A non-contact method for measuring the young's modulus of cells

Abstract

The present application relates to a kind of non-contact measurement cell Young's modulus method, including quantitative phase microscopy system measurement cell phase diagram, by off-axis interference quantitative microscopic imaging system, phase delay caused by cell thickness, cell internal dry matter distribution is obtained by shooting;Further by the derivative and fluctuation of phase delay, qualitative contrast different cell Young's modulus size.The off-axis interference imaging system is composed of reference light path and sample light path, sample light path passes through transparent biological sample, reference light path and sample light path have a certain offset angle, and are coupled with sample light path to obtain the final interference figure;The present application can not only realize non-contact measurement cell demonstration modulus, but also still maintain good effect under low resolution low power lens, provide solution train of thought for large field of view parallel cell cluster Young's modulus measurement.

Description

Technical Field

[0001] This invention relates to a non-contact method for measuring Young's modulus of cells, specifically including cell phase data acquisition, cell phase data analysis, and verification of the method under a low-power, large field of view. It can be mainly applied to the real-time Young's modulus characterization of transparent samples with a large field of view, such as live cell clusters, in biological experiments. Background Technology

[0002] Cell stiffness is an important cellular property associated with migration, adhesion, and growth. For individual cells, stiffness is related to cell fate transition, pattern formation, and stem cell development. For cell monolayers, cell stiffness plays a crucial role in embryonic tissue development, adult tissue differentiation, and wound healing rate. Given the importance of stiffness in physical and biological systems, it is urgent to determine the role of cell stiffness in the collective mixing of cell monolayers. This knowledge gap is due to technological limitations. Currently, atomic force microscopy (AFM) is widely used to measure cell stiffness during migration. AFM directly measures cell stiffness using mechanical principles and has demonstrated its true limits in measuring single-cell stiffness. However, due to the low temporal resolution, limited scanning range, and tendency to damage cells, it is difficult to use AFM for long-term, real-time observation of the dynamic changes in the stiffness of large-area monolayers.

[0003] Recently developed quantitative phase microscopy systems have achieved remarkable results in characterizing the internal structure of single cells. Atomic force microscopy combined with quantitative phase imaging systems has been used for many years, providing a solid foundation for modeling cellular mechanical properties. Based on previous research and existing data, it is believed that phase data is related to cytoskeleton structure. It holds promise for obtaining equivalent cytoskeleton distribution maps and characterizing cell stiffness through phase maps. However, current methods are only effective for high-magnification single-cell characterization, and are computationally complex, with slow processing speeds for large field-of-view, high-resolution images. Summary of the Invention

[0004] The purpose of this invention is to provide a non-contact method for measuring Young's modulus of cells under a large field of view, offering a method for real-time and effective qualitative characterization of Young's modulus in living cells. This invention achieves this by acquiring cell phase data using an off-axis interferometric quantitative phase imaging system, calculating the total variation and fluctuation of the cell phase, and simulating low-magnification to verify the effectiveness of the total variation and fluctuation at low resolution. By correlating cell stiffness with the distribution of the cytoskeleton and the resulting mechanical structure, changes in the cytoskeleton structure are characterized by calculating changes in phase distribution, thus characterizing the cell's mechanical properties.

[0005] The technical solution adopted by the present invention to achieve the above objective is: a non-contact method for measuring Young's modulus of cells, comprising the following steps:

[0006] 1) Obtain the interferogram of the cells and acquire the cell phase map using an off-axis interferometric imaging system;

[0007] 2) Using phase to replace cell thickness, the total variation of phase or the standard deviation of phase is obtained based on the cell phase map to replace the phase derivative, so as to characterize the derivative or fluctuation of cell thickness;

[0008] 3) Construct the relationship between the phase derivative and the Young's modulus of the cell;

[0009] 4) For the cell to be tested, the phase map of the cell to be tested is obtained through step 1). Based on the phase of the cell to be tested, the Young's modulus of the cell to be tested is obtained through the relational formula.

[0010] The samples include one of the following: muscle cells, undifferentiated human gastric cancer cells, human gastric cancer cells, human breast cancer cells, human astrocytoblastoma cells, and human immortalized keratinocytes.

