Micro-device and characterization method for quantitatively characterizing micro-scale cell population expansion force
By recording the displacement field of fluorescent particles under microscopic physical constraints and combining it with an elasticity model, the problem of quantitative measurement of microscale cell population expansion force in existing technologies has been solved, achieving high-precision characterization of cell population expansion force, which has significant potential for academic and clinical applications.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2026-03-06
- Publication Date
- 2026-06-16
AI Technical Summary
Existing cell mechanics measurement techniques are insufficient to quantitatively characterize the outward expansion force of cell populations under physical constraints in real time and directly at the microscale. Traditional methods have low measurement accuracy and cannot meet the need for precise mapping of tumor malignancy.
A micro-physical constraint environment was constructed using a micro-patterned elastic barrier. By recording the displacement field of fluorescent particles before and after cell removal, and combining it with an elasticity analysis model, the population expansion force was accurately measured.
This method enables high-precision quantitative characterization of the expansion capacity of microscale cell populations, significantly improving measurement accuracy and repeatability, and has important academic value and clinical translation potential.
Smart Images

Figure CN122218931A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of biomechanics and micro / nano manufacturing technology, specifically a microscopic device and method for quantitative characterization of the expansion force of microscale cell populations. Background Technology
[0002] Cellular mechanical behavior plays a crucial role in biological processes such as tumor migration, embryonic development, and tissue repair. During the evolution of malignant tumors, tumor cells not only exhibit changes in the mechanical properties of individual cells but also demonstrate an expansionary mechanical response of a large cell population to the surrounding matrix. Among these, the outward expansion force generated by the cell population under spatial physical constraints (i.e., population expansion force) is a key biomechanical indicator reflecting the tumor's invasiveness and malignancy.
[0003] In biomechanics, precise measurements of cellular mechanics are of profound significance for studying tumor evolution mechanisms, developing novel anticancer drugs, and establishing biomechanical diagnostic standards. For example, in mechanotherapy, studying how cell populations overcome physical barriers to expand helps to elucidate the mechanisms by which cancer cells break through the basement membrane from a mechanical perspective.
[0004] However, existing cellular force measurement techniques still have significant limitations. Currently, mainstream traction force microscopy (TFM) primarily focuses on measuring the inward contraction force (traction) generated by cells, and is mostly used for observing single or small numbers of cells. For cell populations under physical constraints, the outward expansion force they generate is often masked by complex basal deformation signals, making it difficult for traditional methods to directly isolate and quantitatively characterize this outward force with a population synergistic effect.
[0005] Furthermore, existing indirect derivation methods and related mechanical measurement platforms typically rely on coarse geometric model assumptions, lacking specialized microscopic devices capable of quantifying the mechanical work done by cell populations to overcome physical limitations in real time and directly at the microscale. Limited by the disconnect between hardware design and supporting algorithms, existing methods often neglect the complex continuous medium mechanical properties during the conversion from displacement field to stress field in data processing, resulting in low measurement accuracy and failing to meet the clinical and research needs for precise mapping of tumor malignancy.
[0006] Therefore, developing a microscopic device that can integrate microenvironmental constraints and high-precision mechanical analysis functions to achieve direct quantitative characterization of the expansion force of microscale cell populations has become a key problem that urgently needs to be solved in the field of biomechanics research. Summary of the Invention
[0007] To address the problems of existing technologies, this invention provides a microscopic device and method for quantitative characterization of microscale cell population expansion force. It utilizes a micro-patterned elastic barrier to construct a microscopic physical constraint environment and spatially confine the cell population. By recording the displacement field of fluorescent particles before and after cell removal triggers mechanical relaxation, combined with an elasticity analytical model, it achieves accurate measurement of population expansion force.
[0008] The present invention provides a microscopic device for quantitative characterization of microscale cell population expansion force, comprising a functionalized modified glass substrate, an elastic barrier layer fixed on the substrate and having a microporous array structure, and fluorescent particles uniformly embedded in the elastic barrier layer for tracking displacement.
