allow the evaluation of the laceration risk of blunt-tipped edges within a computational modeling environment. An axisymmetric tissue finite element model was set up in Abaqus 2021 to match the experimental set-up from a previous study. The model simulated the pressing of penetrometer geometries into dermal tissue, and stress and strain outputs were evaluated at the experimental failure force. Two separate nonlinear hyperelastic material models were calibrated for the dermis to data from the literature (high and low stiffness models). For both the high-stiffness and low-stiffness skin models, the failure force appears to occur near a local maximum in the principal strain. All failures occurred after the maximum strain near or at the top surface is or above 59%, with mid-thickness strain at a similar level. The strain energy density is concentrated near the edge tip for each configuration, indicating highly localized material damage at the point of loading, and increases rapidly prior to the approximate failure force. As the edge is further compressed into the tissue, the stress triaxiality near the edge contacting point decreases towards zero. This study has identified general failure criteria for skin laceration which can be implemented in a computational model. A higher risk for laceration would be indicated with strain energy density larger than 60 mJ/mm3, dermal strain larger than 55%, and stress triaxiality below 0.1. These findings were largely insensitive to the dermal stiffness and broadly applicable across different indenter geometries. It is expected that this framework may be implemented to evaluate hazardous forces for product edges, interactions with robots, and interfaces with medical and drug delivery devices.

The Role of Interface Geometry and Appendages on the Mesoscale Mechanics of the Skin

The skin is the largest organ in the human body and serves various functions, including mechanical protection and mechanosensation. Yet, even though skin's biomechanics are attributed to two main layers - epidermis and dermis-computational models have often treated this tissue as a thin homogeneous material or, when considering multiple layers, have ignored the most prominent heterogeneities of skin seen at the mesoscale. Here we create finite element models of representative volume elements (RVEs) of skin, including the three-dimensional variation of the interface between the epidermis and dermis as well as considering the presence of hair follicles. The sinusoidal interface, which approximates the anatomical features known as Rete ridges, does not affect the homogenized mechanical response of the RVE but contributes to stress concentration, particularly at the valleys of the Rete ridges. The stress profile is three-dimensional due to the skin's anisotropy, leading to high-stress bands connecting the valleys of the Rete ridges through one type of saddle point. The peaks of the Rete ridges and the other class of saddle points of the sinusoidal surface form a second set of low-stress bands under equi-biaxial loading. Another prominent feature of the heterogeneous stress pattern is a switch in the stress jump across the interface, which becomes lower with respect to the flat interface at increasing deformations. These features are seen in both tension and shear loading. The RVE with the hair follicle showed strains concentrating at the epidermis adjacent to the hair follicle, the epithelial tissue surrounding the hair right below the epidermis, and the bulb or base region of the hair follicle. The regions of strain concentration near the hair follicle in equi-biaxial and shear loading align with the presence of distinct mechanoreceptors in the skin, except for the bulb or base region. This study highlights the importance of skin heterogeneities, particularly its potential mechanophysiological role in the sense of touch and the prevention of skin delamination.

A quantitative comparison of devices for in vivo biomechanical characterization of human skin

Non-invasive skin characterization devices are emerging as a valuable tool in clinical skin research. In recent years, the range of available experimental techniques and methods used to determine the biomechanical properties of skin has increased considerably. Although a substantial amount of work has been devoted to assessing the working principle of macroscopic skin characterization devices individually, a rationalization and comparison between them is still lacking. This motivated the present study, which aimed to characterize and compare three commonly used working principles: suction, dynamic shear loading, and indentation. A synthetic model system with tunable mechanical properties was used to assess the three devices, and the results rationalized based on corresponding finite element models. In vivo measurements were performed on healthy volunteers to investigate the capability of differentiating the biomechanical properties of skin at different body locations, and to assess the intra- and inter-rater reliability of each device. The present comparative analysis indicates that the analyzed functional principles perceive the stiffness of human skin differently, with relevant implications for the interpretation of the respective measurement results.

Computational modeling and simulation of epithelial wound closure

Wounds in the epithelium may lead to serious injurious events or chronic inflammatory diseases, however, multicellular organisms have the ability to self-repair wounds through the movement of epithelial cell toward the wound area. Despite intensive studies exploring the mechanism of wound closure, the role of mechanics in epithelial wound closure is still not well explained. In order to investigate the role of mechanical properties on wound closure process, a three-dimensional continuum physics-based computational model is presented in this study. The model takes into account the material property of the epithelial cell, intercellular interactions between neighboring cells at cell-cell junctions, and cell-substrate adhesion between epithelial cells and ECM. Through finite element simulation, it is found that the closure efficiency is related to the initial gap size and the intensity of lamellipodial protrusion. It is also shown that cells at the wound edge undergo higher stress compared with other cells in the epithelial monolayer, and the cellular normal stress dominates over the cellular shear stress. The model presented in this study can be employed as a numerical tool to unravel the mechanical principles behind the complex wound closure process. These results might have the potential to improve effective wound management and optimize the treatment.

