CN109190558B - Method for monitoring real-time three-dimensional dynamic behavior of particles - Google Patents
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Abstract
The invention discloses a method for monitoring real-time three-dimensional dynamic behaviors of particles, which comprises the steps of recording a real-time hologram by adopting a coaxial digital holographic microscope, reconstructing a scattered light field of the particles through numerical values, and obtaining three-dimensional positions of the particles by utilizing the maximum local light intensity; connecting the three-dimensional positions of the particles into a trajectory; calculating the root-mean-square terminal distance of the tracks at different time intervals to obtain an MSD-delta t curve; fitting a curve, and classifying the tracks; calculating the instantaneous speed and the included angle of the instantaneous speed vector and the upward direction z of each particle after classification and the average speed of each track; determining the position of the interface, and calculating the axial distance from each track point to the interface, the spatial distribution of the density and the speed of the particles and the distribution of theta; the invention simultaneously measures a plurality of particles, and the axial positioning precision reaches the submicron level; the real-time three-dimensional coordinates of the particles can be obtained; fluorescent labeling is not needed, and imaging is not damaged; the imaging depth reaches hundreds of microns, and the system is very suitable for dynamic three-dimensional tracking and analysis of the activities of various particles.
Description
Technical Field
The invention relates to the research field of particle three-dimensional position monitoring, in particular to a method for monitoring real-time three-dimensional dynamic behaviors of particles.
Background
Microparticles refer to particles ranging in size from submicron to hundreds of microns, including bacteria, fungi, viruses, nanoparticles, colloids, cells, and the like. The three-dimensional dynamic behavior of the particles in the medium and near the interface is monitored in real time, and the method can be used for researching the response of the particles to the environment (temperature, electric field, pH and the like) and the interaction between the particles and the interface and disclosing the mechanism of the process.
Conventional optical microscopes can only record two-dimensional coordinates of particles at the focal plane and are not suitable for tracking their three-dimensional motion. The confocal microscope can record the information of the particles at different heights in a layer scanning mode, and three-dimensional tracking is realized. However, the time resolution of confocal microscopy is greatly limited by the scanning speed of the instrument and is not suitable for real-time tracking of moving particles such as bacteria. The total internal reflection microscope utilizes the characteristic that evanescent wave intensity is exponentially attenuated in the axial direction, can monitor three-dimensional movement of particles in a real-time and lossless mode, and has axial positioning precision from sub-nanometers to several nanometers. However, the imaging range of the method in the axial direction is only hundreds of nanometers, and the spatial variation range of the movement of the particles can reach tens of microns to hundreds of microns, so that the application of the technology in three-dimensional tracking of the particles is limited.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for monitoring real-time three-dimensional dynamic behaviors of particles.
The purpose of the invention is realized by the following technical scheme:
a method for monitoring real-time three-dimensional dynamic behavior of particles is characterized by comprising the following steps:
s1, recording holograms of different moments on a sample to obtain an original holographic image, and recording a background image in a blank area of the sample, or carrying out light intensity averaging on the original holographic image to obtain a background image, wherein the sample is a particle;
s2, carrying out background subtraction on the original holographic image through the background image to eliminate background noise;
s3, carrying out numerical reconstruction on the background-subtracted holographic image to obtain three-dimensional reconstruction intensity distribution information of each particle at different moments;
s4, carrying out threshold filtering on the three-dimensional reconstructed intensity distribution information of the particles and searching for a local maximum value of light intensity to obtain alternative three-dimensional positions of the particles at different moments;
s5, setting a displacement threshold, determining the three-dimensional positions of the same particle at different moments, and connecting the three-dimensional positions to form a three-dimensional track; calculating the root-mean-square end distance MSD of the track at different time intervals delta t to obtain an MSD-delta t curve;
s6, fitting the MSD-delta t curve, and classifying the particle track according to the motion mode by the index obtained by fitting; calculating the instantaneous speed V of each track point, the included angle theta between the instantaneous speed vector and the upward z direction and the average speed V of each track in different modesTThe average value of the instantaneous speed of all track points in the track is obtained;
wherein the instantaneous speed is:
wherein i is the frame number of the track point in the track, i is 2,3 … N, and N is the total frame number of the track; (x)i，yi，zi) And (x)i-1，yi-1，zi-1) Dt is the position of the same particle in two continuous frames, and dt is the time interval of the two continuous frames;
angle θ of instantaneous velocity vector to z-up direction:
wherein,
is a direction vector of the z-up direction,
in the form of a velocity vector, the velocity vector,
a is
Modulo b is
The mold of (4);
s7, taking the lowest axial position in all track points as the position z of the interface0The axial position of each track point is zi(ii) a Calculating the axial distance z between each track point and the interfaces，zs＝zi-z0；
S8, calculating the spatial distribution of the density and the speed of the particles and the distribution of theta in different motion modes; and analyzing the three-dimensional dynamic behavior of the particles and the interaction between the particles and the interface through the motion characteristic quantity.
