A method for measuring the near-wall height of bacteria and three-dimensional reconstruction based on fluorescence intensity calibration

Abstract

The application provides a kind of bacterial near-wall height measurement and three-dimensional reconstruction method based on fluorescence intensity calibration, the method comprises: constructing oblique incidence fluorescence microscopic imaging system, acquires the fluorescence image sequence containing standard microspheres fixed on the surface of substrate and moving bacteria;Based on the fluorescence image of standard microspheres, by extracting radial intensity distribution and combining spherical geometry, the quantitative calibration relationship between fluorescence intensity and vertical height is established;According to the calibration relationship, the instantaneous height of the moving bacteria is inversed, and the three-dimensional motion trajectory is reconstructed;Based on the rod-shaped geometric model composed of a cylinder and two hemispheres, the principal component analysis is carried out on the three-dimensional point cloud data to determine the long axis direction, the lower hemisphere model is fitted, and the minimum vertical distance between the lowest point of the lower hemisphere and the substrate surface is defined as the gap height.The application realizes nanoscale absolute height measurement, effectively compensates the laser power fluctuation and light bleaching effect, and can accurately analyze the spatial attitude of rod-shaped bacteria.

Description

Technical Field

[0001] This invention relates to the field of microbial detection and optical measurement technology, and in particular to a method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration. Background Technology

[0002] In the fields of microbiology, biophysics, and microfluidics, bacterial movement near solid surfaces is closely related to key processes such as infection and colonization, biofilm formation, and microenvironment perception. Accurate measurement of the height of the gap between bacteria and the substrate is a crucial prerequisite for revealing their near-wall movement mechanisms. Currently, height measurements of near-surface microorganisms mainly employ optical techniques such as total internal reflection fluorescence microscopy (TIRF), digital holographic microscopy, and interferometric reflection microscopy. While TIRF technology offers high axial resolution, its fluorescence signal is susceptible to fluctuations in excitation power, dye photobleaching, and changes in the solution environment, making it difficult to obtain absolute height information and limiting it to qualitative or relative analysis. Holographic and interferometric methods are sensitive to system stability, background noise, and sample scattering characteristics, making it difficult to maintain measurement accuracy in complex biological environments. Especially for rapidly moving or non-spherical bacteria, existing methods still have significant limitations in simultaneously acquiring their spatial position, orientation, and true gap height.

[0003] Therefore, existing technologies have not yet developed a reliable means to achieve non-invasive, high-precision, real-time measurement of the height of the gap between motile bacteria and the surface under conventional fluorescence imaging conditions, and to simultaneously reconstruct their three-dimensional motion posture. Summary of the Invention

[0004] In view of this, the present invention aims to provide a method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration, so as to solve or alleviate the technical problems existing in the prior art.

[0005] The technical solution of this invention is implemented as follows: a method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration, comprising the following steps: Step S1: Construct an oblique incidence fluorescence microscopy imaging system, wherein the incident angle of the excitation light is adjusted to be slightly less than the critical angle of total internal reflection to form an oblique incidence excitation field, and fluorescence image sequences containing standard microspheres fixed on the substrate surface and motile bacteria are acquired. Step S2: Based on the fluorescence image of the standard microspheres, establish a quantitative calibration relationship between fluorescence intensity and vertical height from the substrate surface, wherein the mapping relationship is established by extracting the radial intensity distribution of the standard microspheres and combining it with their spherical geometry. Step S3: Based on the quantitative calibration relationship, the fluorescence image of the motile bacteria is inverted to obtain the instantaneous height of the motile bacteria relative to the substrate surface at each moment; Step S4: Based on the fluorescence image sequence of the motile bacteria and the instantaneous height, reconstruct the three-dimensional motion trajectory of the motile bacteria; Step S5: Based on a preset rod-shaped geometric model, which consists of a cylinder and hemispherical caps at both ends, the three-dimensional point cloud data of the motile bacteria is fitted to determine the spatial posture of the motile bacteria. Principal component analysis is applied to the three-dimensional point cloud data to determine its major axis direction, and the lower hemisphere model is fitted to the point cloud region near the substrate surface. The minimum vertical distance between the lowest point of the fitted lower hemisphere and the substrate surface is defined as the gap height.

[0006] Compared with existing technologies, this invention has the following advantages: By introducing standard microspheres fixed to the substrate surface, this invention establishes a quantitative calibration relationship between fluorescence intensity and vertical height, effectively overcoming the problem of uncontrollable fluorescence intensity caused by laser power fluctuations, photobleaching, and environmental changes in traditional total internal reflection fluorescence microscopy, thus achieving nanometer-level absolute measurement of the height of the gap between bacteria and the substrate. Simultaneously, by constructing an oblique incidence excitation field, this invention expands the axial penetration depth while maintaining near-wall height sensitivity, providing stable support for continuous observation within the 0-500 nanometer range. Furthermore, based on a rod-shaped geometric model composed of a cylinder and two hemispheres, this invention combines principal component analysis to perform three-dimensional attitude analysis of motile bacteria, solving the problem of difficulty in reconstructing the spatial attitude of rod-shaped bacteria and accurately defining the gap height.

[0007] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of the invention will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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.

