JP7318926B2 - Method and apparatus for analyzing elastic property distribution of cells to be measured, and method and apparatus for determining shape parameters of probe of atomic force microscope - Google Patents

Description

TECHNICAL FIELD The present invention relates to a method and apparatus for analyzing the elastic property distribution of cells to be measured, and is particularly suitable for obtaining tissue information useful in determining whether a tissue to be excised is cancerous during surgery for solid cancer. It also relates to a method and apparatus for analyzing elastic property distribution of cells to be measured.
The present invention also relates to a method and apparatus for determining shape parameters of a probe of an atomic force microscope suitable for use in the method and apparatus for analyzing the distribution of elastic properties of cells to be measured.

During surgery for cancer, particularly solid cancer, it is preferable to be able to determine whether or not the tissue to be resected has become cancerous using imaging information or the like before surgery. In addition, in order to increase the possibility of complete cure, including the possibility of metastasis, by appropriately removing the tissue judged to be cancerous, it is necessary to perform the judgment or diagnosis in a short period of time during the surgical excision of the tissue suspected to be cancerous. The advent of medical diagnostic equipment that can

On the other hand, atomic force microscopy (AFM) is widely used to measure local mechanical properties of cells. Patent Document 1 and Non-Patent Document 1 propose a physiological examination method for breast cancer cancer cells using AFM.
Patent document 2 describes a method and system for measuring the complex elastic modulus of cells, which can measure the complex elastic modulus of many cells at high speed without impairing the measurement accuracy required for realizing a cytodynamic diagnostic device. is proposed. Cells are viscoelastic bodies that have both properties of elasticity that maintains their shape and viscosity that deforms and flows. Therefore, the complex elastic modulus of cells is not constant, but is a function of time and frequency.

On the other hand, Patent Document 3 proposes a technique for precisely analyzing the elastic properties of cancer cells. It has become clear that there is a negative correlation between the metastatic potential of cancer cells and the hardness of cancer cells. is being used to suppress cancer metastasis. In such studies, in order to precisely evaluate the drug efficacy of candidate substances, it is necessary to use AFM, which is suitable for precisely analyzing the elastic properties of cancer cells affected by candidate substances, to localize cells. Mechanical physical property measurement techniques have been proposed.

However, in the conventionally known techniques for measuring the local mechanical properties of cells using AFM, the short time required during surgery to measure the mechanical properties of cells or tissues in the field during surgery to remove cancer cells, For example, within 5 minutes, it was difficult to obtain mechanical property information that would help diagnose benign or malignant tumors by tissue examination.
Therefore, there is a need for a method and apparatus for analyzing the elastic properties of cells with high spatial resolution that enable such rapid measurement of the mechanical properties of cells or tissues.
Also, in order to realize a method and apparatus for analyzing elastic properties of cells with high spatial resolution, it was necessary to know the shape of the probe of the atomic force microscope very accurately.

Japanese Patent No. 5809707 Japanese Patent No. 6360735 JP 2019-53019 A

Maria Plodinec, et. al.: “The nanomechanical signature of breast cancer”, NATURE NANOTECHNOLOGY, Vol.7, pages 757-765 (2012-10-21) K. L. Johnson: “Contact Mechanics“, Cambridge University Press (1987) Ken Nakajima, et al., "Development of Quantitative Evaluation Method for Elastic Modulus of Soft Materials Using Atomic Force Microscope," Journal of the Vacuum Society of Japan (2013, Vol. 56, No. 7, pp. 258-266)

The present invention solves the above-mentioned problems, and provides a method and apparatus for analyzing elastic property distribution of cells to be measured with high spatial resolution, which enables rapid measurement of mechanical properties of cells or tissues. aim.
It is also an object of the present invention to provide a method and apparatus for determining the shape parameters of an atomic force microscope tip that can provide a very accurate knowledge of the probe shape of the atomic force microscope.

[1] The method of analyzing the elastic property distribution of cells to be measured according to the present invention is a method of analyzing the elastic property distribution of cells to be measured, for example, as shown in FIG.
Measured values obtained by associating the amount of deformation of the cell and the pressing force of the probe obtained when the probe of the atomic force microscope is pressed against the surface of the cell to be measured are obtained from the measurement target with which the probe is in contact. a step (201) of obtaining together with the measurement position coordinates of the cell, wherein the measurement position coordinates of the cell to be measured are arranged in the upper layer of the nucleus of the cell to be measured and the site surrounding the nucleus;
Using a shape parameter determined according to the shape of the tip of the probe and a model formula representing the relationship between the deformation amount (d) of the cell and the pressing force (F) of the probe, the pressing position of the probe is determined. a step (201) of calculating the relationship between the amount of deformation (d) of the cell at and the pressing force (F) of the probe;
Using the actually measured values obtained by associating the measured amount of deformation of the cell with the pressing force of the probe, and the calculated value calculated by the model formula, the variance value (Δ _T ) of the fitting error is calculated with respect to the parameter R a step (202-205) of calculating a shape parameter with a minimum value;
creating at least one of a stress distribution and an elastic value distribution of the cell to be measured using the minimum shape parameter;
generating at least one of a stress distribution map and an elasticity value distribution map of the nucleus of the cell under measurement and around the nucleus based on at least one of the created stress distribution and elasticity distribution of the cell under measurement;
method including.