[0011] The cell phase map is represented as follows:

[0012]

[0013] Where I represents the interferogram containing samples, G represents the blank background image without any samples, phase represents the final phase image, Image[] represents taking the imaginary part, Real[] represents taking the real part, arctan() represents calculating the arctangent, and unwrap() represents unwrapping the phase.

[0014] The method of using phase to replace cell thickness, and obtaining the total variation of phase or the standard deviation of phase based on the cell phase map to replace the phase derivative, is as follows:

[0015] Calculation of total variation TV based on cell phase maps:

[0016]

[0017] Where p(x,y) represents the phase of point (x,y) in the phase diagram; TV(x,y) represents the total variation of point (x,y) in the cell phase diagram, used to replace the phase derivative.

[0018] The method of using phase to replace cell thickness, and obtaining the total variation of phase or the standard deviation of phase based on the cell phase map to replace the phase derivative, is as follows:

[0019] Phase fluctuation (Std) was calculated based on the cell phase map, and the fluctuation in each 3×3 pixel region is as follows:

[0020]

[0021] Where p(i,j) represents the phase of point (i,j) in the phase map, and n represents the number of pixels in a 3×3 pixel region, which is set to 9. Std(x,y) represents the average pixel value within a 3×3 pixel area, and represents the phase fluctuation of point (x,y) in the cell phase map, used to replace the phase derivative.

[0022] The relationship between the phase derivative and the Young's modulus of the cell is constructed as follows:

[0023]

[0024] Where k and C are constant coefficients, s(x,y) represents the Young's modulus of point (x,y), and p(x,y) represents the phase of point (x,y) in the phase diagram. This represents the phase derivative, which can be replaced by the total variation TV or the phase fluctuation Std.

[0025] The phase is used to replace cell thickness, and the refractive index inside the cell remains unchanged.

[0026] A non-contact system for measuring Young's modulus of cells, comprising:

[0027] The host computer is used to process the interferograms output by the off-axis interferometric imaging system to measure the Young's modulus of cells, including:

[0028] The cell phase map acquisition module is used to acquire cell phase maps based on cell interferograms obtained through an off-axis interferometric imaging system.

[0029] The phase derivative calculation module is used to replace cell thickness with phase, and obtain the phase derivative and fluctuation based on the cell phase map to characterize the derivative and fluctuation of cell thickness;

[0030] The relation building module is used to construct the relationship between the phase derivative and the Young's modulus of the cell.

[0031] The Young's modulus acquisition module is used to obtain the Young's modulus of the cell to be tested based on the phase map of the cell to be tested obtained by the cell phase map acquisition module, and the Young's modulus of the cell to be tested is obtained through a relational expression.

[0032] The off-axis interferometric imaging system includes: a laser, and a first lens, a second lens, a first beam splitter, a first reflector, a sample stage, an objective lens, a second reflector, a second beam splitter, a third lens, an aperture, and a camera, which are sequentially arranged in its output optical path; the second beam splitter is disposed in the reflected optical path of the first beam splitter.

[0033] The laser beam passes through the first lens and the second lens in sequence to produce parallel beams after beam expansion. The first beam splitter generates two beams: the reference beam is directly incident on the second beam splitter; the sample beam passes through the first mirror, passes through the sample stage, and then enters the objective lens, and then enters the second beam splitter through the second mirror.

[0034] After the sample beam passes through the second beam splitter, it merges with the reference beam to form an off-axis interference image field; the off-axis interference image field passes through the third lens and the aperture in sequence, and the camera records the interference pattern.

[0035] The present invention has the following beneficial effects and advantages:

[0036] 1. This invention utilizes an easily implemented optical system and a simple derivative calculation algorithm, and uses phase to replace cell thickness, which not only realizes non-contact, non-destructive measurement, but also makes it possible to observe live cell samples for a long time.

[0037] 2. Simultaneously, this invention enables qualitative comparison of Young's modulus differences between different cell types under large field-of-view and low resolution conditions, including the Young's modulus difference between cancer cells and normal cells. This provides a possibility for real-time measurement of Young's modulus of cell clusters using interferometric methods over a large field of view.

