1
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Chala N, Zhang X, Zambelli T, Zhang Z, Schneider T, Panozzo D, Poulikakos D, Ferrari A. 4D Force Detection of Cell Adhesion and Contractility. NANO LETTERS 2023; 23:2467-2475. [PMID: 36975035 PMCID: PMC10103301 DOI: 10.1021/acs.nanolett.2c03733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Revised: 03/17/2023] [Indexed: 06/18/2023]
Abstract
Mechanical signals establish two-way communication between mammalian cells and their environment. Cells contacting a surface exert forces via contractility and transmit them at the areas of focal adhesions. External stimuli, such as compressive and pulling forces, typically affect the adhesion-free cell surface. Here, we demonstrate the collaborative employment of Fluidic Force Microscopy and confocal Traction Force Microscopy supported by the Cellogram solver to enable a powerful integrated force probing approach, where controlled vertical forces are applied to the free surface of individual cells, while the concomitant deformations are used to map their transmission to the substrate. Force transmission across human cells is measured with unprecedented temporal and spatial resolution, enabling the investigation of the cellular mechanisms involved in the adaptation, or maladaptation, to external mechanical stimuli. Altogether, the system enables facile and precise force interrogation of individual cells, with the capacity to perform population-based analysis.
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Affiliation(s)
- Nafsika Chala
- Laboratory
of Thermodynamics in Emerging Technologies, Department of Mechanical
and Process Engineering, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
| | - Xinyu Zhang
- Laboratory
of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zurich, Gloriastrasse 35, Zurich 8092, Switzerland
| | - Tomaso Zambelli
- Laboratory
of Biosensors and Bioelectronics, Institute for Biomedical Engineering, ETH Zurich, Gloriastrasse 35, Zurich 8092, Switzerland
| | - Ziyi Zhang
- Courant
Institute of Mathematical Sciences, New
York University, 5th Avenue 60, New York, New York 10011, United
States
| | - Teseo Schneider
- Department
of Computer Science, University of Victoria, 3800 Finnerty Road, Engineering
& Computer Science Building, Victoria, BC V8P 5C2, Canada
| | - Daniele Panozzo
- Courant
Institute of Mathematical Sciences, New
York University, 5th Avenue 60, New York, New York 10011, United
States
| | - Dimos Poulikakos
- Laboratory
of Thermodynamics in Emerging Technologies, Department of Mechanical
and Process Engineering, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
| | - Aldo Ferrari
- Laboratory
of Thermodynamics in Emerging Technologies, Department of Mechanical
and Process Engineering, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland
- Experimental
Continuum Mechanics, EMPA, Swiss Federal
Laboratories for Material Science and Technologies, Überlandstrasse 129, 8600 Dübendorf, Switzerland
- Institute
for Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zurich, Leonhardstrasse 21, 8092 Zürich, Switzerland
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2
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Hervas-Raluy S, Wirthl B, Guerrero PE, Robalo Rei G, Nitzler J, Coronado E, Font de Mora Sainz J, Schrefler BA, Gomez-Benito MJ, Garcia-Aznar JM, Wall WA. Tumour growth: An approach to calibrate parameters of a multiphase porous media model based on in vitro observations of Neuroblastoma spheroid growth in a hydrogel microenvironment. Comput Biol Med 2023; 159:106895. [PMID: 37060771 DOI: 10.1016/j.compbiomed.2023.106895] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Revised: 03/09/2023] [Accepted: 04/09/2023] [Indexed: 04/17/2023]
Abstract
To unravel processes that lead to the growth of solid tumours, it is necessary to link knowledge of cancer biology with the physical properties of the tumour and its interaction with the surrounding microenvironment. Our understanding of the underlying mechanisms is however still imprecise. We therefore developed computational physics-based models, which incorporate the interaction of the tumour with its surroundings based on the theory of porous media. However, the experimental validation of such models represents a challenge to its clinical use as a prognostic tool. This study combines a physics-based model with in vitro experiments based on microfluidic devices used to mimic a three-dimensional tumour microenvironment. By conducting a global sensitivity analysis, we identify the most influential input parameters and infer their posterior distribution based on Bayesian calibration. The resulting probability density is in agreement with the scattering of the experimental data and thus validates the proposed workflow. This study demonstrates the huge challenges associated with determining precise parameters with usually only limited data for such complex processes and models, but also demonstrates in general how to indirectly characterise the mechanical properties of neuroblastoma spheroids that cannot feasibly be measured experimentally.
