Viscoelasticity in 3D Cell Culture and Regenerative Medicine: Measurement Techniques and Biological Relevance

Abstract

The field of mechanobiology is gaining prominence due to recent findings that show cells sense and respond to the mechanical properties of their environment through a process called mechanotransduction. The mechanical properties of cells, cell organelles, and the extracellular matrix are understood to be viscoelastic. Various technologies have been researched and developed for measuring the viscoelasticity of biological materials, which may provide insight into both the cellular mechanisms and the biological functions of mechanotransduction. Here, we explain the concept of viscoelasticity and introduce the major techniques that have been used to measure the viscoelasticity of various soft materials in different length- and timescale frames. The topology of the material undergoing testing, the geometry of the probe, the magnitude of the exerted stress, and the resulting deformation should be carefully considered to choose a proper technique for each application. Lastly, we discuss several applications of viscoelasticity in 3D cell culture and tissue models for regenerative medicine, including organoids, organ-on-a-chip systems, engineered tissue constructs, and tunable viscoelastic hydrogels for 3D bioprinting and cell-based therapies.

Figure 1

(a) Axial force causes elongation or compression in the direction of force and inverse deformation on the perpendicular direction of force (Poisson’s ratio). (b) Tangential (shear) force causes shear deformation. (c) Volumetric pressure results in bulk deformation. (d) Shear stress on fluid causes flow of the material.

Figure 2

(a) Relationship between the stress and strain in elastic, plastic, elastic-plastic, and viscoelastic material. (b) Creep test over time for various materials. (c) Relaxation test over time for different material types.

Figure 3

(top) Purely elastic materials show no phase difference between stress and strain. (middle) Viscoelastic materials show phase difference between the stress and strain signal. (bottom) Shear modulus in viscoelastic materials is a vector summation of two orthogonal components, storage (elastic) modulus and loss (viscous) modulus.

Figure 4

The process of mechanotransduction translates the microenvironment viscoelasticity and cell–cell tension forces into chemical signals to regulate the cell processes. Typically, integrin proteins form the focal adhesion between the cell and ECM. Cadherin proteins are responsible for cell–cell forces. Focal adhesion is regulated by environment viscoelasticity and through polymerization of actin and myosin; the mechanical cues are transmitted to the nucleus and result in change of gene and protein expressions. Focal adhesion kinase (FAK); muscle LIM protein (MLP); myocardin-related transcription factor A (MRTFA); yes-associated protein (YAP). Adapted with permission from reference (24). Copyright 2014 Nature Publishing Group.

Figure 5

Nucleus and cytoskeleton connection. Outside the outer nuclear membrane (ONM), different nesprin isoforms connect to F-actin, intermediate filaments (IF), and microtubules (MTs). SUN proteins bind to nesprins in the perinuclear space (PS) and interact with nuclear lamina through lamin A in the inner nuclear membrane (INM). Emerin proteins connect the Sun proteins to lamin A and directly interact with chromatin. Adapted with permission under a Creative Commons [CC-BY 4.0] from reference (37). Copyright 2018 Frontiers Media.

Figure 6

Remodeling of the cervical ECM during pregnancy. (a) The architecture of ECM components in nonpregnant women. (b) The morphological changes near the end of pregnancy. Water contents increased, the diameter of collagen fibers increased, crimping increased, and PGs are loosened in (b). Adapted with permission under a Creative Commons [CC-BY 4.0] from reference (20). Copyright 2020 Sensors.

Figure 7

(a) Controlled Shear Rate system diagram. (b) Controlled Shear Stress system diagram.

Figure 8

Geometries are available for rotational rheometers.

Figure 9

A variety of sizes of cones and plates are available. The larger sizes are recommended for low viscosity materials, and smaller sizes are recommended for high viscosity materials.

Figure 10

Parallel plate vs cone plate. The cone plate applies constant shear rate.

Figure 11

(a) The first drawing of the AFM tip in the vicinity of the sample. (b) Basic system diagram of AFM. By moving the cantilever on the sample surface, the angle of laser reflection from the cantilever changes, which the photodetector records. (c) Information obtained by AFM is in the form of a force–distance curve. Each pixel requires at least one force–distance plot to obtain material property at that point. Adapted with permission from references (64) (Copyright 2003 The American Physical Society) and (65) (Copyright 2021 Portland Press).