[0038] 3. By using phase instead of cell thickness, non-contact, non-destructive measurement is achieved, making it possible to observe live cell samples over a long period of time. Attached Figure Description

[0039] Figure 1 Optical path diagram of an off-axis interferometric microscopy system;

[0040] Among them, S1 is the laser source, S2 is the first lens, S3 is the second lens, S4 is the first beam splitter, S5 is the first mirror, S6 is the sample stage, S7 is the objective lens, S8 is the second mirror, S9 is the second beam splitter, S10 is the lens, S11 is the aperture, and S12 is the camera.

[0041] Figure 2 Diagram showing the relationship between height, Young's modulus, and cytoskeleton; (a) cell thickness diagram, (b) cell Young's modulus diagram, (c) cytoskeleton structure diagram;

[0042] Figure 3 Phase versus cell thickness; (a) cell thickness plot, (b) cell phase plot, (c) total variation plot of cell, (d) total variation plot of cell phase;

[0043] Figure 4 The calculated parameters are inversely proportional to Young's modulus; (a) the phase standard deviation is inversely proportional to Young's modulus, (b) the phase total variation is inversely proportional to Young's modulus;

[0044] Figure 5The proposed method and Young's modulus are plotted under simulated low magnification. (a) Phase plot at 0.2x resolution, (b) Phase plot at 0.1x resolution, (c) Phase standard deviation and Young's modulus at 0.2x resolution, (d) Total variation of phase and Young's modulus at 0.2x resolution, (e) Phase standard deviation and Young's modulus at 0.1x resolution, (f) Total variation of phase and Young's modulus at 0.1x resolution. Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0046] This invention relates to a non-contact method for measuring Young's modulus of cells, comprising: measuring cell phase maps using a quantitative phase microscopy system; capturing phase delays caused by cell thickness and the distribution of dry matter within the cell using an off-axis interferometric quantitative microscopy imaging system; and then qualitatively comparing the Young's modulus of different cells by analyzing the derivative and fluctuation of the phase delay. The off-axis interferometric imaging system consists of a reference optical path and a sample optical path. The sample optical path passes through a transparent biological sample, and the reference optical path and sample optical path have a certain offset angle, coupled with the sample optical path to obtain the final interferogram. The analysis of the derivative and fluctuation of the phase delay involves calculating the total variation of the phase data to obtain the absolute value of the phase derivative, and calculating the phase fluctuation within a certain pixel neighborhood by calculating the standard deviation. The analyzed data is compared with reference data measured by an atomic force microscope, showing that the derivative and fluctuation of the cell phase are inversely proportional to the Young's modulus of the cell. This invention not only enables non-contact measurement of cell demonstration modulus but also maintains good results under low resolution and low magnification, providing a solution for measuring the Young's modulus of parallel cell clusters in a large field of view.

[0047] like Figure 1 As shown, the off-axis interferometric quantitative phase imaging system includes: a laser source S1, a beam expander composed of two lenses S2 and S3, beam splitters S4 and S9, mirrors S5 and S8, an objective lens S7, a sample stage S6, a lens S10, an aperture S11, and a camera S12. The laser beam emitted from the laser source S1, after passing through the first lens S2 and the second lens S3, becomes a beam-expanded parallel beam. This beam is then split by the first beam splitter S4 into two beams. The beam directly from the first beam splitter S4 to the second beam splitter S19 is the reference beam. The beam passing through the first mirror S5 and the sample stage S6, and then incident parallel to the objective lens S7 and the second mirror S8, is the sample beam. The sample beam is combined with the reference beam by the second beam splitter S9 to form an off-axis interferometric image field. This image field, after passing through the third lens S10 and the aperture S11, is then recorded by the camera S12 as an interferogram.

[0048] This invention provides a method for non-contact, large-field-of-view, low-resolution qualitative characterization of cell Young's modulus. It utilizes an off-axis interferometric imaging system to acquire cell phase maps, uses phase to represent cell thickness, and characterizes the derivative and fluctuation of cell thickness by calculating the derivative and fluctuation of phase, which are inversely proportional to cell Young's modulus.

[0049] Cell phase data is used to obtain cell phase maps through off-axis phase recovery algorithms. According to the following formula, the optical phase delay is the product of cell thickness d(x,y) and intercellular refractive index Δn(x,y), where λ represents the wavelength.