Anisotropic mechanical characterization of human skin by in vivo multi-axial ring suction test

Human skin is a soft tissue behaving as an anisotropic material. The anisotropy emerges from the alignment of collagen fibers in the dermis, which causes the skin to exhibit greater stiffness in a certain direction, known as Langer's line. The importance of determining this anisotropy axis lies in assisting surgeons in making incisions that do not produce undesirable scars. In this paper, we introduce an open-source numerical framework, MARSAC (Multi-Axial Ring Suction for Anisotropy Characterization: https://github.com/aflahelouneg/MARSAC), adapted to a commercial device CutiScan CS 100® that applies a suction load on an annular section, causing a multi-axial stretch in the central zone, where in-plane displacements are captured by a camera. The presented framework receives inputs from a video file and converts them into displacement fields through Digital Image Correlation (DIC) technique. From the latter and based on an analytical model, the method assesses the anisotropic material parameters of human skin: Langer's line ϕ, and the elastic moduli E₁ and E₂ along the principal axes, providing that the Poisson's ratio is fixed. The pipeline was applied to a public data repository, https://search-data.ubfc.fr/femto/FR-18008901306731-2021-08-25_In-vivo-skin-anisotropy-dataset-for-a-young-man.html, containing 30 test series performed on a forearm of a Caucasian subject. As a result, the identified parameter averages, ϕˆ=40.9±8.2^∘ and the anisotropy ratio E₁ˆ/E₂ˆ=3.14±1.60, were in accordance with the literature. The intra-subject analysis showed a reliable assessment of ϕ and E₂. As skin anisotropy varies from site to site and from subject to subject, the novelty of the method consists in (i) an optimal utilization of CutiScan CS 100® probe to measure the Langer's line accurately and rapidly on small areas with a minimum diameter of 14mm, (ii) validation of an analytical model based on deformation ellipticity.

Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty

Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.

Computer simulation of the wound process (review of literature)

Relevance. Computer simulation is a mathematical modeling process performed on a computer that is designed to predict the behavior or results of a real or physical system. Computer simulation has a number of advantages over classical models of animal experiments: the cheapness of the method (the need to acquire and maintain animals disappears by itself), the speed of obtaining results, the absence of bioethical problems, the ability to change the conditions of the experiment, etc.

he purpose of this study is to review the methods of computer simulation of the wound process, to identify the shortcomings of the models and propose ways to solve them, as well as to select the best existing model for describing wound regeneration.

Material and methods. In the course of this work, an analysis was made of foreign and domestic literature on the problem of computer modeling of the wound process.

Results. After analyzing the relevant literature on this topic, the problem is seen precisely in the insufficiently studied process of wound regeneration, since many different cells, cytokines, growth factors, enzymes, fibrillar proteins, etc. take part in it. The models that currently exist describe wound regeneration only in an extremely generalized way, which does not allow us to apply them in clinical situations. Analyzing literature sources, we came to the conclusion that both numerical approaches, both cellular-biochemical (the first type of models) and phenomenological (the second type) are applicable in the case of wound modeling and can be used very successfully. The problem is that on the basis of one approach it is impossible to display a complete picture of wound healing, in this way it is possible to predict only individual regeneration parameters necessary for certain purposes due to the complexity and versatility of this typical pathophysiological process.

Conclusion. Computer modeling of wounds is still a controversial and complex topic. Existing models are not intended to describe all the processes occurring in a healing wound. It is much more productive to describe the various phenomena during healing separately. This is due to the fact that many elements are involved in the regeneration of the skin, which are almost impossible to take into account in full. The available models are of exclusively scientific value, consisting in attempts to understand all complex processes and interactions. Practical application is difficult, since existing models require specific input data that require highly specialized equipment. If we abstract from all this, then the best existing model of the first type is the model of the authors Yangyang Wang, Christian F. Guerrero-Juarez, Yuchi Qiu and co-authors, in addition to it, any of the described phenomenological models will do. 

Bayesian Inference With Gaussian Process Surrogates to Characterize Anisotropic Mechanical Properties of Skin From Suction Tests

One of the intrinsic features of skin and other biological tissues is the high variation in the mechanical properties across individuals and different demographics. Mechanical characterization of skin is still a challenge because the need for subject-specific in vivo parameters prevents us from utilizing traditional methods, e.g., uniaxial tensile test. Suction devices have been suggested as the best candidate to acquire mechanical properties of skin noninvasively, but capturing anisotropic properties using a circular probe opening-which is the conventional suction device-is not possible. On the other hand, noncircular probe openings can drive different deformations with respect to fiber orientation and therefore could be used to characterize the anisotropic mechanics of skin noninvasively. We propose the use of elliptical probe openings and a methodology to solve the inverse problem of finding mechanical properties from suction measurements. The proposed probe is tested virtually by solving the forward problem of skin deformation by a finite element (FE) model. The forward problem is a function of the material parameters. In order to solve the inverse problem of determining skin properties from suction data, we use a Bayesian framework. The FE model is an expensive forward function, and is thus substituted with a Gaussian process metamodel to enable the Bayesian inference problem.

New Closed-Form Solution for Quadratic Damped and Forced Nonlinear Oscillator with Position-Dependent Mass: Application in Grafted Skin Modeling

The paper deals with modelling and analytical solving of a strong nonlinear oscillator with position-dependent mass. The oscillator contains a nonlinear restoring force, a quadratic damping force and a constant force which excites vibration. The model of the oscillator is a non-homogenous nonlinear second order differential equation with a position-dependent parameter. In the paper, the closed-form exact solution for periodic motion of the oscillator is derived. The solution has the form of the cosine Ateb function with amplitude and frequency which depend on the coefficient of mass variation, damping parameter, coefficient of nonlinear stiffness and excitation value. The proposed solution is tested successfully via its application for oscillators with quadratic nonlinearity. Based on the exact closed-form solution, the approximate procedure for solving an oscillator with slow-time variable stiffness and additional weak nonlinearity is developed. The proposed method is named the ‘approximate time variable Ateb function solving method’ and is applicable to many nonlinear problems in physical and applied sciences where parameters are time variable. The method represents the extended and adopted version of the time variable amplitude and phase method, which is rearranged for Ateb functions. The newly developed method is utilized for vibration analysis of grafted skin on the human body. It is found that the grafted skin vibration properties, i.e., amplitude, frequency and phase, vary in time and depend on the dimension, density and nonlinear viscoelastic properties of the skin and also on the force which acts on it. The results obtained analytically are compared with numerically and experimentally obtained ones and show good agreement.