[0009] This invention also provides a method for quantitative characterization of the expansion force of microscale cell populations. Using the aforementioned microscopic device for quantitative characterization of the expansion force of microscale cell populations, the process is as follows: A microscopic physical constraint environment is constructed using the microporous array structure of the elastic barrier layer in the microscopic device, precisely restricting the space of the cell population planted within it. The geometric deformation of the elastic barrier layer during mechanical relaxation is captured by recording the positional coordinate deviations of the fluorescent particles before and after cell removal. Subsequently, a continuous displacement field is constructed using a computational module, and combined with a linear elastic constitutive model and principal stress algorithm, the expansion force and strain characterizing the cell population are quantitatively analyzed, achieving precise quantitative characterization of the collective mechanical behavior of cell populations at the microscale.
[0010] The characterization process specifically includes the following steps: 1) Fabrication of a master template with microstructures: forming an array of micropores by etching on the surface of a silicon wafer; 2) Preparation of PDMS transfer template: Polydimethylsiloxane PDMS is coated on the surface of the master template to obtain a PDMS transfer template with a micropillar array; 3) Glass substrate modification: The glass substrate is functionalized to enable its surface to covalently bond with the hydrogel; 4) Preparation of micropatterned hydrogels containing fluorescent particles: Fluorescent particles with a diameter of 500 nm were added to polyethylene glycol diacrylate (PEGDA) and mixed well. Then, a prepolymer solution was dropped onto the surface of a modified glass substrate. The droplets were covered by the PDMS transfer template and crosslinked and cured in situ by UV irradiation. The template was then removed, and a hydrogel barrier with a microporous structure and embedded fluorescent particles was obtained on the surface of the glass substrate. 5) Acquiring load displacement: Target cells are seeded in the micropores of the hydrogel barrier. After the cell density stabilizes, the load position coordinates of the fluorescent particles are obtained using a laser confocal microscope. 6) Acquiring displacement under no-load conditions: Cells were removed using sodium hydroxide solution to trigger mechanical relaxation of the hydrogel, and the coordinates of the no-load position of the fluorescent particles were obtained; 7. Quantitative analysis of expansion force: A continuous displacement field was constructed based on the positional deviation of fluorescent particles before and after cell removal, and the stress and strain fields of the cell monolayer were calculated accordingly.
[0011] Further improvements, in step 2), the preparation process of the PDMS transfer template is as follows: the polydimethylsiloxane (PDMS) base material and the crosslinking agent are mixed at a mass ratio of 10:1 and then covered on the surface of the master template. The mixture is cured at 80°C for 2 hours and demolded with anhydrous ethanol to obtain a PDMS transfer template with a micropillar array.
[0012] Further improvements are made in step 3), where the glass substrate modification process involves immersion in a 2.5 mol / L NaOH solution to induce the generation of hydroxyl functional groups on the glass surface. Subsequently, a dehydration condensation reaction is carried out at 80°C using the silane coupling agent TMSPMA, thereby grafting active methacryloyloxy functional groups onto the substrate surface to achieve covalent bonding between the hydrogel barrier and the glass substrate. Further improvements are made, and the glass substrate modification process in step 3) is as follows: 3.1) Surface hydroxylation pretreatment: High-precision glass slides are placed alternately in a 2.5 mol / L NaOH solution to ensure that the surface of each glass slide can be fully in contact with the alkaline solution. The slides are immersed at room temperature for more than 12 hours to thoroughly remove organic residues from the glass surface through strong alkaline etching and induce the formation of high-density hydroxyl (-OH) functional groups on the surface. 3.2) Cleaning and dehydration: Remove the glass slide from the alkaline solution and rinse it repeatedly with large amounts of deionized water and anhydrous ethanol until the washing solution is neutral and there are no visible residues on the surface. Then, wrap the glass slide tightly with clean aluminum foil and put it in an oven to dry it thoroughly, providing a dry chemical environment for the subsequent silanization reaction. 3.3) Silanization Coupling Reaction: The silane coupling agent 3-(isobutyryloxy)propyltrimethoxysilane TMSPMA was uniformly coated on the surface of the dried glass slide. The slide was wrapped with tin foil to protect it from light and left to stand at room temperature for 1 hour to allow the TMSPMA molecules to undergo preliminary physical adsorption on the glass surface. Subsequently, the wrapped glass slide was placed in an 80°C constant temperature oven and heated overnight. The high temperature promoted the dehydration condensation of the methoxy group of TMSPMA with the hydroxyl group on the glass surface to form a stable Si-O-Si covalent bond. 3.4) Washing and activation treatment: After the reaction is completed, the glass slide is taken out and rinsed repeatedly with anhydrous ethanol to thoroughly wash away the residual TMSPMA physically adsorbed on the surface; it is then wrapped with tin foil and placed in an 80°C oven for 1 hour to complete the final dehydration and activation, and a modified glass substrate with active methacryloyloxy groups grafted on the surface is obtained.
