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Nagle M, Conroy Broderick H, Vedel C, Destrade M, Fop M, Ní Annaidh A. A Gaussian process approach for rapid evaluation of skin tension. Acta Biomater 2024; 182:54-66. [PMID: 38750916 DOI: 10.1016/j.actbio.2024.05.025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Revised: 04/17/2024] [Accepted: 05/10/2024] [Indexed: 05/25/2024]
Abstract
Skin tension plays a pivotal role in clinical settings, it affects scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension or its natural pre-stretch. This study aims to utilise modern machine learning (ML) methods to develop a model that uses non-invasive measurements of surface wave speed to predict clinically useful skin properties such as stress and natural pre-stretch. A large dataset consisting of simulated wave propagation experiments was created using a simplified two-dimensional finite element (FE) model. Using this dataset, a sensitivity analysis was performed, highlighting the effect of the material parameters and material model on the Rayleigh and supersonic shear wave speeds. Then, a Gaussian process regression model was trained to solve the ill-posed inverse problem of predicting stress and pre-stretch of skin using measurements of surface wave speed. This model had good predictive performance (R2 = 0.9570) and it was possible to interpolate simplified parametric equations to calculate the stress and pre-stretch. To demonstrate that wave speed measurements could be obtained cheaply and easily, a simple experiment was devised to obtain wave speed measurements from synthetic skin at different values of pre-stretch. These experimental wave speeds agree well with the FE simulations, and a model trained solely on the FE data provided accurate predictions of synthetic skin stiffness. Both the simulated and experimental results provide further evidence that elastic wave measurements coupled with ML models are a viable non-invasive method to determine in vivo skin tension. STATEMENT OF SIGNIFICANCE: To prevent unfavourable patient outcomes from reconstructive surgery, it is necessary to determine relevant subject-specific skin properties. For example, during a skin graft, it is necessary to estimate the pre-stretch of the skin to account for shrinkage upon excision. Existing methods are invasive or rely on the experience of the clinician. Our work aims to present an innovative framework to non-invasively determine in vivo material properties using the speed of a surface wave travelling through the skin. Our findings have implications for the planning of surgical procedures and provides further motivation for the use of elastic wave measurements to determine in vivo material properties.
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Affiliation(s)
- Matt Nagle
- SFI Centre for Research Training in Foundations of Data Science, University College Dublin, Belfield, Dublin 4, Ireland; School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland.
| | - Hannah Conroy Broderick
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland
| | - Christelle Vedel
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland; EPF School of Engineering, Av. du Président Wilson, Cachan, France
| | - Michel Destrade
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland; School of Mathematical and Statistical Sciences, University of Galway, University Rd, Galway, Ireland
| | - Michael Fop
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.
| | - Aisling Ní Annaidh
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland; Charles Institute of Dermatology, University College Dublin, Belfield, Dublin 4, Ireland.
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Barsimantov Mandel J, Solorio L, Tepole AB. Geometry of adipocyte packing in subcutaneous tissue contributes to nonlinear tissue properties captured through a Gaussian process surrogate model. SOFT MATTER 2024; 20:4197-4207. [PMID: 38477130 DOI: 10.1039/d3sm01661g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/14/2024]
Abstract
Subcutaneous tissue mechanical response is governed by the geometry and mechanical properties at the microscale and drives physiological and clinical processes such as drug delivery. Even though adipocyte packing is known to change with age, disease, and from one individual to another, the link between the geometry of the packing and the overall mechanical response of adipose tissue remains poorly understood. Here we create 1200 periodic representative volume elements (RVEs) that sample the possible space of Laguerre packings describing adipose tissue. RVE mechanics are modeled under tri-axial loading. Equilibrium configuration of RVEs is solved by minimizing an energetic potential that includes volume change contributions from adipocyte expansion, and area change contributions from collagen foam stretching. The resulting mechanical response across all RVE samples is interpolated with the aid of a Gaussian process (GP), revealing how the microscale geometry dictates the overall RVE mechanics. For example, increase in adipocyte size and increase in sphericity lead to adipose tissue softening. We showcase the use of the homogenized model in finite element simulations of drug injection by implementing a Blatz-Ko model, informed by the GP, as a custom material in the popular open-source package FEBio. These simulations show how microscale geometry can lead to vastly different injection dynamics even if the constituent parameters are held constant, highlighting the importance of characterizing individual's adipose tissue structure in the development of personalized therapies.
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Affiliation(s)
| | - Luis Solorio
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, USA
| | - Adrian Buganza Tepole
- School of Mechanical Engineering, Purdue University, 205 Gates Rd, West Lafayette, USA.