Compartmental modeling of skin absorption and desorption kinetics: Donor solvent evaporation, variable diffusion/partition coefficients, and slow equilibration process within stratum corneum

This work expands the recently developed compartmental model for skin transport to model variable diffusion and/or partition coefficients, and the presence of slow equilibration/slow binding kinetics within stratum corneum. The model was validated by comparing it with the diffusion model which was solved numerically using the finite element method. It was found that the new compartmental model predictions agreed well with that of the diffusion model, providing a sufficient number of compartments was used. The compartmental model was applied to two previously published experimental data sets: water penetration and desorption data and the finite dose dermal penetration of testosterone. Significant improvement of the fitting quality for all these data sets was achieved using the compartmental model.

Multiscale Computational Model Predicts Mouse Skin Kinematics Under Tensile Loading

Skin is a complex tissue whose biomechanical properties are generally understood in terms of an incompressible material whose microstructure undergoes affine deformations. A growing number of experiments, however, have demonstrated that skin has a high Poisson's ratio, substantially decreases in volume during uniaxial tensile loading, and demonstrates collagen fiber kinematics that are not affine with local deformation. In order to better understand the mechanical basis for these properties, we constructed multiscale mechanical models (MSM) of mouse skin based on microstructural multiphoton microscopy imaging of the dermal microstructure acquired during mechanical testing. Three models that spanned the cases of highly aligned, moderately aligned, and nearly random fiber networks were examined and compared to the data acquired from uniaxially stretched skin. Our results demonstrate that MSMs consisting of networks of matched fiber organization can predict the biomechanical behavior of mouse skin, including the large decrease in tissue volume and nonaffine fiber kinematics observed under uniaxial tension.

Effect of collagen fibre orientation on the Poisson's ratio and stress relaxation of skin: an ex vivo and in vivo study

During surgical treatment skin undergoes extensive deformation, hence it must be able to withstand large mechanical stresses without damage. Therefore, understanding the mechanical properties of skin becomes important. A detailed investigation on the relationship between the three-dimensional deformation response of skin and its microstructure is conducted in the current study. This study also discloses the underlying science of skin viscoelasticity. Deformation response of skin is captured using digital image correlation, whereas micro-CT, scanning electron microscopy and atomic force microscopy are used for microstructure analysis. Skin shows a large lateral contraction and expansion (auxeticity) when stretched parallel and perpendicular to the skin tension lines, respectively. Large lateral contraction is a result of fluid exudation from the tissue, while large rotation of the stiff collagen fibres in the loading direction explains the skin auxeticity. During stress relaxation, lateral contraction and fluid effluxion from skin reveal that tissue volume loss is the intrinsic science of skin viscoelasticity. Furthermore, the results obtained from in vivo study on human skin show the relevance of the ex vivo study to physiological conditions and stretching of the skin during its treatments.

Bayesian calibration of a computational model of tissue expansion based on a porcine animal model

Tissue expansion is a technique used clinically to grow skin in situ to correct large defects. Despite its enormous potential, lack of fundamental knowledge of skin adaptation to mechanical cues, and lack of predictive computational models limit the broader adoption and efficacy of tissue expansion. In our previous work, we introduced a finite element model of tissue expansion that predicted key patterns of strain and growth which were then confirmed by our porcine animal model. Here we use the data from a new set of experiments to calibrate the computational model within a Bayesian framework. Four 10×10cm2 patches were tattooed in the dorsal skin of four 12 weeks-old minipigs and a total of six patches underwent successful tissue expander placement and inflation to 60cc for expansion times ranging from 1 h to 7 days. Six patches that did not have expanders implanted served as controls for the analysis. We find that growth can be explained based on the elastic deformation. The predicted area growth rate is k∈[0.02,0.08] [h-1]. Growth is anisotropic and reflects the anisotropic mechanical behavior of porcine dorsal skin. The rostral-caudal axis shows greater deformation than the transverse axis, and the time scale of growth in the rostral-caudal direction is given by rate parameters k1∈[0.04,0.1] [h-1] compared to k2∈[0.01,0.05] [h-1] in the transverse direction. Moreover, the calibration results underscore the high variability in biological systems, and the need to create probabilistic computational models to predict tissue adaptation in realistic settings. STATEMENT OF SIGNIFICANCE: Tissue expansion is a widely used technique in reconstructive surgery because it triggers growth of skin for the correction of large skin lesions and for breast reconstruction after mastectomy. Despite of its potential, complications and undesired outcomes persist due to our incomplete understanding of skin mechanobiology. Here we quantify the deformation and growth fields induced by an expander over 7 days in a porcine animal model and use these data to calibrate a computational model of skin growth using finite element simulations and a Bayesian framework. The calibrated model is a leap forward in our understanding skin growth, we now have quantitative understanding of this process: area growth is anisotropic and it is proportional to stretch with a characteristic rate constant of k∈[0.02,0.08] [h-1].