[0009] Figure 1 This is the main flowchart of the method of the present invention; Figure 2 This is a data flow diagram of the present invention; Figure 3This is a flowchart of the attitude analysis algorithm of the present invention; Figure 4 This is a scatter plot comparing the measurement accuracy of the present invention with that of the TIRF method; Figure 5 This is a comparison curve showing the effect of laser power fluctuation on height measurement according to the present invention; Figure 6 This is a comparison curve showing the effect of photobleaching on height measurement according to the present invention. Detailed Implementation

[0010] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0011] This invention proposes a method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration, comprising the following steps: Step S1: Construct an oblique incidence fluorescence microscopy imaging system, wherein the incident angle of the excitation light is adjusted to be slightly less than the critical angle of total internal reflection to form an oblique incidence excitation field, and fluorescence image sequences containing standard microspheres fixed on the substrate surface and motile bacteria are acquired. To construct an oblique incidence fluorescence microscopy imaging system, a commercially available inverted fluorescence microscope can be used, where the excitation light is obliquely incident by adding a prism or mirror assembly to the excitation light path. Alternatively, a custom optical platform can be used to integrate components such as a laser source, beam expander and collimator, scanning galvanometer, and objectives to construct an imaging system with oblique incidence capability.

[0012] The excitation beam incident angle is adjusted to be slightly less than the critical angle for total internal reflection. This adjustment is achieved by manually rotating the objective lens or sample stage to change the relative angle between the excitation beam and the sample interface until a suitable oblique incident excitation effect is obtained. Alternatively, the excitation beam can be incident at the desired angle by adjusting the tilt angle of optical elements such as prisms or mirrors. When the excitation beam is incident at an angle slightly less than the critical angle for total internal reflection, part of the excitation beam penetrates the substrate surface, forming an excitation field in the near-surface region whose intensity decays vertically. This excitation field can excite fluorophores in the sample to produce fluorescence emission.

[0013] Fluorescent image sequences can be acquired using photodetectors such as CCD or CMOS at the eyepiece or side port of the microscope. Image acquisition is set to continuous mode to obtain image frames over a period of time, forming a sequence. Standard microspheres are pre-fixed to the substrate surface via physical adsorption or chemical bonding. Motile bacteria swim freely in the solution, and their fluorescence signals are acquired synchronously with those of the standard microspheres.

[0014] Step S2: Based on the fluorescence image of the standard microspheres, establish a quantitative calibration relationship between fluorescence intensity and vertical height from the substrate surface. This mapping relationship is established by extracting the radial intensity distribution of the standard microspheres and combining it with their spherical geometry. Based on fluorescence images of standard microspheres, a quantitative calibration relationship between fluorescence intensity and vertical height from the substrate surface was established. The acquired fluorescence images of the standard microspheres were analyzed to obtain fluorescence intensity values ​​in different regions of the microspheres. Using the known geometric dimensions of the microspheres, the vertical height from the substrate surface to each point on the microsphere surface was calculated, and these intensity values ​​were correlated with their corresponding vertical heights to form a lookup table or functional relationship.

[0015] This mapping relationship is established by extracting the radial intensity distribution of a standard microsphere and combining it with its spherical geometry. From the fluorescence image of the standard microsphere, with the center of the microsphere as a reference point, the change in fluorescence intensity along the radial direction is measured. Combining this with the spherical geometric features of the microsphere (such as radius), the radial distance is converted into a vertical height. For example, for a point on the microsphere image, its radial distance is... The radius of the microsphere is Its height in the vertical direction can be calculated. .

[0016] Step S3: Based on the quantitative calibration relationship, the fluorescence image of the motile bacteria is inverted to obtain the instantaneous height of the motile bacteria relative to the substrate surface at each moment; Based on the quantitative calibration relationship, the fluorescence images of motile bacteria are inverted. For each frame of fluorescence image of motile bacteria acquired, the fluorescence intensity information of the bacterial region is extracted, and this intensity value is substituted into the quantitative calibration relationship established in step S2 to convert it into the corresponding vertical height value.

[0017] This yields the instantaneous height of the motile bacteria relative to the substrate surface at each moment. The above inversion process is repeated for each frame of the bacterial image in the image sequence to obtain the vertical height data of the bacteria at different time points, i.e., the instantaneous height, reflecting the dynamic position of the bacteria in the vertical direction.

[0018] Step S4: Reconstruct the three-dimensional motion trajectory of the motile bacteria based on the fluorescence image sequence and instantaneous height of the motile bacteria; Based on the fluorescence image sequence and instantaneous height of motile bacteria, the three-dimensional trajectory of the motile bacteria is reconstructed. The positional information of the motile bacteria in the two-dimensional plane, such as the x and y coordinates of the bacterial centroid, is obtained from the fluorescence image sequence and combined with the instantaneous height (z coordinate) of the bacteria at each moment obtained in step S3 to obtain the position coordinates of the bacteria in three-dimensional space. Connecting these three-dimensional coordinate points that change over time forms the three-dimensional trajectory of the bacteria.

[0019] Step S5: Based on the preset rod-shaped geometric model, which consists of a cylinder and hemispherical heads at both ends, the three-dimensional point cloud data of the motile bacteria is fitted to determine the spatial posture of the motile bacteria. Principal component analysis is applied to the three-dimensional point cloud data to determine its major axis direction, and the lower hemisphere model is fitted to the point cloud region near the substrate surface. The minimum vertical distance between the lowest point of the lower hemisphere of the fitted model and the substrate surface is defined as the gap height.

[0020] A pre-defined rod-shaped geometric model is constructed from a cylinder and hemispherical caps at both ends. For example, a cylinder with a specific length and diameter is connected to hemispherical caps at both ends to approximate the true morphology of rod-shaped bacteria.

