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Sachs D, Jakob R, Restivo G, Hafner J, Lindenblatt N, Ehret AE, Mazza E. A quadriphasic mechanical model of the human dermis. Biomech Model Mechanobiol 2024; 23:1121-1136. [PMID: 38489079 DOI: 10.1007/s10237-024-01827-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 02/09/2024] [Indexed: 03/17/2024]
Abstract
The present study investigates the multiphasic nature of the mechanical behavior of human dermis. Motivated by experimental observations and by consideration of its composition, a quadriphasic model of the dermis is proposed, distinguishing solid matrix components, interstitial fluid and charged constituents moving within the fluid, i.e., anions and cations. Compression and tensile experiments with and without change of osmolarity of the bath are performed to characterize the chemo-mechanical coupling in the dermis. Model parameters are determined through inverse analysis. The computations predict a dominant role of the permeability in the determination of the temporal evolution of the mechanical response of the tissue. In line with the previous studies on other tissues, the analysis shows that an ideal model based on Donnan's equilibrium overestimates the osmotic pressure in skin for the case of very dilute solutions. The quadriphasic model is applied to predict changes in dermal cell environment and therefore alterations in what is called the "mechanome," associated with skin stretch. The simulations indicate that skin deformation causes a variation in several local variables, including in particular the electric field associated with a deformation-induced non-homogeneous distribution of fixed charges.
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Affiliation(s)
- David Sachs
- Institute for Mechanical Systems, ETH Zürich, Zurich, Switzerland.
| | - Raphael Jakob
- Institute for Mechanical Systems, ETH Zürich, Zurich, Switzerland
| | - Gaetana Restivo
- Department of Dermatology, University Hospital Zürich, Zurich, Switzerland
| | - Jürg Hafner
- Department of Dermatology, University Hospital Zürich, Zurich, Switzerland
| | - Nicole Lindenblatt
- Department of Plastic Surgery and Hand Surgery, University Hospital Zürich, Zurich, Switzerland
| | - Alexander E Ehret
- Institute for Mechanical Systems, ETH Zürich, Zurich, Switzerland
- Swiss Federal Laboratories for Materials Science and Technology, Experimental Continuum Mechanics, Dübendorf, Switzerland
| | - Edoardo Mazza
- Institute for Mechanical Systems, ETH Zürich, Zurich, Switzerland.
- Swiss Federal Laboratories for Materials Science and Technology, Experimental Continuum Mechanics, Dübendorf, Switzerland.
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2
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Jakob R, Britt BR, Giampietro C, Mazza E, Ehret AE. Discrete network models of endothelial cells and their interactions with the substrate. Biomech Model Mechanobiol 2024; 23:941-957. [PMID: 38351427 PMCID: PMC11101350 DOI: 10.1007/s10237-023-01815-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 12/30/2023] [Indexed: 05/18/2024]
Abstract
Endothelial cell monolayers line the inner surfaces of blood and lymphatic vessels. They are continuously exposed to different mechanical loads, which may trigger mechanobiological signals and hence play a role in both physiological and pathological processes. Computer-based mechanical models of cells contribute to a better understanding of the relation between cell-scale loads and cues and the mechanical state of the hosting tissue. However, the confluency of the endothelial monolayer complicates these approaches since the intercellular cross-talk needs to be accounted for in addition to the cytoskeletal mechanics of the individual cells themselves. As a consequence, the computational approach must be able to efficiently model a large number of cells and their interaction. Here, we simulate cytoskeletal mechanics by means of molecular dynamics software, generally suitable to deal with large, locally interacting systems. Methods were developed to generate models of single cells and large monolayers with hundreds of cells. The single-cell model was considered for a comparison with experimental data. To this end, we simulated cell interactions with a continuous, deformable substrate, and computationally replicated multistep traction force microscopy experiments on endothelial cells. The results indicate that cell discrete network models are able to capture relevant features of the mechanical behaviour and are thus well-suited to investigate the mechanics of the large cytoskeletal network of individual cells and cell monolayers.
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Affiliation(s)
- Raphael Jakob
- Institute for Mechanical Systems, ETH Zurich, CH-8092, Zürich, Switzerland
| | - Ben R Britt
- Institute for Mechanical Systems, ETH Zurich, CH-8092, Zürich, Switzerland
- Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600, Dübendorf, Switzerland
| | - Costanza Giampietro
- Institute for Mechanical Systems, ETH Zurich, CH-8092, Zürich, Switzerland
- Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600, Dübendorf, Switzerland
| | - Edoardo Mazza
- Institute for Mechanical Systems, ETH Zurich, CH-8092, Zürich, Switzerland
- Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600, Dübendorf, Switzerland
| | - Alexander E Ehret
- Institute for Mechanical Systems, ETH Zurich, CH-8092, Zürich, Switzerland.
- Empa, Swiss Federal Laboratories for Materials Science and Technology, CH-8600, Dübendorf, Switzerland.
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3
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Fidalgo DS, Jorge RMN, Parente MPL, Louwagie EM, Malanowska E, Myers KM, Oliveira DA. Pregnancy state before the onset of labor: a holistic mechanical perspective. Biomech Model Mechanobiol 2024:10.1007/s10237-024-01853-3. [PMID: 38758337 DOI: 10.1007/s10237-024-01853-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2024] [Accepted: 04/17/2024] [Indexed: 05/18/2024]
Abstract
Successful pregnancy highly depends on the complex interaction between the uterine body, cervix, and fetal membrane. This interaction is synchronized, usually following a specific sequence in normal vaginal deliveries: (1) cervical ripening, (2) uterine contractions, and (3) rupture of fetal membrane. The complex interaction between the cervix, fetal membrane, and uterine contractions before the onset of labor is investigated using a complete third-trimester gravid model of the uterus, cervix, fetal membrane, and abdomen. Through a series of numerical simulations, we investigate the mechanical impact of (i) initial cervical shape, (ii) cervical stiffness, (iii) cervical contractions, and (iv) intrauterine pressure. The findings of this work reveal several key observations: (i) maximum principal stress values in the cervix decrease in more dilated, shorter, and softer cervices; (ii) reduced cervical stiffness produces increased cervical dilation, larger cervical opening, and decreased cervical length; (iii) the initial cervical shape impacts final cervical dimensions; (iv) cervical contractions increase the maximum principal stress values and change the stress distributions; (v) cervical contractions potentiate cervical shortening and dilation; (vi) larger intrauterine pressure (IUP) causes considerably larger stress values and cervical opening, larger dilation, and smaller cervical length; and (vii) the biaxial strength of the fetal membrane is only surpassed in the cases of the (1) shortest and most dilated initial cervical geometry and (2) larger IUP.