Mechanical modeling and characterization of human skin: A review

This paper reviews the advances made in recent years on modeling approaches and experimental techniques to characterize the mechanical properties of human skin. The skin is the largest organ of the human body that has a complex multi-layered structure with different mechanical behaviors. The mechanical properties of human skin play an important role in distinguishing between healthy and unhealthy skin. Furthermore, knowing these mechanical properties enables computer simulation, skin research, clinical studies, as well as diagnosis and treatment monitoring of skin diseases. This paper reviews the recent efforts on modeling skin using linear, nonlinear, viscoelastic, and anisotropic materials. The work also focuses on aging effects, microstructure analysis, and non-invasive methods for skin testing. A detailed explanation of the skin structure and numerical models, such as finite element models, are discussed in this work. This work also compares different experimental methods that measure the mechanical properties of human skin. The work reviews the experimental results in the literature and shows how the mechanical properties of human skin vary with the skin sites, the layers, and the structure of human skin. The paper also discusses how state-of-the-art technology can advance skin research.

Changes in the three-dimensional microscale topography of human skin with aging impact its mechanical and tribological behavior

Human skin enables interaction with diverse materials every day and at all times. The ability to grasp objects, feel textures, and perceive the environment depends on the mechanical behavior, complex structure, and microscale topography of human skin. At the same time, abrasive interactions, such as sometimes occur with prostheses or textiles, can damage the skin and impair its function. Previous theoretical and computational efforts have shown that skin’s surface topography or microrelief is crucial for its tribological behavior. However, current understanding is limited to adult surface profiles and simplified two-dimensional simulations. Yet, the skin has a rich set of features in three dimensions, and the geometry of skin is known to change with aging. Here we create a numerical model of a dynamic indentation test to elucidate the effect of changes in microscale topography with aging on the skin’s response under indentation and sliding contact with a spherical indenter. We create three different microrelief geometries representative of different ages based on experimental reports from the literature. We perform the indentation and sliding steps, and calculate the normal and tangential forces on the indenter as it moves in three distinct directions based on the characteristic skin lines. The model also evaluates the effect of varying the material parameters. Our results show that the microscale topography of the skin in three dimensions, together with the mechanical behavior of the skin layers, lead to distinctive trends on the stress and strain distribution. The major finding is the increasing role of anisotropy which emerges from the geometric changes seen with aging.

Improving reconstructive surgery design using Gaussian process surrogates to capture material behavior uncertainty

To produce functional, aesthetically natural results, reconstructive surgeries must be planned to minimize stress as excessive loads near wounds have been shown to produce pathological scarring and other complications (Gurtner et al., 2011). Presently, stress cannot easily be measured in the operating room. Consequently, surgeons rely on intuition and experience (Paul et al., 2016; Buchanan et al., 2016). Predictive computational tools are ideal candidates for surgery planning. Finite element (FE) simulations have shown promise in predicting stress fields on large skin patches and in complex cases, helping to identify potential regions of complication. Unfortunately, these simulations are computationally expensive and deterministic (Lee et al., 2018a). However, running a few, well selected FE simulations allows us to create Gaussian process (GP) surrogate models of local cutaneous flaps that are computationally efficient and able to predict stress and strain for arbitrary material parameters. Here, we create GP surrogates for the advancement, rotation, and transposition flaps. We then use the predictive capability of these surrogates to perform a global sensitivity analysis, ultimately showing that fiber direction has the most significant impact on strain field variations. We then perform an optimization to determine the optimal fiber direction for each flap for three different objectives driven by clinical guidelines (Leedy et al., 2005; Rohrer and Bhatia, 2005). While material properties are not controlled by the surgeon and are actually a source of uncertainty, the surgeon can in fact control the orientation of the flap with respect to the skin's relaxed tension lines, which are associated with the underlying fiber orientation (Borges, 1984). Therefore, fiber direction is the only material parameter that can be optimized clinically. The optimization task relies on the efficiency of the GP surrogates to calculate the expected cost of different strategies when the uncertainty of other material parameters is included. We propose optimal flap orientations for the three cost functions and that can help in reducing stress resulting from the surgery and ultimately reduce complications associated with excessive mechanical loading near wounds.

Three-Dimensional Quantification of Collagen Microstructure During Tensile Mechanical Loading of Skin

Skin is a heterogeneous tissue that can undergo substantial structural and functional changes with age, disease, or following injury. Understanding how these changes impact the mechanical properties of skin requires three-dimensional (3D) quantification of the tissue microstructure and its kinematics. The goal of this study was to quantify these structure-function relationships via second harmonic generation (SHG) microscopy of mouse skin under tensile mechanical loading. Tissue deformation at the macro- and micro-scale was quantified, and a substantial decrease in tissue volume and a large Poisson’s ratio was detected with stretch, indicating the skin differs substantially from the hyperelastic material models historically used to explain its behavior. Additionally, the relative amount of measured strain did not significantly change between length scales, suggesting that the collagen fiber network is uniformly distributing applied strains. Analysis of undeformed collagen fiber organization and volume fraction revealed a length scale dependency for both metrics. 3D analysis of SHG volumes also showed that collagen fiber alignment increased in the direction of stretch, but fiber volume fraction did not change. Interestingly, 3D fiber kinematics was found to have a non-affine relationship with tissue deformation, and an affine transformation of the micro-scale fiber network overestimates the amount of fiber realignment. This result, along with the other outcomes, highlights the importance of accurate, scale-matched 3D experimental measurements when developing multi-scale models of skin mechanical function.

