Abstract
Cells and tissues can sense and react to the modifications of the physico-chemical properties of the extracellular environment (ECM) through integrin-based adhesion sites and adapt their physiological response in a process called mechanotransduction. Due to their critical localization at the cell-ECM interface, transmembrane integrins are mediators of bidirectional signaling, playing a key role in “outside-in” and “inside-out” signal transduction. After presenting the basic conceptual fundamentals related to cell mechanobiology, we review the current state-of-the-art technologies that facilitate the understanding of mechanotransduction signaling pathways. Finally, we highlight innovative technological developments that can help to advance our understanding of the mechanisms underlying nuclear mechanotransduction.
Introduction
During the last two decades, increasing evidence has suggested that the physico-chemical properties of the cell microenvironment and the physical forces exerted by cells and tissues play critical roles in the regulation of physiological and pathological situations. In both contexts, cells must adapt their behavior by converting physical signals into biochemical signals and changes in gene expression by using mechanochemical transduction, or mechanotransduction, signaling pathways.
Adherent cells are connected to the extracellular matrix (ECM) through the transmembrane receptor integrins. Mechanical signals can be detected via focal adhesion (FA) sites and translated into biochemical information through integrin-related signaling pathways. The inside tension generated by the actomyosin contractility can be transferred to the ECM through integrins at FAs. As a consequence, FAs serve as crucial sites for both outside-in and inside-out mechanotransduction (Figure 1). Although it is clear that integrins play a crucial role in translating outside-in and inside-out signals, it remains unclear how cells can be able to sense mechanical forces and convert mechanical signals into biological responses (Jaalouk and Lammerding, ). Moreover, this global mechanism is further complicated by the highly dynamic behavior of cells that can adapt their morphology and cytoskeletal organization in response to mechanical forces. In addition, specialized mechanoreceptors can enhance mechanosensation for critical processes such as blood pressure, auditory function or touch sensation by using specific organelles that can detect a wide range of stimulus frequencies (Peng et al., ). For instance, the so-called “hair” cells transduce mechanical vibrations into electrical signals that propagate to the brain. Located on the apical surface of sensory hair cells, hair bundles are filled with actin, named stereocilia. The mechanical deflection of the stereocilia toward the tall edge opens gated ion channels, while opposite deflection closes channels (Katta et al., ). Indeed, the actin filament sliding generates a force that changes the conformation of a transmembrane protein, leading to the transient entry of calcium ions. Other mechanisms such as the modifications of intracellular protein conformations or the direct transmission of forces to the cell nucleus are only being explored (Chu et al., ). To address this issue, the mechanobiology field has become very active at the forefront of current research (Roca-Cusachs et al., ). Mechanobiology is an interdisciplinary field that focuses on physical forces and their impact on cell mechanics. A major challenge in mechanobiology is to understand mechanotransduction mechanisms by which mechanical signals are transduced into a cascade of biochemical events (Humphrey et al., ) and to understand how these molecular events contribute to development, physiology and disease.
Figure 1
To answer these open questions, current studies need to stimulate mechanically living cells and tissues and then determine their mechanical and functional responses. Current studies on cell mechanotransduction are mostly limited by the techniques that are available to impose mechanical stimulation at both single cell and tissue levels and, in turn, allow to measure biomechanical and biochemical cell responses. Here, we introduce some basic concepts of mechanobiology and we review recent experimental developments that have significant implications for addressing challenging questions in cellular mechanotransduction.
Basic Concepts of Mechanobiology
The concept of force in cell biology can be intuitively related to pushing or pulling actions exerted by individual or assembly of cells. Even if the concept of force in cell biology is difficult to define, it exists a wide range of physiological situations where mechanical events are crucial to the establishment of cellular functions. For instance, the division of eukaryote cells requires the assembly of a bipolar spindle, which the morphology mostly depends on the activities of molecular motors that generate pushing or pulling forces on the microtubule-based mitotic spindle (Shimamoto et al., ). The quantification of cellular forces requires the development of micro- or nano-sensors capable of converting forces into mechanical deformations, knowing the material properties of the force sensor (i.e., the spring constant or the elastic modulus). Micro- or nano-sensors provide therefore an exact readout of forces from the material deformation within a range from few piconewtons to hundreds of nanonewtons.