[0050]

[0051] It is impossible to simultaneously obtain cell height and characterize cell refractive index. When the objective magnification and resolution are sufficiently high, the cell thickness between adjacent pixels (e.g., (x,y) and (x+1,y)) in a quantitative phase image is approximately the same. However, for high-throughput measurements, the difference in d(x,y) between adjacent pixels is not negligible. These thickness differences (0-10) are far greater than the differences in refractive index between different cell parts (typically on the order of 10^(-2)). It is assumed that Δn(x,y) within the cell is constant at low resolution because the variation in intracellular dry mass is sufficiently small. Previous studies have shown that cell volume is related to cytoskeleton distribution, suggesting that cell height is related to cytoskeleton distribution.

[0052] The total variation and wave calculation methods directly calculate the derivatives in both directions.

[0053]

[0054] At the same time, there is fluctuation in each 3×3 pixel area.

[0055]

[0056] The experiment simulates low-magnification verification by averaging the signal of a single pixel across its entire field of view, based on the image acquisition principle. Following this principle, pixel values ​​within a specific field of view in a quantitative phase image are averaged, ranging from 1×1 to 10×10. This process effectively reduces the image resolution to 10 distinct subsets. Subsequently, two proposed metrics are applied to images at different resolutions, and their performance is evaluated. The proposed method aims to provide a large field-of-view, low-resolution, non-contact method for characterizing the Young's modulus of living cell clusters. An off-axis interferometric phase system acquires the cell phase map, and the phase derivative is calculated as inversely proportional to the wave amplitude to characterize the Young's modulus. The proposed method still yields good results in simulating low-resolution images.

[0057] The following section introduces a method for characterizing Young's modulus using phase representation. The specific steps are as follows:

[0058] Step 1: Young's modulus of different cell types was determined using atomic force microscopy: muscle cells (C2C12), undifferentiated human gastric cancer cells (HGC-27), human gastric cancer cells (MGC-803), human breast cancer cells (MCF7), human glioblastoma cells (U87), and human immortalized keratinocytes (HaCaT). Cell height was also measured using atomic force microscopy.

[0059] Step two involves obtaining the distribution of the intracellular cytoskeleton (F-actin) through fluorescent staining and comparing it with the data obtained in Step one. It was found that fluctuations in cell height are related to the cytoskeleton. The results are as follows: Figure 2 .

[0060] Step 3, Phase Image Generation: Sub-nanometer precision phase images can be obtained using the off-axis interferometric quantitative phase imaging system according to the following relationship:

[0061]

[0062] Where I represents the interferogram containing samples, G represents the blank background image without any samples, phase represents the final phase image, Image[] represents taking the imaginary part, Real[] represents taking the real part, arctan() represents calculating the arctangent, and xunwrap() represents unwrapping the phase. Comparing the phase data with the cell height data obtained in step one, they are found to be quite similar, as shown in the following results. Figure 3 .

[0063] Step four: Calculate the total variation and phase fluctuations. Assume that Δn(x,y) within the cell is constant at low resolution. The derivatives in both directions are calculated directly.

[0064]

[0065] At the same time, there is fluctuation in each 3×3 pixel area.

[0066]

[0067] The phase derivative can be replaced by either total variation or phase fluctuation.

[0068] Step 5: Relationship between phase derivative and Young's modulus. For adherent cells, quantitative phase imaging reveals the cytoskeleton structure. Furthermore, the total variation of the phase further highlights the cytoskeleton structure, thus establishing a correlation between the cytoskeleton structure and the phase. Additionally, it is noted that the total variation of the phase essentially represents the absolute value of the spatial derivative of the phase under discrete conditions. The relationship between the phase (p) and Young's modulus (s) on the spatial plane (x,y) is as follows.

[0069]

[0070] in, The equation is used to replace the total variation or phase fluctuation, where k and C are constant coefficients, s(x,y) is Young's modulus, and p(x,y) represents the phase at a certain point. If we ignore |·| and derive the above equation, we can not only derive the disorder intensity equation described in existing papers, but also obtain the inverse nonlinear relationship between the phase disorder intensity and Young's modulus.