[0013] Further improvements are made to step 4), specifically the process for preparing the micropatterned hydrogel containing fluorescent particles, as follows: 4.1) Preparation of composite prepolymer solution: Polyethylene glycol diacrylate (PEGDA) was selected as the hydrogel matrix material, and a PEGDA solution was prepared; lithium phenyl (2,4,6-trimethylbenzoyl) phosphate (LAP) photoinitiator was added to the solution; then, fluorescent particles were added for dilution; the fluorescent particles were uniformly dispersed in the prepolymer solution by ultrasonic or mechanical stirring. 4.2) Dropping and Mold Pressing: The above-prepared composite prepolymer liquid is dropped onto the surface of the glass substrate that has been functionalized with TMSPMA. A PDMS transfer template with a micropillar array is vertically pressed onto the surface of the droplet. The prepolymer liquid fills the gaps between the PDMS micropillars through physical extrusion and removes air bubbles. 4.3) In-situ UV crosslinking: Using a UV lamp, the prepolymer liquid in the compression state is irradiated in situ. Under the action of LAP initiator, the PEGDA molecular chain undergoes free radical polymerization and forms covalent bonds with the TMSPMA molecules on the glass substrate surface. 4.4) Demolding and molding: After irradiation, the PDMS transfer template on the surface is removed. Due to the anchoring effect of TMSPMA, the hydrogel layer is firmly adhered to the surface of the glass substrate, and finally a hydrogel barrier with microporous structure and fluorescent particles uniformly embedded inside is obtained.
[0014] Further improvements are made, and the specific process of quantitative analysis of expansion force in step 7) is as follows: 7.1) Calculate the strain tensor components based on the displacement vector components u and v: ; ; ; Where u and v are the displacement vector components of the fluorescent particles within the elastic barrier layer relative to their initial positions in the x-axis and y-axis directions, respectively; x and y are the spatial coordinates in a two-dimensional Cartesian coordinate system. , These represent the normal strain components of the elastic barrier layer in the x and y directions, respectively. For the shear strain components of the elastic barrier layer; 7.2) Calculate the stress components according to Hooke's Law: ; ; ; in, , These represent the normal stress components of the elastic barrier layer in the x and y directions, respectively. denoted as the shear stress component of the elastic barrier layer; E is the Young's modulus of the elastic barrier layer material. The Poisson's ratio of the elastic barrier layer material; 7.3) The maximum principal stress of cell monolayer expansion was calculated. and maximum principal strain : ; .
[0015] The beneficial effects of this invention are as follows: 1. By integrating a micropatterned elastic barrier and a fluorescence tracer module, a standardized microscale physical constraint environment was constructed, filling the gap in the field of biomechanics for direct measurement devices of the outward expansion force of cell populations, and effectively making up for the functional limitation of traditional traction force microscopy devices that can only characterize inward contraction force.
[0016] 2. By utilizing high-precision microimprinting technology and a built-in continuous medium mechanics analytical model, quantitative analysis of population expansion force was achieved, significantly improving the accuracy and experimental repeatability of cross-sample measurements.
[0017] 3. The device and method provided by this invention have shown significant academic value and clinical translation potential in the biomechanical mapping of tumor malignancy, the analysis of cell population migration mechanisms, and the screening of drugs targeting mechanical targets. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 This is a flowchart of the quantitative characterization method for the expansion force of microscale cell populations described in this invention.