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Affiliation(s)
- Daniel S Fidalgo
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465, Porto, Portugal.
- Mechanical Department (DEMec), Faculty of Engineering of University of Porto (FEUP), R. Dr. Roberto Frias, 4200-465, Porto, Portugal.
| | - Renato M Natal Jorge
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465, Porto, Portugal
- Mechanical Department (DEMec), Faculty of Engineering of University of Porto (FEUP), R. Dr. Roberto Frias, 4200-465, Porto, Portugal
| | - Marco P L Parente
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465, Porto, Portugal
- Mechanical Department (DEMec), Faculty of Engineering of University of Porto (FEUP), R. Dr. Roberto Frias, 4200-465, Porto, Portugal
| | - Erin M Louwagie
- Department of Mechanical Engineering, Columbia University, New York, NY, 10027, USA
| | - Ewelina Malanowska
- Department of Gynaecology, Endocrinology and Gynaecologic Oncology, Pomeranian Medical University, Szczecin, Poland
| | - Kristin M Myers
- Department of Mechanical Engineering, Columbia University, New York, NY, 10027, USA
| | - Dulce A Oliveira
- Institute of Science and Innovation in Mechanical and Industrial Engineering (INEGI), R. Dr. Roberto Frias 400, 4200-465, Porto, Portugal
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4
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Mohammadkhah M, Klinge S. Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues. J Mech Behav Biomed Mater 2023; 148:106203. [PMID: 37879165 DOI: 10.1016/j.jmbbm.2023.106203] [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: 06/23/2023] [Revised: 09/25/2023] [Accepted: 10/17/2023] [Indexed: 10/27/2023]
Abstract
Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.
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Affiliation(s)
- Melika Mohammadkhah
- Technische Universität Berlin, Institute of Mechanics, Chair of Structural Mechanics and Analysis, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany.
| | - Sandra Klinge
- Technische Universität Berlin, Institute of Mechanics, Chair of Structural Mechanics and Analysis, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany
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5
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Wahlsten A, Stracuzzi A, Lüchtefeld I, Restivo G, Lindenblatt N, Giampietro C, Ehret AE, Mazza E. Multiscale mechanical analysis of the elastic modulus of skin. Acta Biomater 2023; 170:155-168. [PMID: 37598792 DOI: 10.1016/j.actbio.2023.08.030] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2023] [Revised: 07/27/2023] [Accepted: 08/15/2023] [Indexed: 08/22/2023]
Abstract
The mechanical properties of the skin determine tissue function and regulate dermal cell behavior. Yet measuring these properties remains challenging, as evidenced by the large range of elastic moduli reported in the literature-from below one kPa to hundreds of MPa. Here, we reconcile these disparate results by dedicated experiments at both tissue and cellular length scales and by computational models considering the multiscale and multiphasic tissue structure. At the macroscopic tissue length scale, the collective behavior of the collagen fiber network under tension provides functional tissue stiffness, and its properties determine the corresponding elastic modulus (100-200 kPa). The compliant microscale environment (0.1-10 kPa), probed by atomic force microscopy, arises from the ground matrix without engaging the collagen fiber network. Our analysis indicates that indentation-based elasticity measurements, although probing tissue properties at the cell-relevant length scale, do not assess the deformation mechanisms activated by dermal cells when exerting traction forces on the extracellular matrix. Using dermal-equivalent collagen hydrogels, we demonstrate that indentation measurements of tissue stiffness do not correlate with the behavior of embedded dermal fibroblasts. These results provide a deeper understanding of tissue mechanics across length scales with important implications for skin mechanobiology and tissue engineering. STATEMENT OF SIGNIFICANCE: Measuring the mechanical properties of the skin is essential for understanding dermal cell mechanobiology and designing tissue-engineered skin substitutes. However, previous results reported for the elastic modulus of skin vary by six orders of magnitude. We show that two distinct deformation mechanisms, related to the tension-compression nonlinearity of the collagen fiber network, can explain the large variations in elastic moduli. Furthermore, we show that microscale indentation, which is frequently used to assess the stiffness perceived by cells, fails to engage the fiber network, and therefore cannot predict the behavior of dermal fibroblasts in stiffness-tunable fibrous hydrogels. This has important implications for how to measure and interpret the mechanical properties of soft tissues across length scales.
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Affiliation(s)
- Adam Wahlsten
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, Zurich 8092, Switzerland
| | - Alberto Stracuzzi
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, Zurich 8092, Switzerland; Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, Dübendorf 8600, Switzerland
| | - Ines Lüchtefeld
- Institute for Biomedical Engineering, Department of Information Technology and Electrical Engineering, ETH Zurich, Gloriastrasse 35, Zurich 8092, Switzerland
| | - Gaetana Restivo
- Department of Dermatology, University Hospital Zurich, Zurich 8091, Switzerland
| | - Nicole Lindenblatt
- Department of Plastic and Hand Surgery, University Hospital Zurich, Zurich 8091, Switzerland
| | - Costanza Giampietro
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, Zurich 8092, Switzerland; Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, Dübendorf 8600, Switzerland
| | - Alexander E Ehret
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, Zurich 8092, Switzerland; Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, Dübendorf 8600, Switzerland
| | - Edoardo Mazza
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, Zurich 8092, Switzerland; Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, Dübendorf 8600, Switzerland.