Figure 12

A variety of cantilever tips are available for different material types and stiffnesses. Pyramidal tip shape is mainly used for solids. For softer material, other shapes of the tip should be considered. Each tip has its own computational model to extract the material properties accurately. Adapted with permission from reference (66). Copyright 2019 Springer Nature.

Figure 13

AFM operates in 3 distinct modes. In contact mode (left), the tip of the cantilever touches the surface of the material and scans it. In the noncontact mode (middle), the tip hovers above the surface of the material and oscillates at a very small amplitude. The retention and repulsive forces between the tip and the material of interest cause deflection on the cantilever, which changes the amplitude or the frequency of oscillation. In the semicontact mode (right), while the tip oscillates above the surface of the sample, occasionally touches the material to eliminate the effect of material adhesion and friction. Adapted with permission under a Creative Commons [CC-BY 4.0] from reference (67). Copyright 2018 BioMed Central.

Figure 14

The tip of the AFM can be functionalized to perform other types of measurements in addition to the mechanical properties. Ligands and antibodies could be attached to the tip, and during the scan, they will bind to specific molecules for chemical contrast, molecule recognition, and structural information. If the tip has a conductive layer, it can detect electrochemical information from the surface of the sample. Adapted with permission from reference (78). Copyright 2018 Annual Review of Analytical Chemistry.

Figure 15

(a) Nanoindentation records stress versus displacement at the tip of the indenter and, based on the tip geometry, computes the mechanical properties of the sample. The difference between loading and unloading curves shows the hysteresis of the material, which is an indication of viscoelasticity. (b) and (c) depict different probe tip shapes which result in different load–distance curves. (d) and (e) If the material causes negative changes in the load-distance curve, the effect of adhesion should be subtracted from material mechanical properties. Adapted with permission from reference (79). Copyright 2005 Woodhead Publishing.

Figure 16

(a) A system diagram of the nanoindentation setup. The probe tip contacts the material and, based on displacement and the applied stress, force–distance curves are obtained. (b) The diagram of the recent nanoindentation device that is based on deflection of the ferrule and light interferometry. The tip of this device has a spherical shape and is more suitable for very soft materials such as hydrogels and cells. Adapted with permission from references (80) (Copyright 2003 National Institute of Standards and Technology) and (81) (Copyright 2012 Review of Scientific Instruments).

Figure 17

Representation of the series of processes needed to measure the sample viscoelasticity. (1) Diagram of the sample holder and the flexible membrane with known mechanical properties. The sample is loaded in the sample holder. The diameter and height of the holder are fixed dimensions. (2) After loading the sample into the machine, an ultrasonic probe vibrated the sample inside the holder. An optical system measures the displacement on the surface of the sample and calculates the viscoelasticity of the sample. (3) Elastic and viscous moduli are plotted over time, before, during, and after the gelation. The user can record how long the gelation takes time and how much the gel mechanics have changed. Adapted with permission from reference (83). Copyright 2017 Society for Biomaterials.

Figure 18

Various methods of excitation in the OCE and their comparison with the Brillouin method, which does not need external force. (a) A compression plate applies force uniformly on the sample and deforms it. Light coherent microscopy measures the deformation, and the instrument calculates viscoelasticity based on stress and measures strain. (b) An external force generator applies mechanical waves to generate standing waves in a defined boundary. OCE measures harmonics of standing waves to calculate the mechanical properties. (c) External mechanical waves are applied to the surface of the material, and shear wave velocity is measured, which is related to Young’s modulus. (d) In Brillouin microscopy, there is no external force. Photons interact with phonons inside the sample and measure their vibrations. The Brillouin technique measures longitudinal properties, not the elastic or viscous modulus. Adapted with permission from reference (85). Copyright 2017 Nature Photonics.