[0021] To determine the spatial orientation of motile bacteria, 3D point cloud data is fitted to them. Image processing techniques are used to extract 3D point cloud data from the fluorescence images of the bacteria. A pre-defined rod-shaped geometric model is then matched and fitted to the point cloud data. The fitting process can employ least squares or other optimization algorithms to obtain model parameters (such as position, orientation, and size), thereby determining the bacterial orientation in 3D space.

[0022] Principal component analysis (PCA) is performed on 3D point cloud data to identify the direction with the largest variance in the dataset. This direction corresponds to the long axis direction of the rod-shaped bacteria, thereby obtaining the main extension direction of the bacteria in space.

[0023] Identify the point cloud region closest to the substrate surface from the 3D point cloud data of bacteria, and fit a lower hemisphere model to this region to represent the end part of the bacteria near the substrate surface.

[0024] In the fitted lower hemisphere model, its lowest point in the vertical direction is determined, and the vertical distance from the lowest point to the substrate surface is calculated. This distance is defined as the gap height between the bacteria and the substrate surface.

[0025] As a specific implementation, the present invention further proposes a method for establishing the above-mentioned quantitative calibration relationship, which specifically includes: extracting the radial intensity distribution of the standard microsphere in the fluorescence image; establishing a mapping relationship between the radial intensity distribution and the vertical height based on the known geometric dimensions of the standard microsphere and its spherical geometric relationship; and obtaining a calibration curve in the form of power law or exponential decay by fitting the mapping relationship, as the quantitative calibration relationship.

[0026] In oblique incidence fluorescence microscopy, due to the exponential decay of the excitation light field in the vertical direction, standard microspheres fixed to the substrate surface exhibit a non-uniform fluorescence intensity distribution in the fluorescence image. To accurately capture this characteristic, the radial intensity distribution of the standard microspheres in the fluorescence image is first extracted. Image processing techniques are used to identify the image contour and center position of the standard microspheres. Using the center as a reference, pixel intensities are averaged or sampled along different radial directions or annular regions to obtain the fluorescence intensity variation curve of the microsphere from the center to the edge, serving as the basis for obtaining fluorescence intensity information of the microsphere at different vertical heights.

[0027] Based on this, and according to the known geometric dimensions of the standard microspheres, combined with their spherical geometric relationships, a mapping relationship between the radial intensity distribution and the vertical height is established. The standard microspheres are spheres of known diameter (such as silica microspheres). When fixed to the substrate surface, the distance from the center of the sphere to the substrate surface is determined. The vertical height from any point on the sphere to the substrate surface can be calculated using its radial position in the image and the sphere's geometric dimensions. For example, for a radius of... The microspheres, in the image, are radially distanced from the center of the sphere by [missing information]. The point, its vertical height from the base surface. It can be based on the Pythagorean theorem and the geometric relationships of a sphere (such as...) ,in The distance from the lowest point of the sphere to the base is derived by considering each radial position in the radial intensity distribution. r Its corresponding fluorescence intensity value and calculated vertical height By correlating the data, a series of discrete data points are established between fluorescence intensity and vertical height, forming a preliminary mapping relationship.

[0028] To obtain a continuous, smooth, and predictive quantitative calibration relationship, a calibration curve in the form of power-law or exponential decay needs to be obtained by fitting the mapping relationship. Due to the attenuation characteristics of the obliquely incident excitation light field in the vertical direction, the fluorescence intensity usually decreases non-linearly with vertical height. Common attenuation models include power-law decay (such as...). ) or exponential decay (e.g. ),in Fluorescence intensity Vertical height 、 、 The parameters are used for fitting. Using fitting algorithms such as the least squares method, a calibration curve accurately reflecting the quantitative relationship between fluorescence intensity and vertical height is obtained, serving as the basis for subsequent inversion of the instantaneous height of motile bacteria.

[0029] As a specific implementation, the present invention further proposes to construct an oblique incidence fluorescence microscopy imaging system, specifically including using an oil immersion objective with a high numerical aperture, introducing excitation light through the rear aperture of the objective, and adjusting the incident angle of the excitation light to be slightly smaller than the critical angle of total internal reflection, thereby forming an oblique incidence excitation field. Employing high numerical aperture (NAP) oil immersion objectives can effectively improve imaging resolution and fluorescence signal collection efficiency. By using oil, which has a refractive index similar to glass, oil immersion objectives reduce light refraction loss between the objective and the sample, further increasing the NAP and enhancing resolution and light-gathering ability. In oblique incidence fluorescence microscopy, high NAP objectives are crucial for achieving large-angle excitation light incidence, providing a wider range of incident angles and effectively collecting weak fluorescence signals from near-wall regions.

[0030] Introducing excitation light through the rear aperture of the objective lens is a common method for achieving oblique incidence illumination. The rear aperture of the objective lens is the Fourier plane of the objective lens; introducing excitation light through this plane allows for precise control of the incident angle and illumination mode. By adjusting the position of the beam incident on the rear aperture, the incident angle of the excitation light at the sample interface can be precisely controlled, ensuring that the excitation light is focused near the sample surface, forming a thin-layer excitation field.

[0031] The incident angle of the excitation light is adjusted to be slightly smaller than the critical angle for total internal reflection. The critical angle for total internal reflection is the minimum incident angle at which total internal reflection occurs when light travels from an optically denser medium to an optically less dense medium. When the incident angle is slightly smaller than the critical angle, the light penetrates the interface, but the penetration depth is extremely limited, forming a rapidly decaying evanescent or quasi-evanescent field. This adjustment aims to create an oblique incident excitation field with controllable penetration depth, selectively exciting fluorescent molecules near the substrate surface and effectively suppressing background fluorescence far from the substrate surface. With this configuration, the oblique incident excitation field confines the excitation region to the vicinity of the substrate surface, achieving specific excitation and imaging of bacteria near the substrate wall.