[0071]

[0072] Where Δp represents the difference in phase relative to the average value within a 3×3 pixel region. This represents the mean Young's modulus of a 3×3 pixel region, where C″ represents a constant. This represents the average phase value within a 3×3 pixel area.

[0073] It is proposed that, under normal conditions, the relationship between disorder intensity and Young's modulus lies within a finite, monotonically decreasing interval, where s(r) > 0, as shown in equation [equation missing]. This further confirms that the spatial distribution of phase in adherent cells is characteristic of the cytoskeleton distribution. This provides a potential framework for further exploring the quantitative relationship between phase and cellular mechanical properties. The results are as follows... Figure 4 .

[0074] Step 5: Simulating Low-Resolution Images. To measure cell Young's modulus at high throughput using iQPM technology during cell mass migration, iQPM must have a large field of view, which reduces its resolution. Based on image acquisition principles, a single pixel's signal is averaged across its entire field of view. Mimicking this principle, pixel values ​​within a specific field of view in the quantitative phase image are averaged, ranging from 1×1 to 10×10. This process effectively reduces the image resolution to 10 distinct subsets. Subsequently, the proposed two metrics are applied to images at different resolutions, and their performance is evaluated. The results are as follows: Figure 5 .

[0075] Figure 2 The relationship between cell height, cell rigidity, and cytoskeleton is illustrated. Atomic force microscopy was performed on C2C12 cells. Cell height results are shown below. Figure 2 As shown in (a), the Young's modulus of the cell is as follows: Figure 2 As shown in (b). After AFM scanning, cells were stained with Actin-Tracker Green to observe f-actin (cytoskeleton), and cell nuclei were labeled with Hoechst 33342. Figure 3 (b)). In Figure 3The cytoskeleton aggregation region identified in b was observed to be similar to... Figure 3 The fibrous hard regions in (a) correspond to high Young's modulus values.

[0076] Figure 3 This demonstrates the feasibility of using optical phase retardation as a parameter representing cell thickness. For example... Figure 3 As shown in (a)-(b), the phase represents cell thickness. The total variation of thickness and phase was further calculated, as follows: Figure 3 As shown in (c)-(d). Although the total variation of phase is smaller than the total variation of thickness, there are still similarities between the two.

[0077] Figure 4 The phase derivative and phase fluctuation are inversely proportional to the cell's Young's modulus. To demonstrate the relationship between the cell's Young's modulus and these two indicators, the indicator values ​​were averaged for approximately 10 cells of each type. The relationship between Young's modulus and each indicator is an inverse linear fit. Meanwhile, as... Figure 4 As shown in (a), the r-squared coefficient of the phase ripple is the largest compared to the total phase variation. Interestingly, the total phase variation shows the smallest absolute value of the slope ( Figure 4 (b) This indicates that using total phase variation to represent cell stiffness provides higher resolution. If MGC-803 is excluded, total phase variation is able to classify the other five cell types. In summary, these results suggest an inverse relationship between Young's modulus and both indices.

[0078] Figure 5 The proposed total phase variation and phase fluctuation method demonstrates good performance at low resolution. Figure 5 In (a)-(b), both phase fluctuation and total phase variation increase after resolution reduction, possibly because the physical distance between adjacent pixels is greater in the low-resolution image than in the original image. However, the total phase variation remains relatively uniform. Overall, reducing resolution has a smaller impact on the distribution of the total phase variation in cellular regions. Figure 5 Figures (b)-(c) show the correlation between Young's modulus and corresponding indices at 0.2x resolution. Figure 5 Tables (e)-(f) show the correlation between Young's modulus and the corresponding indices at 0.1x resolution. As the resolution decreases to 0.2x and 0.1x, phase ripple and total phase variation remain inversely proportional in low-resolution images. However, ripples between certain cell types become very similar, even indistinguishable, while the total phase variation maintains the distinction between different cell types.

