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Huang WZ, Li B, Feng XQ. Mechanobiological tissue instability induced by stress-modulated growth. SOFT MATTER 2023; 19:708-722. [PMID: 36602136 DOI: 10.1039/d2sm01195f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The growth of biological tissues, which is regulated by a variety of factors, can induce stresses that may, in turn, destabilize the tissues into diverse patterns. In most previous studies, however, tissue growth was usually assumed as a prescribed parameter independent of stresses, limiting our understanding of the mechanobiological morphogenesis of real tissues. In this paper, we propose a theoretical model to investigate the mechanobiological response of soft tissues undergoing stress-modulated growth. Linear stability analysis is first performed to elucidate the surface instability mechanism induced by stress-modulated volumetric growth. We further conduct finite element simulations to validate the theoretical prediction and, particularly, to capture the post-buckling pattern evolution. Our results show that the non-uniform stresses, which evolve with the tissue growth and morphogenesis, exert mechanical feedback on the growth itself, producing up-down asymmetric surface morphologies as observed in, for example, the gyrification of human brains and brain organoids. It is also revealed that large residual stresses are unnecessary to cause mechanobiological instability and subsequent asymmetric patterning, which has long been believed to be driven by sufficiently high stresses. The present work could help us to understand the morphological changes of biological tissues under physiological and pathological conditions.
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Affiliation(s)
- Wei-Zhi Huang
- Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
| | - Bo Li
- Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
| | - Xi-Qiao Feng
- Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
- State Key Laboratory of Tribology in Advanced Equipment (SKLT), Tsinghua University, Beijing 100084, China
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2
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Erlich A, Étienne J, Fouchard J, Wyatt T. How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale. Interface Focus 2022; 12:20220038. [PMID: 36330322 PMCID: PMC9560792 DOI: 10.1098/rsfs.2022.0038] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 09/08/2022] [Indexed: 10/16/2023] Open
Abstract
Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.
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Affiliation(s)
| | - Jocelyn Étienne
- Université Grenoble Alpes, CNRS, LIPHY, 38000 Grenoble, France
| | - Jonathan Fouchard
- Laboratoire de Biologie du Développement, Institut de Biologie Paris Seine (IBPS), Sorbonne Université, CNRS (UMR 7622), INSERM (URL 1156), 7 quai Saint Bernard, 75005 Paris, France
| | - Tom Wyatt
- Wellcome Trust–Medical Research Council Cambridge Stem Cell Institute, University of Cambridge, Cambridge, UK
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Gou K, Baek S, Lutnesky MMF, Han HC. Growth-profile configuration for specific deformations of tubular organs: A study of growth-induced thinning and dilation of the human cervix. PLoS One 2021; 16:e0255895. [PMID: 34379659 PMCID: PMC8357173 DOI: 10.1371/journal.pone.0255895] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 07/26/2021] [Indexed: 12/02/2022] Open
Abstract
Growth is a significant factor that results in deformations of tubular organs, and particular deformations associated with growth enable tubular organs to perform certain physiological functions. Configuring growth profiles that achieve particular deformation patterns is critical for analyzing potential pathological conditions and for developing corresponding clinical treatments for tubular organ dysfunctions. However, deformation-targeted growth is rarely studied. In this article, the human cervix during pregnancy is studied as an example to show how cervical thinning and dilation are generated by growth. An advanced hyperelasticity theory called morphoelasticity is employed to model the deformations, and a growth tensor is used to represent growth in three principle directions. The computational results demonstrate that both negative radial growth and positive circumferential growth facilitate thinning and dilation. Modeling such mixed growth represents an advancement beyond commonly used uniform growth inside tissues to study tubular deformations. The results reveal that complex growth may occur inside tissues to achieve certain tubular deformations. Integration of further biochemical and cellular activities that initiate and mediate such complex growth remains to be explored.