[2] In the method of analyzing the elastic property distribution of a cell to be measured according to the present invention, at least one of the stress distribution map and the elasticity value distribution map measured in the nucleus and the periphery of the nucleus of the cell to be measured is a malignant tumor. and the elastic property range of normal cells or benign tumors.
[3] In the method of analyzing the elastic property distribution of a cell to be measured according to the present invention, preferably, the relationship between the deformation amount (d) of the cell at the probe pressing position and the pressing force (F) of the probe is expressed. The model formula is
The method for analyzing elastic property distribution of cells according to claim 1 or 2.
Here, R is the tip radius of the probe, σ is the stress of the cell at the position where the probe is pressed, ν is Poisson's ratio of the cell, and E is the elastic modulus.
[4] In the method of analyzing the elastic property distribution of a cell to be measured according to the present invention, preferably, the relationship between the amount of deformation (d) of the cell at the position where the probe is pressed and the pressing force (F) of the probe is expressed. The model formula is
should be

[5] The apparatus for analyzing the distribution of elastic properties of cells to be measured according to the present invention is an analysis system for analyzing the distribution of elastic properties of cells to be measured,
Measured values obtained by associating the amount of deformation of the cell and the pressing force of the probe obtained when the probe of the atomic force microscope is pressed against the surface of the cell to be measured are obtained from the measurement target with which the probe is in contact. a means for acquiring the measurement position coordinates of the cell together with the measurement position coordinates of the cell, wherein the measurement position coordinates of the cell to be measured are arranged in the upper layer of the nucleus of the cell to be measured and the site surrounding the nucleus;
Using a shape parameter determined according to the shape of the tip of the probe and a model formula representing the relationship between the deformation amount (d) of the cell and the pressing force (F) of the probe, the pressing position of the probe is determined. means for calculating the relationship between the deformation amount (d) of the cell at and the pressing force (F) of the probe;
Using the actually measured values obtained by associating the measured amount of deformation of the cell with the pressing force of the probe, and the calculated value calculated by the model formula, the variance value (Δ _T ) of the fitting error is calculated with respect to the parameter R a means for calculating a shape parameter with a minimum value;
means for creating at least one of the stress distribution and the elastic value distribution of the cell to be measured using the minimum shape parameter;
means for generating at least one of a stress distribution map and an elasticity value distribution map of the nucleus and the vicinity of the nucleus of the cell under measurement based on at least one of the created stress distribution and elasticity distribution of the cell under measurement;
It is an analysis system comprising

[6] In the analysis system for analyzing the elastic property distribution of the cell under measurement of the present invention, at least one of the stress distribution map and the elasticity value distribution map measured in the nucleus and the periphery of the nucleus of the cell under measurement is malignant. Means may be provided for generating an indication for comparison with a threshold value of being within the elastic property range of a tumor or being within the elastic property range of normal cells or benign tumors.

[8] The method of determining the shape parameters of the probe of the atomic force microscope for analyzing the elastic properties of cells of the present invention is, for example, as shown in FIGS. a step of obtaining measured values obtained by associating the amount of deformation of the cell with the pressing force of the probe, which are obtained when the probe is pressed against x, y);
A calculated value by a model formula that associates the deformation amount of the cell with the pressing force of the probe is calculated for a plurality of obtained measured values that associate the deformation amount of the cell with the pressing force of the probe. a computing step;
a fitting error calculation step (301) for obtaining a fitting error (Δ _x,y ) between the measured value and the calculated value;
a minimum value calculation step (302) for calculating a minimum fitting error (Δ _{x, y} ^min ) with the tip radius R of the probe as a parameter;
a minimum value determination step (303) for determining whether the minimum fitting error (Δ _x,y ^min ) calculated in the minimum value calculation step is the minimum value for the parameter R;
a step (303) of changing the contact stress parameter of the model formula when it is determined that the minimum value is not the minimum value in the minimum value determining step;
a contact stress parameter setting step (304) for setting the contact stress parameter of the initial value or the contact stress parameter updated in the minimum value determination step in the step of calculating the fitting error;
If the minimum value _{determination} step determines that the minimum ^value a sending step (303);
repeating the step of obtaining the measured value to the step of sending the minimum fitting error of the single measurement point for all measurement points of the cell to be measured;
a fitting error variance value calculation step (305) for obtaining the fitting error variance value (Δ _T ) for all measurement points of the cell to be measured;
a step (306) of calculating the minimum value of the fitting error variance value determining whether the variance value (Δ _T ) of the fitting error calculated in the fitting error variance value computing step is the minimum value for the parameter R;
If it is determined in the step of determining the minimum value of the matching error variance that the variance of the matching error (Δ _T ) is not the minimum value, the step of sending the variance of the matching error Δ _T to the step of calculating the residual. (306) and
A residual calculation step (307) of changing the parameter of the tip radius R of the probe by the Monte Carlo method and sending it to the contact stress parameter setting step;
and determining the parameter R for which the dispersion value (Δ _T ) of the fitting error is determined to be the minimum value in the step of determining the minimum value of the fitting error variance value as the tip shape parameter of the probe (306). It is.

