Thermoelastic modelling of the skin at finite deformations

Noninvasive identification of directionally-dependent elastic properties of soft tissues using full-field optical data

This paper introduces an innovative approach for elastic property characterization of soft tissues, having directional-dependent material behavior, via their vibration response measurement and interpretation. The full-field time-dependent surface displacements as a result of externally excited soft tissues are collected through digital image correlation (DIC). A developed analytical model, capturing the low-amplitude vibration behavior of anisotropic layered human skin with the incorporation of the influence of subcutaneous elasticity and inertia, is employed to accurately predict its resonant frequencies and pertaining displacement field images. An efficient solution approach for the model is implemented into an inverse algorithm to rapidly characterize the anisotropic elastic properties based on importing the vibration characteristics. To show the merit of the approach, a 3-D finite element (FE) simulation model was used to generate full-field data, detected and matched with a set of specific vibration modes via modal assurance criterion (MAC). The validity of the model implemented into the inverse characterization algorithm is demonstrated through a comparison of predicted vibration frequencies and mode-shapes simulated via the 3-D FE model for different cases with anisotropic elastic properties in different layers of the skin. It is shown that modes are influenced differently when anisotropic properties are introduced to the model. Thus, the established inverse characterization algorithm is capable of rapidly predicting the elastic material properties of anisotropic soft sheets with adequate accuracy.

Mechanical characterization of human skin-A non-invasive digital twin approach using vibration-response integrated with numerical methods

This paper proposes an innovative approach to identify elastic material properties and mass density of soft tissues based on interpreting their mechanical vibration response, externally excited by a mechanical indenter or acoustic waves. A vibration test is performed on soft sheets to measure their response to a continuous range of excitation frequencies. The frequency responses are collected with a pair of high-speed cameras in conjunction with 3-D digital image correlation (DIC). Two cases are considered, including suspended/fully-free rectangular neoprene sheets as artificial tissue cutout samples and continuous layered human skin vibrations. An efficient theoretical model is developed to analytically simulate the free vibrations of the neoprene artificial sheet samples as well as the continuous layered human skins. The high accuracy and validity of the presented analytical simulations are demonstrated through comparison with the DIC measurements and the conducted frequency tests, as well as a number of finite element (FE) modeling. The developed analytical approach is implemented into a numerical algorithm to perform an inverse calculation of the soft sheets' elastic properties using the imported experimental vibration results and the predicted system's mass via the system equivalent reduction/expansion process (SEREP) method. It is shown that the proposed frequency-dependent inverse approach is capable of rapidly predicting the material properties of the tested samples with high accuracy.

Infrared Thermography for Real-Time Assessment of the Effectiveness of Scoliosis Braces

This work proposes an innovative method, based on the use of low-cost infrared thermography (IRT) instrumentation, to assess in real time the effectiveness of scoliosis braces. Establishing the effectiveness of scoliosis braces means deciding whether the pressure exerted by the brace on the patient's back is adequate for the intended therapeutic purpose. Traditionally, the evaluation of brace effectiveness relies on empirical, qualitative assessments carried out by orthopedists during routine follow-up examinations. Hence, it heavily depends on the expertise of the orthopedists involved. In the state of the art, the only objective methods used to confirm orthopedists' opinions are based on the evaluation of how scoliosis progresses over time, often exposing people to ionizing radiation. To address these limitations, the method proposed in this work aims to provide a real-time, objective assessment of the effectiveness of scoliosis braces in a non-harmful way. This is achieved by exploiting the thermoelastic effect and correlating temperature changes on the patient's back with the mechanical pressure exerted by the braces. A system based on this method is implemented and then validated through an experimental study on 21 patients conducted at an accredited orthopedic center. The experimental results demonstrate a classification accuracy slightly below 70% in discriminating between adequate and inadequate pressure, which is an encouraging result for further advancement in view of the clinical use of such systems in orthopedic centers.