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6
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Merson J, Parvez N, Picu RC. Probing soft fibrous materials by indentation. Acta Biomater 2023; 163:25-34. [PMID: 35381401 PMCID: PMC9526757 DOI: 10.1016/j.actbio.2022.03.053] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Revised: 03/22/2022] [Accepted: 03/29/2022] [Indexed: 11/27/2022]
Abstract
Indentation is often used to measure the stiffness of soft materials whose main structural component is a network of filaments, such as the cellular cytoskeleton, connective tissue, gels, and the extracellular matrix. For elastic materials, the typical procedure requires fitting the experimental force-displacement curve with the Hertz model, which predicts that f=kδ1.5 and k is proportional to the reduced modulus of the indented material, E/(1-ν2). Here we show using explicit models of fiber networks that the Hertz model applies to indentation in network materials provided the indenter radius is larger than approximately 12lc, where lc is the mean segment length of the network. Using smaller indenters leads to a relation between force and indentation displacement of the form f=kδq, where q is observed to increase with decreasing indenter radius. Using the Hertz model to interpret results of indentations in network materials using small indenters leads to an inferred modulus smaller than the real modulus of the material. The origin of this departure from the classical Hertz model is investigated. A compacted, stiff network region develops under the indenter, effectively increasing the indenter size and modifying its shape. This modification is marginal when large indenters are used. However, when the indenter radius is small, the effect of the compacted layer is pronounced as it changes the indenter profile from spherical towards conical. This entails an increase of exponent q above the value of 1.5 corresponding to spherical indenters. STATEMENT OF SIGNIFICANCE: The article presents a study of indentation in network biomaterials and demonstrates a size effect which precludes the use of the Hertz model to infer the elastic constants of the material. The size effect occurs once the indenter radius is smaller than approximately 12 times the mean segment length of the network. This result provides guidelines for the selection of indentation conditions that guarantee the applicability of the Hertz model. At the same time, the finding may be used to infer the mean segment length of the network based on indentations with indenters of various sizes. Hence, the method can be used to evaluate this structural parameter which is not easily accessible in experiments.
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Affiliation(s)
- J Merson
- Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States
| | - N Parvez
- Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States
| | - R C Picu
- Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, United States.
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7
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Jimenez JM, Tuttle T, Guo Y, Miles D, Buganza-Tepole A, Calve S. Multiscale mechanical characterization and computational modeling of fibrin gels. Acta Biomater 2023; 162:292-303. [PMID: 36965611 PMCID: PMC10313219 DOI: 10.1016/j.actbio.2023.03.026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 02/28/2023] [Accepted: 03/17/2023] [Indexed: 03/27/2023]
Abstract
Fibrin is a naturally occurring protein network that forms a temporary structure to enable remodeling during wound healing. It is also a common tissue engineering scaffold because the structural properties can be controlled. However, to fully characterize the wound healing process and improve the design of regenerative scaffolds, understanding fibrin mechanics at multiple scales is necessary. Here, we present a strategy to quantify both the macroscale (1-10 mm) stress-strain response and the deformation of the mesoscale (10-1000 µm) network structure during unidirectional tensile tests. The experimental data were then used to inform a computational model to accurately capture the mechanical response of fibrin gels. Simultaneous mechanical testing and confocal microscopy imaging of fluorophore-conjugated fibrin gels revealed up to an 88% decrease in volume coupled with increase in volume fraction in deformed gels, and non-affine fiber alignment in the direction of deformation. Combination of the computational model with finite element analysis enabled us to predict the strain fields that were observed experimentally within heterogenous fibrin gels with spatial variations in material properties. These strategies can be expanded to characterize and predict the macroscale mechanics and mesoscale network organization of other heterogeneous biological tissues and matrices. STATEMENT OF SIGNIFICANCE: Fibrin is a naturally-occurring scaffold that supports cellular growth and assembly of de novo tissue and has tunable material properties. Characterization of meso- and macro-scale mechanics of fibrin gel networks can advance understanding of the wound healing process and impact future tissue engineering approaches. Using structural and mechanical characteristics of fibrin gels, a theoretical and computational model that can predict multiscale fibrin network mechanics was developed. These data and model can be used to design gels with tunable properties.
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Affiliation(s)
- Julian M Jimenez
- Weldon School of Biomedical Engineering, Purdue University, 206 South Martin Jischke Drive, West Lafayette, IN 47907, United States
| | - Tyler Tuttle
- Paul M. Rady Department of Mechanical Engineering, University of Colorado Boulder, 1111 Engineering Dr, Boulder, CO 80309, United States
| | - Yifan Guo
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, United States
| | - Dalton Miles
- Chemical and Biological Engineering, University of Colorado Boulder, 3415 Colorado Ave, Boulder, CO 80303, United States
| | - Adrian Buganza-Tepole
- Weldon School of Biomedical Engineering, Purdue University, 206 South Martin Jischke Drive, West Lafayette, IN 47907, United States; School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, United States.
| | - Sarah Calve
- Weldon School of Biomedical Engineering, Purdue University, 206 South Martin Jischke Drive, West Lafayette, IN 47907, United States; Paul M. Rady Department of Mechanical Engineering, University of Colorado Boulder, 1111 Engineering Dr, Boulder, CO 80309, United States.
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8
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Yu X, Zhang Y. A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density. J Mech Behav Biomed Mater 2022; 134:105396. [PMID: 35963022 PMCID: PMC10368519 DOI: 10.1016/j.jmbbm.2022.105396] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Revised: 07/13/2022] [Accepted: 07/19/2022] [Indexed: 10/16/2022]
Abstract
Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.
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9
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Merson J, Picu RC. Random Fiber Network Loaded by a Point Force. JOURNAL OF APPLIED MECHANICS 2022; 89:044501. [PMID: 35783110 PMCID: PMC9247584 DOI: 10.1115/1.4053329] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
This article presents the displacement field produced by a point force acting on an athermal random fiber network (the Green function for the network). The problem is defined within the limits of linear elasticity, and the field is obtained numerically for nonaffine networks characterized by various parameter sets. The classical Green function solution applies at distances from the point force larger than a threshold which is independent of the network parameters in the range studied. At smaller distances, the nonlocal nature of fiber interactions modifies the solution.