[0032] As a specific implementation, the present invention further proposes to invert the fluorescence image of motile bacteria, specifically including: acquiring the fluorescence image of the motile bacteria frame by frame; extracting the fluorescence intensity information of the whole or local area of ​​the motile bacteria; substituting the extracted fluorescence intensity information into the quantitative calibration relationship to calculate the instantaneous height.

[0033] Fluorescence images of motile bacteria are acquired frame-by-frame. By continuously acquiring a series of independent image frames, the distribution of fluorescence signals of motile bacteria at different time points is recorded. Typically, a high frame rate camera is combined with a fluorescence microscopy system to ensure that the acquisition frame rate is sufficient to capture the rapid movement of bacteria and avoid information loss due to motion blur or insufficient sampling. Each image frame serves as an independent data unit, carrying the two-dimensional spatial information and fluorescence intensity information of the bacteria at that instant, providing fundamental data for dynamic analysis.

[0034] Extracting fluorescence intensity information from the whole or localized regions of motile bacteria is a crucial step in connecting image data with height calibration. In practice, the motile bacteria in each frame are first segmented to identify their contour regions. Depending on the analytical requirements, the average fluorescence intensity, maximum fluorescence intensity, or total fluorescence intensity of the entire bacterial region can be extracted to represent the overall fluorescence signal of the bacteria at that moment. Alternatively, fluorescence intensity information from specific localized regions of the bacteria (such as the central region, the edge region near the substrate surface, or multiple discrete points) can also be extracted. This extraction method is adaptable to different bacterial morphologies, fluorescence label uniformity, and research objectives, ensuring that the extracted fluorescence intensity data accurately reflects the distance relationship between the bacteria and the substrate surface.

[0035] The extracted fluorescence intensity information is substituted into a quantitative calibration relationship to calculate the instantaneous height. This quantitative calibration relationship, pre-established based on standard microspheres, describes a mapping function (such as a power-law or exponential decay form) between fluorescence intensity and vertical height from the substrate surface. By using the fluorescence intensity value of motile bacteria at a specific moment as input and substituting it into this mapping function, the instantaneous vertical height of the bacteria relative to the substrate surface at that moment can be directly calculated. This process converts optical measurements into physical spatial height, achieving a transformation from two-dimensional image information to three-dimensional height information.

[0036] As a specific implementation, this invention further proposes a specific method for fitting based on a preset rod-shaped geometric model in step S5 above. First, the motile bacteria are modeled as a rod-shaped three-dimensional structure composed of a cylinder and hemispherical caps at both ends. This modeling method provides an accurate geometric representation of the bacterial morphology. The shape of rod-shaped bacteria (such as Escherichia coli) can be approximated as a cylinder with hemispherical caps at both ends. By preset or optimizing parameters such as the length and radius of the cylinder and the radius of the hemispherical caps during the fitting process, a geometric model that highly matches the actual bacterial morphology is constructed, laying the foundation for subsequent three-dimensional point cloud data fitting and ensuring the physical rationality of the fitting results.

[0037] Secondly, principal component analysis (PCA) was applied to the extracted 3D point cloud data of motile bacteria to determine its major axis direction. PCA can extract the main direction of change from high-dimensional data. By performing PCA on the 3D point cloud data of motile bacteria obtained from fluorescence image sequences and instantaneous height data, the direction of the longest distribution of point cloud data was identified, i.e., the geometric major axis of the bacteria. This provides a key reference for the initial pose of the rod-shaped model, enabling the subsequent fitting process to converge to the correct bacterial spatial pose more efficiently and accurately.

[0038] Next, a lower hemisphere model is fitted to the point cloud region near the substrate surface to determine the center of the lower hemisphere, and thus the lowest point of the lower hemisphere. When determining the gap height between the bacteria and the substrate surface, the point where the bacteria are closest to the substrate surface must be accurately located. This is achieved by filtering the 3D point cloud data... For regions with lower coordinate values ​​(i.e., closer to the base surface), a lower hemisphere model is fitted to these points, effectively smoothing noise in the point cloud data and obtaining a continuous, mathematically definable lower hemisphere surface. Once the lower hemisphere model (including the coordinates of the center and radius) is determined, its lowest point in the vertical direction can be accurately calculated. For example, if the coordinates of the center are... , radius is The coordinates of the lowest point are This process ensures that the gap height is calculated based on a smooth and physically meaningful model surface, rather than discrete, potentially noisy points.

[0039] As a specific implementation method, the present invention further proposes a method for screening and statistically analyzing the three-dimensional motion trajectory, which specifically includes the following steps: removing trajectories with a duration less than a first preset threshold; calculating the standard deviation of the gap height within the window using the sliding time window method; determining windows with a standard deviation less than a second preset threshold as near-wall stable motion states; merging continuous stable windows to form stable motion segments, and screening out trajectories with a stable motion segment ratio exceeding a third preset threshold for subsequent analysis.