Further, the light intensity averaging of the original holographic image is specifically calculated by a formula as follows:
wherein, Ib(x, y) is the gray scale value of the pixel at the (x, y) position in the background image, N is the total frame number of the holographic image, t is the time, It(x, y) is the gray value of the pixel at the (x, y) position in the original holographic image at the time t;
further, in step S2, the background subtraction is performed on the original holographic image, specifically: reading gray values of pixel points in the original holographic image and the background image, and subtracting the gray value I of the pixel points in the background holographic images(x, y) is:
Is(x,y)＝It(x,y)-Ib(x,y)，
wherein, Ib(x, y) is the gray scale value of the pixel at the (x, y) position in the background image, It(x, y) is the gray value of the pixel at the (x, y) position in the original hologram at the time t;
further, in step S3, the specific process is as follows:
U(r,z)＝FT-1(FT(Is(r,0)·H(q,-z)))，
wherein h (r, -z) is a propagation operator, r is an initial transverse coordinate of the particle, and z is an initial axial coordinate of the particle; i is an imaginary unit; k is the wave number; r is the light propagation distance; i issIs the light intensity of the sample; FT-1Is inverse Fourier transform; FT is Fourier transform; h (q, -z) is the Fourier transform of H (r, -z);
the value of the reconstruction axial interval is larger than the axial imaging range of the instrument, and the step is that the size of the pixel is divided by the magnification factor of the objective lens;
further, the threshold value is filtered, and the light intensity threshold value is less than 10%;
further, in step S5, the specific process is as follows: setting a displacement threshold T according to the motion characteristics of the particles, wherein if the displacement value between two positions in two continuous frames is less than the threshold, the two positions belong to the same particle; meanwhile, the length of the track is set to be not less than W points, wherein W is 30, so that the correctness of the root-mean-square terminal distance calculated by the track connection and the subsequent steps is ensured;
further, the displacement threshold T is the particle velocity VsMultiplied by the exposure time teThe result is: t ═ Vste；
Further, the fitting of the MSD- Δ t curve specifically includes:
the point 10% before the MSD- Δ t curve was fitted by the following formula:
MSD(Δt)＝6D(Δt)ν，
dividing the track of the particles according to the motion mode by the index nu obtained by fitting, and obtaining the result as follows: the index nu is less than 0.95 and is a first mode; the index nu is more than or equal to 0.95 and less than or equal to 1.05 and is a second mode; the index nu is more than 1.05 and is a third mode;
further, the first mode is a limited diffusion mode; the second mode is a free diffusion mode; the third mode is an active motion mode;
compared with the prior art, the invention has the following advantages:
the invention adopts Rayleigh-Sommerfeld algorithm to position the three-dimensional position of the particle, can measure a plurality of particles simultaneously, and the axial positioning precision reaches submicron level; the real-time three-dimensional coordinates of the particles can be obtained; it does not need fluorescent mark, and is a nondestructive imaging method. The imaging depth of the device can reach dozens of hundreds of microns, and the device is very suitable for dynamically tracking the activities of various particles.