Figure 19

(top) Optical system block diagram of the OCE. (bottom) Comparison of the OCE with other viscoelasticity techniques over spatial resolution and field of view. AFM (atomic force microscopy), OT (optical tweezers), UE (ultrasound elastography), MRE (magnetic resonance elastography), MPM (multiphoton microscopy), CBM (confocal Brillouin microscopy), LSI (laser speckle imaging), HI (holographic imaging). Adapted with permission from reference (88). Copyright 2015 Wiley-VCH.

Figure 20

(left) Light scattering from a solid-like material (for example, collagen fibers) and liquid-like material (cytosol). (right) The Brillouin frequency shift is larger in solid-like materials compared with liquid-like materials, but the line width is smaller in rigid materials compared with liquid-like materials. Adapted with permission under a Creative Commons [CC-BY 4.0] from reference (97). Copyright 2019 Nature Methods.

Figure 21

Three configurations for microfluidic devices have been introduced to measure rheologically complex fluids. (a) The capillary devices are used for measuring shear viscosities. The viscosity is a function of flow rate Q and pressure drop ΔP throughout the length of the channel L. w and d represent the width and depth of the channel, respectively. Two main approaches of controlled pressure drop and controlled flow are identified for capillary viscometry. Viscosities in the range of 0.001–10 Pa·s have been measured over a range of shear rate of 0.1–0.001/s. In some cases, a sample volume in the range of nanoliters was successfully measured. (b) The stagnation point flow is used for extensional deformation. Near the stagnation point, the flow is in a vorticity-free state, which can result in orientation of the microstructural components of the fluid. Video or fluorescent microscopy is used for observing the flow birefringence at the stagnation point to obtain the rheological information. (c) Contraction devices measure the sudden pressure drop in an imposed flow. Adapted with permission from reference (104). Copyright 2009 Elsevier.

Figure 22

(A) A simple diagram of the micropipette aspiration technique. By applying negative pressure to the tip, the particle will gradually move into the pipet. The experiment is done either by constant pressure or by constant ramp pressure. (B) The pressure changes either in step function or by a ramp function over time. (C) The length of the material drawn into the pipet changes over time, and the curve of change of the length depends on the change in pressure. Adapted with permission from reference (108). Copyright 2019 Biophysical Society.

Figure 23

The micropipette aspiration technique can be combined with other technologies such as (A) microindenter, (B) fluorescent labeling, (C, D, E) secondary pipet, (F) spheroid manipulation, (G) microfluidic devices, and (H) branches of biopolymers or growing fungal cell. Adapted with permission from reference (108). Copyright 2019 Biophysical Society.

Figure 24

(a) PEG and genetically encoded tension sensor extension. (b) Tension gauge tether rupture. (c) DNA hairpin extension. (d) Change in force of genetically encoded tension sensors translates into an analog change in fluorescence. (e) Rupturing the tension gauge causes an abrupt (digital) change in fluorescence that is reversible. (f) Change in DNA hairpin force translates into a digital and irreversible change in fluorescence. Adapted with permission under a Creative Commons [CC-BY 4.0] from reference (123). Copyright 2021 ACS.

Figure 25

Schematic of the optical path and the converging beam. The focal point is aligned with the center of the material thickness. Adapted with permission under a Creative Commons [CC-BY] from reference (140). Copyright 1970 Physical Review Letters.

Figure 26

Basic schematic diagram for optical trapping. Adapted with permission from reference (87). Copyright 2018 ACS Macro Letters.

Figure 27

(a) Illustration of the focused acoustic beam in the vicinity of the particle. (b) Configuration of trapping forces applied to the particle. (c) A pair of interdigit transducers to generate a planar standing-wave field for 3D manipulation of a particle. (d) Numerical simulation of an acoustic beam near the particle in 3D. Adapted with permission under a Creative Commons [CC-BY 4.0] from references (147) (Copyright 2015 Elsevier) and (144) (Copyright 2018 Nature Publishing Group).

Figure 28

(top) Strain elastography method. (middle) ARFI. (bottom) Shear Wave Measurements. Adapted with permission under a Creative Commons [CC-BY 4.0] from references (153,162). Copyright 2018 Springer Nature. Copyright 2015 Elsevier.

Figure 29

Some material properties that are critical for 3D printing.