Force assays allow to probe the mechanical properties of cells, which describe the cell deformation over time in response to an applied stress. The elastic modulus corresponds to the scaling between stress and strain of cells and depends on the deformation mode (Figures 2A–C). The Young's modulus corresponds to the cell elasticity with a unit of pascals (Pa) under extension. This fundamental property of living cells and tissues is involved in the establishment of their three-dimensional (3D) shapes under a mechanical stress. However, one must consider that living cells and tissues need to be considered as viscoelastic living materials (Figure 2D). Viscoelastic materials undergoing a mechanical deformation store and dissipate mechanical energy (Coppée et al., ). The viscoelastic behavior of cells and tissues leads to the relaxation of the mechanical stress and the increase of the deformation over time (Moeendarbary and Harris, ) (Figures 2E,F). Various rheological models, such as the standard linear solid model, have been proposed to describe the viscoelastic behavior of cells and tissues (Figure 2D).
Figure 2
In addition to the investigation of the mechanical properties of cells themselves, forces applied by cells on their surrounding are key for understanding inside-out mechanotransduction pathways. Contractile cellular forces are transmitted to other cellular neighbors via cell-cell adhesive interactions (i.e., cadherins) and to their local microenvironment through cell-matrix interactions (i.e., integrins). Cellular tractions forces occur across small-length scales (nano- to micrometers) in the range of pico to nanonewtons, making challenging a direct experimental measurement. Interestingly, ion channels have been proposed for decades to be central for sensing mechanical forces, but their identity remained largely elusive until the discovery of Piezo 1 and Piezo 2 channels (Coste et al.,
In the human body, the magnitude of forces exerted by cells varies significantly and mainly depends on the physiological location of the cells. Indeed, each type of tissue construct is characterized by both specific physico-chemical and mechanical properties. For this reason, a large effort has been made in the last two decades to propose novel synthetic materials that can recapitulate the physico-chemical properties of the complex native cellular microenvironment.
Synthetic Matrices to Reproduce the Complexity of the Native Cell Microenvironment
In human tissues, the ECM is a highly 3D dynamic structure where cells have interactions with a myriad of biochemical (e.g., soluble factors) and biophysical (e.g., stiffness/stress) cues that direct their functions. Cells are constantly remodeling the ECM through synthesis, degradation and chemical modifications. These processes imply important changes in ECM properties (e.g., stiffness and porosity), which in turn drive cell fate and maintain tissue homeostasis (Baker et al.,
Hydrogels are defined as crosslinked water-swollen biomacromolecules that form a three-dimensional structure. The large amount of water in hydrogels allows the diffusion of biomolecules secreted by cells. The design of hydrogels suitable for cell culture requires to reproduce both the biochemical and mechanical properties of their native microenvironment. Water-swollen polymers such as poly(ethyleneglycol) (PEG), poly(vinyl alcohol) (PVA), poly(2-hydroxyethylmethacrylate) (PHEMA) and poly(acrylamide) (PAAm) can form elastic hydrogels that can reproduce some basic mechanical aspects of soft tissues (Figure 3A) (Annabi et al.,
Figure 3

(A) The elasticity of living tissues spans a wide range of rigidities which are organized in three domains: soft (0.1 ≤ E ≤ 1kPa), intermediate (1 ≤ E ≤ 10 kPa) and stiff (10 ≤ E ≤ 100 kPa). (B) Acrylamide (AAm, in black) and bisacrylamide (bis-AAm, in blue) and N-hydroxyethylacrylamide (HEA, in red) monomers were co-polymerized to form a hydrophilic network of polyacrylamide containing hydroxyl groups (hydroxy-PAAm) by random radical polymerization (Grevesse et al.,
In addition to these works, magnetic hydrogels (M-gel systems) (Niland et al.,
Even if considerable efforts have been made to design synthetic hydrogels with finely tunable physico-chemical and mechanical properties, ECM fiber networks remain more complex than their synthetic analogs. Indeed, native ECM fibers can be mechanically stretched by cell-generated forces that will upregulate their Young's modulus (Liu et al.,
Standardizing Cell-Substrate Interactions With Microfabricated Tools
Interactions of cells with the ECM determine their fate through the modulation of cell shape, cell-surface adhesions and cell spreading. The ability to produce precisely engineered surfaces for cell culture that can provide robust in vitro assays to control cell adhesion is crucial for understanding inside-out and outside-in mechanotransduction signals.
