Non-contact cell Young modulus measuring method

Abstract

The invention relates to a method for measuring Young modulus of cells in a non-contact manner, which comprises the following steps: measuring a cell phase diagram by using a quantitative phase microscopic imaging system, and shooting by using an off-axis interference quantitative microscopic imaging system to obtain phase delay caused by cell thickness and dry matter distribution in the cells; further, the Young moduli of different cells are qualitatively compared by analyzing the derivative and fluctuation of the phase delay. The off-axis interference imaging system is composed of a reference light path and a sample light path, the sample light path penetrates through the transparent biological sample, a certain deviation angle exists between the reference light path and the sample light path, and the reference light path is coupled with the sample light path to obtain a final interferogram; according to the invention, non-contact measurement of the cell demonstration modulus can be realized, a good effect is still maintained under a low-resolution low-power lens, and a solution thought is provided for measurement of the Young modulus of a large-view-field parallel cell cluster.

Description

Technical Field

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

[0002] Cell stiffness is an important cell property associated with migration, adhesion, and growth. For single cells, stiffness is associated with cell fate switching, pattern formation, and stemness. For cell monolayers, cell stiffness plays a crucial role in the development of embryonic tissues, the differentiation function of adult tissues, and the speed of wound healing. 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 monomers. This knowledge gap is partly due to technical limitations. Currently, atomic force microscopy is widely used to measure cell stiffness during migration. Atomic force microscopy uses mechanical principles to directly measure cell stiffness and has demonstrated its true limit in measuring single cell stiffness. However, due to the low temporal resolution, limited scanning range, and easy damage to cells, it is difficult to use atomic force microscopy to observe the dynamic changes of cell stiffness in large monolayers in real time for a long time. .

[0003] Recently developed quantitative phase microscopy systems have achieved remarkable results in characterizing the internal structure of single cells. In the prior art, atomic force microscopes and quantitative phase imaging systems have been used for many years, and have a good foundation for modeling cell mechanical properties. Based on previous studies and existing data, it is believed that phase data is related to cytoskeletal structure. It is promising to obtain equivalent cytoskeletal distribution maps and characterize cell hardness through phase images. However, current research methods are only effective in characterizing single cells at high magnification, and the calculations are complex, and the processing speed for large field of view and high-resolution images is slow. Summary of the invention

[0004] The purpose of the present invention is to provide a non-contact method for measuring the Young's modulus of cells under a large field of view, and to provide a method that can be used to qualitatively characterize the Young's modulus of living cells in real time and effectively. The implementation method of the present invention obtains cell phase data through an off-axis interferometric quantitative phase imaging system, calculates the total variation and fluctuation of the cell phase, and simulates a low-power microscope to verify the effect of the total variation and fluctuation at low resolution. When the cell hardness is associated with the distribution of the cytoskeleton and the mechanical structure formed by it, the changes in the skeleton structure are characterized by calculating the changes in the phase distribution, and the mechanical properties of the cell are characterized.

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

[0006] 1) Obtain the interference pattern of the cell using the off-axis interferometric imaging system and obtain the cell phase map;

[0007] 2) Using phase instead of 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 to characterize the derivative or fluctuation of cell thickness;

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

[0009] 4) For the cells to be tested, a phase image of the cells to be tested is obtained through step 1), and based on the phase of the cells to be tested, Young's modulus of the cells to be tested is obtained through a relationship.

[0010] The sample comprises one of muscle cells, undifferentiated human gastric cancer cells, human gastric cancer cells, human breast cancer cells, human brain astroglioma cells, and human immortalized keratinocytes.

[0011] The cell phase diagram is represented by:

[0012]

[0013] Among them, I represents the interference pattern 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 inverse tangent, and unwrap() represents phase unwrapping.

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

[0015] Calculate the total variation TV based on the cell phase map:

[0016]

[0017] Among them, p(x,y) represents the phase of point (x,y) in the phase map; TV(x,y) represents the total variation of point (x,y) in the cell phase map, which is used to replace the phase derivative.