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Affiliation(s)
- Silvia Hervas-Raluy
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, University of Zaragoza, Aragon Institute for Engineering Research (I3A), Maria de Luna 3, Zaragoza, 50018, Spain.
| | - Barbara Wirthl
- Institute for Computational Mechanics, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics & Computation, Boltzmannstraße 15, Garching b. Munich, 85748, Germany
| | - Pedro E Guerrero
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, University of Zaragoza, Aragon Institute for Engineering Research (I3A), Maria de Luna 3, Zaragoza, 50018, Spain
| | - Gil Robalo Rei
- Institute for Computational Mechanics, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics & Computation, Boltzmannstraße 15, Garching b. Munich, 85748, Germany
| | - Jonas Nitzler
- Institute for Computational Mechanics, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics & Computation, Boltzmannstraße 15, Garching b. Munich, 85748, Germany; Professorship for Data-Driven Materials Modeling, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics & Computation, Boltzmannstraße 15, Garching b. Munich, 85748, Germany
| | - Esther Coronado
- Clinical and Translational Oncology Research Group, Instituto de Investigación La Fe,, Fernando Abril Martorell 106, Valencia, 46026, Spain
| | - Jaime Font de Mora Sainz
- Clinical and Translational Oncology Research Group, Instituto de Investigación La Fe,, Fernando Abril Martorell 106, Valencia, 46026, Spain
| | - Bernhard A Schrefler
- Department of Civil, Environmental and Architectural Engineering, University of Padua, Marzolo 9, Padua, 35131, Italy; Institute for Advanced Study, Technical University of Munich, Boltzmannstraße 15, Garching b. Munich, 85748, Germany
| | - Maria Jose Gomez-Benito
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, University of Zaragoza, Aragon Institute for Engineering Research (I3A), Maria de Luna 3, Zaragoza, 50018, Spain
| | - Jose Manuel Garcia-Aznar
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, University of Zaragoza, Aragon Institute for Engineering Research (I3A), Maria de Luna 3, Zaragoza, 50018, Spain
| | - Wolfgang A Wall
- Institute for Computational Mechanics, Technical University of Munich, TUM School of Engineering and Design, Department of Engineering Physics & Computation, Boltzmannstraße 15, Garching b. Munich, 85748, Germany
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3
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Aryeetey OJ, Frank M, Lorenz A, Pahr DH. Fracture toughness determination of porcine muscle tissue based on AQLV model derived viscous dissipated energy. J Mech Behav Biomed Mater 2022; 135:105429. [DOI: 10.1016/j.jmbbm.2022.105429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Revised: 08/17/2022] [Accepted: 08/22/2022] [Indexed: 10/31/2022]
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4
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Substrate viscosity impairs temozolomide-mediated inhibition of glioblastoma cells' growth. Biochim Biophys Acta Mol Basis Dis 2022; 1868:166513. [PMID: 35932892 DOI: 10.1016/j.bbadis.2022.166513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Revised: 07/16/2022] [Accepted: 07/29/2022] [Indexed: 11/20/2022]
Abstract
BACKGROUND The mechanical state of the extracellular environment of the brain cells considerably affects their phenotype during the development of central nervous system (CNS) pathologies, and when the cells respond to drugs. The reports on the evaluation of the viscoelastic properties of different brain tumors have shown that both tissue stiffness and viscosity can be altered during cancer development. Although a compelling number of reports established the role of substrate stiffness on the proliferation, motility, and drug sensitivity of brain cancer cells, there is a lack of parallel data in terms of alterations in substrate viscosity. METHODS Based on viscoelasticity measurements of rat brain samples using strain rheometry, polyacrylamide (PAA) hydrogels mimicking elastic and viscous parameters of the tissues were prepared. Optical microscopy and flow cytometry were employed to assess the differences in glioblastoma cells morphology, proliferation, and cytotoxicity of anticancer drug temozolomide (TZM) due to increased substrate viscosity. RESULTS Our results indicate that changes in substrate viscosity affect the proliferation of untreated glioma cells to a lesser extent, but have a significant impact on the apoptosis-associated depolarization of mitochondria and level of DNA fragmentation. This suggests that viscosity sensing and stiffness sensing machinery can activate different signaling pathways in glioma cells. CONCLUSION Collected data indicate that viscosity should be considered an important parameter in in vitro polymer-based cell culture systems used for drug screening.