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Affiliation(s)
- J Merson
- Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180
| | - R C Picu
- Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180
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10
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Stracuzzi A, Britt BR, Mazza E, Ehret AE. Risky interpretations across the length scales: continuum vs. discrete models for soft tissue mechanobiology. Biomech Model Mechanobiol 2022; 21:433-454. [PMID: 34985590 PMCID: PMC8940853 DOI: 10.1007/s10237-021-01543-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 11/28/2021] [Indexed: 11/29/2022]
Abstract
Modelling and simulation in mechanobiology play an increasingly important role to unravel the complex mechanisms that allow resident cells to sense and respond to mechanical cues. Many of the in vivo mechanical loads occur on the tissue length scale, thus raising the essential question how the resulting macroscopic strains and stresses are transferred across the scales down to the cellular and subcellular levels. Since cells anchor to the collagen fibres within the extracellular matrix, the reliable representation of fibre deformation is a prerequisite for models that aim at linking tissue biomechanics and cell mechanobiology. In this paper, we consider the two-scale mechanical response of an affine structural model as an example of a continuum mechanical approach and compare it with the results of a discrete fibre network model. In particular, we shed light on the crucially different mechanical properties of the 'fibres' in these two approaches. While assessing the capability of the affine structural approach to capture the fibre kinematics in real tissues is beyond the scope of our study, our results clearly show that neither the macroscopic tissue response nor the microscopic fibre orientation statistics can clarify the question of affinity.
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Affiliation(s)
- Alberto Stracuzzi
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600, Dübendorf, Switzerland.
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zürich, Switzerland.
| | - Ben R Britt
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600, Dübendorf, Switzerland
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zürich, Switzerland
| | - Edoardo Mazza
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600, Dübendorf, Switzerland
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zürich, Switzerland
| | - Alexander E Ehret
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600, Dübendorf, Switzerland.
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zürich, Switzerland.
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11
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Witt NJ, Woessner AE, Quinn KP, Sander EA. Multiscale Computational Model Predicts Mouse Skin Kinematics Under Tensile Loading. J Biomech Eng 2022; 144:041008. [PMID: 34729595 PMCID: PMC8719047 DOI: 10.1115/1.4052887] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Revised: 10/11/2021] [Indexed: 11/08/2022]
Abstract
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.
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Affiliation(s)
- Nathan J. Witt
- Roy J. Carver Department of Biomedical Engineering, College of Engineering, University of Iowa, Iowa City, IA 52242
| | - Alan E. Woessner
- Department of Biomedical Engineering, University of Arkansas, Fayetteville, AR 72701
| | - Kyle P. Quinn
- Department of Biomedical Engineering, University of Arkansas, Fayetteville, AR 72701
| | - Edward A. Sander
- Roy J. Carver Department of Biomedical Engineering, College of Engineering, University of Iowa, 5629 Seamans Center, Iowa City, IA 52242; Department of Orthopedics and Rehabilitation, Carver College of Medicine, University of Iowa, Iowa City, IA 52242
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12
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Eichinger JF, Grill MJ, Kermani ID, Aydin RC, Wall WA, Humphrey JD, Cyron CJ. A computational framework for modeling cell-matrix interactions in soft biological tissues. Biomech Model Mechanobiol 2021; 20:1851-1870. [PMID: 34173132 PMCID: PMC8450219 DOI: 10.1007/s10237-021-01480-2] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 06/08/2021] [Indexed: 01/10/2023]
Abstract
Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.
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Affiliation(s)
- Jonas F Eichinger
- Institute for Computational Mechanics, Technical University of Munich, Garching, 85748, Germany.,Institute for Continuum and Materials Mechanics, Hamburg University of Technology, Hamburg, 21073, Germany
| | - Maximilian J Grill
- Institute for Computational Mechanics, Technical University of Munich, Garching, 85748, Germany
| | - Iman Davoodi Kermani
- Institute for Computational Mechanics, Technical University of Munich, Garching, 85748, Germany
| | - Roland C Aydin
- Institute of Material Systems Modeling, Helmholtz-Zentrum Hereon, Geesthacht, 21502, Germany
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, Garching, 85748, Germany
| | - Jay D Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, CT, 06520, USA
| | - Christian J Cyron
- Institute for Continuum and Materials Mechanics, Hamburg University of Technology, Hamburg, 21073, Germany. .,Institute of Material Systems Modeling, Helmholtz-Zentrum Hereon, Geesthacht, 21502, Germany.
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13
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Eichinger JF, Haeusel LJ, Paukner D, Aydin RC, Humphrey JD, Cyron CJ. Mechanical homeostasis in tissue equivalents: a review. Biomech Model Mechanobiol 2021; 20:833-850. [PMID: 33683513 PMCID: PMC8154823 DOI: 10.1007/s10237-021-01433-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 02/04/2021] [Indexed: 12/20/2022]
Abstract
There is substantial evidence that growth and remodeling of load bearing soft biological tissues is to a large extent controlled by mechanical factors. Mechanical homeostasis, which describes the natural tendency of such tissues to establish, maintain, or restore a preferred mechanical state, is thought to be one mechanism by which such control is achieved across multiple scales. Yet, many questions remain regarding what promotes or prevents homeostasis. Tissue equivalents, such as collagen gels seeded with living cells, have become an important tool to address these open questions under well-defined, though limited, conditions. This article briefly reviews the current state of research in this area. It summarizes, categorizes, and compares experimental observations from the literature that focus on the development of tension in tissue equivalents. It focuses primarily on uniaxial and biaxial experimental studies, which are well-suited for quantifying interactions between mechanics and biology. The article concludes with a brief discussion of key questions for future research in this field.
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Affiliation(s)
- Jonas F Eichinger
- Institute for Computational Mechanics, Technical University of Munich, 85748, Munich, Germany
- Institute of Continuum and Materials Mechanics, Hamburg University of Technology, 21073, Hamburg, Germany
| | - Lea J Haeusel
- Institute for Computational Mechanics, Technical University of Munich, 85748, Munich, Germany
| | - Daniel Paukner
- Institute of Continuum and Materials Mechanics, Hamburg University of Technology, 21073, Hamburg, Germany
- Institute of Material Systems Modeling, Helmholtz-Zentrum Geesthacht, 21502, Geesthacht, Germany
| | - Roland C Aydin
- Institute of Material Systems Modeling, Helmholtz-Zentrum Geesthacht, 21502, Geesthacht, Germany
| | - Jay D Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, CT, 06520, USA
| | - Christian J Cyron
- Institute of Continuum and Materials Mechanics, Hamburg University of Technology, 21073, Hamburg, Germany.
- Institute of Material Systems Modeling, Helmholtz-Zentrum Geesthacht, 21502, Geesthacht, Germany.