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

[0019] The phase fluctuation Std is calculated based on the cell phase map, and the fluctuation in each 3×3 pixel area is as follows:

[0020]

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

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

[0023]

[0024] Where k and C are constant coefficients, s(x,y) represents the Young's modulus at point (x,y), and p(x,y) represents the phase at point (x,y) in the phase diagram. Represents the phase derivative, used to replace the total variation TV or phase fluctuation Std.

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

[0026] A system for non-contact measurement of Young's modulus of a cell, comprising:

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

[0028] A cell phase image acquisition module, used for acquiring a cell phase image based on a cell interference image obtained by an off-axis interference imaging system;

[0029] A phase derivative calculation module, used for using phase to replace cell thickness, obtaining phase derivatives and fluctuations based on the cell phase map, so as to characterize the derivatives and fluctuations of cell thickness;

[0030] A relationship building module is used to build the relationship between the phase derivative and the cell Young's modulus;

[0031] The Young's modulus acquisition module is used to obtain the phase image of the cell to be tested through the cell phase image acquisition module, and obtain the Young's modulus of the cell to be tested through a relationship based on the phase of the cell to be tested.

[0032] The off-axis interferometric imaging system comprises: 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 arranged in sequence on the output light path of the laser; the second beam splitter is arranged on the reflected light path of the first beam splitter;

[0033] The light beam emitted by the laser passes through the first lens and the second lens in sequence to generate parallel light after beam expansion, and then generates two light beams through the first beam splitter: the reference beam is directly incident on the second beam splitter; the sample beam passes through the first reflector, passes through the sample stage, and is incident on the objective lens, and is incident on the second beam splitter through the second reflector;

[0034] The sample beam passes through the second beam splitter and is combined 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 interference pattern is recorded by the camera.

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

[0036] 1. The present invention utilizes an optical system that is easy to implement, a derivative calculation algorithm that is simple to calculate, and phase instead of cell thickness, which not only realizes non-contact and non-destructive measurement, but also provides the possibility for long-term observation of living cell samples.

[0037] 2. At the same time, the present invention achieves qualitative comparison of the Young's modulus differences between different types of cells under large field of view and low resolution, including the difference between cancer cells and normal cells, making it possible to provide interferometry with large field of view and real-time measurement of Young's modulus of cell clusters.

[0038] 3. Using phase instead of cell thickness not only realizes non-contact and non-destructive measurement, but also makes it possible to observe living cell samples for a long time. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is the optical path diagram of the off-axis interferometric microscopy imaging system;

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

[0041] Figure 2 Relationship diagram 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 and cell thickness correlation diagram; (a) cell thickness map, (b) cell phase map, (c) cell total variation map, (d) cell phase total variation map;

[0043] Figure 4 The inverse relationship between the calculated parameters and Young's modulus; (a) the inverse relationship between the phase standard deviation and Young's modulus, (b) the inverse relationship between the phase total variation and Young's modulus;

[0044] Figure 5The inverse relationship between the proposed method and Young's modulus under simulated low-power microscope; (a) phase image at 0.2 times resolution, (b) phase image at 0.1 times resolution, (c) inverse relationship between phase standard deviation and Young's modulus at 0.2 times resolution, (d) inverse relationship between phase total variation and Young's modulus at 0.2 times resolution, (e) inverse relationship between phase standard deviation and Young's modulus at 0.1 times resolution, (f) inverse relationship between phase total variation and Young's modulus at 0.1 times resolution. DETAILED DESCRIPTION

[0045] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0046] The present invention relates to a method for non-contact measurement of cell Young's modulus, including a quantitative phase microscopy system to measure a cell phase map, and to obtain a phase delay caused by cell thickness and dry matter distribution inside the cell by an off-axis interference quantitative microscopy imaging system; and then to qualitatively compare the Young's modulus of different cells by analyzing the derivative and fluctuation of the phase delay. The off-axis interference imaging system is composed of a reference optical path and a sample optical path, and the sample optical path passes through a transparent biological sample, and the reference optical path and the sample optical path have a certain offset angle, and are coupled with the sample optical path to obtain a final interference map; the derivative and fluctuation of the phase delay are analyzed, and the absolute value of the phase derivative is obtained by calculating the total variation of the phase data, and the phase fluctuation in the pixel neighborhood is calculated by calculating the standard deviation in a certain pixel neighborhood; the data obtained by analysis are compared with the reference data measured by an atomic force microscope, and the derivative and fluctuation of the cell phase are inversely proportional to the Young's modulus of the cell. The present invention can not only realize non-contact measurement of cell demonstration modulus, but also maintain good results under low-resolution and low-power microscopes, and provide a solution for the measurement of Young's modulus of large field parallel cell clusters.

