A method of microbiological analysis

Abstract

This invention relates to the field of biofilm microbial imaging and lineage analysis technology, and discloses a microbial analysis and processing method. The three-dimensional lineage tracking of individual microorganisms includes: identifying individual microorganisms in the biofilm through three-dimensional connectivity analysis; establishing individual movement trajectories across time points using a three-dimensional Kalman filter algorithm; detecting division events and establishing parent-child lineage associations based on trajectory changes, volume conservation, and spatial proximity; and finally assembling a four-dimensional spatiotemporal lineage diagram structure to represent the complete microbial proliferation and evolution process. This invention solves the technical problems of broken three-dimensional biofilm lineage tracking and loss of spatial diffusion trajectories in traditional two-dimensional analysis methods.

Description

Technical Field

[0001] This invention relates to the field of biofilm microbial detection and lineage analysis technology, and more specifically, to a microbial analysis and processing method, particularly to a technique for three-dimensional spatial localization, movement trajectory tracking, division event detection, and lineage association of individual microorganisms in a three-dimensional biofilm. Background Technology

[0002] In the field of biofilm formation and development dynamics research, researchers need to track the proliferation lineage and spatial diffusion processes of individual microorganisms within a three-dimensional biofilm structure. Biofilms exhibit a multi-layered three-dimensional structure, with microorganisms distributed and proliferating at different focal depths.

[0003] Existing microbial lineage tracing technologies are mainly based on two-dimensional planar image analysis, and they face the following major technical challenges when processing three-dimensional biofilm structures:

[0004] The connectivity of microorganisms at different focal plane depths is difficult to determine, which leads to the same microorganism being mistakenly identified as multiple independent individuals in the projection of adjacent focal planes, resulting in repeated counting across focal planes;

[0005] After splitting, offspring may migrate across the focal plane to different depth layers, and traditional methods cannot establish parent-offspring relationships across depth layers;

[0006] The changes in the number of trajectories caused by the splitting event are difficult to distinguish from the repeated counting across the focal plane, resulting in the breakage of the phylogenetic tree in the depth direction and the loss of spatial diffusion trajectories. Summary of the Invention

[0007] This invention provides a method for microbial analysis and processing, which solves the technical problems of broken microbial lineage tracking and loss of spatial diffusion trajectories in three-dimensional biofilm structures.

[0008] This invention discloses a microbial analysis and processing method, comprising the following steps:

[0009] A multi-focal-plane time-series confocal microscopic image sequence of a biofilm is obtained. The multi-focal-plane images at each time point are sorted by focal plane depth and stacked and assembled to output a four-dimensional image dataset, which includes three-dimensional spatial coordinates and time coordinates.

[0010] Three-dimensional connectivity analysis is performed on the stack of three-dimensional images at each time point in the four-dimensional image dataset to identify connected regions across the focal plane and extract the three-dimensional attribute data of each microbial individual. The three-dimensional attribute list of microbial individuals at each time point is output, and the three-dimensional attribute data includes three-dimensional centroid coordinates and volume parameters.

[0011] Spatial matching is performed on the three-dimensional attribute lists of microbial individuals at adjacent time points. The three-dimensional Kalman filter algorithm is used to predict the three-dimensional position of each individual at the next moment, establish the correspondence between individuals across time points, and output a set of three-dimensional motion trajectories.

[0012] During the trajectory association process, split events are detected. When two new individuals appear near a certain 3D position at a certain moment and there is a parent individual with increased volume at the previous moment, it is marked as a split event and a parent-child lineage association is established. The set of lineage association edges is output.

[0013] All individual microorganisms are treated as nodes and phylogenetic association edges are treated as directed edges, and a four-dimensional spatiotemporal phylogenetic graph structure is assembled to output the phylogenetic graph data of biofilm microorganisms.

[0014] Furthermore, the three-dimensional connectivity analysis includes:

[0015] Pixel-by-pixel position comparison is performed on the images of adjacent focal planes in the 3D image stack. When a pixel position belongs to the foreground region in both adjacent focal planes, it is determined that there is a cross-focal plane connectivity relationship at that position.

[0016] Based on cross-focal plane connectivity, the projection regions of the same microbial individual on multiple focal planes are merged into a single three-dimensional connected domain.

[0017] The three-dimensional centroid coordinates and volume parameters are extracted for each three-dimensional connected domain. The three-dimensional centroid coordinates are calculated by weighted average of the two-dimensional centroids of each focal plane, and the volume parameters are calculated by accumulating the product of the projected area of ​​each focal plane and the focal plane spacing.

[0018] Furthermore, the three-dimensional centroid coordinates are calculated as follows: the projected area on each focal plane is used as a weight, and the two-dimensional centroid coordinates and focal plane depth coordinates on each focal plane are weighted and averaged to obtain the horizontal, vertical and depth coordinates of the three-dimensional centroid.