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14
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Morch A, Astruc L, Mayeur O, Witz JF, Lecomte-Grosbras P, Brieu M. Is there any objective and independent characterization and modeling of soft biological tissues? J Mech Behav Biomed Mater 2020; 110:103915. [PMID: 32771881 DOI: 10.1016/j.jmbbm.2020.103915] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Revised: 04/28/2020] [Accepted: 06/04/2020] [Indexed: 10/23/2022]
Abstract
The characterization of soft tissue raises several difficulties. Indeed, soft biological tissues usually shrink when dissected from their in vivo location. This shrinkage is characteristic of the release of residual stresses, since soft tissues are indeed often pre-stressed in their physiological configuration. During experimental loading, large extension at very low level of force are expected and assumed to be related to the progressive recruitment and stretching of fibers. However, the first phase of the mechanical test is also aiming at recovering the pre-stressed in vivo behavior. As a consequence, the initial phase, corresponding to the recovering of prestress and/or recruitment of fiberes, is questionable and frequently removed. One of the preferred methods to erase it consists in applying a preforce or prestress to the sample: this allows to easily get rid of the sample retensioning range. However this operation can impact the interpretation of the identified mechanical parameters. This study presents an evaluation of the impact of the data processing on the mechanical properties of a numerically defined material. For this purpose, a finite element simulation was performed to replicate a uniaxial tensile test on a biological soft tissue sample. The influence of different pre-stretches on the mechanical parameters of a second order Yeoh model was investigated. The Yeoh mechanical parameters, or any other strain energy density, depend strongly on any pre- and post-processing choices: they adapt to compensate the error made when choosing an arbitrary level of prestretch or prestress. This observation spreads to any modeling approach used in soft tissues. Mechanical parameters are indeed naturally bound to the choice of the pre-stretch (or pre-stress) through the elongation and the constitutive law. Regardless of the model, it would therefore be pointless to compare mechanical parameters if the conditions for the processing of experimental raw data are not fully documented.
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Affiliation(s)
- A Morch
- Univ. Lille, CNRS, Centrale Lille, UMR 9013 LaMcube Laboratoire de mécanique multiphysique et multiéchelle, F-59000, Lille, France
| | - L Astruc
- Univ. Lille, CNRS, Centrale Lille, UMR 9013 LaMcube Laboratoire de mécanique multiphysique et multiéchelle, F-59000, Lille, France
| | - O Mayeur
- Univ. Lille, CNRS, Centrale Lille, UMR 9013 LaMcube Laboratoire de mécanique multiphysique et multiéchelle, F-59000, Lille, France
| | - J-F Witz
- Univ. Lille, CNRS, Centrale Lille, UMR 9013 LaMcube Laboratoire de mécanique multiphysique et multiéchelle, F-59000, Lille, France
| | - P Lecomte-Grosbras
- Univ. Lille, CNRS, Centrale Lille, UMR 9013 LaMcube Laboratoire de mécanique multiphysique et multiéchelle, F-59000, Lille, France.
| | - M Brieu
- Univ. Lille, CNRS, Centrale Lille, UMR 9013 LaMcube Laboratoire de mécanique multiphysique et multiéchelle, F-59000, Lille, France; California State University, Los Angeles College Engineering, Computer Science and Technology, Dept. Mechanical Engineering, USA
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15
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Domaschke S, Morel A, Kaufmann R, Hofmann J, Rossi RM, Mazza E, Fortunato G, Ehret AE. Predicting the macroscopic response of electrospun membranes based on microstructure and single fibre properties. J Mech Behav Biomed Mater 2020; 104:103634. [DOI: 10.1016/j.jmbbm.2020.103634] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Revised: 12/31/2019] [Accepted: 01/08/2020] [Indexed: 01/29/2023]
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16
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Pissarenko A, Ruestes CJ, Meyers MA. Constitutive description of skin dermis: Through analytical continuum and coarse-grained approaches for multi-scale understanding. Acta Biomater 2020; 106:208-224. [PMID: 32014584 DOI: 10.1016/j.actbio.2020.01.026] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Revised: 01/01/2020] [Accepted: 01/20/2020] [Indexed: 11/30/2022]
Abstract
Although there are many successful descriptions of the mechanical response of dermis at different levels of complexity and incorporating varying degrees of the physical phenomena involved in deformation, observations indicate that the unraveling of fibers involves a complex three-dimensional process in which they interact in ways that resemble a braided pattern. Here we develop two complementary treatments to gain a better understanding of the mechanical response of dermis: a) an analytical treatment incorporating fibril stiffness, interfibrillar frictional sliding, and the effect of lateral fibers on the extension of a primary fiber; b) a coarse-grained molecular dynamics model comprised of an array of parallel curved fibrils simulating a fiber. Interfibrillar frictional sliding and stiffness are also captured. Both analytical and molecular dynamics models operate at a scale compatible with the wavelength of collagen fibers (~10 µm). The constitutive description presented here incorporates important physical processes taking place during deformation of dermis and thus represents an advance in our understanding of these phenomena. STATEMENT OF SIGNIFICANCE: Microstructural observations of the dermis of skin during tensile deformation indicate that the unraveling of fibers involves a complex three-dimensional process which replicates the effects of braiding. Two complementary constitutive modeling treatments were developed to gain a better understanding of the mechanical response of dermis: an analytical treatment incorporating fibril stiffness, interfibrillar sliding, and the effect of transverse fibers; and a coarse-grained molecular dynamics model describing the fibril bundling effect. An important novel aspect of the current contribution is the recognition that tridimensional collagen fiber arrangements play an important role in the mechanical response. The constitutive description presented here incorporates physical processes taking place during deformation of the dermis and thus represents an advance in our understanding of these phenomena.
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Affiliation(s)
| | - Carlos J Ruestes
- Instituto Interdisciplinario de Ciencias Básicas, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Cuyo, CONICET, Mendoza, Argentina
| | - Marc A Meyers
- University of California, San Diego, CA, United States.