[0020] Figure 2 This is a schematic diagram of the overall structure and micropatterned physical constraint environment of the microscopic device for quantitative characterization of microscale cell population expansion force as described in this invention.
[0021] Figure 3This image shows a comparison of the expansion capacity of various malignant cell lines obtained using the microscopic device and characterization method described in this invention. Detailed Implementation
[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0023] This invention provides a microscopic device for quantitative characterization of microscale cell population expansion force, the steps of which are as follows: Figure 1 As shown, the process includes glass substrate modification, preparation of PDMS transfer template, preparation of micropatterned hydrogels containing fluorescent particles, cell seeding, measurement of displacement under loaded and unloaded states, and quantitative analysis of the mechanical field.
[0024] A specific implementation process of the present invention is as follows: Figure 1 As shown, taking the measurement and quantitative comparison of the population expansion capacity of human breast cell lines with different malignant progression gradients—from normal epithelial cells (MCF-10A) to precancerous cells (MCF-10AT)—under microscale physical constraints as an example, the specific implementation steps are as follows: 1) Preparation of PDMS transfer template: A microporous array master template with a height of 50 μm was obtained on a silicon wafer by photolithography using a mask. The PDMS base material and crosslinking agent were mixed at a mass ratio of 10:1 and degassed, and then covered on the surface of the master template. The mixture was cured at 80°C for 2 hours, and demolded with anhydrous ethanol to obtain a PDMS transfer template with a micropillar array on the surface.
[0025] 2) Glass substrate modification: Glass slides were alternately placed and immersed in a 2.5 mol / L NaOH solution and left to stand overnight. After removal, they were washed with deionized water and anhydrous ethanol, wrapped in aluminum foil and dried. A silane coupling agent TMSPMA was uniformly coated onto the glass slides. After standing at room temperature in the dark for 1 hour, the slides were placed in an 80°C oven for overnight reaction. After removal, residual TMSPMA was washed away with anhydrous ethanol, and finally, the slides were baked in an 80°C oven for 1 hour.
[0026] 3) Preparation of micropatterned hydrogels containing fluorescent particles: A prepolymer solution was prepared containing 10% wt / wt PEGDA (Mn=10,000Da), 1% LAP photoinitiator, and 500nm fluorescent particles diluted 1:50. The prepolymer solution was dropped onto a modified glass surface, and the liquid layer thickness was controlled by pressing with a PDMS template. In-situ curing was completed by irradiation with a 254nm UV lamp for 3 minutes. The template was then removed to obtain a hydrogel barrier with a microporous structure and embedded fluorescent particles.
[0027] 4) Loading state measurement: MCF-10A and MCF-10AT cells were seeded in microwells and cultured until the monolayer density stabilized. The coordinates of the fluorescent particles (loading state) were captured and recorded using a laser confocal microscope, such as... Figure 2 As shown.
[0028] 5) Triggering mechanical relaxation and unloaded measurement: Add 50 μl of 0.1 mol / L NaOH solution to remove cells, causing mechanical relaxation of the hydrogel. After the displacement stabilizes, re-image the coordinates of the fluorescent particles (unloaded state). Figure 2 As shown.
[0029] 6) Quantitative analysis of collective expansion force: A continuous displacement field is constructed based on the discrete displacements before and after the particles. The maximum principal stress and strain distribution are calculated by substituting these values into the constitutive equations. Figure 3 As shown, the displacement vector field, maximum principal stress field, maximum principal strain field, and comparison diagram of the expansion force of the two cell lines are shown, which include cell lines from normal epithelial cells (MCF-10A) to precancerous cells (MCF-10AT).
[0030] ; ; ; Stress components (assuming Young's modulus E = 5 kPa, Poisson's ratio V = 0.49): ; ; ; ; .
[0031] For the micropore region planted with MCF-10A and MCF-10AT cell populations, the average maximum principal stress within 20 μm of the physical boundary of the micropore was extracted and calculated to obtain the cell population expansion force. MCF-10A: ; MCF-10AT: .