[9] In the method of determining the shape parameter of the probe of an atomic force microscope for analyzing the elastic properties of cells of the present invention, preferably, the shape parameter of the probe of the atomic force microscope is the tip radius R Therefore, the formula representing the tip radius R is preferably expressed by the following formula.
Here, R is the tip radius of the probe, a, b, c, r are the fitting parameters, z is the height direction coordinate of the cell, ∂z/∂x is the x-axis tilt of the cell, ∂z/∂y is the slope of the cell in the y-axis direction, and d is the amount of depression at the location of the cell pressed by the probe,
[10] In the method of determining shape parameters of the probe of an atomic force microscope for analyzing elastic properties of cells according to the present invention, the model formula is preferably represented by the following formula.
Here, F is the pressing force of the probe, R is the tip radius of the probe, d is the amount of depression of the cell at the position where the probe is pressed, σ is the membrane stress of the cell, ν is the Poisson's ratio of the cell, and E is the thickness of the cell. is the elastic modulus,
[11] In the method of determining the shape parameters of the probe of an atomic force microscope for analyzing the elastic properties of cells of the present invention, preferably, the contact stress parameters of the model formula are the elastic modulus E of the cell and the membrane of the cell contains the stress σ,
The formula for obtaining the matching error (Δ _x,y ) is preferably expressed by the following formula.
Here, the pressing force F _l ^cal of the calculated value uses the pressing force F _l of the Hertz+membrane stress model, and the pressing force F _l ^Exp of the actual measurement uses the depression amount d as a parameter.

The method and apparatus of the present invention for analyzing the distribution of elastic properties of cells to be measured uses an optimum model formula determined according to the shape of the tip of the cantilever probe, so data analysis can be performed with high spatial resolution. Therefore, even if the movement of the cantilever probe is performed only once, the distribution of elastic properties of the cells to be measured can be accurately analyzed, so that the mechanical properties of cells or tissues can be rapidly measured.
The method and apparatus for determining the shape parameters of the tip of the atomic force microscope of the present invention determine the shape parameters of the model formula determined according to the tip shape of the cantilever probe by machine learning using the Monte Carlo method or the like. Therefore, the probe shape of the atomic force microscope can be known very accurately.

1 is a system configuration diagram of a cell elasticity analysis system showing an embodiment of the present invention; FIG. It is a flowchart explaining the process which acquires the pressing force and the amount of depression measurement data. FIG. 4 is an explanatory diagram defining measurement positions arranged in a grid on the surface directly above the nucleus of a cell to be measured; 4 is a flow chart for explaining a process of calculating stress distribution and elastic value distribution of a cell to be measured. FIG. 4 is a configuration diagram of the essential parts for explaining the force interaction between the probe of the AFM tip and the cell body; It is an enlarged view of the main part explaining various mechanical models between the tip of the AFM tip and the cell body, including mechanical analysis information. FIG. 4 is an enlarged view of a main part explaining that the tip of the AFM tip has a mechanical relationship depending on the inclination of the surface shape of the cell body; FIG. 4 is a diagram for explaining measured value distributions according to various mechanical models between the probe of the AFM tip and the cell body; FIG. 4 is a diagram for explaining predicted value error distributions according to various mechanical models between the probe of the AFM tip and the cell body; FIG. 10 is an evaluation diagram of the life and death state of cells based on a stress map formed by AFM. It is a figure which shows an example of (A) a three-dimensional height distribution state diagram of a to-be-measured cell, (B) stress distribution, (C) elastic value distribution, and (D) force spectrum. FIG. 4 is a functional block diagram of a machine learning algorithm for calculating cell body prestress for optimizing AFM tip geometry, illustrating one embodiment of the present invention. FIG. 13 is an enlarged view of a main part of a first loop for calculating a fitting error (fitting error) Δ from an elastic modulus E and a stress σ in the functional block diagram of the machine learning algorithm of FIG. 12; FIG. 4 is a diagram for explaining the relationship between the amount of cell deformation (the amount of depression: nm) and the pressing force (nN) of the probe in various contact pressure models. Evolution map of stress using tip shape parameters generated by Monte Carlo method. FIG. 10 illustrates the evolution of dispersion using tip shape parameters generated by the Monte Carlo method;

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, the present invention will be described with reference to the embodiments shown in the drawings, but the present invention is not limited to the embodiments shown in the drawings. In addition, in each figure referred to below, the same reference numerals are used for common elements, and the description thereof will be omitted as appropriate.
FIG. 1 schematically shows the system configuration of a cell elasticity analysis system showing one embodiment of the present invention. As shown in FIG. 1 , the cell analysis of this embodiment includes an atomic force microscope (AFM) 20 and a computer 10 . In addition, a position adjustment drive unit 32 and a controller 34 are provided as a position adjustment mechanism for adjusting the relative positions of the cell and the probe of the cantilever.