Refined Dual-Phase-Lag Theory for the 1D Behavior of Skin Tissue under Ramp-Type Heating

In this article, a mathematical analysis of thermoelastic skin tissue is presented based on a refined dual-phase-lag (DPL) thermal conduction theory that considers accounting for the effect of multiple time derivatives. The thin skin tissue is regarded as having mechanically clamped surfaces that are one-dimensional. Additionally, the skin tissue undergoes ramp-type heating on its outer surface, whereas its inner surface keeps the assessed temperature from vanishing. Some of the previous generalized thermoelasticity theories were obtained from the proposed model. The distributions of temperature, displacement, dilatation, and stress are attained by applying the Laplace transform and its numerical reversal approaches. The outcomes are explicitly illustrated to examine the significant influences on the distributions of the field variables. The refined DPL bioheat conduction model in this study predicts temperature, and the findings revealed that the model is located among the existing generalized thermoelastic theories. These findings offer a more thorough understanding of how skin tissue behaves when exposed to a particular boundary condition temperature distribution.

Development of a numerical multi-layer model of skin subjected to pulsed laser irradiation to optimise thermal stimulation in photorejuvenation procedure

BACKGROUND AND OBJECTIVE

This paper presents the development of a 3D physics-based numerical model of skin capable of representing the laser-skin photo-thermal interactions occurring in skin photorejuvenation treatment procedures. The aim of this model was to provide a rational and quantitative basis to control and predict temperature distribution within the layered structure of skin. Ultimately, this mathematical and numerical modelling platform will guide the design of an automatic robotic controller to precisely regulate skin temperature at desired depths and for specific durations.

METHODS

The Pennes bioheat equation was used to account for heat transfer in a 3D multi-layer model of skin. The effects of blood perfusion, skin pigmentation and various convection conditions are also incorporated in the proposed model. The photo-thermal effect due to pulsed laser light on skin is computed using light diffusion theory. The physics-based constitutive model was numerically implemented using a combination of finite volume and finite difference techniques. Direct sensitivity routines were also implemented to assess the influence of constitutive parameters on temperature. A stability analysis of the numerical model was conducted.

RESULTS

Finally, the numerical model was exploited to assess its ability to predict temperature distribution and thermal damage via a multi-parametric study which accounted for a wide array of biophysical parameters such as light coefficients of absorption for individual skin layers and melanin levels (correlated with ethnicity). It was shown how critical is the link between melanin content, laser light characteristics and potential thermal damage to skin.

CONCLUSIONS

The developed photo-thermal model of skin-laser interactions paves the way for the design of an automated simulation-driven photorejuvenation robot, thus alleviating the need for inconsistent and error-prone human operators.

Biaxial mechanics of thermally denaturing skin - Part 1: Experiments

The mechanics of collagenous soft tissues, such as skin, are sensitive to heat. Thus, quantifying and modeling thermo-mechanical coupling of skin is critical to our understanding of skin's physiology, pathophysiology, and its treatment. However, key gaps persist in our knowledge about skin's coupled thermo-mechanics. Among them, we haven't quantified the role of skin's microstructural organization in its response to superphysiological loading. To fill this gap, we conducted a comprehensive set of experiments in which we combined biaxial mechanical testing with histology and two-photon imaging under liquid heat treatment at temperatures ranging from 37^∘C to 95^∘C lasting between 2 seconds and 5 minutes. Among other observations, we found that unconstrained skin, when exposed to high temperatures, shrinks anisotropically with the principal direction of shrinkage being aligned with collagen's principal orientation. Additionally, we found that when skin is isometrically constrained, it produces significant forces during denaturation that are also anisotropic. Finally, we found that denaturation significantly alters the mechanical behavior of skin. For short exposure times, this alteration is reflected in a reduction of stiffness at high strains. At long exposure times, the tissue softened to a point where it became untestable. We supplemented our findings with confirmation of collagen denaturation in skin via loss of birefringence and second harmonic generation. Finally, we captured all time-, temperature-, and direction-dependent experimental findings in a hypothetical model. Thus, this work fills a fundamental gap in our current understanding of skin thermo-mechanics and will support future developments in thermal injury prevention, thermal injury management, and thermal therapeutics of skin. STATEMENT OF SIGNIFICANCE: Our work experimentally explores how skin reacts to being heated. That is, it measures how much skin shrinks, what forces it produces, and how its mechanical properties change; all as a function of temperature, but also of direction and time. Additionally, our work connects these measurements to changes in skin's microscopic make-up. This knowledge is important to our understanding of skin's function and dysfunction, especially during burn injuries or heat-dependent treatments.