Drawings
FIG. 1 is a block flow diagram of a method for monitoring real-time three-dimensional dynamic behavior of particles according to the present invention;
FIG. 2 is a block diagram of a coaxial digital holographic microscopy imaging system according to an embodiment of the invention;
FIG. 3 is an original hologram of E.coli in the embodiment of the present invention;
FIG. 4 is a background image obtained by averaging the light intensity of a sequence of holographic images according to an embodiment of the present invention;
FIG. 5 is a background-subtracted hologram according to an embodiment of the present invention;
FIG. 6 is a diagram showing the movement trace of Escherichia coli near the interface in the embodiment of the present invention;
FIG. 7 is a MSD- Δ t plot of a limited diffusion trace in an embodiment of the invention;
FIG. 8 is a MSD- Δ t plot of active motion trajectory in the described embodiment of the invention;
FIG. 9 is a graph of the density distribution of E.coli in the active motor mode in the embodiment of the present invention;
FIG. 10 is a spatial distribution plot of E.coli in the active motor mode according to an embodiment of the present invention;
FIG. 11 is a distribution diagram of the angle θ between the velocity vector of the E.coli in the active motion mode and the upward z-direction in the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Examples
A method for monitoring real-time three-dimensional dynamic behavior of microparticles, as shown in fig. 1, comprises the following steps:
the first step is as follows: recording holograms of different moments on a sample by using a coaxial digital holographic microscopic imaging system to obtain an original holographic image, and recording a background image in a blank area of the sample or carrying out light intensity averaging on the original holographic image to obtain a background image; the sample is a microparticle; the average light intensity is calculated as follows:
wherein, Ib(x, y) is the gray value of the pixel at the (x, y) position in the background image, N is the original valueTotal number of frames of the starting hologram, t is time, It(x, y) is the gray value of the pixel at the (x, y) position in the original holographic image at the time t;
in this example, the microparticles were selected to be wild-type E.coli;
the coaxial digital holographic microscopic imaging system is shown in fig. 2 and comprises a first light source 1 and a second light source 1' of two mutually perpendicular LED light sources, a first plane reflector 7, a sample stage 8, a microscope objective 9, a second plane reflector 10 and an sCMOS camera 11; the two LED light sources are designed by adopting coaxial cage type light paths, and the light paths are simple and can flexibly change incident wavelengths; the LED light sources each comprise a first LED lamp 2 and a second LED lamp 2 ', a first microscope objective spatial filter 3 and a second microscope objective spatial filter 3', a first diaphragm 4 and a second diaphragm 4 ', and a first convex lens 5 and a second convex lens 5' with a focal length f equal to 50mm, and the LED light source 1 further comprises a third plane mirror 6; the microscope objective (with magnification of 10, 20, 40, 60 and 100) is mounted on the objective changer, and the objective can be flexibly switched.
The second step is that: carrying out background deduction on the original holographic image through a background image to eliminate background noise; the method specifically comprises the following steps: reading gray values of pixel points in the original holographic image and the background image, and subtracting the gray value I of the pixel points in the background holographic images(x, y) is:
Is(x,y)＝It(x,y)-Ib(x,y)，
wherein, Ib(x, y) is the gray scale value of the pixel at the (x, y) position in the background image, It(x, y) is the gray value of the pixel at the (x, y) position in the original hologram at the time t; FIG. 3 is an original hologram of E.coli in the embodiment of the present invention; FIG. 4 is a background image obtained by averaging the light intensity of a sequence of holographic images according to an embodiment of the present invention; fig. 5 is a background-subtracted hologram in an embodiment of the invention.
The third step: carrying out numerical reconstruction on the background-subtracted holographic image according to a Rayleigh-Sommerfeld algorithm to obtain the intensity distribution information of the reconstructed light field of all escherichia coli in a set three-dimensional space in a visual field range, and calculating as follows:
U(r,z)＝FT-1(FT(Is(r,0)·H(q,-z)))，
wherein h (r, -z) is a propagation operator, r is an initial transverse coordinate of the escherichia coli, and z is an initial axial coordinate of the escherichia coli; i is an imaginary unit; k is the wave number; r is the light propagation distance; i issIs the light intensity of the sample; FT-1Is inverse Fourier transform; FT is Fourier transform; h (q, -z) is the Fourier transform of H (r, -z);
the fourth step: filtering the obtained three-dimensional reconstruction intensity distribution information of the escherichia coli through a threshold value and searching for a local maximum value of light intensity to obtain alternative three-dimensional positions of the particles at different moments; the method comprises the specific steps of firstly setting a light intensity threshold value which is usually less than 10 percent and is set to be 7 percent, filtering noise in a reconstructed light field, and then finding a local maximum light intensity point by point in a cube with the side length of w (taking bacteria as an example, w is an integral value close to the sum of the length of a bacterial flagella and a body) in the cube with the side length of 13 mu m, and finding and recording the three-dimensional position of the maximum light intensity point by point.