[0032] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, for the device embodiments, the above descriptions are merely preferred embodiments of the present invention. Since they are fundamentally similar to the method embodiments, the descriptions are relatively simple, and relevant parts can be referred to the descriptions of the method embodiments. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention, without departing from the principle of the present invention, should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A microscopic device for quantitative characterization of microscale cell population expansion force, characterized in that: It includes a functionalized modified glass substrate, an elastic barrier layer fixed on the substrate and having a microporous array structure, and fluorescent particles uniformly embedded in the elastic barrier layer for tracking displacement.
2. A method for quantitative characterization of microscale cell population expansion force, using the microscopic apparatus for quantitative characterization of microscale cell population expansion force as described in claim 1, characterized in that: The microporous array structure of the elastic barrier layer in the microscopic device used for quantitative characterization of the expansion force of the microscale cell population is used to construct a microscopic physical constraint environment to precisely restrict the space of the cell population planted therein. By recording the position coordinate deviation of the fluorescent particles before and after cell removal, the geometric deformation of the elastic barrier layer during mechanical relaxation is captured. Subsequently, a continuous displacement field was constructed using the computation module, and combined with the linear elastic constitutive model and principal stress algorithm, the expansion force and strain characterizing the cell population were quantitatively analyzed, thus achieving a precise quantitative characterization of the collective mechanical behavior of the cell population at the microscale.
3. The method for quantitative characterization of microscale cell population expansion force according to claim 2, characterized in that: The characterization process specifically includes the following steps: 1) Fabrication of a master template with microstructures: forming an array of micropores by etching on the surface of a silicon wafer; 2) Preparation of PDMS transfer template: Polydimethylsiloxane PDMS is coated on the surface of the master template to obtain a PDMS transfer template with a micropillar array; 3) Glass substrate modification: The glass substrate is functionalized to enable its surface to covalently bond with the hydrogel; 4) Preparation of micropatterned hydrogel containing fluorescent particles: Fluorescent particles were added to polyethylene glycol diacrylate (PEGDA) and mixed well. Then, a prepolymer solution was dropped onto the surface of a modified glass substrate. The droplet was covered by the PDMS transfer template and crosslinked and cured in situ by UV irradiation. The template was then removed to obtain a hydrogel barrier with a microporous structure and embedded fluorescent particles on the surface of the glass substrate. 5) Acquiring load displacement: Target cells are seeded in the micropores of the hydrogel barrier. After the cell density stabilizes, the load position coordinates of the fluorescent particles are obtained using a laser confocal microscope. 6) Acquiring displacement under no-load conditions: Cells were removed using sodium hydroxide solution to trigger mechanical relaxation of the hydrogel, and the coordinates of the no-load position of the fluorescent particles were obtained; 7. Quantitative analysis of expansion force: A continuous displacement field was constructed based on the positional deviation of fluorescent particles before and after cell removal, and the stress and strain fields of the cell monolayer were calculated accordingly.
4. The method for quantitative characterization of microscale cell population expansion force according to claim 2, characterized in that: Step 2) The specific process of preparing the PDMS transfer template is as follows: after mixing polydimethylsiloxane PDMS base material and crosslinking agent at a mass ratio of 10:1, the mixture is applied to the surface of the master template and cured at 80°C for 2 hours. Anhydrous ethanol is used to assist in demolding to obtain a PDMS transfer template with a micropillar array.
5. The method for quantitative characterization of microscale cell population expansion force according to claim 2, characterized in that: Step 3) The glass substrate modification process involves immersion in NaOH solution to induce the generation of hydroxyl functional groups on the glass surface. Subsequently, a dehydration condensation reaction is carried out at 80°C using the silane coupling agent TMSPMA, thereby grafting active methacryloyloxy functional groups onto the substrate surface to achieve covalent bonding between the hydrogel barrier and the glass substrate.