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17
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On the homogeneity and isotropy of planar long fibre network computational models. SN APPLIED SCIENCES 2020. [DOI: 10.1007/s42452-020-2524-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022] Open
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18
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Bircher K, Merluzzi R, Wahlsten A, Spiess D, Simões-Wüst AP, Ochsenbein-Kölble N, Zimmermann R, Deprest J, Mazza E. Influence of osmolarity and hydration on the tear resistance of the human amniotic membrane. J Biomech 2019; 98:109419. [PMID: 31679754 DOI: 10.1016/j.jbiomech.2019.109419] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2019] [Revised: 08/15/2019] [Accepted: 10/13/2019] [Indexed: 12/20/2022]
Abstract
The amnion is considered to be the load-bearing part of the fetal membranes. We investigated the influence of osmolarity of the testing medium and hydration on its fracture toughness. Mode I fracture tests revealed that physiological variations in the bath osmolarity do not influence the tear resistance of amnion, while larger changes, i.e. from physiological saline solution to distilled water, lead to a significant reduction of the fracture toughness. Uniaxial tensile tests on collagen hydrogels confirmed the reduction in toughness, suggesting that lower bath osmolarity triggers changes in the failure properties of single collagen fibers. Prenatal surgeries, in particular fetoscopic procedures with partial amniotic carbon dioxide insufflation, might result in dehydration of the amnion. Dehydration induced a brittle behavior; however, subsequent rehydration for 15 min resulted in a similar tear resistance as for the fresh tissue.
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Affiliation(s)
- Kevin Bircher
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland
| | - Riccardo Merluzzi
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland
| | - Adam Wahlsten
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland
| | - Deborah Spiess
- University Hospital Zurich, Department of Obstetrics, 8091 Zurich, Switzerland
| | | | | | - Roland Zimmermann
- University Hospital Zurich, Department of Obstetrics, 8091 Zurich, Switzerland
| | - Jan Deprest
- University Hospitals Leuven, Department of Obstetrics and Gynecology, 3000 Leuven, Belgium; Institute of Women's Health, Research Department of Maternal Fetal Medicine, University College London, London, UK
| | - Edoardo Mazza
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland; Empa, Swiss Federal Laboratories for Materials Science and Technology, 8600 Dübendorf, Switzerland.
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19
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Ayyalasomayajula V, Pierrat B, Badel P. A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia. Biomech Model Mechanobiol 2019; 18:1507-1528. [PMID: 31065952 PMCID: PMC6748894 DOI: 10.1007/s10237-019-01161-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2018] [Accepted: 04/26/2019] [Indexed: 12/11/2022]
Abstract
Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force-displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress-stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure-function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.
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Affiliation(s)
- Venkat Ayyalasomayajula
- Mines Saint-Étienne, Univ Lyon, Univ Jean Monnet, INSERM, U1059 SAINBIOSE, Centre CIS, 42023, Saint-Étienne, France.
| | - Baptiste Pierrat
- Mines Saint-Étienne, Univ Lyon, Univ Jean Monnet, INSERM, U1059 SAINBIOSE, Centre CIS, 42023, Saint-Étienne, France
| | - Pierre Badel
- Mines Saint-Étienne, Univ Lyon, Univ Jean Monnet, INSERM, U1059 SAINBIOSE, Centre CIS, 42023, Saint-Étienne, France
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20
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Bircher K, Ehret AE, Spiess D, Ehrbar M, Simões-Wüst AP, Ochsenbein-Kölble N, Zimmermann R, Mazza E. On the defect tolerance of fetal membranes. Interface Focus 2019; 9:20190010. [PMID: 31485307 DOI: 10.1098/rsfs.2019.0010] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 05/15/2019] [Indexed: 11/12/2022] Open
Abstract
A series of mechanical experiments were performed to quantify the strength and fracture toughness of human amnion and chorion. The experiments were complemented with computational investigations using a 'hybrid' model that includes an explicit representation of the collagen fibre network of amnion. Despite its much smaller thickness, amnion is shown to be stiffer, stronger and tougher than chorion, and thus to determine the mechanical response of fetal membranes, with respect to both, deformation and fracture behaviour. Data from uniaxial tension and fracture tests were used to inform and validate the computational model, which was then applied to rationalize measurements of the tear resistance of tissue samples containing crack-like defects. Experiments and computations show that the strength of amnion is not significantly reduced by defects smaller than 1 mm, but the crack size induced by perforations for amniocentesis and fetal membrane suturing during fetal surgery might be larger than this value. In line with previous experimental observations, the computational model predicts a very narrow near field at the crack tip of amnion, due to localized fibre alignment and collagen compaction. This mechanism shields the tissue from the defect and strongly reduces the interaction of multiple adjacent cracks. These findings were confirmed through corresponding experiments, showing that no interaction is expected for multiple sutures for an inter-suture distance larger than 1 mm and 3 mm for amnion and chorion, respectively. The experimental procedures and numerical models applied in the present study might be used to optimize needle and/or staple dimensions and inter-suture distance, and thus to reduce the risk of iatrogenic preterm premature rupture of the membranes from amniocentesis, fetoscopic and open prenatal surgery.
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Affiliation(s)
- Kevin Bircher
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland
| | - Alexander E Ehret
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland.,Empa, Swiss Federal Laboratories for Materials Science and Technology, 8600 Dübendorf, Switzerland
| | - Deborah Spiess
- Department of Obstetrics, University Hospital Zurich, 8091 Zurich, Switzerland
| | - Martin Ehrbar
- Department of Obstetrics, University Hospital Zurich, 8091 Zurich, Switzerland
| | | | | | - Roland Zimmermann
- Department of Obstetrics, University Hospital Zurich, 8091 Zurich, Switzerland
| | - Edoardo Mazza
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland.,Empa, Swiss Federal Laboratories for Materials Science and Technology, 8600 Dübendorf, Switzerland
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21
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Abstract
Fracture toughness characterizes the ability of a material to maintain a certain level of strength despite the presence of a macroscopic crack. Understanding this tolerance for defects in soft collagenous tissues (SCT) has high relevance for assessing the risks of fracture after cutting, perforation or suturing. Here we investigate the peculiar toughening mechanisms of SCT through dedicated experiments and multi-scale simulations, showing that classical concepts of fracture mechanics are inadequate to quantify and explain the high defect tolerance of these materials. Our results demonstrate that SCT strength is only modestly reduced by defects as large as several millimeters. This defect tolerance is achieved despite a very narrow process zone at the crack tip and even for a network of brittle fibrils. The fracture mechanics concept of tearing energy fails in predicting failure at such defects, and its magnitude is shown to depend on the chemical potential of the liquid environment.