In conventional two-dimensional (2D) cultures, cells grow until confluence without any specific spatial organization. Major drawbacks of conventional cultures are therefore the difficulty to manage complex parameters involved in mechanotransduction signaling pathways. To address this limitation, a large effort has been made during the last two decades to develop robust micropatterning techniques for manipulating cell adhesion patterns. Although the first micropatterning methods were introduced more than 40 years ago (Carter,
Figure 4

(A) Microcontact printing allows to from 2D micropatterns of proteins on flat culture substrates from a PDMS structured microstamp (Grevesse et al.,
The design of well-defined micro- and nano-structured surfaces can help to understand interactions of cells with topographical features. It has been observed that epithelial cells align along the preferential direction of nano-grooves, suggesting that the ECM topography encountered by cells in vivo is involved in cell polarization (Teixeira et al.,
Mechanical Probing of Mechanotransduction Signaling Pathways
The characterization of the cells mechanical properties requires to apply well-controlled external forces to induce measurable deformations. The quantification of the mechanical deformation as a function of time and its dependence on the loading frequency allows to determine the viscoelastic behaviors of living cells and tissues. Over the last few years, original methods have been developed to apply well-controlled forces to living cells and tissues. For instance, a parallel plate method based on the bending of glass microplates of calibrated stiffness enables quantifying either passive (i.e., cell deformability) or active (i.e., cell traction) forces. Interestingly, this technique can be combined with confocal microscopy or total internal reflection fluorescence (TIRF) microscopy for studying the dynamics of cell-substrate interactions (Mitrossilis et al.,
However, the implementation of these techniques in the broader biological community remains challenging due to the inherently multidisciplinary expertise required to conduct and interpret mechanical measurements. Interestingly, some of these force assays can be also used for studying how external forces are transduced into biochemical and functional responses and to identify the corresponding mechanotranduction signaling pathways, in normal or pathological situations (Chen,
Figure 5

Examples of force-application techniques used to probe the rheological properties of cells or to apply well-defined external loads for studying mechanotransduction pathways. From left to right: atomic force microscopy (AFM), micropipette aspiration, optical tweezers, magnetic tweezers and uniaxial stretcher.
At the lowest force levels, Atomic Force Microscopy (AFM) has progressively emerged as a key platform for mapping the mechanical properties of living biological samples on spatially defined areas ranging from few nanometers to several tens of micrometers. By using AFM to probe fibroblasts seeded on polyacrylamide hydrogels with varying stiffness, Solon et al. demonstrated that fibroblasts are able to adapt their own stiffness to match the elastic modulus of its substrate (Solon et al.,
For larger levels of forces, other techniques have emerged such as optical tweezers (Killian et al.,
Magnetic tweezers rely on the manipulation of paramagnetic beads by applying a controlled magnetic field that exerts pulling forces on the beads. Paramagnetic beads can be chemically functionalized to present adhesion proteins at their surface that can be recognized by the cell cytoskeleton. For instance, Grevesse et al. used fibronectin-coated microbeads to link the cytoskeleton of cortical neurons and probe the mechanical properties of the two main subcellular compartments (soma vs. axon) (Grevesse et al.,
Micropipette aspiration partially aspirates a single cell by applying a subatmospheric pressure through a glass micropipette. This technique was first used on circulating white blood cells (Tsai et al.,
Other techniques, such as membrane stretching, allow to apply a fixed strain to single cells or a cell sheet by deforming an elastic substrate. The mechanical deformation is thus transmitted to the cells through integrin-related adhesions and involved outside-in mechanotransduction signaling pathways. Silicone elastomers such a poly(dimethylsiloxane), PDMS, are usually used to form elastic membranes. Strain rates commonly vary from 0.1 to 10 Hz with a typical strain percentage ranging from 1 to 30% to keep the membrane deformation in the linear elastic regime. Uniaxial or biaxial strain field can be applied, depending on the complexity of the strain device. One dimensional (1D), or uniaxial strain, corresponds to the membrane stretch in one direction. In this configuration, the two free edges must be constrained