A biphasic multilayer computational model of human skin

The present study investigates the layer-specific mechanical behavior of human skin. Motivated by skin’s histology, a biphasic model is proposed which differentiates between epidermis, papillary and reticular dermis, and hypodermis. Inverse analysis of ex vivo tensile and in vivo suction experiments yields mechanical parameters for each layer and predicts a stiff reticular dermis and successively softer papillary dermis, epidermis and hypodermis. Layer-specific analysis of simulations underlines the dominating role of the reticular dermis in tensile loading. Furthermore, it shows that the observed out-of-plane deflection in ex vivo tensile tests is a direct consequence of the layered structure of skin. In in vivo suction experiments, the softer upper layers strongly influence the mechanical response, whose dissipative part is determined by interstitial fluid redistribution within the tissue. Magnetic resonance imaging-based visualization of skin deformation in suction experiments confirms the deformation pattern predicted by the multilayer model, showing a consistent decrease in dermal thickness for large probe opening diameters.

Challenges and opportunities for small volumes delivery into the skin

Each individual's skin has its own features, such as strength, elasticity, or permeability to drugs, which limits the effectiveness of one-size-fits-all approaches typically found in medical treatments. Therefore, understanding the transport mechanisms of substances across the skin is instrumental for the development of novel minimal invasive transdermal therapies. However, the large difference between transport timescales and length scales of disparate molecules needed for medical therapies makes it difficult to address fundamental questions. Thus, this lack of fundamental knowledge has limited the efficacy of bioengineering equipment and medical treatments. In this article, we provide an overview of the most important microfluidics-related transport phenomena through the skin and versatile tools to study them. Moreover, we provide a summary of challenges and opportunities faced by advanced transdermal delivery methods, such as needle-free jet injectors, microneedles, and tattooing, which could pave the way to the implementation of better therapies and new methods.

How stiff is skin?

The measurement of the mechanical properties of skin (such as stiffness, extensibility and strength) is a key step in characterisation of both dermal ageing and disease mechanisms and in the assessment of tissue-engineered skin replacements. However, the biomechanical terminology and plethora of mathematical analysis approaches can be daunting to those outside the field. As a consequence, mechanical studies are often inaccessible to a significant proportion of the intended audience. Furthermore, devices for the measurement of skin function in vivo generate relative values rather than formal mechanical measures, therefore limiting the ability to compare studies. In this viewpoint essay, we discuss key biomechanical concepts and the influence of technical and biological factors (including the nature of the testing apparatus, length scale, donor age and anatomical site) on measured mechanical properties such as stiffness. Having discussed the current state-of-the-art in macro-mechanical and micromechanical measuring techniques and in mathematical and computational modelling methods, we then make suggestions as to how these approaches, in combination with 3D X-ray imaging and mechanics methods, may be adopted into a single strategy to characterise the mechanical behaviour of skin.

Extracting the elasticity of the human skin in microscale and in-vivo from atomic force microscopy experiments using viscoelastic models

Detecting mechanical properties of the intact skin in-vivo leads to a novel quantitative method to diagnose skin diseases and to monitor skin conditions in clinical settings. Current research and clinical methods that detect skin mechanics have major limitations. The in-vitro experiments are done in non-physiological conditions and in-vivo clinical methods measurer unwanted mechanics of underneath fat and muscle tissues but report the measurement as skin mechanics. An ideal skin mechanics should be captured at skin scale (i.e., micron-scale) and in-vivo. However, extreme challenges of capturing the in-vivo skin mechanics in micron-scale including skin motion due to heart beep, breathing and movement of the subject, has hindered measurement of skin mechanics in-vivo.This study for the first time captures micro-scale mechanics (elasticity and viscoelasticity) of top layers of skin (i.e., the stratum corneum (SC) and stratum granulosum (SG)) in-vivo. In this study, the relevant literature is reviewed and Atomic Force Microscopy (AFM) was used to capture force-indentation curves on the fingertip skin of four human subjects at a high indentation speed of 40 μm/s. The skin of the same subject were tested in-vitro at 10 different indentation speeds ranging from 0.125 to 40 μm/s by AFM. This study extracts the in-vivo elasticity of SC and SG by detecting time-dependency of tested tissue using a fractional viscoelastic standard linear model developed for indentation. The in-vivo elasticity of SC and SG were smaller in females and in-vitro elasticity were higher than that of in-vivo results. The results were consistent with previous observations.

Personalized Computational Models of Tissue-Rearrangement in the Scalp Predict the Mechanical Stress Signature of Rotation Flaps

OBJECTIVE

To elucidate the mechanics of scalp rotation flaps through 3D imaging and computational modeling. Excessive tension near a wound or sutured region can delay wound healing or trigger complications. Measuring tension in the operating room is challenging, instead, noninvasive methods to improve surgical planning are needed.

DESIGN

Multi-view stereo allows creation of 3D patient-specific geometries based on a set of photographs. The patient-specific 3D geometry is imported into a finite element (FE) platform to perform a virtual procedure. The simulation is compared with the clinical outcome. Additional simulations quantify the effect of individual flap parameters on the resulting tension distribution.

PARTICIPANTS

Rotation flaps for reconstruction of scalp defects following melanoma resection in 2 cases are presented. Rotation flaps were designed without preoperative FE preparation.

MAIN OUTCOME MEASURE

Tension distribution over the operated region.