Biaxial mechanics of thermally denaturing skin - Part 2: Modeling

Understanding the response of skin to superphysiological temperatures is critical to the diagnosis and prognosis of thermal injuries, and to the development of temperature-based medical therapeutics. Unfortunately, this understanding has been hindered by our incomplete knowledge about the nonlinear coupling between skin temperature and its mechanics. In Part I of this study we experimentally demonstrated a complex interdependence of time, temperature, direction, and load in skin's response to superphysiological temperatures. In Part II of our study, we test two different models of skin's thermo-mechanics to explain our observations. In both models we assume that skin's response to superphysiological temperatures is governed by the denaturation of its highly collageneous microstructure. Thus, we capture skin's native mechanics via a microstructurally-motivated strain energy function which includes probability distributions for collagen fiber orientation and waviness. In the first model, we capture skin's response to superphysiological temperatures as a transition between two states that link the kinetics of collagen fiber denaturation to fiber coiling and to the transformation of each fiber's constitutive behavior from purely elastic to viscoelastic. In the second model, we capture skin's response to superphysiological temperatures instead via three states in which a sequence of two reactions link the kinetics of collagen fiber denaturation to fiber coiling, followed by a state of fiber damage. Given the success of both models in qualitatively and quantitatively capturing our observations, we expect that our work will provide guidance for future experiments that could probe each model's assumptions toward a better understanding of skin's coupled thermo-mechanics and that our work will be used to guide the engineering design of heat treatment therapies. STATEMENT OF SIGNIFICANCE: Quantifying and modeling skin thermo-mechanics is critical to our understanding of skin physiology, pathophysiology, as well as heat-based treatments. This work addresses a lack of theoretical and computational models of the coupled thermo-mechanics of skin. Our model accounts for skin microstructure through modeling the probability of fiber orientation and fiber stress-free states. Denaturing induces changes in the stress-free configuration of collagen, as well as changes in fiber stiffness and viscoelastic properties. We propose two competing models that fit all of our experimental observations. These models will enable future developments of thermal-therapeutics, prevention and management of skin thermal injuries, and set a foundation for improved mechanistic models of skin thermo-mechanics.

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.

Multifactorial Effects of Gelling Conditions on Mechanical Properties of Skin-Like Gelatin Membranes Intended for In Vitro Experimentation and Artificial Skin Models

The development of new cosmetic products, skin contact medical devices, skin medicaments, wound care devices, tattooing and piercing has experienced an impressive growth in recent years. In parallel, new restrictions to in vivo experimentation in animals and humans have been widely implemented by regulatory authorities. New knowledge about alternative materials for in vitro skin-related experimentation is required to overcome these severe limitations. This paper presents a set of three 4-D surface response equations describing the mechanical properties of skin-like gelatin membranes intended for use as an alternative biomaterial for in vitro skin-related experimentation. The membranes were obtained by a sol-gel method. The novelty of this contribution is the establishment of the cross-dependency effects of key synthesis conditions on the final mechanical properties of gelatin membranes. The results of this work are useful to produce gelatin membranes with tailored mechanical properties mimicking different types of human skins. In particular, membranes with Young’s modulus of 1 MPa and maximum tensile strength of 0.85 MPa were obtained.