An atomic force microscope 20 includes a semiconductor laser 22 , a cantilever 23 having a pyramidal probe 24 at its tip, a photodetector 25 and a preamplifier 26 . In the atomic force microscope 20, a laser beam emitted from a semiconductor laser 22 is irradiated onto the back surface of a cantilever 23, and the reflected light is incident on a photodetector 25 having a four-divided light receiving surface. In response to this, the photodetector 25 outputs a current proportional to the power of the incident light, which is converted to a voltage value via the preamplifier 26 .
The preamplifier 26 obtains the sum of the voltage values corresponding to the upper two light receiving surfaces and the sum of the voltage values corresponding to the lower two light receiving surfaces among the voltage values corresponding to the four light receiving surfaces of the photodetector 25. Furthermore, by taking the difference between the sum of the voltage values for the two upper light receiving surfaces and the sum of the voltage values for the two lower light receiving surfaces, the deflection amount of the cantilever 23 is output as a voltage value, and the output deflection amount is A representative voltage value is entered into the computer 10 .

The position adjustment driving unit 32 includes, for example, an XYZ-axis stage having a movement amount of millimeter order in the three-axis directions of XYZ, and a piezo actuator arranged on the XYZ-axis stage and capable of position adjustment with nanometer accuracy in the three-axis directions of XYZ. and a driving element. The controller 34 controls the XYZ-axis stage and the piezo driving elements, and controls the position of the probe 24 so as to raster-scan the cell to be measured, for example. The plate 40 is placed on the XYZ-axis stage of the position adjustment drive unit 32, on which cells to be analyzed are placed. The controller 34 controls the position adjustment drive section 32 and inputs the movement amount (displacement amount) of the position adjustment drive section 32 to the computer 10 . The movement amount (displacement amount) of the position adjustment drive unit 32 corresponds to the movement amount of the plate 40, that is, the cell to be measured.

The computer 10 is an information processing device that controls the position adjustment driving section 32 via the controller 34 and executes cell analysis processing described below based on inputs from the preamplifier 26 and the controller 34 . It should be noted that the computer 10 is not limited in its form, and may be a personal computer, or an embedded computer or workstation specialized for the use of the present invention.

The system configuration of the cell analysis system has been described above. Subsequently, the cell analysis processing executed by the computer 10 will be described. In the following description, FIG. 1 will be referred to as appropriate.

In this embodiment, the computer 10 performs roughly two processes. In the first process, the work of pressing the probe 24 of the cantilever 23 against the cell placed on the plate 40 is repeated to acquire measurement data of the amount of pressing force indentation for a plurality of probe pressing points. In the subsequent second processing, the elastic properties of the cells to be analyzed are visualized and displayed on the display screen based on the obtained measurement data of the pressing force indentation amount.

Here, first, an example of processing for acquiring the measurement data of the pressing force and the amount of depression will be described based on the flowchart shown in FIG.
In step 101 , the position adjustment driving section 32 is controlled to position the probe 24 in the measurement area of the cell to be measured placed on the plate 40 . Here, in this embodiment, as shown in FIG. 3, measurement positions are defined that are arranged in a grid on the surface directly above the nucleus of the cell. In the example shown in FIG. 3, a range of 40 μm×40 μm centering on the center of the nucleus was defined as the measurement area on the surface of the cell, and the center of each section obtained by dividing this measurement area into squares of 256×256 pixels was searched. It is defined as the measurement position of the tip that the needle 24 pushes. As this coordinate system, for example, (i, j); i=1 to 256, j=1 to 256 may be used, and may be aligned with the XY axis plane of the XYZ axis stage.

In the subsequent step 102, the XY piezo elements of the position adjustment driving section 32 are driven to align the probe 24 of the cantilever 23 with the first measurement position (i, j) among 256.times.256 measurement positions.

In the subsequent step 103, the Z piezo element of the position adjustment driving section 32 is driven to move upward by a predetermined unit amount.

In the subsequent step 104, the following (1) to (3) are calculated, and set data having these as elements are stored in a predetermined storage area.
(1) Movement amount z in the cell height direction from the origin of the Z piezo element (hereinafter referred to as movement amount z)
(2) Deflection amount Δ of cantilever 23 (hereinafter referred to as deflection amount Δ)
(3) Force F applied to probe 24 (hereinafter referred to as force F)

In subsequent step 105, it is determined whether the force F exceeds a predetermined threshold value, and steps 103 and 104 are repeatedly executed until the force F exceeds the predetermined threshold value (step 105, No).

In this embodiment, steps 103 and 104 described above are repeatedly executed to move the Z piezo element upward at a constant speed, and along with this, the plate 40 arranged on the Z piezo element moves upward. Moving. Then, at a certain point, the probe 24 of the cantilever 23 contacts the surface of the cell at the first measurement position aligned in the previous step 102, and after that, as the plate 40 moves further upward, The cell surface is pressed against the probe 24 and elastically deformed, and the cantilever 23 bends accordingly.

During this time, the computer 10 calculates the "movement amount z" based on the input from the controller 34, acquires the "deflection amount Δ" based on the voltage value input from the preamplifier 26, and obtains the "deflection amount Δ". is multiplied by the spring constant of the cantilever 23 to calculate the “force F”.

After that, when the force F exceeds a predetermined threshold value (step 105, Yes), the process proceeds to step 106, where the storage of the set data (movement amount z, deflection amount Δ, force F) is terminated, and position adjustment is performed. The Z piezo element of the drive unit 32 is returned to the origin, and the probe 24 is pulled away from the cell. At this point, a data set consisting of a plurality of sets of data (movement amount z, deflection amount Δ, force F) is stored in a predetermined storage area.