[0040] After obtaining the three-dimensional motion trajectories of motile bacteria, a preliminary screening is performed. The duration of each trajectory is calculated (e.g., by counting the number of image frames contained in the trajectory or the actual length of time) and compared with a pre-set first threshold. Trajectories with a duration less than this threshold are considered transient events, measurement noise, or unrepresentative short-lived movements and are discarded to ensure that the trajectories for subsequent analysis have sufficient persistence and reliability. The first preset threshold can be flexibly set according to experimental conditions, bacterial species, and their typical motility cycles; for example, it can be set to several seconds or dozens of image frames.

[0041] After initial screening, the gap height was analyzed using a sliding time window method to identify the stable near-wall motility of bacteria. For each retained motility trajectory, a fixed-length sliding time window was defined, moving along the trajectory's time axis at preset step sizes (e.g., sliding one or several frames at a time). Within each sliding window, gap height data for all moments within that window were collected, and their standard deviation was calculated. The standard deviation serves as an indicator of data dispersion, reflecting the fluctuations in near-wall motility of bacteria within that window. The length of the sliding window is determined based on the bacterial motility characteristics and the analysis timescale, and can be set to, for example, from tens to hundreds of frames.

[0042] The standard deviation of the gap height calculated within each sliding window is compared with a second preset threshold. If the standard deviation of the gap height within a window is less than the threshold, the near-wall movement of the motile bacteria within that window is determined to be in a relatively stable state, i.e., a near-wall stable movement state. The second preset threshold defines the quantitative standard of "stability," which is determined based on experimental data and empirical knowledge of stable bacterial movement; for example, it can be set as a small range of gap height fluctuations.

[0043] All consecutive windows determined to be in a near-wall stable motion state are merged to form a longer stable motion segment. For example, if windows A, B, and C are consecutive and all determined to be stable, they are merged into one stable motion segment. For each trajectory, the proportion of the total duration of all its stable motion segments to the total duration of the trajectory is calculated. Only when this proportion exceeds a third preset threshold is the trajectory selected for subsequent detailed analysis. The third preset threshold is set according to research needs, for example, it can be set to 50%, 70%, or higher, to ensure that the selected trajectories have significant stable motion characteristics.

[0044] As one specific implementation, the present invention further proposes that the subsequent analysis includes: statistically analyzing the distribution of the gap height, calculating the curvature of the three-dimensional motion trajectory, and calculating the swimming speed of the motile bacteria.

[0045] The distribution of gap height is statistically analyzed to quantify the preference of bacteria for maintaining a vertical distance from the substrate surface during stable near-wall movement. By statistically analyzing gap height data obtained within the stable movement segment, a frequency distribution map or probability density function of gap height is generated, visually displaying the proportion or probability of bacteria spending time at different heights. This helps reveal the "comfort zone" of bacteria in the near-wall region or the characteristics of their interaction with the wall (such as whether there is a specific adsorption or repulsion distance). In practice, instantaneous gap height values ​​within all stable movement segments are collected, divided into several height intervals, the number of height values ​​in each interval is counted, and a histogram is plotted.

[0046] The curvature of a three-dimensional motion trajectory is calculated to quantify the degree of bending in the bacterial trajectory, reflecting the frequency and abruptness of turning during movement. Curvature is a geometric quantity describing the local bending of a curve, revealing the turning behavior of bacteria near the wall (such as straight swimming, large-radius turns, or abrupt U-turns), and assessing the bacterial's mobility and directional control. In practice, discrete trajectory point data is used to approximate the curvature of each point through numerical differentiation or fitting local curve segments (such as circular arcs or spline curves). For example, for continuous three-dimensional trajectories... Its curvature Through formula Calculation, where and These are the first and second derivatives of the trajectory with respect to time, respectively. For discrete points, the finite difference method or a circle approximation based on three adjacent points can be used for calculation.

[0047] Calculating the swimming speed of motile bacteria is used to quantify their movement rate in three-dimensional space and is a key parameter for assessing bacterial motility and activity. Swimming speed is divided into instantaneous speed and average speed. Instantaneous speed reflects the speed of bacterial movement at a specific moment, while average speed reflects the overall motility efficiency over a period of time. By calculating swimming speed, we can understand the motility performance of bacteria under different environmental conditions or physiological states (such as their response to nutrient gradients or chemical stimuli). In practice, instantaneous speed is obtained by dividing the spatial distance between adjacent trajectory points by the corresponding time interval. For example, for two consecutive trajectory points... and During the time interval The instantaneous velocity is approximately equal to .

[0048] As a specific embodiment, this invention further proposes that the standard microspheres are silica microspheres, whose dimensions are known and fixed to the substrate surface. Specifically, the silica microspheres are made of high-purity silica material, possessing excellent chemical stability, optical transparency, and good biocompatibility. They are not easily reactive with the environment and maintain stable optical properties under fluorescence excitation. Furthermore, silica microspheres are easily prepared into spherical particles with uniform size and smooth surfaces, providing an ideal physical basis for accurate geometric modeling and fluorescence intensity distribution analysis. Known size means that the diameter or radius of the standard microsphere has a precise preset value or a value obtained through high-precision measurement. When establishing a quantitative calibration relationship between fluorescence intensity and vertical height, calculations must be performed in conjunction with the spherical geometry of the microspheres. Accurate size information is a prerequisite for geometric calculations and directly affects the accuracy of the calibration curve. Fixing to the substrate surface means that the standard microspheres are firmly attached to the substrate surface of the imaging system through physical adsorption, chemical bonding or the use of specific adhesives, so that they remain stationary throughout the calibration and measurement process. This ensures the spatial stability of the microspheres as a height reference and avoids measurement errors caused by microsphere drift or shaking, thereby ensuring the accurate establishment of the fluorescence intensity decay curve.