[0019] Furthermore, the method of predicting the three-dimensional position of each object at the next moment using the three-dimensional Kalman filter algorithm includes:

[0020] Based on the three-dimensional position and movement velocity of each microbial individual at the previous moment, the predicted position at the current moment is calculated using the prediction equation of Kalman filtering.

[0021] The actual location of the microbial individual detected at the current moment is matched with each predicted location. The three-dimensional Euclidean distance between the predicted location and the actual location is calculated. Pairs with the smallest distance and less than a preset threshold are established as cross-time point correspondences of the same individual.

[0022] The Kalman filter update equation is used to correct the predicted values ​​based on the actual detection location and update the state estimates of each body.

[0023] Furthermore, in the matching process, when there are multiple candidate matches, the Hungarian algorithm is used to perform the global optimal matching so as to minimize the overall matching cost.

[0024] Furthermore, the detection of split events includes:

[0025] The number of detected trajectories changes between adjacent time points. When the number of newly added individuals exceeds the number of disappeared individuals, the three-dimensional location region where the newly added individuals are located is marked as a split candidate region.

[0026] Within the splitting candidate region, check whether there is a single individual with a volume parameter greater than a preset threshold in the previous moment. If so, mark the individual as a parent candidate.

[0027] Based on the spatial proximity and volume conservation relationships between the parent candidate and the two newly added individuals at the current moment, the split event is confirmed, and directed edge relationships from the parent node to the two child nodes are established.

[0028] Furthermore, the volume conservation relationship refers to the ratio of the volume of the parent body to the sum of the volumes of the two daughter bodies being in the range of 0.8 to 1.2.

[0029] Furthermore, it also includes a three-dimensional morphological verification step: checking whether the parent candidate exhibits the characteristics of gradually expanding volume and gradually stretching shape in several frames of images before splitting. If the trend of the feature change is detected, the authenticity of the splitting event is further confirmed. If the trend of the feature change is not detected, the candidate is marked as a suspected false detection.

[0030] Furthermore, before sorting and stacking the multi-focal images at each time point according to focal depth, an image preprocessing step is also included: grayscale conversion and background subtraction of each focal image to generate a binarized foreground mask image.

[0031] The present invention discloses a microbial analysis and processing system, comprising: a computing unit and a storage unit for performing the various steps of the microbial analysis and processing method described in the present invention.

[0032] This invention overcomes the problem of traditional two-dimensional analysis methods misclassifying the projections of the same microorganism on different focal planes as multiple independent individuals by using three-dimensional connectivity analysis to merge the microbial projection regions across focal planes, thus avoiding counting errors caused by repeated counting across focal planes. It also overcomes the difficulty of cross-frame association caused by microbial movement in three-dimensional space by using a three-dimensional Kalman filter algorithm to predict and match the three-dimensional motion trajectories of individual microorganisms, thereby establishing continuous individual motion trajectories in three-dimensional space. Furthermore, it overcomes the difficulty of identifying parent-child relationships caused by the migration of offspring across focal planes after division by using a splitting event detection strategy based on trajectory quantity changes, volume parameters, and spatial proximity, thus achieving lineage association across depth layers. Finally, it overcomes the problem of traditional two-dimensional tracking methods being unable to express the lineage evolution process in three-dimensional space by using a four-dimensional spatiotemporal lineage diagram structure to uniformly represent individual microorganisms and their splitting relationships, thus solving the technical problems of broken lineage tracking and lost spatial diffusion trajectories in the three-dimensional structure of biofilms, achieving a complete, accurate, and multi-dimensional characterization of the microbial proliferation process. Attached Figure Description

[0033] Figure 1 This is a flowchart of the overall process of a microbial analysis and processing method according to the present invention;

[0034] Figure 2 This is a detailed flowchart of the three-dimensional connectivity analysis steps of the present invention;

[0035] Figure 3 This is a detailed flowchart of the invention's use of a three-dimensional Kalman filter algorithm for spatial matching and trajectory tracking;

[0036] Figure 4 This is a detailed flowchart of the splitting event detection steps of the present invention. Detailed Implementation

[0037] In the field of biofilm formation and development dynamics research, researchers need to track the proliferation lineage and spatial diffusion processes of individual microorganisms within a three-dimensional biofilm structure. Biofilms exhibit a multi-layered three-dimensional structure, with microorganisms distributed and proliferating at different focal depths. The progeny cells after division may migrate to different depth layers to settle, forming a complex three-dimensional lineage structure.