RESULTS

The tension from FE shows peaks at the base and distal ends of the scalp rotation flap. The predicted geometry from the simulation aligns with postoperative photographs. Simulations exploring the flap design parameters show variation in the tension. Lower tensions were achieved when rotation was oriented with respect to skin tension lines (horizontal tissue fibers) and smaller rotation angles.

CONCLUSIONS

Tension distribution following rotation of scalp flaps can be predicted through personalized FE simulations. Flaps can be designed to reduce tension using FE, which may greatly improve the reliability of scalp reconstruction in craniofacial surgery, critical in complex cases when scalp reconstruction is essential for coverage of hardware, implants, and/or bone graft.

General method for classification of fiber families in fiber-reinforced materials: application to in-vivo human skin images

Fiber structures play a major role for the function of fiber-reinforced materials such as biological tissue. An objective classification of the fiber orientations into fiber families is crucial to understand its mechanical properties. We introduce the Fiber Image Network Evaluation Algorithm (FINE algorithm) to classify and quantify the number of fiber families in scientific images. Each fiber family is characterized by an amplitude, a mean orientation, and a dispersion. A new alignment index giving the averaged fraction of aligned fibers is defined. The FINE algorithm is validated by realistic grayscale Monte-Carlo fiber images. We apply the algorithm to an in-vivo depth scan of second harmonic generation images of dermal collagen in human skin. The derived alignment index exhibits a crossover at a critical depth where two fiber families with a perpendicular orientation around the main tension line arise. This strongly suggests the presence of a transition from the papillary to the reticular dermis. Hence, the FINE algorithm provides a valuable tool for a reliable classification and a meaningful interpretation of in-vivo collagen fiber networks and general fiber reinforced materials.

Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression

A key feature of living tissues is their capacity to remodel and grow in response to environmental cues. Within continuum mechanics, this process can be captured with the multiplicative split of the deformation gradient into growth and elastic contributions. The mechanical and biological response during tissue adaptation is characterized by inherent variability. Accounting for this uncertainty is critical to better understand tissue mechanobiology, and, moreover, it is of practical importance if we aim to develop predictive models for clinical use. However, the current gold standard in computational models of growth and remodeling remains the use of deterministic finite element (FE) simulations. Here we focus on tissue expansion, a popular technique in which skin is stretched by a balloon-like device inducing its growth. We construct FE models of tissue expansion with various levels of detail, and show that a sufficiently broad set of FE simulations from these models can be used to train an accurate and efficient multi-fidelity Gaussian process (GP) surrogate. The approach is not limited to simulation data, rather, it can fuse different kinds of data, including from experiments. The main appeal of the framework relies on the common experience that highly detailed models (or experiments) are more accurate but also more costly, while simpler models (or experiments) can be easily evaluated but are bound to have some error. In these situations, doing uncertainty analysis tasks with the high fidelity models alone is not feasible and, conversely, relying solely on low fidelity approximations is also undesirable. We show that a multi-fidelity GP outperforms the high fidelity GP and low fidelity GP when tested against the most detailed FE model. In turn, having trained the multi-fidelity GP model, we showcase the propagation of uncertainty from the mechanical and biological response parameters to the spatio-temporal growth outcomes. We expect that the methods and applications in this paper will enable future research in parameter calibration under uncertainty and uncertainty propagation in real clinical scenarios involving tissue growth and remodeling.

Morphology and composition play distinct and complementary roles in the tolerance of plantar skin to mechanical load

Plantar skin on the soles of the feet has a distinct morphology and composition that is thought to enhance its tolerance to mechanical loads, although the individual contributions of morphology and composition have never been quantified. Here, we combine multiscale mechanical testing and computational models of load bearing to quantify the mechanical environment of both plantar and nonplantar skin under load. We find that morphology and composition play distinct and complementary roles in plantar skin's load tolerance. More specifically, the thick stratum corneum provides protection from stress-based injuries such as skin tears and blisters, while epidermal and dermal compositions provide protection from deformation-based injuries such as pressure ulcers. This work provides insights into the roles of skin morphology and composition more generally and will inform the design of engineered skin substitutes as well as the etiology of skin injury.

Linking microvascular collapse to tissue hypoxia in a multiscale model of pressure ulcer initiation

Pressure ulcers are devastating injuries that disproportionately affect the older adult population. The initiating factor of pressure ulcers is local ischemia, or lack of perfusion at the microvascular level, following tissue compression against bony prominences. In turn, lack of blood flow leads to a drop in oxygen concentration, i.e, hypoxia, that ultimately leads to cell death, tissue necrosis, and disruption of tissue continuity. Despite our qualitative understanding of the initiating mechanisms of pressure ulcers, we are lacking quantitative knowledge of the relationship between applied pressure, skin mechanical properties as well as structure, and tissue hypoxia. This gap in our understanding is, at least in part, due to the limitations of current imaging technologies that cannot simultaneously image the microvascular architecture, while quantifying tissue deformation. We overcome this limitation in our work by combining realistic microvascular geometries with appropriate mechanical constitutive models into a microscale finite element model of the skin. By solving boundary value problems on a representative volume element via the finite element method, we can predict blood volume fractions in response to physiological skin loading conditions (i.e., shear and compression). We then use blood volume fraction as a homogenized variable to couple tissue-level skin mechanics to an oxygen diffusion model. With our model, we find that moderate levels of pressure applied to the outer skin surface lead to oxygen concentration contours indicative of tissue hypoxia. For instance, we show that applying a pressure of 60 kPa at the skin surface leads to a decrease in oxygen partial pressure from a physiological value of 65 mmHg to a hypoxic level of 31 mmHg. Additionally, we explore the sensitivity of local oxygen concentration to skin thickness and tissue stiffness, two age-related skin parameters. We find that, for a given pressure, oxygen concentration decreases with decreasing skin thickness and skin stiffness. Future work will include rigorous calibration and validation of this model, which may render our work an important tool toward developing better prevention and treatment tools for pressure ulcers specifically targeted toward the older adult patient population.