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Affiliation(s)
- Kun Gou
- Department of Mathematical, Physical, and Engineering Sciences, Texas A&M University-San Antonio, San Antonio, Texas, United States of America
- * E-mail:
| | - Seungik Baek
- Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan, United States of America
| | - Marvin M. F. Lutnesky
- Department of Life Sciences, Texas A&M University-San Antonio, San Antonio, Texas, United States of America
| | - Hai-Chao Han
- Department of Mechanical Engineering, The University of Texas at San Antonio, San Antonio, Texas, United States of America
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Abstract
Cells of the vascular wall are exquisitely sensitive to changes in their mechanical environment. In healthy vessels, mechanical forces regulate signaling and gene expression to direct the remodeling needed for the vessel wall to maintain optimal function. Major diseases of arteries involve maladaptive remodeling with compromised or lost homeostatic mechanisms. Whereas homeostasis invokes negative feedback loops at multiple scales to mediate mechanobiological stability, disease progression often occurs via positive feedback that generates mechanobiological instabilities. In this review, we focus on the cell biology, wall mechanics, and regulatory pathways associated with arterial health and how changes in these processes lead to disease. We discuss how positive feedback loops arise via biomechanical and biochemical means. We conclude that inflammation plays a central role in overriding homeostatic pathways and suggest future directions for addressing therapeutic needs.
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Affiliation(s)
- Jay D Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, Connecticut 06520, USA;
| | - Martin A Schwartz
- Department of Biomedical Engineering, Yale University, New Haven, Connecticut 06520, USA;
- Department of Cell Biology, Department of Internal Medicine (Cardiology), and Cardiovascular Research Center, Yale University, New Haven, Connecticut 06520, USA
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张 晗, 张 愉, 陈 诗, 崔 新, 彭 坤, 乔 爱. [Review of studies on the biomechanical modelling of the coupling effect between stent degradation and blood vessel remodeling]. SHENG WU YI XUE GONG CHENG XUE ZA ZHI = JOURNAL OF BIOMEDICAL ENGINEERING = SHENGWU YIXUE GONGCHENGXUE ZAZHI 2020; 37:956-966. [PMID: 33369334 PMCID: PMC9929987 DOI: 10.7507/1001-5515.202008007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Indexed: 11/03/2022]
Abstract
The dynamic coupling of stent degradation and vessel remodeling can influence not only the structural morphology and material property of stent and vessel, but also the development of in-stent restenosis. The research achievements of biomechanical modelling and analysis of stent degradation and vessel remodeling were reviewed; several noteworthy research perspectives were addressed, a stent-vessel coupling model was developed based on stent damage function and vessel growth function, and then concepts of matching ratio and risk factor were established so as to evaluate the treatment effect of stent intervention, which may lay the scientific foundation for the structure design, mechanical analysis and clinical application of biodegradable stent.
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Affiliation(s)
- 晗冰 张
- 北京工业大学 环境与生命学部(北京 100124)Faculty of Environment and Life, Beijing University of Technology, Beijing 100124, P.R.China
| | - 愉 张
- 北京工业大学 环境与生命学部(北京 100124)Faculty of Environment and Life, Beijing University of Technology, Beijing 100124, P.R.China
| | - 诗亮 陈
- 北京工业大学 环境与生命学部(北京 100124)Faculty of Environment and Life, Beijing University of Technology, Beijing 100124, P.R.China
| | - 新阳 崔
- 北京工业大学 环境与生命学部(北京 100124)Faculty of Environment and Life, Beijing University of Technology, Beijing 100124, P.R.China
| | - 坤 彭
- 北京工业大学 环境与生命学部(北京 100124)Faculty of Environment and Life, Beijing University of Technology, Beijing 100124, P.R.China
| | - 爱科 乔
- 北京工业大学 环境与生命学部(北京 100124)Faculty of Environment and Life, Beijing University of Technology, Beijing 100124, P.R.China
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Almet AA, Byrne HM, Maini PK, Moulton DE. The role of mechanics in the growth and homeostasis of the intestinal crypt. Biomech Model Mechanobiol 2020; 20:585-608. [PMID: 33219879 PMCID: PMC7979635 DOI: 10.1007/s10237-020-01402-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Accepted: 11/03/2020] [Indexed: 11/29/2022]
Abstract
We present a mechanical model of tissue homeostasis that is specialised to the intestinal crypt. Growth and deformation of the crypt, idealised as a line of cells on a substrate, are modelled using morphoelastic rod theory. Alternating between Lagrangian and Eulerian mechanical descriptions enables us to precisely characterise the dynamic nature of tissue homeostasis, whereby the proliferative structure and morphology are static in the Eulerian frame, but there is active migration of Lagrangian material points out of the crypt. Assuming mechanochemical growth, we identify the necessary conditions for homeostasis, reducing the full, time-dependent system to a static boundary value problem characterising a spatially heterogeneous "treadmilling" state. We extract essential features of crypt homeostasis, such as the morphology, the proliferative structure, the migration velocity, and the sloughing rate. We also derive closed-form solutions for growth and sloughing dynamics in homeostasis, and show that mechanochemical growth is sufficient to generate the observed proliferative structure of the crypt. Key to this is the concept of threshold-dependent mechanical feedback, that regulates an established Wnt signal for biochemical growth. Numerical solutions demonstrate the importance of crypt morphology on homeostatic growth, migration, and sloughing, and highlight the value of this framework as a foundation for studying the role of mechanics in homeostasis.