[0038] Existing microbial lineage tracing technologies are mainly based on two-dimensional planar images for analysis. When processing three-dimensional biofilm structures, they have the following technical problems: it is difficult to determine the connectivity of microorganisms at different focal plane depths, which leads to the same microorganism being mistaken for multiple independent individuals when projected onto adjacent focal planes; after division, offspring may migrate across focal planes, and traditional methods cannot establish parent-child relationships across depth layers; it is difficult to distinguish between changes in the number of trajectories caused by division events and repeated counting across focal planes, resulting in breaks in the lineage tree in the depth direction and loss of spatial diffusion trajectories.

[0039] According to an embodiment of this invention, a microbial analysis and processing method is provided to solve the technical problems of broken microbial lineage tracking and loss of spatial diffusion trajectory in the above-mentioned three-dimensional biofilm structure.

[0040] It should be understood that the execution of this embodiment requires the following hardware environment: a confocal microscope or a microscopic imaging device with multifocal plane imaging capability, used to acquire multifocal plane time-series images of biofilm samples; and a computing device with image processing and data analysis capabilities, used to execute the data processing steps described in this embodiment.

[0041] The method of this embodiment includes the following steps;

[0042] Step 100: Obtain a multi-focal-plane time-series confocal microscopic image sequence of the biofilm, sort the multi-focal-plane images at each time point according to the focal plane depth and stack them to assemble, and output a four-dimensional image dataset.

[0043] According to an embodiment of this implementation, the four-dimensional image dataset includes three-dimensional spatial coordinates and time coordinates, wherein the three-dimensional space is composed of planar coordinates and focal depth coordinates of multiple focal planes, and the time coordinates are composed of the acquisition time series.

[0044] It should be noted that the acquisition methods for multi-focal plane images include, but are not limited to: obtaining optical section images at different depths by scanning layer by layer using a confocal microscope; and performing multi-layer imaging by sequentially adjusting the focal plane position at each time point using a microscope with motorized focusing function. The images of each focal plane are then stacked and assembled after being sorted according to their corresponding depth coordinate values ​​from smallest to largest.

[0045] For example, in a study monitoring the development of *Pseudomonas aeruginosa* biofilms, confocal microscopy was used to continuously image its growth in a culture vessel. The imaging parameters for the confocal microscope were set as follows: pixel physical size of 0.125 μm / pixel, focal plane spacing of 0.5 μm, and 20 focal plane images (focal plane depth range from 0 to 9.5 μm) were acquired at each time point. Data was collected every 30 minutes for 6 hours, resulting in a total of 13 time points. The multifocal image data from the first time point was stacked and assembled to form a four-dimensional image dataset, where the 10th focal plane (corresponding to depth coordinates)... (micrometers) and the 11th focal plane (corresponding to depth coordinates) The image resolution (in micrometers) is 1024×1024 pixels.

[0046] Step 200: Perform three-dimensional connectivity analysis on the stack of three-dimensional images at each time point in the four-dimensional image dataset, identify connected regions across the focal plane, extract the three-dimensional attribute data of each microbial individual, and output the three-dimensional attribute list of microbial individuals at each time point.

[0047] According to an embodiment of this implementation, three-dimensional connectivity analysis includes the following processing steps:

[0048] Step 201: Perform pixel-by-pixel position comparison on the images of adjacent focal planes in the 3D image stack. When a pixel position belongs to the foreground region in both adjacent focal planes, it is determined that there is a cross-focal plane connectivity relationship at that position.

[0049] Furthermore, the "pixel-by-pixel position comparison" refers to for each For a given planar coordinate location, check if both adjacent focal planes in the depth direction contain foreground pixels. If so, the pixel location is considered to have connectivity in the depth direction. "Adjacent focal planes" refer to two consecutive focal plane layers in the focal plane depth sequence.

[0050] Step 202: Based on the cross-focal plane connectivity, merge the projection regions of the same microbial individual on multiple focal planes into a single three-dimensional connected domain to avoid duplicate counting.

[0051] Furthermore, the identification of the three-dimensional connected components refers to grouping and labeling pixel sets with connected paths in the three-dimensional image stack based on the inter-focal plane connectivity established in step 201. Specifically, this is achieved by analyzing each... The connectivity of voxel locations is used to identify pixel sets that satisfy the following conditions: there is a connected path between any two pixels in the set (i.e., it is possible to reach another pixel from one pixel through a continuous connection between adjacent pixels), and all pixels in the set belong to the foreground region. Such a set of connected pixels is identified as a three-dimensional connected domain, corresponding to a microbial individual.

[0052] Step 203: Extract the three-dimensional centroid coordinates and volume parameters for each three-dimensional connected domain. The three-dimensional centroid coordinates are calculated by weighted average of the two-dimensional centroids of each focal plane, and the volume parameters are calculated by multiplying and summing the projected area of ​​each focal plane and the distance between the focal planes.