to avoid compression in the direction perpendicular to the strain as a result of the Poisson effect. In two-dimensional (2D) strain devices, a uniform biaxial deformation is obtained from the stretching of a thin elastic membrane. Membrane stretching presents the advantage of being applicable on 2D tissues, providing an average readout from millions of cells. In addition, PDMS membranes are optically transparent and could be prepared with thicknesses ranging from 50 to 250 μm, which are particularly well-suited to perform live stretching experiments on an inverted microscope. Uniaxial stretching experiments have been performed to mimic the deformation of brain tissues during traumatic events. Indeed, it was found that traumatic stimulations of integrins are an important etiological contributor to mild Traumatic Brain Injury (mTBI). Cultures of cortical neurons were stretched with an abrupt one-dimensional strain to reproduce in vitro TBI. Stretching experiments revealed that the Rho signaling pathway can be activated through integrins and may contribute to the diffuse axonal injury reported in mTBI (Hemphill et al.,
Measuring Quantitatively Protrusive and Contractile Forces
Actin filaments (AFs) are semiflexible polymers with a persistence length of ~17 μm (Gittes et al.,
To test this experimentally, Prass and coworkers introduced a very elegant way to directly measure the protrusive forces exerted by the leading edge (Prass et al.,
Figure 6

(A) Protrusive forces exerted by the lamellipodia of migrating cells can be quantified by measuring the deflection of an AFM cantilever over time. A cantilever of calibrated spring constant is placed vertically perpendicular to the surface in front of the leading edge and its vertical position is measured optically over time. The polymerization of actomyosin filaments exerts a load force that pushes on the cell membrane that deflects the cantilever. (B) Traction force microscopy (TFM) measures the contractile forces exerted by adherent cells on an elastic hydrogel that contains fluorescent embedded beads of ~200 nm in diameter. Cell spreads on the hydrogel, leading to its contraction (stressed state in green). After trypsin detachment, the contractile stress is released, and the fluorescent beads relax (in red). The differences of bead position between stressed and relaxed states serve as markers to visualize the hydrogel deformation in a 2D plane. (C) Gel deformations are estimated using a Fourier-based difference-with-interpolation image analysis. To characterize the contractile forces of each cell, the elastic strain energy stored in the polyacrylamide gel due to cell tractions is calculated as the product of local tractions and deformations, integrated over the spreading area of the cells. The scale bar is 20 μm.
The actomyosin cytoskeleton of adherent cells generates contractile forces which are transmitted to the ECM through integrin-based adhesions (Figure 1). Contractile forces are crucial for physiological processes such as embryo morphogenesis or wound healing (DuFort et al.,
In this context, PAAm hydrogels with embedded fluorescent beads of ~200 nm in diameter has emerged as a robust method to determine quantitatively traction forces exerted by adherent cells (Figures 6B,C). Adherent cells deform the substrate with cellular tractions that have a very small magnitude (pN—nN) and occur across small length scales (nm—μm). Due to their superior optical and mechanical properties, PAAm hydrogels are now considered as the substrate of choice to perform continuous traction force measurements. Indeed, PAAm hydrogels are optically transparent and their mechanical properties are also ideal since they are linearly elastic over a wide range of deformations. Traction forces can be estimated by comparing two images of fluorescent images of fluorescent markers embedded in the elastic hydrogel (Figure 6B). The first image corresponds to the stressed state where the cell is applying traction forces on the substrate, whereas the second corresponds to the fully relaxed state of the substrate. This reference image is obtained by detaching cells with a trypsin treatment. Although TFM was originally conceived to compute a 2D force field exerted by a single cell on a flat substrate (Han et al.,
In vivo cells exist within three-dimensional (3D) matrices, however measuring tractions of cells in 3D remains difficult and the nonlinear nature of collagen type I hydrogels, which is already used for 3D cell culture, prevents calculation of traction forces. To address this challenge, vertical cantilevers were molded from silicone elastomers in order to measure forces from tissue constructs composed of few 100 of cells (Legant et al.,
Determining Mechanical and Functional Properties of the Cell Nucleus