A linear viscoelastic model to understand skin mechanical behaviour and for cosmetic formulation design

OBJECTIVES

Skin is arguably one of the most important organs that plays an active role in our everyday biological functions after brain. Owing to the wide range of applications in medicine, cosmetics industry and more recently robotics, skin research has gained tremendous attention with respect to its mechanical behaviour. Various macro modelling approaches are available for modelling skin's mechanical behaviour. The objective of this paper is to study skin's mechanical property change with age and demonstrate anti-ageing effects of cosmetic formulations from skin mechanical property change perspective.

METHODS

In this study, skin's mechanical behaviour was modelled using a 1D linear viscoelastic phenomenological model and the model was validated using two sets of experimentally observed skin data (strain, stress relaxation and cyclical loading). The model was further modified to study the effect of the presence of a thin layer of cosmetic polymer and to demonstrate anti-ageing effects of the cosmetic polymer from the perspective of change in the mechanical behaviour of skin with cosmetic layer.

RESULTS

The estimated values of skin mechanical properties from the model agree with those in literature. The extracted model features show good correlation with skin age (viscosity and time constant). The results from our model indicate that the cosmetic polymers enhance the mechanical properties of skin significantly.

CONCLUSIONS

This work will find its applications in designing and testing anti-ageing formulations. This model can be used to filter various combinations of cosmetic formulations by knowing the mechanical response of polymer on skin, thereby accelerating the product development.

On fibre dispersion modelling of soft biological tissues: a review

Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. This paper provides a timely and critical review of the continuum modelling of fibre dispersion, specifically, the angular integration and the generalized structure tensor models. The models are used in representative numerical examples to fit sets of experimental data that have been obtained from mechanical tests and fibre structural information from second-harmonic imaging. In particular, patches of healthy and diseased aortic tissues are investigated, and it is shown that the predictions of the models fit very well with the data. It is straightforward to use the models described herein within a finite-element framework, which will enable more realistic (and clinically relevant) boundary-value problems to be solved. This also provides a basis for further developments of material models and points to the need for additional mechanical and microstructural data that can inform further advances in the material modelling.

Tensile behavior and structural characterization of pig dermis

Skin, the outermost layer of the body, fulfills a broad range of functions, protecting internal organs from damage and infection, while regulating the body's temperature and water content via the exchange of heat and fluids. It must be able to withstand and recover from extensive deformation and damage that can occur during growth, movement, and potential injuries. A detailed investigation of the evolution of the collagen architecture of the dermis as a function of deformation is conducted, which reveals new aspects that help us to understand the mechanical response of skin. Juvenile pig is used as a model material because of its similarity to human skin. The dermis is found to have a tridimensional woven structure of collagen fibers, which evolves with deformation. After failure, we observe that the fibers have straightened and aligned in the direction of tension. The effects of strain-rate change, cyclic loading, stress relaxation, and orientation are quantitatively established. Digital image correlation techniques are implemented to quantify skin's anisotropy; measurements of the Poisson ratio are reported. This is coupled with transmission electron microscopy which enables obtaining quantitative strain parameters evaluated through the orientation and curvature of the collagen fibers and their changes, for the first time in all three dimensions of the tissue. A model experiment using braided human hair in tension exhibits a similar J-curve response to skin, and we propose that this fiber configuration is at least partially responsible for the monotonic increase of the tangent modulus of skin with strain. The obtained results are intended to serve as a basis for structurally-based models of skin. STATEMENT OF SIGNIFICANCE: Our study reveals a new aspect of the dermis: it is comprised of a tridimensional woven structure of collagen fibers, which evolves with deformation. This is enabled by primarily two techniques, transmission electron microscopy on three perpendicular planes and confocal images with second harmonic generation fluorescence of collagen, captured at different intervals of depth. After failure, the fibers have straightened and aligned in the direction of tension. Digital image correlation techniques are implemented to quantify skin's anisotropy; measurements of the Poisson ratio are reported. A model experiment using braided human hair in tension exhibits a similar J-curve response to skin, and we propose that this fiber configuration is at least partially responsible for the monotonic increase of the tangent modulus of skin with strain.

On the compressibility and poroelasticity of human and murine skin

A total of 37 human and 33 murine skin samples were subjected to uniaxial monotonic, cyclic, and relaxation experiments. Detailed analysis of the three-dimensional kinematic response showed that skin volume is significantly reduced as a consequence of a tensile elongation. This behavior is most pronounced in monotonic but persists in cyclic tests. The dehydration associated with volume loss depends on the osmolarity of the environment, so that tension relaxation changes as a consequence of modifying the ionic strength of the environmental bath. Similar to ex vivo observations, complementary in vivo stretching experiments on human volar forearms showed strong in-plane lateral contraction. A biphasic homogenized model is proposed which allows representing all relevant features of the observed mechanical response.