[0053] Furthermore, the aforementioned focal plane spacing refers to the physical distance between adjacent focal planes in the depth direction. This focal plane spacing parameter is determined by the scanning step size of the microscopic imaging equipment during image acquisition and can be directly obtained from the equipment metadata or depth coordinate information in the image header file. The two-dimensional centroid coordinates of each focal plane refer to the centroid coordinates of the foreground region on each focal plane, which can be obtained by considering all pixels contained in the three-dimensional connected region on that focal plane. and The coordinates are averaged separately. The formula for calculating the volume parameter is:

[0054]

[0055] in, This represents the focal plane spacing.

[0056] It should be noted that the above-mentioned three-dimensional attribute data includes, but is not limited to: three-dimensional centroid coordinates. Volume parameters Geometric features include the sequence of projected areas of each focal plane, and the ratio of major and minor axes of the shape. The formula for calculating the three-dimensional centroid coordinates is:

[0057]

[0058] in, This represents the number of focal planes spanned by the three-dimensional connected domain. For the first The projected area on each focal plane For the first Two-dimensional centroid coordinates on a focal plane, For the first Depth coordinates of each focal plane.

[0059] In this embodiment, an image preprocessing step may be included before step 200: grayscale conversion and background subtraction are performed on each focal plane image to generate a binarized foreground mask image, thereby improving the accuracy of subsequent connectivity analysis. Background subtraction may employ a sliding window local mean method or a Gaussian mixture background model.

[0060] For the above biofilm samples at the first time point ( Three-dimensional connectivity analysis was performed on three-dimensional images (min). Microbial individuals with cross-focal plane connectivity were detected at focal plane depths of 4.5 μm and 5.0 μm. For example, the projected region of an individual M1 on these two adjacent focal planes was... Location If there are connected pixels at a certain location, determine the location at that position. and It exhibits connectivity. Based on 3D connected component identification, the connected pixel set of this individual M1 contains approximately 320 pixels from the 10th focal plane and approximately 310 pixels from the 11th focal plane. According to the volume calculation formula, the projected areas of this individual are respectively... micrometer and micrometer Focal plane spacing If the value is in micrometers, then the volume is... cubic micrometers. Three-dimensional centroid coordinates are... Micrometer.

[0061] At the same time point, a total of 25 microbial individuals were identified through similar analysis. The table below lists the three-dimensional attribute data of 6 representative individuals:

[0062] Table 1. Three-dimensional attribute data of microbial individuals at the first time point;

[0063]

[0064] Step 300: Spatial matching of the three-dimensional attribute lists of microbial individuals at adjacent time points, prediction of the three-dimensional position of each individual at the next moment using the three-dimensional Kalman filter algorithm, establishment of cross-time point individual correspondence, and output of a set of three-dimensional motion trajectories.

[0065] According to an embodiment of this implementation, a three-dimensional Kalman filter algorithm is used to predict the trajectory of individual microorganisms in three-dimensional space. The input of the three-dimensional Kalman filter algorithm is the three-dimensional position coordinates and velocity information of the individual microorganism at adjacent time points. The state vector contains three-dimensional position coordinates and three-dimensional velocity components. The output is the predicted position coordinates of each individual at the next time point.

[0066] Furthermore, the state vector in the Kalman filter algorithm is defined as follows: ,in Indicates transpose. Indicates the time of a microbial individual The three-dimensional position coordinates, This represents the velocity components in three directions. The state transition matrix should be based on the time sampling interval. The structure, in the form of:

[0067]

[0068] Indicates from time At the time The state change relationship. Process noise covariance matrix. The settings should be based on the irregularity of actual microbial movement, and can be estimated based on historical trajectory data to reflect unexpected acceleration fluctuations; measure the noise covariance matrix. The settings should be adjusted according to the image detection accuracy to reflect the uncertainty of position coordinate detection. Parameters Q and R should be adjusted offline based on sample data in the early stages of tracking to ensure that the filter can reasonably balance the degree of confidence in the predicted and measured values.

[0069] It should be noted that before performing 3D spatial matching and distance calculation, the 3D coordinates need to undergo unit-standardized data preprocessing. Specifically, this involves... , The pixel coordinates of the orientation are converted to physical units (such as micrometers) by multiplying by the pixel's physical size. The focal plane depth coordinates in all directions are unified to the same physical unit to ensure that the coordinates in the three directions are in the same metric space, thereby ensuring the accuracy of subsequent three-dimensional Euclidean distance calculations.

[0070] Step 301: Based on the three-dimensional position and movement velocity of each microbial individual at the previous moment, calculate the predicted position at the current moment using the prediction equation of Kalman filtering.

[0071] Step 302: Match the actual detected microbial individual locations with each predicted location, calculate the three-dimensional Euclidean distance between the predicted and actual locations, and establish the pairings with the smallest distance that is less than a preset threshold as the cross-time point correspondence of the same individual.