[0049] As a specific embodiment, this invention further proposes that the excitation field penetration depth of the oblique incidence fluorescence microscopy system covers a range of 0 to 500 nanometers. The excitation field penetration depth refers to the distance from which the intensity of the excitation light after entering the sample is sufficient to effectively excite the fluorescent probe. In the oblique incidence fluorescence microscopy system, by precisely controlling the incident angle of the excitation light to be slightly less than the critical angle of total internal reflection, a shallow excitation field with controllable penetration depth is formed. Precisely limiting this penetration depth to 0 to 500 nanometers means that the system can specifically excite and detect fluorescence signals located on the substrate surface within the 0 to 500 nanometer range. This range is of great significance for studying the near-wall behavior of bacteria and other microorganisms, as many microbial interactions, attachments, and near-wall movements with surfaces occur within this nanoscale range. Achieving this precise penetration depth requires fine adjustment of the incident angle, wavelength, and numerical aperture of the excitation light, combined with refractive index matching between the sample and the substrate. For example, by adjusting the incident angle of the laser to keep the difference between it and the critical angle of total internal reflection within a very small range, the attenuation characteristics and penetration depth of the excitation field can be precisely controlled.

[0050] Experimental Example: Comparative Experiment with Traditional TIRF Method: I. Experimental Objective By systematically comparing the method with the traditional total internal reflection fluorescence microscopy (TIRF) method, the effectiveness of the method of the present invention in terms of measurement accuracy, anti-interference ability, and attitude resolution is verified.

[0051] II. Experimental Materials and Equipment: 2.1 Test Materials:

[0052] 2.2 Test Equipment

[0053] 2.3 Experimental Grouping

[0054] III. Experimental Methods: 3.1 Establishment of Calibration Curve Before starting the comparative experiment, it is necessary to establish a fluorescence intensity-height calibration curve for the method of this invention. Calibration is performed using silica microspheres fixed to the substrate surface.

[0055] Calibration method: Silica microspheres were fixed onto the surface of a coverslip, with the microsphere density controlled to be approximately 50-100 per field of view.

[0056] Inject PBS buffer containing fluorescent dye (Alexa Fluor 488 labeled BSA, 1 mg / mL).

[0057] Fluorescence images of the microspheres were acquired using an oblique incidence fluorescence microscopy system (incident angle 2° below the critical angle).

[0058] Extract the radial intensity distribution of the microspheres, and combine it with the spherical geometry (h = R - √(R)). 2 -r 2 Establish the mapping relationship between fluorescence intensity and vertical height.

[0059] The exponential decay curve is fitted using the nonlinear least squares method: .

[0060] Calibration curve results:

[0061]

[0062]

[0063]

[0064] 3.2 Bacterial Sample Preparation Bacillus subtilis was inoculated into LB medium and cultured at 37°C and 200 rpm until the logarithmic growth phase. ).

[0065] Take 1 mL of bacterial culture, centrifuge at 5000 rpm for 5 minutes, and discard the supernatant.

[0066] Add 1 mL of FM4-64 fluorescent dye (final concentration 5 μg / mL) and incubate in the dark for 10 minutes.

[0067] Centrifuge and wash twice to remove excess dye.

[0068] Resuspend in PBS buffer containing F-BSA and adjust the concentration to approximately 10. 7 per mL.

[0069] Add the bacterial sample to the sample cell with the immobilized microspheres and let it stand for 5 minutes to allow some bacteria to settle near the wall.

[0070] 3.3 Imaging System Settings: 3.3.1 Setting of the method of the present invention (oblique incidence mode):

[0071] 3.3.2 Traditional TIRF Method Setup:

[0072] 3.3.3 Confocal Reference Method Settings:

[0073] IV. Comparative Experiment 1: Measurement Accuracy Comparison 4.1 Test Methods: Thirty bacteria in a near-wall stable motion state (interstitial height <500 nm) were randomly selected.

[0074] The same bacterium was imaged and its height measured using both the method of this invention and the conventional TIRF method.

[0075] The measurement errors of the two methods were calculated using the three-dimensional scanning results of confocal microscopy as a reference standard.

[0076] Traditional TIRF methods for obtaining "height": Traditional TIRF methods cannot directly obtain absolute height values; they can only qualitatively determine them through fluorescence intensity. In this experiment, for quantitative comparison, an empirical calibration curve was used to convert fluorescence intensity into relative height (roughly calibrated using microspheres of known height).

[0077] 4.2 Test Results: Table 1. Comparison of Measurement Accuracy Test Results (1)

[0078] Table 1. Comparison of Measurement Accuracy Test Results (2)

[0079] Table 2 Summary of Measurement Accuracy

[0080] 4.3 Accuracy Comparison Conclusion: The experimental results show that: The method of this invention measures height with a root mean square error of only 3.5 nm compared to the confocal reference standard, and the maximum error does not exceed 4 nm, achieving nanometer-level absolute height measurement.

[0081] The traditional TIRF method has a measurement error as high as 118.5 nm, and the error accumulates and amplifies with increasing height, providing only qualitative or semi-quantitative information.

[0082] The measurement accuracy of the method of this invention is 97% higher than that of the traditional TIRF method, achieving a leap from the micrometer to the nanometer scale.

[0083] V. Comparative Experiment 2: Comparison of Resistance to Laser Power Fluctuations 5.1 Test Methods: Ten bacteria in a stable near-wall state were randomly selected and their positions were fixed.