The mechanical stability of the nucleus defines its capability of maintaining a three-dimensional shape by minimizing deformations and recovering strain after a mechanical deformation. Interestingly, it has been demonstrated that large nuclear deformations increase the risk of modifying nuclear architecture and may lead to DNA damages and ultimately cell death (Versaevel et al.,
The quantifications of deformations and recovery of nuclei are required for understanding the mechanisms involved in the nuclear response to forces and in the maintenance of its mechanical stability. To address this challenge, micropipette aspiration has been shown to be an interesting method by providing a robust way to characterize nuclear viscoelastic properties. This technique was used by Guilak and coworkers to demonstrate the individual contribution of each nuclear components. The authors conclude that nuclei behave as a viscoelastic material which is 3–4 times stiffer than the cytoplasm and nearly twice as viscous as the cytoplasm (Guilak et al.,
It has been shown that genome expression is affected by spatial positioning and chromatin motions (Misteli,
Figure 7

(A) LINC complexes are made of the inner nuclear membrane (INM), SUN protein trimers, the outer nuclear membrane (ONM) and KASH proteins. KASH protein mediates interactions with actin cables through Nesprin 2. (B) A-type and B-type lamins (orange and blue, respectively) form individual polymer networks which are juxtaposed on the inside of the nuclear envelope. Both lamin types are found at the interface between chromatin and the cytoskeleton (Swift and Discher,
The overall nuclear stiffness is mainly established by the remodeling of lamina and chromatin. It is therefore important to decipher their individual roles for a better understanding of the nuclear mechanics and the regulation of cellular functions. It has been shown that chromatin controls the resistance to small deformations, while lamina dictates the nuclear strain stiffening that dominates resistance to large deformations (Stephens et al.,
Cell shape changes have been found to modulate nuclear shape, DNA expression (Versaevel et al.,
Optogenetic Methods to Interrogate Mechanotransduction Pathways
Optogenetics is a rapidly evolving technology that aims to control optically and precisely specific events in genetically targeted living cells and tissues. Optogenetic methods allow to deliver an optical control at high temporal (millisecond-scale) and spatial resolution in physiological or pathological situations (Deisseroth,
Figure 8

(A) The optogenetic principle is based on light-sensitive proteins from algae called opsins. (B) Opsins can be expressed in single cells, cell clusters or tissues by using transfection with a gene construct inserted in viruses. By using different wavelengths, optogenetics allows to activate or inhibit for instance neurotransmission, or specific mechanotransduction signaling pathways in living cells, such as neurons.
In 1979 Francis Crick described one of the major challenges facing neuroscience by the need to control one cell type in the brain while leaving other cell types unaltered. Since electrodes cannot be used to precisely target defined cells, Crick envisioned that light might be used to control and monitor the activity of genetically defined neuronal populations. However, it took more than 30 years for neuroscientists to develop the first approaches for optogenetics. In the early 2000s, Zemelman and Miesenbock (Sloan- Kettering Cancer center, New York) (Zemelman et al.,
Although it arose from neurosciences, optogenetics has started to address recently open questions about mechanotransduction mechanisms in various cell types. For instance, Bruegman et al. showed that optogenetic stimulations of skeletal muscles expressing the light-sensitive channel ChR2 can generate large forces, which could be useful for studying mechanotransduction signaling pathways in muscle cells (Bruegmann et al.,
Summary and Future Perspectives
Novel techniques developed to probe cellular forces have reported a wide range of mechanisms acting over multiple length scales (from molecular forces to supra-cellular force patterns). As a consequence, physical forces cannot be only considered as basic switches of mechanotransduction signals, but as the key mechanism to propagate signals between cells. Interestingly, recent technological developments allow to study the molecular mechanisms used by cellular forces to alter gene activities by modulating the conversion of mechanical stimuli into biochemical signals. Advancements in force measurement methods will therefore permit to address many remaining open questions surrounding cell-substrate but also cell-cell interactions, such as cadherins. For instance, understanding how mechanical tension exerted on cadherins is converted into biochemical signals and how this signaling in turn leads to changes in cell expression remains an open question in cell biology.