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Affiliation(s)
- A A Almet
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.,NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, Irvine, CA, USA.,Department of Mathematics, University of California, Irvine, Irvine, CA, USA
| | - H M Byrne
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
| | - P K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
| | - D E Moulton
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK.
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Linka K, Peirlinck M, Kuhl E. The reproduction number of COVID-19 and its correlation with public health interventions. COMPUTATIONAL MECHANICS 2020; 66:1035-1050. [PMID: 32836597 PMCID: PMC7385940 DOI: 10.1007/s00466-020-01880-8] [Citation(s) in RCA: 87] [Impact Index Per Article: 21.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 07/06/2020] [Indexed: 05/09/2023]
Abstract
Throughout the past six months, no number has dominated the public media more persistently than the reproduction number of COVID-19. This powerful but simple concept is widely used by the public media, scientists, and political decision makers to explain and justify political strategies to control the COVID-19 pandemic. Here we explore the effectiveness of political interventions using the reproduction number of COVID-19 across Europe. We propose a dynamic SEIR epidemiology model with a time-varying reproduction number, which we identify using machine learning. During the early outbreak, the basic reproduction number was 4.22 ± 1.69, with maximum values of 6.33 and 5.88 in Germany and the Netherlands. By May 10, 2020, it dropped to 0.67 ± 0.18, with minimum values of 0.37 and 0.28 in Hungary and Slovakia. We found a strong correlation between passenger air travel, driving, walking, and transit mobility and the effective reproduction number with a time delay of 17.24 ± 2.00 days. Our new dynamic SEIR model provides the flexibility to simulate various outbreak control and exit strategies to inform political decision making and identify safe solutions in the benefit of global health.
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Affiliation(s)
- Kevin Linka
- Department of Mechanical Engineering, Stanford University, Stanford, CA USA
| | - Mathias Peirlinck
- Department of Mechanical Engineering, Stanford University, Stanford, CA USA
| | - Ellen Kuhl
- Department of Mechanical Engineering, Stanford University, Stanford, CA USA
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Linka K, Peirlinck M, Kuhl E. The reproduction number of COVID-19 and its correlation with public health interventions. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2020:2020.05.01.20088047. [PMID: 32676611 PMCID: PMC7359536 DOI: 10.1101/2020.05.01.20088047] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Throughout the past six months, no number has dominated the public media more persistently than the reproduction number of COVID-19. This powerful but simple concept is widely used by the public media, scientists, and political decision makers to explain and justify political strategies to control the COVID-19 pandemic. Here we explore the effectiveness of political interventions using the reproduction number of COVID-19 across Europe. We propose a dynamic SEIR epidemiology model with a time-varying reproduction number, which we identify using machine learning. During the early outbreak, the basic reproduction number was 4.22+/-1.69, with maximum values of 6.33 and 5.88 in Germany and the Netherlands. By May 10, 2020, it dropped to 0.67+/-0.18, with minimum values of 0.37 and 0.28 in Hungary and Slovakia. We found a strong correlation between passenger air travel, driving, walking, and transit mobility and the effective reproduction number with a time delay of 17.24+/-2.00 days. Our new dynamic SEIR model provides the flexibility to simulate various outbreak control and exit strategies to inform political decision making and identify safe solutions in the benefit of global health.