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Helisaz H, Bacca M, Chiao M. Quasi-Linear Viscoelastic Characterization of Soft Tissue-Mimicking Materials. J Biomech Eng 2021; 143:061007. [PMID: 33537722 DOI: 10.1115/1.4050036] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Indexed: 11/08/2022]
Abstract
We present a novel method based on the quasi-linear viscoelastic (QLV) theory to describe the time-dependent behavior of soft materials. Unlike previous methods for deriving QLV parameters, we characterize the elastic and viscous behavior of materials separately by using two different sets of experiments. To model the nonlinear elastic behavior, we fit the elastic stress response with a one-term Ogden model. Then, we model the relaxation behavior with a Prony series to compare the stress relaxation of the material at different timescales. This new method allows us to characterize materials with narrow confidence intervals (high accuracy), independently from the loading conditions. We validate our model using samples made of phantom materials that mimic normal and cancerous prostate tissues in terms of Young's modulus. Our model is shown to distinguish materials with similar elastic (viscous) properties but different viscous (elastic) properties. Drawing a precise distinction between the phantoms, this method could be useful for prostate cancer (PCa) diagnosis; but significant clinical studies will be needed in the future.
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Affiliation(s)
- Hamed Helisaz
- Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Mattia Bacca
- Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Mu Chiao
- Department of Mechanical Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
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6
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Pokki J, Zisi I, Schulman E, Indana D, Chaudhuri O. Magnetic probe-based microrheology reveals local softening and stiffening of 3D collagen matrices by fibroblasts. Biomed Microdevices 2021; 23:27. [PMID: 33900463 PMCID: PMC8076128 DOI: 10.1007/s10544-021-00547-2] [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] [Indexed: 12/14/2022]
Abstract
Changes in extracellular matrix stiffness impact a variety of biological processes including cancer progression. However, cells also actively remodel the matrices they interact with, dynamically altering the matrix mechanics they respond to. Further, cells not only react to matrix stiffness, but also have a distinct reaction to matrix viscoelasticity. The impact of cell-driven matrix remodeling on matrix stiffness and viscoelasticity at the microscale remains unclear, as existing methods to measure mechanics are largely at the bulk scale or probe only the surface of matrices, and focus on stiffness. Yet, establishing the impact of the matrix remodeling at the microscale is crucial to obtaining an understanding of mechanotransduction in biological matrices, and biological matrices are not just elastic, but are viscoelastic. Here, we advanced magnetic probe-based microrheology to overcome its previous limitations in measuring viscoelasticity at the cell-size-scale spatial resolution within 3D cell cultures that have tissue-relevant stiffness levels up to a Young's modulus of 0.5 kPa. Our magnetic microrheometers exert controlled magnetic forces on magnetic microprobes within reconstituted extracellular matrices and detect microprobe displacement responses to measure matrix viscoelasticity and determine the frequency-dependent shear modulus (stiffness), the loss tangent, and spatial heterogeneity. We applied these tools to investigate how microscale viscoelasticity of collagen matrices is altered by fibroblast cells as they contract collagen gels, a process studied extensively at the macroscale. Interestingly, we found that fibroblasts first soften the matrix locally over the first 32 hours of culture, and then progressively stiffen the matrix thereafter. Fibroblast activity also progressively increased the matrix loss tangent. We confirmed that the softening is caused by matrix-metalloproteinase-mediated collagen degradation, whereas stiffening is associated with local alignment and densification of collagen fibers around the fibroblasts. This work paves the way for the use of measurement systems that quantify microscale viscoelasticity within 3D cell cultures for studies of cell-matrix interactions in cancer progression and other areas.