[0047] like Figure 1 As shown, the off-axis interferometric quantitative phase imaging system includes: a laser light source S1, a beam expander composed of two lenses S2 and S3, beam splitters S4 and S9, reflectors S5 and S8, an objective lens S7, a sample stage S6, a lens S10, an aperture S11, and a camera S12. The light beam emitted by the laser light source S1 generates parallel light after beam expansion after passing through the first lens S2 and the second lens S3, and generates two light beams after passing through the first beam splitter S4. The light beam directly from the first beam splitter S4 to the second beam splitter S19 is the reference beam, and the light beam that passes through the sample stage S6 through the first reflector S5 and is parallel to the objective lens S7 and the second reflector S8 is the sample beam. The sample beam is combined with the reference beam through the second beam splitter S9 to form an off-axis interference image field. After the image field passes through the third lens S10 and the aperture S11, the interference pattern is recorded by the camera S12.

[0048] The present invention provides a method for non-contact, large-field-of-view, low-resolution qualitative characterization of cell Young's modulus. The method uses an off-axis interferometric imaging system to obtain a cell phase map, uses the phase to replace the cell thickness, and calculates the derivative and fluctuation of the phase to characterize the derivative and fluctuation of the cell thickness, which is inversely proportional to the cell Young's modulus.

[0049] Cell phase data,The cell phase map is obtained by off-axis phase retrieval algorithm. According to the following formula, the optical phase delay is the product of the cell thickness d(x,y) and the intercellular refractive index Δn(x,y), where λ represents the wavelength.

[0050]

[0051] It is not possible to simultaneously obtain cell height and characterize cell refractive index. When the objective magnification and resolution are high enough, the cell thickness between adjacent pixels in the quantitative phase image (such as (x, y) and (x+1, y)) is roughly the same. However, for high-throughput measurements, the difference in d(x, y) between adjacent pixels cannot be ignored. These thickness differences (0-10) are much larger than the refractive index differences between different cell parts (usually on the order of 10^(-2)). It is assumed that Δn(x, y) within the cell is constant at low resolution because the change in dry mass within the cell is small enough. Previous studies have shown that cell volume is related to cytoskeleton distribution, and it is believed that cell height is related to cytoskeleton distribution.

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

[0053]

[0054] Simultaneous fluctuations over each 3×3 pixel area.

[0055]

[0056] The simulation of low-power microscope verification shows that according to the principle of image acquisition, a single pixel averages the signal of its entire field of view. Imitating this principle, the 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 resolution of the image to 10 different subsets. Subsequently, the two proposed metrics were applied to images of different resolutions, and their performance was evaluated. This experiment is conceived as a method for non-contact characterization of the Young's modulus of cells with a large field of view and low resolution for living cell clusters. The off-axis interferometric phase system acquires the cell phase map, and the phase derivative is calculated to characterize the size of the cell Young's modulus inversely proportional to the fluctuation. The proposed method still has good results in simulating low-resolution images.

[0057] Next, we will introduce the method of phase characterization of Young's modulus. The specific steps are as follows:

[0058] Step 1: Use atomic force microscopy to calibrate the Young's modulus of different cell types: muscle cells (C2C12), undifferentiated human gastric cancer cells (HGC-27), human gastric cancer cells (MGC-803), human breast cancer cells (MCF7), human brain glioblastoma cells (U87), and human immortalized keratinocytes (HaCaT). At the same time, the cell height is measured by atomic force microscopy.

[0059] Step 2: The distribution of the cytoskeleton (F-actin) inside the cell was obtained by fluorescent staining and compared with the data obtained in step 1. It was found that the fluctuation of cell height was related to the cytoskeleton. The results were as follows Figure 2 .