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22
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Ji Z, Wang B, Yan K, Dong L, Meng G, Shi L. A linear programming computational framework integrates phosphor-proteomics and prior knowledge to predict drug efficacy. BMC SYSTEMS BIOLOGY 2017; 11:127. [PMID: 29322918 PMCID: PMC5763468 DOI: 10.1186/s12918-017-0501-6] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Background In recent years, the integration of ‘omics’ technologies, high performance computation, and mathematical modeling of biological processes marks that the systems biology has started to fundamentally impact the way of approaching drug discovery. The LINCS public data warehouse provides detailed information about cell responses with various genetic and environmental stressors. It can be greatly helpful in developing new drugs and therapeutics, as well as improving the situations of lacking effective drugs, drug resistance and relapse in cancer therapies, etc. Results In this study, we developed a Ternary status based Integer Linear Programming (TILP) method to infer cell-specific signaling pathway network and predict compounds’ treatment efficacy. The novelty of our study is that phosphor-proteomic data and prior knowledge are combined for modeling and optimizing the signaling network. To test the power of our approach, a generic pathway network was constructed for a human breast cancer cell line MCF7; and the TILP model was used to infer MCF7-specific pathways with a set of phosphor-proteomic data collected from ten representative small molecule chemical compounds (most of them were studied in breast cancer treatment). Cross-validation indicated that the MCF7-specific pathway network inferred by TILP were reliable predicting a compound’s efficacy. Finally, we applied TILP to re-optimize the inferred cell-specific pathways and predict the outcomes of five small compounds (carmustine, doxorubicin, GW-8510, daunorubicin, and verapamil), which were rarely used in clinic for breast cancer. In the simulation, the proposed approach facilitates us to identify a compound’s treatment efficacy qualitatively and quantitatively, and the cross validation analysis indicated good accuracy in predicting effects of five compounds. Conclusions In summary, the TILP model is useful for discovering new drugs for clinic use, and also elucidating the potential mechanisms of a compound to targets. Electronic supplementary material The online version of this article (10.1186/s12918-017-0501-6) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Zhiwei Ji
- School of Electronical and Information Engineering, Anhui University of Technology, Maanshan, 243002, China. .,School of Information & Electronic Engineering, Zhejiang Gongshang University, 18 Xuezheng Road, Hangzhou, 310018, China.
| | - Bing Wang
- School of Electronical and Information Engineering, Anhui University of Technology, Maanshan, 243002, China.
| | - Ke Yan
- College of Information Engineering, China Jiliang University, 258 Xueyuan Streat, Hangzhou, 310018, China
| | - Ligang Dong
- School of Information & Electronic Engineering, Zhejiang Gongshang University, 18 Xuezheng Road, Hangzhou, 310018, China
| | - Guanmin Meng
- Department of Clinical Laboratory, Tongde Hospital of Zhejiang Province, 234 Gucui Road, Hangzhou, 310012, China
| | - Lei Shi
- School of Information & Electronic Engineering, Zhejiang Gongshang University, 18 Xuezheng Road, Hangzhou, 310018, China
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23
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Ehret AE, Bircher K, Stracuzzi A, Marina V, Zündel M, Mazza E. Inverse poroelasticity as a fundamental mechanism in biomechanics and mechanobiology. Nat Commun 2017; 8:1002. [PMID: 29042539 PMCID: PMC5714996 DOI: 10.1038/s41467-017-00801-3] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2017] [Accepted: 07/28/2017] [Indexed: 01/14/2023] Open
Abstract
Understanding the mechanisms of deformation of biological materials is important for improved diagnosis and therapy, fundamental investigations in mechanobiology, and applications in tissue engineering. Here we demonstrate the essential role of interstitial fluid mobility in determining the mechanical properties of soft tissues. Opposite to the behavior expected for a poroelastic material, the tissue volume of different collagenous membranes is observed to strongly decrease with tensile loading. Inverse poroelasticity governs monotonic and cyclic responses of soft biomembranes, and induces chemo-mechanical coupling, such that tensile forces are modulated by the chemical potential of the interstitial fluid. Correspondingly, the osmotic pressure varies with mechanical loads, thus providing an effective mechanism for mechanotransduction. Water mobility determines the tissue's ability to adapt to deformation through compaction and dilation of the collagen fiber network. In the near field of defects this mechanism activates the reversible formation of reinforcing collagen structures which effectively avoid propagation of cracks.How soft tissues respond to mechanical load is essential to their biological function. Here, the authors discover that - contrary to predictions of poroelasticity - fluid mobility in collagenous tissues induces drastic volume decrease with tensile loading and pronounced chemo-mechanical coupling.
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Affiliation(s)
- Alexander E Ehret
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zurich, Switzerland. .,Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600, Dübendorf, Switzerland.
| | - Kevin Bircher
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zurich, Switzerland
| | - Alberto Stracuzzi
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zurich, Switzerland
| | - Vita Marina
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zurich, Switzerland
| | - Manuel Zündel
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zurich, Switzerland
| | - Edoardo Mazza
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092, Zurich, Switzerland. .,Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600, Dübendorf, Switzerland.
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24
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Zündel M, Mazza E, Ehret AE. A 2.5D approach to the mechanics of electrospun fibre mats. SOFT MATTER 2017; 13:6407-6421. [PMID: 28875212 DOI: 10.1039/c7sm01241a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this paper, a discrete random network modelling approach specific to electrospun networks is presented. Owing to the manufacturing process, fibres in these materials systems have an enormous length, as compared to their diameters, and form sparse networks since fibre contact over thickness is limited to a narrow range. Representative volume elements are generated, in which fibres span the entire domain, and a technique is developed to apply computationally favourable periodic boundary conditions despite the initial non-periodicity of the networks. To capture sparsity, a physically motivated method is proposed to distinguish true fibre cross-links, in which mechanical interaction takes place, from mere fibre intersections. The model is exclusively informed by experimentally accessible parameters, demonstrates excellent agreement with the mechanical response of electrospun fibre mats, captures typical microscopic deformation patterns, and provides information on the kinematics of fibres and pores. This ability to address relevant mechanisms of deformation at both micro- and macroscopic length scales, together with the moderate computational cost, render the proposed modelling approach a highly qualified tool for the computer-based design and optimization of electrospun networks.
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Affiliation(s)
- Manuel Zündel
- ETH Zurich, Institute for Mechanical Systems, 8092 Zurich, Switzerland.