[0072] Furthermore, the formula for calculating the above three-dimensional Euclidean distance is as follows:

[0073]

[0074] in, The location predicted by the Kalman filter. This represents the actual detected location at the current moment. The aforementioned preset threshold refers to the upper bound of the three-dimensional spatial distance determined based on the characteristics of microbial movement speed and time intervals. The preset threshold should be set as the maximum reasonable movement distance of microorganisms within the interval between adjacent time points, denoted as... The judgment condition is Typically, this can be determined based on historical trajectory data or prior biological knowledge.

[0075] Step 303: Using the update equation of Kalman filtering, correct the predicted values ​​according to the actual detection positions and update the state estimates of each body.

[0076] In the aforementioned biofilm study, the second time point ( Trajectory tracking of individual microorganisms (minutes) was performed. The three-dimensional position of individual M1 at the first time point was used as the basis for this tracking. Micrometer and initial velocity estimation Prediction is performed using Kalman filtering at micrometers per minute. The time sampling interval is set. Minutes later, according to the state transition matrix, the predicted position of M1 at the second time point is: Micrometers. The actual detected position of M1 at the second time point was... micrometers, three-dimensional Euclidean distance is micrometers, smaller than the preset matching threshold Micrometers are used to confirm the matching relationship. The state estimate is corrected using a Kalman filter update equation, and the rate estimate for updating M1 is given. Micrometers per minute.

[0077] A similar matching process was performed on the 25 individuals identified between the first and second time points. 21 individuals successfully established cross-time correspondences, while 4 individuals failed to match due to excessive distance. Three new individuals were detected at the second time point (possibly due to cell division). The motion trajectory data of individuals M1-M6 between the two time points are as follows:

[0078] Table 2. Three-dimensional motion trajectory data of microbial individuals M1-M6 between two time points;

[0079]

[0080] It should be noted that in the above three-dimensional spatial matching process, when there are multiple candidate matches, the Hungarian algorithm is used for global optimal matching. The input of the Hungarian algorithm is the three-dimensional Euclidean distance matrix between the predicted position and the actual detection position, and the output is the optimal pairing scheme that minimizes the overall matching cost, so as to establish the cross-time point correspondence of each microbial individual.

[0081] Step 400: Detect split events during trajectory association. When two new individuals appear near a certain 3D position at a certain moment and there is a parent individual with increased volume at the previous moment, mark it as a split event and establish a parent-child lineage association, and output the lineage association edge set.

[0082] Furthermore, the "volume increase" refers to the trend of volume parameter increase of the candidate parent individual in the observation of multiple adjacent time points, that is, the candidate parent individual gradually accumulates volume in several time points before division, rather than just an accidental increase at a single time point.

[0083] According to an embodiment of this implementation, the detection criteria for splitting events include:

[0084] Step 401: Detect the change in the number of trajectories in adjacent time steps. When the number of newly added individuals exceeds the number of disappeared individuals, mark the three-dimensional location region where the newly added individuals are located as a split candidate region.

[0085] Furthermore, the term "newly added individual" refers to an individual detected at the current moment that does not meet the matching criteria with any tracked individual from the previous moment, while "disappeared individual" refers to a tracked individual that existed at the previous moment but has not yet had a cross-time point correspondence established at the current moment. The "three-dimensional location region" refers to the cubic neighborhood surrounding the three-dimensional centroid coordinates of the newly added individual, and the side length of the neighborhood should be set to twice the maximum reasonable movement distance of the microorganism within the interval between adjacent time points. The criterion for determining that "the number of newly added individuals exceeds the number of disappeared individuals" is as follows: Let the number of newly added individuals at the current moment be... The number of individuals who failed to establish a corresponding relationship at the previous moment was ,when At that time, it was considered that there was a net increase in the number of trajectories, and a splitting event may have occurred at that moment.

[0086] Step 402: Within the splitting candidate region, check if there is a single individual with a volume parameter greater than a preset threshold in the previous moment. If so, mark the individual as a parent candidate.

[0087] Furthermore, the aforementioned "single individual" refers to the largest tracked individual within the candidate division region that is spatially adjacent to the candidate division region at the previous moment. If multiple candidate individuals exist within the candidate division region, the individual with the largest volume exceeding a preset threshold should be selected as the parent candidate. The preset threshold for the aforementioned volume parameter should be set as the average volume of the microorganism before division. The preset threshold for the volume parameter refers to the lower limit of the volume that a parent individual with division potential should meet, which can typically be determined based on the average volume characteristics of microorganisms in the sample.

[0088] Step 403: Based on the spatial proximity and volume conservation relationships between the parent candidate and the two newly added individuals at the current moment, confirm the splitting event and establish directed edge relationships from the parent node to the two child nodes.