[0060] Step 3, phase image generation: The off-axis interferometric quantitative phase imaging system can be used to obtain a sub-nanometer precision phase image according to the following relationship:

[0061]

[0062] Where I represents the interference pattern containing samples, G represents the blank background image without any samples, phase represents the final phase image, Image[] represents the imaginary part, Real[] represents the real part, arctan() represents the inverse tangent, and xunwrap() represents phase unwrapping. Comparing the phase data with the cell height data obtained in step 1, we find that they are quite similar. The results are as follows Figure 3 .

[0063] Step 4: Calculate the total variation and phase fluctuation. Assume that Δn(x,y) in the cell is constant at low resolution. Directly calculate the derivatives in two directions.

[0064]

[0065] Simultaneous fluctuations over each 3×3 pixel area.

[0066]

[0067] Either total variation or phase fluctuation is used to replace the phase derivative.

[0068] Step 5, the relationship between phase derivative and Young's modulus. For adherent cells, the quantitative phase image shows the cytoskeletal structure. In addition, the total variation of the phase further highlights the cytoskeletal structure, thereby establishing a correlation between the cytoskeletal structure and the phase. In addition, the total variation of the phase further highlights the cytoskeletal structure, thereby establishing a correlation between the total variation of the phase and Young's modulus. In addition, it is also 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, It is used to replace the total variation or phase fluctuation, 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 |·| is ignored and the above equation is derived, not only can the disorder intensity equation described in the existing paper be derived, but also the anti-nonlinear relationship between the phase disorder intensity and Young's modulus can be obtained.

[0071]

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

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

[0074] Step 5: Simulate low-resolution images. To use the iQPM technology to measure the Young's modulus of cells with high throughput during collective cell migration, iQPM must have a large field of view, which reduces its resolution. According to the principle of image acquisition, a single pixel averages the signal of its entire field of view. Imitating this principle, the 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 resolution of the image to 10 different subsets. Subsequently, the two proposed metrics were applied to images of different resolutions, and their performance was evaluated. The results are shown in the figure. Figure 5 .

[0075] Figure 2 The relationship between cell height, cell stiffness and cytoskeleton is shown. Atomic force microscopy was performed on C2C12 cells. The cell height results are shown in Figure 2. Figure 2 As shown in (a), the cell Young's modulus is Figure 2 As shown in (b). After AFM scanning, cells were stained with Actin-Tracker Green to observe f-actin (cytoskeleton), and Hoechst 33342 was used to label the nucleus ( Figure 3 (b)). Figure 3The cytoskeleton aggregation areas identified in b were observed to be Figure 3 Similar fibrous hard areas in (a) correspond to high Young’s modulus values.

[0076] Figure 3 The feasibility of using optical phase delay as a parameter to represent cell thickness is demonstrated. Figure 3 As shown in (a)-(b), the phase represents the cell thickness. The total variation of thickness and phase is further calculated, as Figure 3 Although the total variation of phase is smaller than that 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 indices, the indicator values ​​of about 10 cells of each type were averaged. The relationship between Young's modulus and each indicator is a linear fit inverse relationship. At the same time, Figure 4 As shown in (a), the phase fluctuation has the largest r-squared coefficient compared to the total phase variation. Interestingly, the total phase variation shows the smallest absolute slope ( Figure 4 (b), indicating that the total phase variation provides a higher resolution for representing cell stiffness. If MGC-803 is excluded, the total phase variation is able to classify the other five cell types. Together, these results suggest an inverse relationship between Young's modulus and both metrics.

[0078] Figure 5 The proposed total phase variation and phase fluctuation have good effects at low resolution. Figure 5 In (a)-(b), after the resolution is reduced, the phase fluctuation and total phase variation values ​​increase, which may be because the physical distance between adjacent pixels in the low-resolution image is larger than that in the original image. However, the total phase variation is still relatively uniform. In general, the distribution of the total phase variation in the cell area is less affected after the resolution is reduced. Figure 5 (b)-(c) show the correlation between Young's modulus and corresponding indicators at 0.2 times resolution. Figure 5 (e)-(f) show the correlation between Young's modulus and corresponding indicators at 0.1x resolution. As the resolution decreases to 0.2x and 0.1x, the phase fluctuation and total phase variation maintain an inverse relationship in low-resolution images. However, the fluctuations between certain types of cells become very close and even difficult to distinguish, while the total phase variation maintains the distinction between different types of cells.