[0084] The laser power is controlled by an adjustable attenuator, and fluctuates randomly within ±10% and ±20% of the nominal value (5mW).

[0085] The height of bacterial gaps was continuously measured using both the method of this invention and the traditional TIRF method, with each power value measured for 100 frames.

[0086] Calculate the change in height measurement with laser power (based on the measurement at 5mW).

[0087] 5.2 Test Results: Table 3. The Influence of Laser Power Fluctuation on Height Measurement

[0088] Table 4 Power Fluctuation Response Statistics

[0089] 5.3 Conclusion on resistance to power fluctuations: The experimental results show that: When the laser power fluctuates by ±10%, the height measurement value of the method of the present invention changes by only ±0.9nm, while the traditional TIRF method changes by ±8.8nm.

[0090] The method of this invention effectively compensates for the influence of excitation light intensity variation on high inversion by normalizing the calibration curve, and improves the anti-interference ability by 90% compared with the traditional TIRF method.

[0091] Both methods exhibit good linearity in their responses, but the variation range of the method in this invention is much smaller than that of the traditional TIRF method.

[0092] VI. Comparative Test 3: Comparison of Resistance to Photobleaching 6.1 Test Methods: Ten bacteria in a stable near-wall state were randomly selected and their positions were fixed.

[0093] Under continuous imaging conditions (excitation power 5mW, exposure time 10ms, frame rate 100fps), the height of bacterial interstitial spaces was continuously measured for 5 minutes using both the method of this invention and the traditional TIRF method.

[0094] Record the change in altitude measurement over time (based on the initial measurement value).

[0095] 6.2 Test Results: Table 5. Effects of photobleaching on height measurement

[0096] Table 6 Statistics on the impact of photobleaching

[0097] 6.3 Conclusion on resistance to photobleaching: The experimental results show that: After 5 minutes of continuous imaging, the height measurement value of the method of the present invention drifted by only 2.8 nm, with an average drift rate of 0.56 nm / min.

[0098] The traditional TIRF method results in a height measurement drift of up to 31.0 nm, with an average drift rate of 6.20 nm / min.

[0099] The method of this invention effectively compensates for the influence of photobleaching on fluorescence intensity through real-time updating and normalization of the calibration curve, and improves the resistance to photobleaching by 91% compared with the traditional TIRF method.

[0100] VII. Comparative Experiment Four: Comparison of Attitude Resolution Capabilities 7.1 Test Methods: Rod-shaped bacterial samples with different orientation angles (0°, 15°, 30°, 45°) were prepared (controlled by an electric rotating stage).

[0101] The same bacterium was imaged using both the method of this invention and the conventional TIRF method.

[0102] The method of the present invention performs attitude analysis according to step S5; the traditional TIRF method cannot obtain three-dimensional point cloud data and can only estimate the attitude angle through the major axis direction of the two-dimensional image (with limited accuracy).

[0103] Using the three-dimensional reconstruction results of confocal microscopy as a reference standard, the attitude angle analytical error of the two methods was calculated.

[0104] 7.2 Test Results: Table 7. Results of the comparative test on attitude resolution capability

[0105] Table 8. Statistics on Attitude Resolution Capability

[0106] 7.3 Attitude Analysis Conclusion: The experimental results show that: The method of this invention can accurately resolve the spatial attitude of rod-shaped bacteria with an attitude angle resolution error of only 0.23°, which is highly consistent with the confocal reference standard.

[0107] Traditional TIRF methods can only estimate the major axis direction from two-dimensional images and cannot obtain three-dimensional pose information. Moreover, the estimation error is as high as 3.45°, which is greater than that of the method of this invention.

[0108] More importantly, traditional TIRF methods cannot define the gap height between bacteria and the substrate (due to a lack of geometric model and three-dimensional information), while the method of this invention achieves a gap height definition with clear geometric meaning through lower hemisphere fitting.

[0109] VIII. Comprehensive Comparative Analysis: 8.1 Summary of Overall Performance Comparison: Table 9. Comparison of overall performance between the method of this invention and the traditional TIRF method.

[0110] 8.2 Visualization of Improvement Magnitude in Each Dimension

[0111] IX. Experimental Conclusions: 9.1 Conclusion on the comparison of measurement accuracy: The root mean square error of the height measurement method of this invention compared to the confocal reference standard is only 3.5 nm, which is 97% higher than the 118.5 nm of the traditional TIRF method. This result shows that this invention, through fixed microsphere calibration and quantitative inversion, achieves a leap from qualitative / semi-quantitative measurement to absolute quantitative measurement with nanometer-level precision, solving the problem that the traditional TIRF method cannot obtain absolute height information.

[0112] 9.2 Conclusion on the comparison of anti-interference capabilities: Under laser power fluctuations of ±10%, the height measurement value of the method of this invention changes by only ±0.9 nm, while the traditional TIRF method changes by ±8.8 nm, indicating a 90% improvement in the anti-interference capability of the method of this invention. Under continuous imaging conditions of 5 minutes, the drift of the method of this invention is only 2.8 nm, while the drift of the traditional TIRF method reaches 31.0 nm, indicating a 91% improvement in the anti-photobleaching capability of the method of this invention. These results demonstrate that the normalization of fluorescence intensity through calibration curves effectively compensates for the influence of excitation light power fluctuations and photobleaching on the measurement results, significantly enhancing the environmental adaptability and long-term stability of the method.