[0089] Furthermore, the "two newly added individuals" should simultaneously meet the following conditions: both of the newly added individuals are located within the candidate region of division, and the three-dimensional centroid distance between them and the candidate parent is less than a preset spatial proximity threshold. The preset spatial proximity threshold should be determined based on the maximum deviation distance of the offspring individual relative to the parent during the microbial division process.

[0090] It should be noted that the volume conservation relationship refers to the ratio of the parent volume to the sum of the volumes of the two daughter volumes being within a preset range. The range for judging the volume conservation relationship can be set as follows: This allows for volume measurement errors during the splitting process. Specifically, the mathematical form of the volume conservation judgment is:

[0091]

[0092] in, For the parent volume, and Let be the volumes of the two daughter bodies. When the above inequality holds, it is assumed that the volume conservation relationship is satisfied between the parent and daughter bodies.

[0093] In this embodiment, to improve the accuracy of splitting event detection, a three-dimensional morphological verification step can be added to step 400: checking whether the parent candidate exhibits characteristics of gradual volume expansion and morphological stretching in several frames of images before splitting. If such characteristic trends are detected, the authenticity of the splitting event is further confirmed; if no such characteristic trends are detected, the splitting event candidate is marked as a suspected false detection. The morphological stretching feature can be evaluated by calculating the rate of change of the major and minor axis ratios of each focal plane projection region.

[0094] Furthermore, the major-minor axis ratio refers to the ratio of the major and minor axes of the microbial projection area on each focal plane after elliptical fitting. When a microorganism expands in volume before division, the shape of its projection area gradually stretches from an approximately circular shape to an ellipse, resulting in an increase in the major-minor axis ratio. By comparing the changing trends of the major-minor axis ratio at multiple adjacent time points, it can be determined whether there is a morphological stretching feature.

[0095] At the fourth time point of the above biofilm monitoring ( A splitting event was detected at (minutes). At this time, the number of newly added individuals was 2, and the number of lost individuals was 0, satisfying the condition. The conditions are met, therefore the candidate region for splitting is located near the location of the newly added individual. The three-dimensional centroid coordinates of the two newly added individuals are respectively... micrometers and Micrometers. At the previous time point ( (Minutes), examining individuals within the candidate splitting region. The candidate with the largest volume was found to be individual M1_mother, whose three-dimensional centroid coordinates are... micrometers, volume is The volume is measured in cubic micrometers (a significant increase compared to 39.38 cubic micrometers at the first time point, indicating a clear trend of increasing volume). The volumes of the two newly added individuals are respectively... cubic micrometer and cubic micrometers. Calculate the volume conservation relationship:

[0096]

[0097] This ratio is within the preset range. Within this range, the volume conservation condition is satisfied. The three-dimensional centroid distances between the two newly added individuals and the parent candidate are respectively... micrometer, Micrometers, all smaller than the preset spatial proximity threshold of 8 micrometers. Examining the morphological characteristics of M1_mother at multiple time points before splitting revealed that it... The major and minor axis ratios at the minute intervals were 1.25, 1.48, and 1.72, respectively, showing an upward trend, and the volume also gradually increased (39.38→55.12→68.50 cubic micrometers), confirming the authenticity of the splitting event. The splitting relationship was established: M1_mother → M1_child1, M1_child2.

[0098] Step 500: Assemble all individual microorganisms as nodes and phylogenetic association edges as directed edges into a four-dimensional spatiotemporal phylogenetic graph structure, and output the phylogenetic graph data of biofilm microorganisms.

[0099] According to an embodiment of this implementation, the four-dimensional spatiotemporal phylogenetic graph is a directed acyclic graph structure, in which each node corresponds to the state of a microbial individual at a certain moment, and the node attributes include three-dimensional position coordinates, time coordinates, volume parameters, etc.; the directed edges represent the parent-child relationship generated by the division, and the direction of the edges points from the parent node to the child node.

[0100] Furthermore, the assembly process of the phylogenetic graph includes: for each observation of each microbial individual at each time moment, creating a corresponding graph node, the identifier of which consists of the individual number and the time number; establishing temporal continuity edges between adjacent time moment nodes of the same individual based on the trajectory association obtained in step 300; and establishing directed edges of splitting relationships between parent nodes and daughter nodes based on the splitting event results obtained in step 400. Through the above node creation and edge connection process, a complete four-dimensional spatiotemporal phylogenetic graph is generated.

[0101] In this embodiment of the application, in addition to step 500, a spatial diffusion analysis step may be included: based on the pedigree structure, the three-dimensional spatial diffusion direction and proliferation rate of each pedigree branch are calculated. The spatial diffusion direction is obtained by calculating the mean displacement vector of the offspring individual relative to the ancestral individual in the same pedigree branch; the proliferation rate is obtained by counting the number of splitting events in each pedigree branch per unit time.