In the subsequent step 107, an Fz curve is acquired based on a data set consisting of a plurality of sets of data (movement amount z, deflection amount Δ, force F) stored in a predetermined storage area. Specifically, a plurality of sets of data (movement amount z, deflection amount Δ, force F) are extracted from a plurality of sets of data (movement amount z, deflection amount Δ, force F) stored in a predetermined storage area. The paired data (movement amount z, force F) is plotted on orthogonal coordinates with the movement amount z as the X axis and the force F as the Y axis to obtain an Fz curve.

In the subsequent step 108, the Fz curve obtained in the previous step 107 is used to obtain the Fd curve in the following procedure.

The following equation (5) holds between the movement amount z ₀ of the Z piezo from the origin when the cantilever 23 contacts the cell surface, the deformation amount d of the cell, the movement amount z, and the deflection amount Δ.

Therefore, in step 108, first, a plotted point (hereinafter referred to as a contact point) on the F-z curve corresponding to the time when the cantilever 23 contacts the cell surface is specified, and the movement amount is calculated from the X coordinate value of the specified contact point. Find _z0 . Next, for each of a plurality of sets of data (movement amount z, deflection amount Δ, force F) stored in a predetermined storage area, the movement amount z and deflection amount Δ, which are elements thereof, and the obtained movement amount z ₀ is substituted into the above formula (5) to calculate the deformation amount d, and the calculated deformation amount d and the set data (deformation amount d, force F). Finally, a plurality of sets of data (deformation amount d, force F) thus generated are plotted on an orthogonal coordinate system with the deformation amount d as the X axis and the force F as the Y axis to obtain an F-d curve. to get

In subsequent step 109, the Fd curve acquired in previous step 108 is stored in a predetermined storage area as "measurement data of pressing force depression amount" relating to the first measurement position ( ). After that, the process returns to step 102 again to drive the XY piezo of the position adjustment drive unit 32 to align the probe 24 of the cantilever 23 with the second measurement position (i, j+1). After that, the steps 103 to 108 described above are executed to acquire the Fd curve, and in the subsequent step 109, the acquired Fd curve is used as the measurement data of the pressing force depression amount related to the second measurement position, and storage area. After that, steps 102 to 109 described above are repeated until the measurement data of the amount of pressing force indentation for all the measurement positions defined on the surface of the cell to be measured is acquired.
The measurement data acquisition processing of the pressing force depression amount has been described above.

Next, the process of calculating the stress distribution and elastic value distribution of the cell to be measured using a model formula determined according to the tip shape of the probe and the membrane structure of the cell to be measured will be described.
FIG. 4 is a flow chart for explaining the process of calculating the stress distribution and elasticity value distribution of the cell to be measured.
As shown in step 200, as the measurement area of the cell to be measured, for example, grid point-like measurement positions + arranged in the center of each section divided by a square of 256×256 pixels are defined. The probe 24 is pressed to this measurement position +.

In step 201, using the actual measurement value Exp at the measurement position + and the calculated value Cal according to the dynamic model between the probe of the AFM tip and the cell body, the pressing force and the amount of depression are plotted on a measurement data chart. Regarding this dynamic model, the probe shape of the AFM tip will be described in detail later using FIGS. 5 to 9. FIG. Further, a flowchart using the measured value Exp and the calculated value Cal by machine learning will be described later in detail with reference to FIGS. 12 and 13. FIG.
In step 202, for a single _measurement position (i, j)=(x, y), the fitting error Δ Find _{x and y} .

Here, the tip radius R of the probe is expressed by the following formula.
where a, b, c, r are the fitting parameters, z is the height coordinate of the cell, ∂z/∂x is the x-axis tilt of the cell, and ∂z/∂y is the y-axis tilt of the cell. , d is the amount of depression at the location of the pressed cell of the probe.
Regarding the optimization by machine learning related to the tip radius R of the probe, using the fitting error variance value calculation unit 305, the minimum fitting error variance value determination unit calculation unit 306, and the residual calculation unit 307 shown in FIG. Details will be explained later.
Then, the minimum matching error Δ _x,y ^min that minimizes the matching error Δ _x,y is obtained.

In step 203, for all measured positions (i, j); i = 1 to 256, j = 1 to 256, the minimum fitting error Δ _{x , y} ^min .
In step 204, the average fitting error Δ x, _y ^mean is determined from the minimum fitting error Δ _x,y ^min for all measured positions (i,j); i=1-256, j=1-256.
At step 205, the variance value _ΔT of the fitting error is determined.

FIG. 5 is a configuration diagram of the essential parts explaining the force interaction between the probe of the AFM tip and the cell body.
The probe 24 of the AFM tip has a tip with a tip radius R and is pressed against the cell to be measured. The cell to be measured has a deformation amount d as a depression amount with respect to the tip position of the probe 24 . A stress σ is generated on the surface of the cell under measurement according to the pressing force F that the tip of the probe 24 acts on the surface of the cell under measurement in the vertical direction. The pressing force F _l of the probe 24 is the sum and balance of two components: the resistance F _s due to the tensile stress σ (prestress) on the surface of the cell to be measured, and the _Fe due to the amount of deformation d considered in the usual Hertzian model. is taken.
In the cell elasticity analysis system of the present invention, measurement data indicating the relationship between the pressing force F and the amount of deformation d can be obtained by changing the positional relationship between the probe 24 and the cell to be measured.