Claims

1. A non-contact method for measuring Young's modulus of cells, characterized in that, Includes the following steps: 1) Obtain the interferogram of the cells and acquire the cell phase map using an off-axis interferometric imaging system; 2) Using phase to replace cell thickness, the total variation of phase or the standard deviation of phase is obtained based on the cell phase map to replace the phase derivative, so as to characterize the derivative or fluctuation of cell thickness; 3) Construct the relationship between the phase derivative and the Young's modulus of the cell; 4) For the cell to be tested, the phase map of the cell to be tested is obtained through step 1). Based on the phase of the cell to be tested, the Young's modulus of the cell to be tested is obtained through the relationship. The relationship between the phase derivative and the Young's modulus of the cell is constructed as follows: ； in, and It is a constant coefficient. Point Young's modulus, Points in the phase diagram phase, Represents the phase derivative, used for substitution with total variation. or phase fluctuation .

2. The non-contact method for measuring Young's modulus of cells according to claim 1, characterized in that, The cells include one of the following: muscle cells, undifferentiated human gastric cancer cells, human gastric cancer cells, human breast cancer cells, human astrocytoblastoma cells, and human immortalized keratinocytes.

3. The non-contact method for measuring Young's modulus of cells according to claim 1, characterized in that, The cell phase map is represented as follows: ； in, This represents an interferogram containing samples. This represents a blank background image that does not contain any samples. This represents the final phase diagram. This indicates taking the imaginary part. Indicates taking the real part, Indicates the need for the opposite tangent. This indicates phase unwrapping.

4. The non-contact method for measuring Young's modulus of cells according to claim 1, characterized in that, The method of using phase to replace cell thickness, and obtaining the total variation of phase or the standard deviation of phase based on the cell phase map to replace the phase derivative, is as follows: Total variation calculation based on cell phase map : ； in, Points in the phase diagram The phase; Points in the cell phase map The total variation is used to replace the phase derivative.

5. The non-contact method for measuring Young's modulus of cells according to claim 1, characterized in that, The method of using phase to replace cell thickness, and obtaining the total variation of phase or the standard deviation of phase based on the cell phase map to replace the phase derivative, is as follows: Phase fluctuations calculated based on cell phase maps The fluctuations in each 3×3 pixel area are as follows: ； in, Points in the phase diagram phase, This represents the number of pixels in a 3x3 pixel area, and is set to 9. This represents the average pixel value within a 3×3 pixel area. Points in the cell phase map The phase fluctuation is used to replace the phase derivative.

6. A non-contact system for measuring Young's modulus of cells, characterized in that, include: The host computer is used to process the interferograms output by the off-axis interferometric imaging system to measure the Young's modulus of cells, including: The cell phase map acquisition module is used to acquire cell phase maps based on cell interferograms obtained through an off-axis interferometric imaging system. The phase derivative calculation module is used to replace cell thickness with phase, and obtain the phase derivative and fluctuation based on the cell phase map to characterize the derivative and fluctuation of cell thickness; The relation building module is used to construct the relationship between the phase derivative and the Young's modulus of the cell. The relationship between the phase derivative and the Young's modulus of the cell is constructed as follows: ； in, and It is a constant coefficient. Point Young's modulus, Points in the phase diagram phase, Represents the phase derivative, used for substitution with total variation. or phase fluctuation ; The Young's modulus acquisition module is used to obtain the Young's modulus of the cell to be tested based on the phase map of the cell to be tested obtained by the cell phase map acquisition module, and the Young's modulus of the cell to be tested is obtained through a relational expression.

7. A non-contact system for measuring Young's modulus of cells according to claim 6, characterized in that, The off-axis interferometric imaging system includes: a laser, and a first lens, a second lens, a first beam splitter, a first reflector, a sample stage, an objective lens, a second reflector, a second beam splitter, a third lens, an aperture, and a camera, which are sequentially arranged in its output optical path; the second beam splitter is disposed in the reflected optical path of the first beam splitter. The laser beam passes through the first lens and the second lens in sequence to produce parallel beams after beam expansion. The first beam splitter generates two beams: the reference beam is directly incident on the second beam splitter; the sample beam passes through the first mirror, passes through the sample stage, and then enters the objective lens, and then enters the second beam splitter through the second mirror. After the sample beam passes through the second beam splitter, it merges with the reference beam to form an off-axis interference image field; the off-axis interference image field passes through the third lens and the aperture in sequence, and the camera records the interference pattern.

Images