Claims

1. A non-contact method for measuring Young's modulus of cells, characterized in that: The following steps are involved: 1) Obtain the interference pattern of the cell using the off-axis interferometric imaging system and obtain the cell phase map; 2) Using phase instead of 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 to characterize the derivative or fluctuation of cell thickness; 3) construct the relationship between the phase derivative and the cell Young's modulus; 4) For the cells to be tested, a phase image of the cells to be tested is obtained through step 1), and based on the phase of the cells to be tested, Young's modulus of the cells to be tested is obtained through a relationship.

2. A non-contact method for measuring cell Young's modulus according to claim 1, characterized in that: The sample comprises one of muscle cells, undifferentiated human gastric cancer cells, human gastric cancer cells, human breast cancer cells, human brain astroglioma cells, and human immortalized keratinocytes.

3. A non-contact method for measuring cell Young's modulus according to claim 1, characterized in that: The cell phase diagram is represented by: Among them, I represents the interference pattern 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 inverse tangent, and unwrap() represents phase unwrapping.

4. A non-contact method for measuring cell Young's modulus according to claim 1, characterized in that: The phase is used to replace the cell thickness, and the total phase variation or the phase standard deviation is obtained based on the cell phase map to replace the phase derivative, as follows: Calculate the total variation TV based on the cell phase map: Among them, p(x,y) represents the phase of point (x,y) in the phase map; TV(x,y) represents the total variation of point (x,y) in the cell phase map, which is used to replace the phase derivative.

5. A non-contact method for measuring cell Young's modulus according to claim 1, characterized in that: The phase is used to replace the cell thickness, and the total phase variation or the phase standard deviation is obtained based on the cell phase map to replace the phase derivative, as follows: The phase fluctuation Std is calculated based on the cell phase map, and the fluctuation in each 3×3 pixel area is as follows: Where p(i,j) represents the phase of point (i,j) in the phase map, n represents the number of pixels in the 3×3 pixel area, and takes the value of 9. It represents the average value of pixels in a 3×3 pixel area, and Std(x,y) represents the phase fluctuation of point (x,y) in the cell phase map, which is used to replace the phase derivative.

6. A non-contact method for measuring cell Young's modulus according to claim 1, characterized in that: The relationship between the phase derivative and the cell Young's modulus is constructed as follows: Where k and C are constant coefficients, s(x,y) represents the Young's modulus at point (x,y), and p(x,y) represents the phase at point (x,y) in the phase diagram. Represents the phase derivative, used to replace the total variation TV or phase fluctuation Std.

7. A non-contact method for measuring cell Young's modulus according to claim 1, characterized in that: The phase is used to replace the cell thickness, and the refractive index inside the cell remains unchanged.

8. A non-contact system for measuring cell Young's modulus, characterized in that: include: The host computer is used to process the interference pattern output by the off-axis interferometric imaging system to measure the cell Young's modulus, including: A cell phase image acquisition module, used for acquiring a cell phase image based on a cell interference image obtained by an off-axis interference imaging system; A phase derivative calculation module, used for using phase to replace cell thickness, obtaining phase derivatives and fluctuations based on the cell phase map, so as to characterize the derivatives and fluctuations of cell thickness; A relationship building module is used to build the relationship between the phase derivative and the cell Young's modulus; The Young's modulus acquisition module is used to obtain the phase image of the cell to be tested through the cell phase image acquisition module, and obtain the Young's modulus of the cell to be tested through a relationship based on the phase of the cell to be tested.

9. A non-contact cell Young's modulus measurement system according to claim 8, characterized in that: The off-axis interferometric imaging system comprises: 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 arranged in sequence on the output light path of the laser; the second beam splitter is arranged on the reflected light path of the first beam splitter; The light beam emitted by the laser passes through the first lens and the second lens in sequence to generate parallel light after beam expansion, and then generates two light beams through the first beam splitter: the reference beam is directly incident on the second beam splitter; the sample beam passes through the first reflector, passes through the sample stage, and is incident on the objective lens, and is incident on the second beam splitter through the second reflector; The sample beam passes through the second beam splitter and is combined 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 interference pattern is recorded by the camera.

Images