A Method to Determine Human Skin Heat Capacity Using a Non-Invasive Calorimetric Sensor

A calorimetric sensor has been designed to measure the heat flow dissipated by a 2 x 2 cm² skin surface. In this work, a non-invasive method is proposed to determine the heat capacity and thermal conductance of the area of skin where the measurement is made. The method consists of programming a linear variation of the temperature of the sensor thermostat during its application to the skin. The sensor is modelled as a two-inputs and two-outputs system. The inputs are 1) the power dissipated by the skin and transmitted by conduction to the sensor, and 2) the power dissipated in the sensor thermostat to maintain the programmed temperature. The outputs are 1) the calorimetric signal and 2) the thermostat temperature. The proposed method consists of a sensor modelling that allows the heat capacity of the element where dissipation takes place (the skin) to be identified, and the transfer functions (TF) that link the inputs and outputs are constructed from its value. These TFs allow the determination of the heat flow dissipated by the surface of the human body as a function of the temperature of the sensor thermostat. Furthermore, as this variation in heat flow is linear, we define and determine an equivalent thermal resistance of the skin in the measured area. The method is validated with a simulation and with experimental measurements on the surface of the human body.

Modeling of One-Dimensional Thermoelastic Dual-Phase-Lag Skin Tissue Subjected to Different Types of Thermal Loading

This work introduces a mathematical model of thermoelastic skin tissue in the context of the dual-phase-lag heat conduction law. One-dimensional skin tissue has been considered with a small thickness and its outer surface traction free. The bounding plane of the skin tissue is subjected to three different types of thermal loading; thermal shock, ramp type heating, and harmonic heating. The inner surface has no temperature increment and traction free. Laplace transform techniques have been used, and its inversions have been calculated by using the Tzuo method. The numerical results have been represented in figures. The thermal shock time parameter, the ramp-type heat parameter, and the angular thermal parameter have significant effects on the temperature increment, the strain, the displacement, and the stress distributions, and they play vital roles in the speed propagation of the thermomechanical waves through the skin tissue.

Vibration analysis of healthy skin: toward a noninvasive skin diagnosis methodology

Several noninvasive imaging techniques have been developed to monitor the health of skin and enhance the diagnosis of skin diseases. Among them, skin elastography is a popular technique used to measure the elasticity of the skin. A change in the elasticity of the skin can influence its natural frequencies and mode shapes. We propose a technique to use the resonant frequencies and mode shapes of the skin to monitor its health. Our study demonstrates how the resonant frequencies and mode shapes of skin can be obtained using numerical and experimental analysis. In our study, natural frequencies and mode shapes are obtained via two methods: (1) finite element analysis: an eigensolution is performed on a finite element model of normal skin, including stratum corneum, epidermis, dermis, and subcutaneous layers and (2) digital image correlation (DIC): several in-vivo measurements have been performed using DIC. The experimental results show a correlation between the DIC and FE results suggesting a noninvasive method to obtain vibration properties of the skin. This method can be further examined to be eventually used as a method to differentiate healthy skin from diseased skin. Prevention, early diagnosis, and treatment are critical in helping to reduce the incidence, morbidity, and mortality associated with skin cancer; thus, making the current study significant and important in the field of skin biomechanics.

HEATING ANALYSIS OF SOFT TISSUE AT FINITE DEFORMATION DURING THERMAL ABLATION

Heating analysis of soft tissue at finite deformation is of importance during treatment planning process for thermal ablation. This paper presents a method by combining non-Fourier bio-heat transfer and nonlinear biomaterial model to simulate thermal and mechanical responses of soft tissues under combined thermal and mechanical loads. At the same time, anisotropic feature of biological tissue is also concerned by including the stored energy of collagen fiber bundles into the traditional neo-Hookean free energy function. Simulation results demonstrate that in spite of relatively small thermal-induced displacement, the resultant thermal strain and stress contribution is nonnegligible and can be used as theoretical basis to measure tissue pain during thermal ablation process.

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.