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Affiliation(s)
- Juho Pokki
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA. .,Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland.
| | - Iliana Zisi
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
| | - Ester Schulman
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
| | - Dhiraj Indana
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
| | - Ovijit Chaudhuri
- Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
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7
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Shakiba D, Alisafaei F, Savadipour A, Rowe RA, Liu Z, Pryse KM, Shenoy VB, Elson EL, Genin GM. The Balance between Actomyosin Contractility and Microtubule Polymerization Regulates Hierarchical Protrusions That Govern Efficient Fibroblast-Collagen Interactions. ACS NANO 2020; 14:7868-7879. [PMID: 32286054 DOI: 10.1021/acsnano.9b09941] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Fibroblasts undergo a critical transformation from an initially inactive state to a morphologically different and contractile state after several hours of being embedded within a physiologically relevant three-dimensional (3D) fibrous collagen-based extracellular matrix (ECM). However, little is known about the critical mechanisms by which fibroblasts adapt themselves and their microenvironment in the earliest stage of cell-matrix interaction. Here, we identified the mechanisms by which fibroblasts interact with their 3D collagen fibrous matrices in the early stages of cell-matrix interaction and showed that fibroblasts use energetically efficient hierarchical micro/nano-scaled protrusions in these stages as the primary means for the transformation and adaptation. We found that actomyosin contractility in these protrusions in the early stages of cell-matrix interaction restricts the growth of microtubules by applying compressive forces on them. Our results show that actomyosin contractility and microtubules work in concert in the early stages of cell-matrix interaction to adapt fibroblasts and their microenvironment to one another. These early stage interactions result in responses to disruption of the microtubule network and/or actomyosin contractility that are opposite to well-known responses to late-stage disruption and reveal insight into the ways that cells adapt themselves and their ECM recursively.
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Affiliation(s)
- Delaram Shakiba
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130 United States
| | - Farid Alisafaei
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Alireza Savadipour
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130 United States
| | - Roger A Rowe
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130 United States
| | - Zhangao Liu
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130 United States
| | - Kenneth M Pryse
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130 United States
| | - Vivek B Shenoy
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Elliot L Elson
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, Missouri 63110, United States
| | - Guy M Genin
- NSF Science and Technology Center for Engineering Mechanobiology and Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130 United States
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8
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Wang M, Liu S, Xu Z, Qu K, Li M, Chen X, Xue Q, Genin GM, Lu TJ, Xu F. Characterizing poroelasticity of biological tissues by spherical indentation: an improved theory for large relaxation. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2020; 138:103920. [PMID: 33132418 PMCID: PMC7595329 DOI: 10.1016/j.jmps.2020.103920] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Flow of fluids within biological tissues often meets with resistance that causes a rate- and size-dependent material behavior known as poroelasticity. Characterizing poroelasticity can provide insight into a broad range of physiological functions, and is done qualitatively in the clinic by palpation. Indentation has been widely used for characterizing poroelasticity of soft materials, where quantitative interpretation of indentation requires a model of the underlying physics, and such existing models are well established for cases of small strain and modest force relaxation. We showed here that existing models are inadequate for large relaxation, where the force on the indenter at a prescribed depth at long-time scale drops to below half of the initially peak force (i.e., F(0)/F(∞) > 2). We developed an indentation theory for such cases of large relaxation, based on Biot theory and a generalized Hertz contact model. We demonstrated that our proposed theory is suitable for biological tissues (e.g., spleen, kidney, skin and human cirrhosis liver) with both small and large relaxations. The proposed method would be a powerful tool to characterize poroelastic properties of biological materials for various applications such as pathological study and disease diagnosis.