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25
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Pensalfini M, Meneghello S, Lintas V, Bircher K, Ehret AE, Mazza E. The suture retention test, revisited and revised. J Mech Behav Biomed Mater 2017; 77:711-717. [PMID: 28867371 DOI: 10.1016/j.jmbbm.2017.08.021] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Revised: 08/10/2017] [Accepted: 08/15/2017] [Indexed: 11/16/2022]
Abstract
A systematic investigation of the factors affecting the suture retention test is performed. The specimen width w and the distance a of the suture bite from the specimen free edge emerge as the most influential geometrical parameters. A conservative approach for the quantification of suture retention strength is identified, based on the use of a camera to monitor the incipient failure and detect the instant of earliest crack propagation. The corresponding critical force, called break starting strength, is extremely robust against test parameter variations and its dependence on the specimen geometry becomes negligible when a≥ 2mm and w≥ 10mm. Comparison of suture retention and mode I crack opening tests reveals a linear correlation between break starting strength and tearing energy. This suggests that the defect created by the needle and the load applied by the suture thread lead to a fracture mechanics problem, which dominates the initiation of failure.
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Affiliation(s)
- M Pensalfini
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, 8092 Zurich, Switzerland.
| | - S Meneghello
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, 8092 Zurich, Switzerland
| | - V Lintas
- Institute for Regenerative Medicine, University of Zurich, Moussonstrasse 13, 8044 Zurich, Switzerland
| | - K Bircher
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, 8092 Zurich, Switzerland
| | - A E Ehret
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, 8092 Zurich, Switzerland; Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
| | - E Mazza
- Institute for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, 8092 Zurich, Switzerland; Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
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26
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Bircher K, Ehret AE, Mazza E. Microstructure based prediction of the deformation behavior of soft collagenous membranes. SOFT MATTER 2017; 13:5107-5116. [PMID: 28492654 DOI: 10.1039/c7sm00101k] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The response of human amnion (HA) and bovine Glisson's capsule (GC) to uniaxial and biaxial tensile loading is analyzed on tissue (∼mm) and collagen fiber (∼μm) length scales. The mechanical behavior of the membranes is rationalized based on a discrete fiber network model that relates model parameters with microstructural features of the tissues. Parameters were first determined for GC based on the quantity and organization of collagen fibers in the tissue. Next, parameters for HA were defined by comparing the microstructures of the two membranes, which differ in fiber organization in that collagen forms μm-thick fiber bundles in GC while 50 nm-thin fibrils constitute the network in HA. The flexural behavior of these structures is phenomenologically represented in the model, indicating that shear forces are transmitted through fibrils within GC bundles, but to a much lesser extent than in a corresponding solid cross section. The model provides excellent predictions of the uniaxial and biaxial mechanical response, as well as of the progressive reorientation of fibers associated with uniaxial loading. The results are particularly relevant since model parameters were not obtained through a fitting procedure of the tissue's tension-stretch curve. Furthermore, simulations of representative in vivo deformation states indicated that a large part of the fibers are expected to be un-crimped under physiological loading conditions. Thus, the crimped shape of collagen fibers in the initial test configuration, and typically observed in histological analyses, might be a consequence of the contraction occurring when membranes are extracted from their environment in the body.
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Affiliation(s)
- Kevin Bircher
- Institute for Mechanical Systems, ETH Zurich, 8092 Zurich, Switzerland.
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Lynch B, Bancelin S, Bonod-Bidaud C, Gueusquin JB, Ruggiero F, Schanne-Klein MC, Allain JM. A novel microstructural interpretation for the biomechanics of mouse skin derived from multiscale characterization. Acta Biomater 2017; 50:302-311. [PMID: 28043893 DOI: 10.1016/j.actbio.2016.12.051] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Revised: 11/15/2016] [Accepted: 12/29/2016] [Indexed: 11/17/2022]
Abstract
Skin is a complex, multi-layered organ, with important functions in the protection of the body. The dermis provides structural support to the epidermal barrier, and thus has attracted a large number of mechanical studies. As the dermis is made of a mixture of stiff fibres embedded in a soft non-fibrillar matrix, it is classically considered that its mechanical response is based on an initial alignment of the fibres, followed by the stretching of the aligned fibres. Using a recently developed set-up combining multiphoton microscopy with mechanical assay, we imaged the fibres network evolution during dermis stretching. These observations, combined with a wide set of mechanical tests, allowed us to challenge the classical microstructural interpretation of the mechanical properties of the dermis: we observed a continuous alignment of the collagen fibres along the stretching. All our results can be explained if each fibre contributes by a given stress to the global response. This plastic response is likely due to inner sliding inside each fibre. The non-linear mechanical response is due to structural effects of the fibres network in interaction with the surrounding non-linear matrix. This multiscale interpretation explains our results on genetically-modified mice with a simple alteration of the dermis microstructure. STATEMENT OF SIGNIFICANCE Soft tissues, as skin, tendon or aorta, are made of extra-cellular matrix, with very few cells embedded inside. The matrix is a mixture of water and biomolecules, which include the collagen fibre network. The role of the collagen is fundamental since the network is supposed to control the tissue mechanical properties and remodeling: the cells attach to the collagen fibres and feel the network deformations. This paper challenges the classical link between fibres organization and mechanical properties. To do so, it uses multiscale observations combined to a large set of mechanical loading. It thus appears that the behaviour at low stretches is mostly controlled by the network structural response, while, at large stretches, the fibre inner-sliding dominate.
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Affiliation(s)
- Barbara Lynch
- LMS, Ecole Polytechnique, CNRS, Université Paris-Saclay, Palaiseau, France
| | - Stéphane Bancelin
- LOB, Ecole Polytechnique, CNRS, INSERM, Université Paris-Saclay, Palaiseau, France
| | - Christelle Bonod-Bidaud
- Institut de Génomique Fonctionnelle de Lyon, ENS-Lyon, CNRS, Université de Lyon, Lyon, France
| | | | - Florence Ruggiero
- Institut de Génomique Fonctionnelle de Lyon, ENS-Lyon, CNRS, Université de Lyon, Lyon, France
| | | | - Jean-Marc Allain
- LMS, Ecole Polytechnique, CNRS, Université Paris-Saclay, Palaiseau, France; Inria, Université Paris-Saclay, Palaiseau, France.
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