[0113] 9.3 Comparison of Attitude Resolution Capabilities: The method of this invention can accurately resolve the spatial attitude of rod-shaped bacteria with an attitude angle resolution error of only 0.23°, and can provide a geometrically meaningful gap height definition through lower hemisphere fitting. Traditional TIRF methods can only estimate the major axis direction from two-dimensional images with an error of 3.45°, and cannot obtain three-dimensional attitude information or define the gap height. This result demonstrates that this invention, through a rod-shaped geometric model and principal component analysis, achieves a leap from two-dimensional imaging to three-dimensional attitude reconstruction, solving the technical challenge of resolving the spatial attitude of rod-shaped bacteria in existing technologies.

[0114] 9.4 Overall Conclusion This experimental example, through a systematic comparison with the traditional TIRF method, fully demonstrates the superiority of the present invention in three dimensions: measurement accuracy, anti-interference capability, and attitude resolution capability. Measurement accuracy: This invention achieves nanometer-level absolute height measurement (RMSE=3.5nm), which is 97% higher than the traditional TIRF method; Interference resistance: The sensitivity of this invention to laser power fluctuations and photobleaching is reduced by more than 90% compared to the traditional TIRF method; Attitude resolution capability: This invention achieves accurate resolution of the three-dimensional spatial attitude of rod-shaped bacteria (error 0.23°), which is not possible with the traditional TIRF method.

[0115] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in the present invention, and these should all 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 method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration, characterized in that, Includes the following steps: Step S1: Construct an oblique incidence fluorescence microscopy imaging system, wherein the incident angle of the excitation light is adjusted to be slightly less than the critical angle of total internal reflection to form an oblique incidence excitation field, and fluorescence image sequences containing standard microspheres fixed on the substrate surface and motile bacteria are acquired. Step S2: Based on the fluorescence image of the standard microspheres, establish a quantitative calibration relationship between fluorescence intensity and vertical height from the substrate surface, wherein the mapping relationship is established by extracting the radial intensity distribution of the standard microspheres and combining it with their spherical geometry. Step S3: Based on the quantitative calibration relationship, the fluorescence image of the motile bacteria is inverted to obtain the instantaneous height of the motile bacteria relative to the substrate surface at each moment; Step S4: Based on the fluorescence image sequence of the motile bacteria and the instantaneous height, reconstruct the three-dimensional motion trajectory of the motile bacteria; Step S5: Based on a preset rod-shaped geometric model, which consists of a cylinder and hemispherical caps at both ends, the three-dimensional point cloud data of the motile bacteria is fitted to determine the spatial posture of the motile bacteria. Specifically, principal component analysis is applied to the three-dimensional point cloud data to determine its major axis direction, and the lower hemisphere model is fitted to the point cloud region near the substrate surface. The minimum vertical distance between the lowest point of the fitted lower hemisphere and the substrate surface is defined as the gap height.

2. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 1, characterized in that, The establishment of the quantitative calibration relationship in step S2 specifically includes: Extract the radial intensity distribution of the standard microspheres in the fluorescence image; Based on the known geometric dimensions of the standard microspheres and their spherical geometric relationships, a mapping relationship between the radial intensity distribution and the vertical height is established. By fitting the mapping relationship, a calibration curve in the form of power law or exponential decay is obtained, which serves as the quantitative calibration relationship.

3. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 1, characterized in that, The construction of the oblique incidence fluorescence microscopy imaging system in step S1 specifically includes: An oil immersion objective with a high numerical aperture is used to introduce excitation light through the rear aperture of the objective. Adjust the incident angle of the excitation light to be slightly smaller than the critical angle of total internal reflection to form an oblique incident excitation field.

4. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 1, characterized in that, The inversion of the fluorescence image of motile bacteria in step S3 specifically includes: The fluorescence images of the motile bacteria were acquired frame by frame; Extract fluorescence intensity information of the entire or local area of ​​the motile bacteria; The extracted fluorescence intensity information is substituted into the quantitative calibration relationship to calculate the instantaneous height.

5. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 1, characterized in that, Step S5, which involves fitting based on a preset rod-shaped geometric model, specifically includes: The motile bacteria were modeled as a rod-shaped three-dimensional structure consisting of a cylinder and hemispherical caps at both ends; Principal component analysis was applied to the extracted three-dimensional point cloud data of the motile bacteria to determine its major axis direction; A lower hemisphere model is fitted to the point cloud region near the base surface to determine the center position of the lower hemisphere, and then the lowest point of the lower hemisphere of the model is determined.

6. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 1, characterized in that, It also includes step S6: screening and statistical analysis of the three-dimensional motion trajectory, specifically including: Trajectories with a duration less than a first preset threshold are removed; The standard deviation of the gap height within the window is calculated using the sliding time window method; A window with a standard deviation less than a second preset threshold is defined as a near-wall stable motion state; The continuous stable windows are merged to form stable motion segments, and the trajectories with a stable motion segment ratio exceeding the third preset threshold are selected for subsequent analysis.

7. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 6, characterized in that, The subsequent analysis includes: statistically analyzing the distribution of the gap height, calculating the curvature of the three-dimensional motion trajectory, and calculating the swimming speed of the motile bacteria.

8. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 1, characterized in that, The standard microspheres are silica microspheres, whose size is known and fixed to the surface of the substrate.

9. The method for measuring and reconstructing the near-wall height of bacteria based on fluorescence intensity calibration according to claim 1, characterized in that, The excitation light field penetration depth of the oblique incidence fluorescence microscopy system covers the range of 0 to 500 nanometers.

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