FIG. 6 is an enlarged view of the main part explaining various mechanical models between the probe of the AFM tip and the cell body, (A) is a parabolic Hertz model (Hertz Model Parabolic), (B) is a conical model (C) is a cortical shell-liquid core model, and (D) is a Hertz + stress membrane model.

The Hertzian model is a classical one, and it is the stress or pressure applied to elastic contact parts such as spherical surfaces and cylindrical surfaces, cylindrical surfaces and cylindrical surfaces, arbitrary curved surfaces and curved surfaces, and is also called Hertzian contact stress. The feature is that the pressure distribution on the contact surface is assumed without considering the friction on the contact surface. For a paraboloid, the following equation holds.
Here, F is the pressing force of the probe, ν is Poisson's ratio of the cell, E is the elastic modulus of the cell, R is the radius of the tip of the probe, and d is the amount of depression of the cell at the position where the probe is pressed.

The Sneddon model is the contact dynamics when an axisymmetric probe is pressed into an elastic body. For measurements without the effect of adhesion, this formula gives the elastic modulus of the sample.
Here, F is the pressing force of the probe, ν is the Poisson's ratio of the cell, E is the elastic modulus of the cell, θ is the inclination angle of the tip conical surface of the probe, and d is the amount of depression of the cell at the position where the probe is pressed. be.

The cutaneous shell-liquid nucleus model deals with mechanical deformation in contact between a spherical cell such as an egg and a cylindrical stylus.
where F is the pressing force of the probe, T is the cortex tension of the skin, r is the radius of the cell, E is the elastic modulus of the cell, R is the tip radius of the probe, and θ is the tip cone of the probe. The tilt angle of the surface, d, is the amount of depression of the cell at the position where the probe is pressed.

The Hertz+membrane stress model is obtained by taking into consideration the membrane stress of the cell in the Hertz model and taking into consideration the friction between the contact surface of the probe and the cell. For example, the JKR (Johnson-Kendall-Roberts) model and the DMT (Derjaguin-Muller-Toporov) model are known. When the tip of the probe is a paraboloid, the following formula holds.
Here, F is the pressing force of the probe, R is the tip radius of the probe, d is the amount of depression of the cell at the position where the probe is pressed, σ is the membrane stress of the cell, ν is the Poisson's ratio of the cell, and E is the thickness of the cell. modulus of elasticity.

FIG. 7 is an enlarged view of a main part explaining that the tip of the AFM tip has a mechanical relationship depending on the inclination of the surface shape of the cell body.
FIG. 7A shows the relationship between the tip radius R of the probe 24 and the slope of the surface shape of the cell body (∂z/∂x, ∂z/∂y). FIG. 7B shows the relationship between the tip radius R of the probe 24 and the deformation amount d of the cell at the position where the probe is pressed. In FIGS. 7A and 7B the dependence of the tip radius on the surface topography gradient is represented.
FIG. 7(C) shows the tip radius R of the probe 24, the inclination of the surface shape of the cell body at the position where the probe is pressed, and the deformation amount of the cell (∂z/∂x, ∂z/∂y, d). showing relationships. FIG. 7(D) shows the tip radius R of the probe 24, the inclination of the surface shape of the cell body at the position where the probe is pressed, and the deformation amount of the cell (∂z/∂x, ∂z/∂y, d). This shows a different relationship, in which the surface shape of the cell body is deeply depressed due to the large amount of deformation of the cell. 7(C) and (D) show the dependence of the tip tip radius on the deformation amount d of the cell.

FIG. 8 is a diagram explaining measured value distributions according to various mechanical models between the probe of the AFM tip and the cell body. As the mechanical model, the above-mentioned (A) Hertz Model Parabolic, (B) Sneddon Model Cone, (C) Cortical Shell Model - liquid core model), (D) Hertz + membrane stress model (Hertz Model + stress membrane) was used.

FIG. 9 is a diagram explaining the predicted value error distribution according to various mechanical models between the probe of the AFM tip and the cell body. The (D) Hertz+membrane stress model shows the smallest predicted value error distribution, with a median value of 0.005% and a narrow confidence range of ±0.0005%. (A) The parabolic Hertzian model shows the next smallest predicted value error distribution, and its median value is 0.30%, but the confidence range is dispersed over a wide range of ±0.02%.

On the other hand, (C) the cutaneous shell liquid core model and (B) the conical Sneddon model show large prediction error distributions. (C) The cutaneous shell liquid nucleus model has a median prediction error distribution of 0.09% with a confidence range of ±0.01%. (B) The conical Sneddon model has a median prediction error distribution of 0.10% and a confidence range of ±0.03%.
Therefore, the (D) Hertz+membrane stress model is the most preferred, and the second best is the (A) parabolic Hertz model.