The fifth step: setting a displacement threshold value to be 3.7 mu m, determining the three-dimensional positions of the same escherichia coli at different moments, and connecting the three-dimensional positions into a three-dimensional track; if the displacement value between two positions in two continuous frames is smaller than the threshold value, the two positions belong to the same escherichia coli; the track length is set to be not less than 30 points so as to ensure the correctness of the root-mean-square terminal distance calculated by the track connection and the subsequent steps; FIG. 6 is a diagram showing the movement trace of Escherichia coli near the interface in the embodiment of the present invention; calculating the root-mean-square end distance MSD of the track at different time intervals delta t to obtain an MSD-delta t curve:
MSD(Δt)＝<|r(t0+Δt)-r(t0)|2>，
wherein, the value of Δ t is 0.05N s, N is 1,2,3 … N-1, and N is the length of the track; FIG. 7 is a MSD- Δ t plot of a limited diffusion trace in an embodiment of the invention; FIG. 8 is a MSD- Δ t plot of active motion trajectory in the described embodiment of the invention;
and a sixth step: fitting the MSD- Δ t curve, the first 10% of points of the fitted curve:
MSD(Δt)＝6D(Δt)ν，
classifying the tracks of the escherichia coli according to the motion mode by the indexes obtained by fitting, and dividing the tracks into a limited diffusion mode, a free diffusion mode and an active motion mode; wherein the index nu is less than 0.95 and is a limited diffusion mode; the index nu is more than or equal to 0.95 and less than or equal to 1.05, and is a free diffusion mode; the index nu is 1.05 which is more than the active movement mode; the embodiment aims at analyzing the complete three-dimensional dynamic behavior of escherichia coli near an interface, tracks with v being more than or equal to 1 are all regarded as active movement, and subsequent data processing is only limited to the actively moving escherichia coli;
calculating the instantaneous speed V of each track point, the included angle theta between the instantaneous speed vector and the upward z direction and the average speed of each track in different modes
The average value of the instantaneous speed of all track points in the track is obtained;
wherein the instantaneous speed is:
wherein i is the frame number of the track point in the track, i is 2,3 … N, and N is the total frame number of the track; (x)i，yi，zi) And (x)i-1，yi-1，zi-1) Dt is the position of the same particle in two continuous frames, and dt is the time interval of the two continuous frames;
angle θ of instantaneous velocity vector to z-up direction:
wherein,
is a direction vector of the z-up direction,
in the form of a velocity vector, the velocity vector,
a is
Modulo b is
Die of
The seventh step: the lowest axial position in all the track points is taken as the position z of the interface0The axial position of each track point is zi(ii) a Calculating the axial distance z between each track point and the interfacesNamely: z is a radical ofs＝zi-z0；
Eighth step: calculating the spatial distribution of the density and the speed of the particles and the distribution of theta in different motion modes; analyzing the three-dimensional dynamic behavior of the particles and the interaction between the particles and the interface through the motion characteristic quantity;
taking dz to be 5 μm (far larger than the resolution of axial positioning to be 400nm) and d theta to be 5 degrees, and calculating the spatial distribution of the density and the speed of the actively moving escherichia coli and the distribution of theta;
and analyzing the three-dimensional dynamic behavior of the escherichia coli and the interaction between the escherichia coli and the interface through the motion characteristic quantity. As can be seen from the figure, the movement of E.coli near the interface is mainly influenced by hydrodynamic effects. The specific analysis is as follows: the spatial distribution of the density of E.coli near the interface shown in FIG. 9 is consistent with a theoretical model of the distribution of particles near the interface under hydrodynamic action:
in the formula, L⊥Distance of action for hydrodynamic action, H isThe thickness of the sample cell, p is a force dipole, eta is the viscosity of a medium, and D is a diffusion coefficient; shown in FIG. 10 at z<At 5 μm, the phenomenon that the movement speed of escherichia coli increases with the decrease of z and the phenomenon that θ is mainly distributed at 90 ° in fig. 11 conform to the theoretical model that particles are subject to hydrodynamic action near the interface and tend to move in the direction parallel to the interface, and the speed increases.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
Claims (9)
1. A method for monitoring real-time three-dimensional dynamic behavior of particles is characterized by comprising the following steps:
s1, recording holograms of different moments on a sample to obtain an original holographic image, and recording a background image in a blank area of the sample, or carrying out light intensity averaging on the original holographic image to obtain a background image, wherein the sample is a particle;
s2, carrying out background subtraction on the original holographic image through the background image to eliminate background noise;
s3, carrying out numerical reconstruction on the background-subtracted holographic image to obtain three-dimensional reconstruction intensity distribution information of each particle at different moments;