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, USA
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Song G, Gosain AK, Buganza Tepole A, Rhee K, Lee T. Exploring uncertainty in hyper-viscoelastic properties of scalp skin through patient-specific finite element models for reconstructive surgery. Comput Methods Biomech Biomed Engin 2024:1-15. [PMID: 38339988 DOI: 10.1080/10255842.2024.2313067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 01/10/2024] [Indexed: 02/12/2024]
Abstract
Understanding skin responses to external forces is crucial for post-cutaneous flap wound healing. However, the in vivo viscoelastic behavior of scalp skin remains poorly understood. Personalized virtual surgery simulations offer a way to study tissue responses in relevant 3D geometries. Yet, anticipating wound risk remains challenging due to limited data on skin viscoelasticity, which hinders our ability to determine the interplay between wound size and stress levels. To bridge this gap, we reexamine three clinical cases involving scalp reconstruction using patient-specific geometric models and employ uncertainty quantification through a Monte Carlo simulation approach to study the effect of skin viscoelasticity on the final stress levels from reconstructive surgery. Utilizing the generalized Maxwell model via the Prony series, we can parameterize and efficiently sample a realistic range of viscoelastic response and thus shed light on the influence of viscoelastic material uncertainty in surgical scenarios. Our analysis identifies regions at risk of wound complications based on reported threshold stress values from the literature and highlights the significance of focusing on long-term responses rather than short-term ones.
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Affiliation(s)
- Gyohyeon Song
- Department of Intelligent Robotics, Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Arun K Gosain
- Surgery (Pediatric Surgery), Plastic Surgery, Lurie Children's Hospital of Chicago, Northwestern Feinberg School of Medicine, Chicago 60611, IL, United States
| | - Adrian Buganza Tepole
- Department of Mechanical Engineering, Purdue University, West Lafayette 47907, IN, United States
| | - Kyehan Rhee
- Department of Mechanical Engineering, Myongji University, Yongin, 17058, Republic of Korea
| | - Taeksang Lee
- Department of Mechanical Engineering, Myongji University, Yongin, 17058, Republic of Korea
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Toaquiza Tubon J, Sree VD, Payne J, Solorio L, Tepole AB. Mechanical damage in porcine dermis: Micro-mechanical model and experimental characterization. J Mech Behav Biomed Mater 2023; 147:106143. [PMID: 37778167 DOI: 10.1016/j.jmbbm.2023.106143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Revised: 05/25/2023] [Accepted: 09/20/2023] [Indexed: 10/03/2023]
Abstract
Skin is subjected to extreme mechanical loading during needle insertion and drug delivery to the subcutaneous space. There is a rich literature on the characterization of porcine skin biomechanics as the preeminent animal model for human skin, but the emphasis has been on the elastic response and specific anatomical locations such as the dorsal and the ventral regions. During drug delivery, however, energy dissipation in the form of damage, softening, and fracture, is expected. Similarly, reports on experimental characterization are complemented by modeling efforts, but with similar gaps in microstructure-driven modeling of dissipative mechanisms. Here we contribute to the bridging of these gaps by testing porcine skin from belly and breast regions, in two different orientation with respect to anatomical axes, and to progressively higher stretches in order to show damage accumulation and stiffness degradation. We complement the mechanical test with imaging of the collagen structure and a micro-mechanics modeling framework. We found that skin from the belly is stiffer with respect to the breast region when comparing the calf stiffness of the J-shaped stress-stretch response observed in most collagenous tissues. No significant direction dependent properties were found in either anatomical location. Both locations showed energy dissipation due to damage, evident though a softening of the stress-stretch response. The microstructure model was able to capture the elastic and damage progression with a small set of parameters, some of which were determined directly from imaging. We anticipate that data and model fits can help in predictive simulations for device design in situations where skin is subject to supra-physiological deformation such as in subcutaneous drug delivery.
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Affiliation(s)
| | - Vivek D Sree
- School of Mechanical Engineering Purdue University, West Lafayette, IN, USA
| | - Jordanna Payne
- Weldon School of Biomedical Engineering Purdue University, West Lafayette, IN, USA
| | - Luis Solorio
- Weldon School of Biomedical Engineering Purdue University, West Lafayette, IN, USA
| | - Adrian Buganza Tepole
- School of Mechanical Engineering Purdue University, West Lafayette, IN, USA; Weldon School of Biomedical Engineering Purdue University, West Lafayette, IN, USA.