FIG. 10 is an evaluation diagram of the state of cells based on a stress map formed by AFM, and is shown using FIGS. 10(a) to 10(f).
FIG. 10(a) is an optical microscope image of living cancer cells.
FIG. 10(b) is an AFM height map of live cancer cells.
FIG. 10(c) is an AFM stress map of living cancer cells.
FIG. 10(d) is an optical microscope image of dead cancer cells.
FIG. 10(e) is an AFM height map of dead cancer cells.
FIG. 10(f) is an AFM stress map of dead cancer cells.
The prestress around the nuclear region of living cells is higher than that of dead cells.

FIG. 11 shows an example of (A) a three-dimensional height distribution state diagram of a cell to be measured, (B) stress distribution, (C) elastic value distribution, and (D) force spectrum. (E) shows the calculation formula of the Hertz+membrane stress model.

FIG. 12 is a functional block diagram of a machine learning algorithm for calculating cell body pre-stress for optimizing AFM tip geometry that illustrates one embodiment of the present invention.
FIG. 13 is an enlarged view of the main part of the first loop for calculating the fitting error Δ from the elastic modulus E and the stress σ in the functional block diagram of the machine learning algorithm of FIG. 12 .

In FIGS. 12 and 13, the matching error calculation unit 301 calculates the actual measurement value Exp and the pressing force _Fl with the depression amount d as a parameter for a single measurement position (i, j)=(x, y). Determine the Fitting Error Δ _x,y of the value Cal.
Here, for the calculated value of the pressing force F _l ^cal , for example, the pressing force F _l of the Hertz+membrane stress model is used, but a parabolic Hertz model or other models may also be used. The actually measured pressing force F _l ^Exp uses the depression amount d as a parameter.

The minimum value calculator 302 calculates the minimum fitting error Δ _x,y ^min with the tip radius R of the probe 24 as a parameter. The minimum value determination unit 303 determines whether the minimum fitting error Δ _x,y ^min calculated by the minimum value calculation unit 302 is the minimum value for the parameter R. If not, the cell elastic modulus E and the cell membrane stress σ It is changed and sent to the elastic modulus E/membrane stress σ setting unit 304 .
The elastic modulus E/membrane stress σ setting unit 304 supplies the initial values of the elastic modulus E/membrane stress σ to the matching error calculating unit 301 or the elastic modulus E/membrane stress σ updated by the minimum value determining unit 303 to the matching error calculating unit 304. Set to 301.

Next, the second loop shown in FIG. 12 for changing the parameter R by the Monte Carlo method and finding the variance value _ΔT of the fitting error will be described. A Monte Carlo method, as used herein, refers to a Markov chain Monte Carlo method in which sampling of posterior probabilities is performed using random numbers. This method was used herein to search for maximizing factors of posterior probabilities. This is the parameter set to achieve the best fit.
In FIG. 12, when the minimum value determining section 303 determines that the parameter R is the minimum value, it sends the minimum fitting error Δ _{x, y} ^min of the measurement point (x, y) to the fitting error variance value calculating section 305 .
The fitting error variance value calculator 305 obtains the variance value _ΔT of the fitting error for all the measurement points of the cells to be measured.

The minimum fitting error variance value determining unit computing unit 306 determines whether the fitting error variance value _ΔT computed by the fitting error variance value computing unit 305 is the minimum value for the parameter R. If not, the residual computing unit 307. The residual calculation unit 307 changes the tip radius R of the probe 24 by the Monte Carlo method, and sends it to the elastic modulus E/membrane stress σ setting unit 304 .
If it is judged as the minimum value by the minimum value judgment unit calculation unit 306 of the adaptive error variance value, the predicted value error P _i (N) is obtained, and the process ends.

In the present invention, machine learning is performed on the measurement data to optimize the parameters of the Hertz+membrane stress model. A supercomputer is used to compare goodness-of-fit index values (fitting scores) of Monte Carlo searches for optimized chip geometries.

FIG. 14 is a diagram for explaining the relationship between the amount of cell deformation (the amount of depression: nm) and the pressing force (nN) of the probe in various contact pressure models. In the figure, the dotted circle line means the experimental data obtained directly by AFM. The four curves represent fitting data calculated with different models. The best fit curve is the Hertz+membrane stress model.
This result is consistent with FIG.

FIG. 15 is an evolution map of stress using tip shape parameters generated by the Monte Carlo method.
With the tip parameters automatically generated by the Monte Carlo method, the stress distribution clearly shows the nucleus, filopodia and lamellipodia. The optimal stress map is due to (e) optimized tip geometry parameters.

FIG. 16 is an evolution map of dispersion using probe shape parameters generated by the Monte Carlo method, where (a) is an overall view and (b) is an enlarged view of a main part of (a).
As the number of iterations increases, the fitting error decreases. A minimum fitting error means that optimized tip shape parameters are generated.

According to the method and apparatus for analyzing the elastic property distribution of the cell to be measured according to the present invention, the optimum model formula determined according to the tip shape of the cantilever probe is used, so data analysis can be performed with high spatial resolution. Rapid measurement of the mechanical properties of cells or tissues is possible, and it can be used, for example, as an intraoperative tissue examination device in a clinical setting.
The method and apparatus for determining the shape parameter of the probe of the atomic force microscope of the present invention can know the shape of the probe of the atomic force microscope very accurately, and the method and apparatus for analyzing the elastic property distribution of the cell to be measured. Suitable for use in devices.