The understanding of the molecular mechanisms involved in outside-in and inside-out mechanotransduction signaling pathways requires to elaborate integrated strategies combining super resolution fluorescence microscopy (e.g., stimulated emission depletion, STED—photo-activated localization microscopy, PALM—stochastic optical reconstruction microscopy, STORM) with biophysical probes and multipatterning of proteins. In addition to these combined imaging techniques, FRET biosensors could be applied to examine force transmission across the cytoskeleton to nuclear envelope proteins, chromatin remodeling or mechanically induced changes within the nucleus. FRET between fluorophores of a single type, known as homoFRET, is a promising method to visualize and quantitatively measure changes in protein ratios upon force application, based on the signal produced when molecules labeled with enhanced green fluorescent protein, such as G-actin, assemble into actin filaments.
A further challenge should be devoted to a better understanding of how ECM sensing can activate specific transcription factors and translocates them to the cell nucleus. Indeed, it remains unclear whether chromosome configurations can be altered in response to the modifications of the mechanical properties of the nucleus that can be modulated by changes in the ECM physico-chemical properties. Furthermore, several aspects of Piezo channels must be addressed in the near future to determine the role of specific mechanotransduction processes in regulating physiological and pathological processes. For instance, it will be important to decouple the role of Piezo 1 and 2 that makes them such versatile mechanosensors. In addition, questions about conformational changes leading to channel (in-)activation remain to be answered.
Finally, a major technical challenge in cellular mechanotransduction concerns the development of synthetic models of the stem cell niche to manipulate the biophysical and biochemical properties of the stem cell microenvironment. Indeed, the discovery of induced pluripotent stem (iPS) cells as patient-specific stem cells represents a breakthrough for the basic cell biology and new therapies. Understanding how stem cell behavior can be regulated by mechanical forces can provide fundamental insights for the design of artificial niches for regenerative therapies. In this context, we envision exciting technical developments for the light-controlled activation of cellular forces, dynamic organoid systems and synthetic niches with a spatiotemporally controlled release of proteins and growth factors. Smart stem cell niches that integrate the control of material properties (stiffness, topography, etc.) and protein patterning to recapitulate cell-cell and cell-matrix interactions is required to identify the ECM cues which are relevant to niche-like regulation of stem cell fate. By guiding collections of stem cells that can assemble in 3D, organ-on-a-chip platforms represent a valuable technology to form realistic in vitro models of organ-level systems required to interrogate mechanotransduction pathways in stem cells but also to realize a precision medicine approach by testing important differences in varied patient cohorts.
Statements
Author contributions
DM and SG designed the content of the article. All authors performed literature survey, prepared the figures and wrote the article. All authors edited and reviewed the article before submission.
Funding
This work was financially supported by the FEDER project PROSTEM, the Belgian National Fund for Scientific Research (F.R.S.-FNRS, Crédits de Recherches–J009916F and J0191.17) and the MAT(T)ISSE project financially supported by Interreg France-Wallonie-Vlaanderen (Fonds Européen de Développement Régional, FEDER-ERDF). DM, LA, CB, EV, ML, and AP are financially supported by FRIA (F.R.S.-FNRS). The Mechanobiology and Soft Matter group belongs to the French research consortium GDR 3070 CellTiss.
Acknowledgments
The authors apologize to the many colleagues whose work could not be cited due to space constraints.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Summary
Keywords
mechanobiology, mechanotransduction, cytoskeleon, integrins, microsystem and macrosystem approaches, force, signaling/signaling pathways
Citation
Mohammed D, Versaevel M, Bruyère C, Alaimo L, Luciano M, Vercruysse E, Procès A and Gabriele S (2019) Innovative Tools for Mechanobiology: Unraveling Outside-In and Inside-Out Mechanotransduction. Front. Bioeng. Biotechnol. 7:162. doi: 10.3389/fbioe.2019.00162
Received
31 January 2019
Accepted
20 June 2019
Published
16 July 2019
Volume
7 - 2019
Edited by
Sara Baratchi, RMIT University, Australia
Reviewed by
Yubing Sun, University of Massachusetts Amherst, United States; Gerald A. Meininger, University of Missouri, United States; Anthony John Ricci, Stanford University, United States
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Copyright
© 2019 Mohammed, Versaevel, Bruyère, Alaimo, Luciano, Vercruysse, Procès and Gabriele.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Sylvain Gabriele sylvain.gabriele@umons.ac.be
This article was submitted to Biomechanics, a section of the journal Frontiers in Bioengineering and Biotechnology
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