s4, carrying out three-dimensional reconstruction on intensity distribution information of the particles, and filtering and searching a local maximum value of light intensity through a light intensity threshold value to obtain alternative three-dimensional positions of the particles at different moments;
s5, setting a displacement threshold, determining the three-dimensional positions of the same particle at different moments, and connecting the three-dimensional positions to form a three-dimensional track; calculating the root-mean-square end distance MSD of the track at different time intervals delta t to obtain an MSD-delta t curve;
s6, fitting the MSD-delta t curve, and classifying the particle track according to the motion mode by the index obtained by fitting; calculating the instantaneous speed V and the angle theta between the instantaneous speed vector and the upward z direction of each track point in different modes, and calculating the angle theta between each track point and the upward z directionAverage velocity
The average value of the instantaneous speed of all track points in the track is obtained;
wherein the instantaneous speed is:
wherein i is the frame number of the track point in the track, i is 2,3 … N, and N is the total frame number of the track; (x)i，yi，zi) And (x)i-1，yi-1，zi-1) Dt is the position of the same particle in two continuous frames, and dt is the time interval of the two continuous frames;
angle θ of instantaneous velocity vector to z-up direction:
wherein,
is a direction vector of the z-up direction,
in the form of a velocity vector, the velocity vector,
a is
Modulo b is
The mold of (4);
s7, taking the lowest axial position in all track points as the position z of the interface0The axial position of each track point is zi(ii) a Calculating the axial distance z between each track point and the interfaces，zs＝zi-z0；
S8, calculating the spatial distribution of the density and the speed of the particles and the distribution of theta in different motion modes; and analyzing the three-dimensional dynamic behavior of the particles and the interaction between the particles and the interface through the motion characteristic quantity.
2. The method for monitoring the real-time three-dimensional dynamic behavior of particles as claimed in claim 1, wherein in step S1, the light intensity average of the original holographic image is calculated by the following formula:
wherein, Ib(x, y) is the gray value of the pixel at the (x, y) position in the background image, N is the total frame number of the original holographic image, t is the time, It(x, y) is the gray value of the pixel at the (x, y) position in the original holographic image at time t.
3. The method for monitoring the real-time three-dimensional dynamic behavior of particles as claimed in claim 1, wherein in step S2, the background subtraction is performed on the original holographic image, specifically: reading gray values of pixel points in the original holographic image and the background image, and subtracting the gray value I of the pixel points in the original holographic image after the background is deducteds(x, y) is:
Is(x,y)＝It(x,y)-Ib(x,y)，
wherein, Ib(x, y) is the gray scale value of the pixel at the (x, y) position in the background image, It(x, y) is the gray value of the pixel at the (x, y) position in the original hologram at time t.
4. The method for monitoring the real-time three-dimensional dynamic behavior of particles as claimed in claim 1, wherein the step S3 comprises the following steps:
U(r,z)＝FT-1(FT(Is(r,0)·H(q,-z)))，
wherein h (r, -z) is a propagation operator, r is an initial transverse coordinate of the particle, and z is an initial axial coordinate of the particle; i is an imaginary unit; k is the wave number; r is the light propagation distance; i issIs the light intensity of the sample; FT-1Is inverse Fourier transform; FT is Fourier transform; h (q, -z) is the Fourier transform of H (r, -z);
the value of the reconstruction axial interval is larger than the axial imaging range of the instrument, and the stepping is that the size of the pixel is divided by the magnification of the objective lens.
5. The method as claimed in claim 1, wherein in step S4, the light intensity threshold is less than 10%.
6. The method for monitoring the real-time three-dimensional dynamic behavior of particles as claimed in claim 1, wherein the step S5 comprises the following steps: setting a displacement threshold T according to the motion characteristics of the particles, wherein if the displacement value between two positions in two continuous frames is smaller than the threshold, the two positions belong to the same particle; meanwhile, the length of the set track is not less than W points, and W is 30.
7. The method as claimed in claim 6, wherein the displacement threshold T is a particle velocity VsMultiplied by the exposure time teThe result is: t ═ Vste。
8. The method for monitoring the real-time three-dimensional dynamic behavior of particles according to claim 1, wherein in step S6, the fitting of the MSD- Δ t curve specifically comprises:
the top 10% point of the MSD- Δ t curve was fitted by the formula:
MSD(Δt)＝6D(Δt)ν，
dividing the track of the particles according to the motion mode by the index nu obtained by fitting, wherein the index nu is less than 0.95 and is a first mode; the index nu is more than or equal to 0.95 and less than or equal to 1.05 and is a second mode; the index nu of 1.05 is the third mode.
9. The method for monitoring the real-time three-dimensional dynamic behavior of particles as claimed in claim 8, wherein the first mode is a limited diffusion mode; the second mode is a free diffusion mode; the third mode is an active motion mode.
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