Development of a Load-Cell Based Palpation Sensor Suitable for Ophthalmic Anesthesia Training

Palpation is the process of using one's hand to perform a physical examination. Ophthalmic anaesthetists palpate the orbital bone around the eye, to locate anatomical markers to help them guide the needle safely for regional needle block into the orbital cavity. The anaesthetists are provided very little training on palpation procedure due to the lack of a suitable training system. Inadvisable palpation can cause damage to the soft tissue if the applied force is more than required. There is a necessity to provide ophthalmic anaesthetists with the relevant knowledge about palpation and the force exerted during this procedure. In this paper, a load cell based palpation sensor which can be integrated with recently developed ophthalmic anaesthesia training systems with a virtual instrument environment that is capable of mimicking the skin reaction to applied palpation with the variable warning threshold is proposed.

Graft orientation influences meshing ratio

OBJECTIVES

The technique of meshed skin grafting is known since 1960s. It was shown that there is a difference between the declared and real expansion ratio of the skin meshed graft. We hypothesize that the orientation of the Langer's lines in a split thickness skin graft is a key parameter in the resulting expansion ratio.

METHODS

The skin graft meshing process was analyzed in two steps. In the first step, ex vivo uniaxial tests of human skin were performed. This served as an input for the constitutive model used for numerical simulations. In the second step, finite element analyses were performed so that stress distributions and expansion ratios could be determined.

RESULTS

It was shown that peaks of true stress tended to be concentrated around the vertex of the mesh pattern region for all cases. The declared expansion was impossible to obtain for all expansion ratios having the meshing incision perpendicular to the Langer's lines. The highest difference between declared and real expansion ratio reaches 37%.

CONCLUSIONS

With regard to literature dealing with expansion of skin grafts by meshing, a high scatter amongst data results is observed. This finding was also explained by our research, demonstrating the significance of Langer's lines and their relative orientation to the direction of meshing.

Improving tissue expansion protocols through computational modeling

Tissue expansion is a common technique in reconstructive surgery used to grow skin in vivo for correction of large defects. Despite its popularity, there is a lack of quantitative understanding of how stretch leads to growth of new skin. This has resulted in several arbitrary expansion protocols that rely on the surgeon's personal training and experience rather than on accurate predictive models. For example, choosing between slow or rapid expansion, or small or large inflation volumes remains controversial. Here we explore four tissue expansion protocols by systematically varying the inflation volume and the protocol duration in a porcine model. The quantitative analysis combines three-dimensional photography, isogeometric kinematics, and finite growth theory. Strikingly, all four protocols generate similar peak stretches, but different growth patterns: Smaller filling volumes of 30 ml per inflation did not result in notable expander-induced growth neither for the short nor for the long protocol; larger filling volumes of 60 ml per inflation trigger skin adaptation, with larger expander-induced growth in regions of larger stretch, and more expander-induced growth for the 14-day compared to the 10-day expansion protocol. Our results suggest that expander-induced growth is not triggered by the local stretch alone. While stretch is clearly a driver for growth, the local stretch at a given point is not enough to predict the expander-induced growth at that location. From a clinical perspective, our study suggests that longer expansion protocols are needed to ensure sufficient growth of sizable skin patches.

Ultrasound elastography reliably identifies altered mechanical properties of burned soft tissues

Although burn injury to the skin and subcutaneous tissues is common in both civilian and military scenarios, a significant knowledge gap exists in quantifying changes in tissue properties as a result of burns. In this study, we present a noninvasive technique based on ultrasound elastography which can reliably assess altered nonlinear mechanical properties of a burned tissue. In particular, ex vivo porcine skin tissues have been exposed to four different burn conditions: (i) 200°F for 10s, (ii) 200°F for 30s, (iii) 450°F for 10s, and (iv) 450°F for 30s. A custom-developed instrument including a robotically controlled ultrasound probe and force sensors has been used to compress the tissue samples to compute two parameters (C₁₀ and C₂₀) of a reduced second-order polynomial hyperelastic material model. The results indicate that while the linear model parameter (C₁₀) does not show a statistically significant difference between the test conditions, the nonlinear model parameter (C₂₀) reliably identifies three (ii-iv) of the four cases (p<0.05) when comparing burned with unburned tissues with a classification accuracy of 60-87%. Additionally, softening of the tissue is observed because of the change in structure of the collagen fibers. The ultrasound elastography-based technique has potential for application under in vivo conditions, which is left for future work.

On skin microrelief and the emergence of expression micro-wrinkles

Over the course of a life time, as a result of adaptive mechanobiological processes (e.g. ageing), or the action of external physical factors such as mechanical loading, the human skin is subjected to, and hosts complex biophysical processes. These phenomena typically operate through a complex interplay, that, ultimately, is responsible for the evolutive geometrical characteristics of the skin surface. Wrinkles are a manifestation of these effects. Although numerous theoretical models of wrinkles arising in multi-layered structures have been proposed, they typically apply to idealised geometries. In the case of skin, which can be viewed as a geometrically complex multi-layer assembly, it is pertinent to question whether the natural skin microrelief could play a significant role in conditioning the characteristics of compression-induced micro-wrinkles by acting as an array of geometrical imperfections. Here, we explore this question through the development of an anatomically-based finite strain parametric finite element model of the skin, represented as a stratum corneum layer on top of a thicker and softer substrate. Our study suggests that skin microrelief could be the dominant factor conditioning micro-wrinkle characteristics for moderate elastic modulus ratios between the two layers. Beyond stiffness ratios of 100, other factors tend to overwrite the effects of skin microrelief. Such stiffness ratio fluctuations can be induced by changes in relative humidity or particular skin conditions and can therefore have important implications for skin tribology.