[0102] Furthermore, the "ancestral individual" refers to the root node in each lineage branch, that is, the initial individual in that branch without a parent-child relationship. The displacement vector of a descendant individual relative to the ancestral individual is the three-dimensional centroid coordinates of the descendant individual minus the three-dimensional centroid coordinates of the ancestral individual. The spatial diffusion direction of that branch is obtained by averaging the displacement vectors of all descendant individuals within the same lineage branch. The formula for calculating the spatial diffusion direction is:

[0103]

[0104] in, The vector represents the spatial diffusion direction. This represents the total number of offspring individuals in this lineage branch. For the first The three-dimensional centroid coordinates of each offspring individual. The coordinates of the centroid of the progenitor individual are three-dimensional.

[0105] The formula for calculating the proliferation rate is:

[0106]

[0107] in, For the proliferation rate, This represents the total number of splitting events that occurred within this lineage branch during the observation period. The moment when the progenitor first appeared. This refers to the moment when the last division event of this lineage occurred or the moment the observation ended. The introduction of this time dimension allows the proliferation rate to reflect the average proliferation frequency of the microbial branch throughout the entire observation period.

[0108] A four-dimensional spatiotemporal phylogenetic graph was constructed for the entire 6-hour monitoring period. During the observations at 13 time points, approximately 180 microbial individual nodes were identified (each node represents the observation state of an individual at a specific moment). Through trajectory correlation, 159 temporally continuous edges were established, connecting observations of the same individual at adjacent time points. Through splitting event detection, a total of 8 splitting events were identified, and 8 directed edges establishing splitting relationships were established. The four-dimensional spatiotemporal phylogenetic graph consists of the following nodes and edges: the progenitor individual of one major phylogenetic branch is M_root, in... When it first appeared in the position Micrometers. This lineage branch underwent three splitting events, occurring at... Minutes passed. The final splitting event occurred... Minutes, therefore the observation period for this lineage branch is , Minutes. Total number of split events. The proliferation rate is:

[0109]

[0110] This lineage branch produced a total of 8 offspring individuals during the 6-hour observation period (which expanded from a single ancestral individual through 3 splits).

[0111] Based on the four-dimensional spatiotemporal phylogenetic diagram structure, the spatial diffusion direction and proliferation parameters of this main phylogenetic branch were calculated. The three-dimensional centroid coordinates of the six leaf individuals (last-generation individuals that did not undergo further division) produced by this branch during the observation period are as follows: , , , , , Micrometers. The three-dimensional centroid coordinates of the ancestral individual are... Micrometers. The displacement vectors of each individual leaf relative to the progenitor individual are as follows:

[0112]

[0113]

[0114] The spatial diffusion direction vector is:

[0115]

[0116] The magnitude of the vector is:

[0117]

[0118] This indicates that the lineage branch diffused 115.65 micrometers along an average direction from the ancestral individual. The direction cosine is:

[0119]

[0120] This indicates that the lineage branch is mainly in In-plane diffusion, The diffusion in the direction (depth direction) is relatively small.

[0121] The trajectory data of each individual between the two time points are summarized as follows:

[0122] Table 3 Spatial evolution data of key individuals in major phylogenetic branches;

[0123]

[0124] The microbial analysis and processing method provided in this embodiment uses three-dimensional connectivity analysis to merge the microbial projection areas across focal planes, overcoming the problem of traditional two-dimensional analysis methods misjudging the projections of the same microorganism on different focal planes as multiple independent individuals, thereby avoiding counting deviations caused by repeated counting across focal planes.

[0125] Furthermore, by using a three-dimensional Kalman filter algorithm to predict and match the three-dimensional motion trajectories of individual microorganisms, the difficulties in cross-frame association caused by the movement of microorganisms in three-dimensional space were overcome, thus establishing continuous individual motion trajectories in three-dimensional space.

[0126] Furthermore, by employing a splitting event detection strategy based on changes in trajectory number, volume parameters, and spatial proximity, the difficulty in identifying parent-child relationships caused by offspring migration across focal planes after splitting was overcome, thus achieving phylogenetic association across depth layers.

[0127] Furthermore, by using a four-dimensional spatiotemporal phylogenetic diagram structure to uniformly represent individual microorganisms and their division relationships, it overcomes the inability of traditional two-dimensional tracking methods to express the phylogenetic evolution process in three-dimensional space, thereby solving the technical problems of broken microbial phylogenetic tracking and loss of spatial diffusion trajectories in the three-dimensional structure of biofilms.