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Affiliation(s)
- Kevin Linka
- Department of Mechanical Engineering, Stanford University, Stanford, California, United States
| | - Mathias Peirlinck
- Department of Mechanical Engineering, Stanford University, Stanford, California, United States
| | - Ellen Kuhl
- Department of Mechanical Engineering, Stanford University, Stanford, California, United States
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Erlich A, Jones GW, Tisseur F, Moulton DE, Goriely A. The role of topology and mechanics in uniaxially growing cell networks. Proc Math Phys Eng Sci 2020; 476:20190523. [PMID: 32082058 PMCID: PMC7016545 DOI: 10.1098/rspa.2019.0523] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Accepted: 12/10/2019] [Indexed: 01/18/2023] Open
Abstract
In biological systems, the growth of cells, tissues and organs is influenced by mechanical cues. Locally, cell growth leads to a mechanically heterogeneous environment as cells pull and push their neighbours in a cell network. Despite this local heterogeneity, at the tissue level, the cell network is remarkably robust, as it is not easily perturbed by changes in the mechanical environment or the network connectivity. Through a network model, we relate global tissue structure (i.e. the cell network topology) and local growth mechanisms (growth laws) to the overall tissue response. Within this framework, we investigate the two main mechanical growth laws that have been proposed: stress-driven or strain-driven growth. We show that in order to create a robust and stable tissue environment, networks with predominantly series connections are naturally driven by stress-driven growth, whereas networks with predominantly parallel connections are associated with strain-driven growth.
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Affiliation(s)
- Alexander Erlich
- Laboratoire Interdisciplinaire de Physique (LIPhy), Université Grenoble Alpes, CNRS, Grenoble 38000, France
| | - Gareth W. Jones
- School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Françoise Tisseur
- School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | - Derek E. Moulton
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
| | - Alain Goriely
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
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Ambrosi D, Ben Amar M, Cyron CJ, DeSimone A, Goriely A, Humphrey JD, Kuhl E. Growth and remodelling of living tissues: perspectives, challenges and opportunities. J R Soc Interface 2019; 16:20190233. [PMID: 31431183 PMCID: PMC6731508 DOI: 10.1098/rsif.2019.0233] [Citation(s) in RCA: 76] [Impact Index Per Article: 15.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Accepted: 07/26/2019] [Indexed: 12/29/2022] Open
Abstract
One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.
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Affiliation(s)
- Davide Ambrosi
- Dipartimento di Matematica, Politecnico di Milano, Milan, Italy
| | - Martine Ben Amar
- Laboratoire de Physique Statistique, Ecole Normale Supérieure, Paris, France
| | - Christian J. Cyron
- Institute of Continuum Mechanics and Materials, Hamburg University of Technology, Hamburg, Germany
- Institute of Materials Research, Helmholtz-Zentrum Geesthacht, Geesthacht, Germany
| | - Antonio DeSimone
- Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
| | - Alain Goriely
- Mathematical Institute, University of Oxford, Oxford, UK
| | - Jay D. Humphrey
- Department of Biomedical Engineering, Yale University, New Haven, CT, USA
| | - Ellen Kuhl
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
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Latorre M, Humphrey JD. Mechanobiological Stability of Biological Soft Tissues. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2019; 125:298-325. [PMID: 31543547 PMCID: PMC6754118 DOI: 10.1016/j.jmps.2018.12.013] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Like all other materials, biological soft tissues are subject to general laws of physics, including those governing mechanical equilibrium and stability. In addition, however, these tissues are able to respond actively to changes in their mechanical and chemical environment. There is, therefore, a pressing need to understand such processes theoretically. In this paper, we present a new rate-based constrained mixture formulation suitable for studying mechanobiological equilibrium and stability of soft tissues exposed to transient or sustained changes in material composition or applied loading. These concepts are illustrated for canonical problems in arterial mechanics, which distinguish possible stable versus unstable mechanobiological responses. Such analyses promise to yield insight into biological processes that govern both health and disease progression.
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Affiliation(s)
- Marcos Latorre
- Department of Biomedical Engineering Yale University, New Haven, CT 06520, USA
- Corresponding author: (Marcos Latorre), (Jay D. Humphrey)
| | - Jay D. Humphrey
- Department of Biomedical Engineering Yale University, New Haven, CT 06520, USA
- Vascular Biology and Therapeutics Program Yale School of Medicine, New Haven, CT 06520, USA
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