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Affiliation(s)
- Ming Wang
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Shaanxi, 710049, P.R. China
- Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, P.R. China
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China
| | - Shaobao Liu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China
- Nanjing Center for Multifunctional Lightweight Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 21006, P.R. China
| | - Zhimin Xu
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P.R. China
| | - Kai Qu
- Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, P.R. China
- Department of Hepatobiliary Surgery, The First Affiliated Hospital of Xi’an Jiaotong University, Xi’an 710061, China
| | - Moxiao Li
- Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, P.R. China
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P.R. China
| | - Xin Chen
- Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, P.R. China
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P.R. China
| | - Qing Xue
- Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, P.R. China
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P.R. China
| | - Guy M. Genin
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Shaanxi, 710049, P.R. China
- Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, P.R. China
- National Science Foundation Science and Technology Center for Engineering Mechanobiology, Washington University, St. Louis, MO 63130, USA
| | - Tian Jian Lu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China
- Nanjing Center for Multifunctional Lightweight Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 21006, P.R. China
| | - Feng Xu
- The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Shaanxi, 710049, P.R. China
- Bioinspired Engineering & Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an 710049, P.R. China
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9
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Liu S, Tao R, Wang M, Tian J, Genin GM, Lu TJ, Xu F. Regulation of Cell Behavior by Hydrostatic Pressure. APPLIED MECHANICS REVIEWS 2019; 71:0408031-4080313. [PMID: 31700195 PMCID: PMC6808007 DOI: 10.1115/1.4043947] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Revised: 05/18/2019] [Indexed: 06/10/2023]
Abstract
Hydrostatic pressure (HP) regulates diverse cell behaviors including differentiation, migration, apoptosis, and proliferation. Abnormal HP is associated with pathologies including glaucoma and hypertensive fibrotic remodeling. In this review, recent advances in quantifying and predicting how cells respond to HP across several tissue systems are presented, including tissues of the brain, eye, vasculature and bladder, as well as articular cartilage. Finally, some promising directions on the study of cell behaviors regulated by HP are proposed.
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Affiliation(s)
- Shaobao Liu
- State Key Laboratory of Mechanics andControl of Mechanical Structures,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China
- The Key Laboratory of Biomedical InformationEngineering of Ministry of Education,
School of Life Science and Technology,
Xi'an Jiaotong University,
Xi'an 710049, China
- Department of Biomedical Engineering,Bioinspired Engineering and Biomechanics Center (BEBC),
Xi'an Jiaotong University,
Xi'an 710049, China
| | - Ru Tao
- The Key Laboratory of Biomedical InformationEngineering of Ministry of Education,
School of Life Science and Technology,
Xi'an Jiaotong University,
Xi'an 710049, China
- Department of Biomedical Engineering,Bioinspired Engineering and Biomechanics Center (BEBC),
Xi'an Jiaotong University,
Xi'an 710049, China
| | - Ming Wang
- The Key Laboratory of Biomedical InformationEngineering of Ministry of Education,
School of Life Science and Technology,
Xi'an Jiaotong University,
Xi'an 710049, China
- Department of Biomedical Engineering,Bioinspired Engineering and Biomechanics Center (BEBC),
Xi'an Jiaotong University,
Xi'an 710049, China
| | - Jin Tian
- Department of Biomedical Engineering,Bioinspired Engineering and Biomechanics Center (BEBC),
Xi'an Jiaotong University,
Xi'an 710049, China
- State Key Laboratory for Strength andVibration of Mechanical Structures,
Xi'an Jiaotong University,
Xi'an 710049, China
| | - Guy M. Genin
- The Key Laboratory of Biomedical Information
Engineering of Ministry of Education,
School of Life Science and Technology,
Xi'an Jiaotong University,
Xi'an 710049, China
- Department of Biomedical Engineering,Bioinspired Engineering and Biomechanics Center (BEBC),
Xi'an Jiaotong University,
Xi'an 710049, China
- Department of Mechanical Engineering &
Materials Science,
National Science Foundation Science and
Technology Center for Engineering Mechanobiology,
Washington University,
St. Louis, MO 63130
| | - Tian Jian Lu
- State Key Laboratory of Mechanics andControl of Mechanical Structures,
Nanjing University of Aeronautics and Astronautics,
Nanjing 210016, China
- Department of Structural Engineering & Mechanics,
Nanjing Center for Multifunctional LightweightMaterials and Structures,
Nanjing University of Aeronautics and Astronautics,
Nanjing 21006, China;
State Key Laboratory for Strength andVibration of Mechanical Structures,
Xi'an Jiaotong University,
Xi'an 710049, China
| | - Feng Xu
- The Key Laboratory of Biomedical InformationEngineering of Ministry of Education,
School of Life Science and Technology,
Xi'an Jiaotong University,
Xi'an 710049, China
- Department of Biomedical Engineering,Bioinspired Engineering and Biomechanics Center (BEBC),
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail:
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