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Nagle M, Price S, Trotta A, Destrade M, Fop M, Ní Annaidh A. Analysis of In Vivo Skin Anisotropy Using Elastic Wave Measurements and Bayesian Modelling. Ann Biomed Eng 2023:10.1007/s10439-023-03185-2. [PMID: 37022652 DOI: 10.1007/s10439-023-03185-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 03/13/2023] [Indexed: 04/07/2023]
Abstract
In vivo skin exhibits viscoelastic, hyper-elastic and non-linear characteristics. It is under a constant state of non-equibiaxial tension in its natural configuration and is reinforced with oriented collagen fibers, which gives rise to anisotropic behaviour. Understanding the complex mechanical behaviour of skin has relevance across many sectors including pharmaceuticals, cosmetics and surgery. However, there is a dearth of quality data characterizing the anisotropy of human skin in vivo. The data available in the literature is usually confined to limited population groups and/or limited angular resolution. Here, we used the speed of elastic waves travelling through the skin to obtain measurements from 78 volunteers ranging in age from 3 to 93 years old. Using a Bayesian framework allowed us to analyse the effect that age, gender and level of skin tension have on the skin anisotropy and stiffness. First, we propose a new measurement of anisotropy based on the eccentricity of angular data and conclude that it is a more robust measurement when compared to the classic "anisotropic ratio". Our analysis then concluded that in vivo skin anisotropy increases logarithmically with age, while the skin stiffness increases linearly along the direction of Langer Lines. We also concluded that the gender does not significantly affect the level of skin anisotropy, but it does affect the overall stiffness, with males having stiffer skin on average. Finally, we found that the level of skin tension significantly affects both the anisotropy and stiffness measurements employed here. This indicates that elastic wave measurements may have promising applications in the determination of in vivo skin tension. In contrast to earlier studies, these results represent a comprehensive assessment of the variation of skin anisotropy with age and gender using a sizeable dataset and robust modern statistical analysis. This data has implications for the planning of surgical procedures and questions the adoption of universal cosmetic surgery practices for very young or elderly patients.
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Affiliation(s)
- Matt Nagle
- SFI Centre for Research Training in Foundations of Data Science, University College Dublin, Belfield, Dublin 4, Ireland.
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland.
| | - Susan Price
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland
| | - Antonia Trotta
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland
| | - Michel Destrade
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland
- School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland
| | - Michael Fop
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.
| | - Aisling Ní Annaidh
- School of Mechanical and Materials Engineering, University College Dublin, Belfield, Dublin 4, Ireland
- Charles Institute of Dermatology, University College Dublin, Belfield, Dublin 4, Ireland
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Aggarwal A, Jensen BS, Pant S, Lee CH. Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2023; 404:115812. [PMID: 37235184 PMCID: PMC10208436 DOI: 10.1016/j.cma.2022.115812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantage of a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed framework is verified against an artificial dataset based on the Gasser-Ogden-Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulation-based predictions.
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Affiliation(s)
- Ankush Aggarwal
- Glasgow Computational Engineering Centre, James Watt School of Engineering, University of Glasgow, Glasgow, G12 8LT, Scotland, United Kingdom
| | - Bjørn Sand Jensen
- School of Computing Science, University of Glasgow, Glasgow, G12 8LT, Scotland, United Kingdom
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
| | - Sanjay Pant
- Zienkiewicz Centre for Computational Engineering, Swansea University, Swansea, SA18EP, Wales, United Kingdom
| | - Chung-Hao Lee
- School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, 73019, OK, United States of America
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Song G, An J, Tepole AB, Lee T. Bayesian Inference With Gaussian Process Surrogates to Characterize Anisotropic Mechanical Properties of Skin From Suction Tests. J Biomech Eng 2022; 144:121003. [PMID: 35788269 PMCID: PMC9445318 DOI: 10.1115/1.4054929] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Revised: 06/23/2022] [Indexed: 11/08/2022]
Abstract
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.
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Affiliation(s)
- Gyohyeon Song
- Department of Mechanical Engineering, Myongji University, Yongin 17058, South Korea
| | - Jaehee An
- Department of Mechanical Engineering, Myongji University, Yongin 17058, South Korea
| | - Adrian Buganza Tepole
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907; Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN 47907
| | - Taeksang Lee
- Department of Mechanical Engineering, Myongji University, Yongin 17058, South Korea
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Guo Y, Mofrad MRK, Tepole AB. On modeling the multiscale mechanobiology of soft tissues: Challenges and progress. BIOPHYSICS REVIEWS 2022; 3:031303. [PMID: 38505274 PMCID: PMC10903412 DOI: 10.1063/5.0085025] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 07/12/2022] [Indexed: 03/21/2024]
Abstract
Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.
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Affiliation(s)
- Yifan Guo
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
| | - Mohammad R. K. Mofrad
- Departments of Bioengineering and Mechanical Engineering, University of California Berkeley, Berkeley, California 94720, USA
| | - Adrian Buganza Tepole
- School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907, USA
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Spagnoli A, Alberini R, Raposio E, Terzano M. Simulation and optimization of reconstructive surgery procedures on human skin. J Mech Behav Biomed Mater 2022; 131:105215. [DOI: 10.1016/j.jmbbm.2022.105215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Revised: 03/16/2022] [Accepted: 04/01/2022] [Indexed: 11/25/2022]
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