Claims

1. A method for microbial analysis and processing, characterized in that, Includes the following steps: A multi-focal-plane time-series confocal microscopic image sequence of a biofilm is obtained. The multi-focal-plane images at each time point are sorted by focal plane depth and stacked and assembled to output a four-dimensional image dataset, which includes three-dimensional spatial coordinates and time coordinates. Three-dimensional connectivity analysis is performed on the stack of three-dimensional images at each time point in the four-dimensional image dataset to identify connected regions across the focal plane and extract the three-dimensional attribute data of each microbial individual. The three-dimensional attribute list of microbial individuals at each time point is output, and the three-dimensional attribute data includes three-dimensional centroid coordinates and volume parameters. Spatial matching is performed on the three-dimensional attribute lists of microbial individuals at adjacent time points. The three-dimensional Kalman filter algorithm is used to predict the three-dimensional position of each individual at the next moment, establish the correspondence between individuals across time points, and output a set of three-dimensional motion trajectories. During the trajectory association process, split events are detected. When two new individuals appear near a certain 3D position at a certain moment and there is a parent individual with increased volume at the previous moment, it is marked as a split event and a parent-child lineage association is established. The set of lineage association edges is output. All individual microorganisms are treated as nodes and phylogenetic association edges are treated as directed edges, and a four-dimensional spatiotemporal phylogenetic graph structure is assembled to output the phylogenetic graph data of biofilm microorganisms.

2. The microbial analysis and processing method according to claim 1, characterized in that, The three-dimensional connectivity analysis includes: Pixel-by-pixel position comparison is performed on the images of adjacent focal planes in the 3D image stack. When a pixel position belongs to the foreground region in both adjacent focal planes, it is determined that there is a cross-focal plane connectivity relationship at that position. Based on cross-focal plane connectivity, the projection regions of the same microbial individual on multiple focal planes are merged into a single three-dimensional connected domain. The three-dimensional centroid coordinates and volume parameters are extracted for each three-dimensional connected domain. The three-dimensional centroid coordinates are calculated by weighted average of the two-dimensional centroids of each focal plane, and the volume parameters are calculated by accumulating the product of the projected area of ​​each focal plane and the focal plane spacing.

3. The microbial analysis and processing method according to claim 2, characterized in that, The three-dimensional centroid coordinates are calculated as follows: the projected area on each focal plane is used as the weight, and the two-dimensional centroid coordinates and focal plane depth coordinates on each focal plane are weighted and averaged to obtain the horizontal, vertical and depth coordinates of the three-dimensional centroid.

4. The microbial analysis and processing method according to claim 1, characterized in that, The method of predicting the three-dimensional position of each object at the next moment using the three-dimensional Kalman filter algorithm includes: Based on the three-dimensional position and movement velocity of each microbial individual at the previous moment, the predicted position at the current moment is calculated using the prediction equation of Kalman filtering. The actual location of the microbial individual detected at the current moment is matched with each predicted location. The three-dimensional Euclidean distance between the predicted location and the actual location is calculated. Pairs with the smallest distance and less than a preset threshold are established as cross-time point correspondences of the same individual. The Kalman filter update equation is used to correct the predicted values ​​based on the actual detection location and update the state estimates of each body.

5. The microbial analysis and processing method according to claim 4, characterized in that, In the matching process, when there are multiple candidate matches, the Hungarian algorithm is used to perform the global optimal matching so as to minimize the overall matching cost.

6. The microbial analysis and processing method according to claim 1, characterized in that, The detected split events include: The number of detected trajectories changes between adjacent time points. When the number of newly added individuals exceeds the number of disappeared individuals, the three-dimensional location region where the newly added individuals are located is marked as a split candidate region. Within the splitting candidate region, check whether there is a single individual with a volume parameter greater than a preset threshold in the previous moment. If so, mark the individual as a parent candidate. Based on the spatial proximity and volume conservation relationships between the parent candidate and the two newly added individuals at the current moment, the split event is confirmed, and directed edge relationships from the parent node to the two child nodes are established.

7. The microbial analysis and processing method according to claim 6, characterized in that, The volume conservation relationship refers to the ratio of the volume of the parent body to the sum of the volumes of the two daughter bodies being in the range of 0.8 to 1.

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8. The microbial analysis and processing method according to claim 6, characterized in that, It also includes a three-dimensional morphological verification step: checking whether the parent candidate exhibits the characteristics of gradually expanding volume and gradually stretching shape in several frames of images before splitting. If the trend of the feature change is detected, the authenticity of the splitting event is further confirmed. If the trend of the feature change is not detected, the candidate is marked as a suspected false detection.

9. The microbial analysis and processing method according to claim 1, characterized in that, Before sorting and stacking the multi-focal images at each time point according to focal depth, an image preprocessing step is also included: grayscale conversion and background subtraction of each focal image to generate a binarized foreground mask image.

10. A microbial analysis and processing system, characterized in that, The system is used to perform the microbial analysis and processing method as described in any one of claims 1 to 9.

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