6. The method for quantitative characterization of microscale cell population expansion force according to claim 5, characterized in that: Step 3) describes the glass substrate modification process as follows: 3.1) Surface hydroxylation pretreatment: High-precision glass slides are placed alternately in NaOH solution to ensure that the surface of each glass slide can be fully in contact with the alkaline solution. The slides are immersed at room temperature for more than 12 hours to thoroughly remove organic residues from the glass surface through strong alkaline erosion and induce the formation of high-density hydroxyl (-OH) functional groups on the surface. 3.2) Cleaning and dehydration: Remove the glass slide from the alkaline solution and rinse it repeatedly with large amounts of deionized water and anhydrous ethanol until the washing solution is neutral and there are no visible residues on the surface. Then, wrap the glass slide tightly with clean aluminum foil and put it in an oven to dry it thoroughly, providing a dry chemical environment for the subsequent silanization reaction. 3.3) Silanization Coupling Reaction: The silane coupling agent 3-(isobutyryloxy)propyltrimethoxysilane TMSPMA was uniformly coated on the surface of the dried glass slide. The slide was wrapped with tin foil to protect it from light and left to stand at room temperature for 1 hour to allow the TMSPMA molecules to undergo preliminary physical adsorption on the glass surface. Subsequently, the wrapped glass slide was placed in an 80°C constant temperature oven and heated overnight. The high temperature promoted the dehydration condensation of the methoxy group of TMSPMA with the hydroxyl group on the glass surface to form a stable Si-O-Si covalent bond. 3.4) Washing and activation treatment: After the reaction is completed, the glass slide is taken out and rinsed repeatedly with anhydrous ethanol to thoroughly wash away the residual TMSPMA physically adsorbed on the surface; it is then wrapped with tin foil and placed in an 80°C oven for 1 hour to complete the final dehydration and activation, and a modified glass substrate with active methacryloyloxy groups grafted on the surface is obtained.
7. The method for quantitative characterization of microscale cell population expansion force according to claim 2, characterized in that: Step 4) describes the specific process for preparing the micropatterned hydrogel containing fluorescent particles as follows: 4.1) Preparation of composite prepolymer solution: Polyethylene glycol diacrylate (PEGDA) was selected as the hydrogel matrix material, and a PEGDA solution was prepared; lithium phenyl (2,4,6-trimethylbenzoyl) phosphate (LAP) photoinitiator was added to the solution; then, fluorescent particles were added for dilution; the fluorescent particles were uniformly dispersed in the prepolymer solution by ultrasonic or mechanical stirring. 4.2) Dropping and Mold Pressing: The above-prepared composite prepolymer liquid is dropped onto the surface of the glass substrate that has been functionalized with TMSPMA. A PDMS transfer template with a micropillar array is vertically pressed onto the surface of the droplet. The prepolymer liquid fills the gaps between the PDMS micropillars through physical extrusion and removes air bubbles. 4.3) In-situ UV crosslinking: Using a UV lamp, the prepolymer liquid in the compression state is irradiated in situ. Under the action of LAP initiator, the PEGDA molecular chain undergoes free radical polymerization and forms covalent bonds with the TMSPMA molecules on the glass substrate surface. 4.4) Demolding and molding: After irradiation, the PDMS transfer template on the surface is removed. Due to the anchoring effect of TMSPMA, the hydrogel layer is firmly adhered to the surface of the glass substrate, and finally a hydrogel barrier with microporous structure and fluorescent particles uniformly embedded inside is obtained.
8. The method for quantitative characterization of microscale cell population expansion force according to claim 2, characterized in that: Step 7) The specific process of quantitative analysis of expansion force is as follows: 7.1) Calculate the strain tensor components based on the displacement vector components u and v: ; ; ; Where u and v are the displacement vector components of the fluorescent particles within the elastic barrier layer relative to their initial positions in the x-axis and y-axis directions, respectively; x and y are the spatial coordinates in a two-dimensional Cartesian coordinate system. , These represent the normal strain components of the elastic barrier layer in the x and y directions, respectively. For the shear strain components of the elastic barrier layer; 7.2) Calculate the stress components according to Hooke's Law: ; ; ; in, , These represent the normal stress components of the elastic barrier layer in the x and y directions, respectively. denoted as the shear stress component of the elastic barrier layer; E is the Young's modulus of the elastic barrier layer material. The Poisson's ratio of the elastic barrier layer material; 7.3) The maximum principal stress of cell monolayer expansion was calculated. and maximum principal strain : ; 。