10 computer 20 atomic force microscope 22 semiconductor laser 23 cantilever 24 probe 25 photodetector 26 preamplifier 32 position adjustment driving unit 34 controller 40 plate 301 fitting error calculation unit 302 minimum value calculation unit 303 minimum value determination unit 304 elastic modulus E/membrane stress σ setting unit 305 matching error variance value calculation unit 306 matching error variance minimum value determination unit calculation unit 307 prediction error storage unit 308 residual calculation unit

Claims (13)

A method for analyzing the elastic property distribution of a cell to be measured, comprising:
Measured values obtained by associating the amount of deformation of the cell and the pressing force of the probe obtained when the probe of the atomic force microscope is pressed against the surface of the cell to be measured are obtained from the measurement target with which the probe is in contact. a step of obtaining together with the measurement position coordinates of the cell, wherein the measurement position coordinates of the cell to be measured are arranged in the upper layer of the nucleus of the cell to be measured and the site surrounding the nucleus;
Using a shape parameter determined according to the shape of the tip of the probe and a model formula representing the relationship between the deformation amount (d) of the cell and the pressing force (F) of the probe, the pressing position of the probe is determined. calculating the relationship between the deformation amount (d) of the cell at and the pressing force (F) of the probe;
Using the actually measured values obtained by associating the measured deformation amount of the cell with the pressing force of the probe, and the calculated value calculated by the model formula, the variance value (Δ _T ) of the fitting error is obtained by the probe calculating a shape parameter that is the minimum value for the parameter R related to the tip radius of
creating at least one of a stress distribution and an elastic value distribution of the cell to be measured using the minimum shape parameter;
generating at least one of a stress distribution map and an elasticity value distribution map of the nucleus of the cell under measurement and around the nucleus based on at least one of the created stress distribution and elasticity distribution of the cell under measurement;
method including. Further, at least one of the stress distribution map and the elastic value distribution map measured around the nucleus and the periphery of the cell to be measured is included in the elastic characteristic range of a malignant tumor, or the elastic characteristic range of a normal cell or a benign tumor. 2. The method of analyzing the elastic property distribution of a measured cell according to claim 1, comprising the step of generating an indication that is compared with a threshold value of whether it is contained in . A model formula representing the relationship between the deformation amount (d) of the cell at the pressing position of the probe and the pressing force (F) of the probe is

The method for analyzing elastic property distribution of cells according to claim 1 or 2.
Here, R is the tip radius of the probe, σ is the stress of the cell at the position where the probe is pressed, ν is Poisson's ratio of the cell, and E is the elastic modulus of the cell. A model formula representing the relationship between the deformation amount (d) of the cell at the pressing position of the probe and the pressing force (F) of the probe is

The method for analyzing elastic property distribution of cells according to claim 1 or 2.
Here, R is the tip radius of the probe, ν is the Poisson's ratio of the cell, and E is the elastic modulus. An analysis system for analyzing elastic property distribution of cells to be measured,
Measured values obtained by associating the amount of deformation of the cell and the pressing force of the probe obtained when the probe of the atomic force microscope is pressed against the surface of the cell to be measured are obtained from the measurement target with which the probe is in contact. a means for acquiring the measurement position coordinates of the cell together with the measurement position coordinates of the cell, wherein the measurement position coordinates of the cell to be measured are arranged in the upper layer of the nucleus of the cell to be measured and the site surrounding the nucleus;
Using a shape parameter determined according to the shape of the tip of the probe and a model formula representing the relationship between the deformation amount (d) of the cell and the pressing force (F) of the probe, the pressing position of the probe is determined. means for calculating the relationship between the deformation amount (d) of the cell at and the pressing force (F) of the probe;
Using the actually measured values obtained by associating the measured deformation amount of the cell with the pressing force of the probe, and the calculated value calculated by the model formula, the variance value (Δ _T ) of the fitting error is obtained by the probe means for calculating a shape parameter that is the minimum value for the parameter R related to the tip radius of
means for creating at least one of the stress distribution and the elastic value distribution of the cell to be measured using the minimum shape parameter;
means for generating at least one of a stress distribution map and an elasticity value distribution map of the nucleus and the vicinity of the nucleus of the cell under measurement based on at least one of the created stress distribution and elasticity distribution of the cell under measurement;
Analysis system with Furthermore, at least one of the stress distribution map and the elastic value distribution map measured around the nucleus and the periphery of the cell to be measured is included in the elastic characteristic range of a malignant tumor or in the elastic characteristic range of a normal cell or a benign tumor. 6. The analysis system according to claim 5, comprising means for generating a display for comparison with a threshold value for determining whether the elastic property distribution of the cell under measurement is analyzed. to the computer,
Measured values obtained by associating the amount of deformation of the cell and the pressing force of the probe obtained when the probe of the atomic force microscope is pressed against the surface of the cell to be measured are obtained from the measurement target with which the probe is in contact. a step of obtaining together with the measurement position coordinates of the cell, wherein the measurement position coordinates of the cell to be measured are arranged in the upper layer of the nucleus of the cell to be measured and the site surrounding the nucleus;
Using a shape parameter determined according to the shape of the tip of the probe and a model formula representing the relationship between the deformation amount (d) of the cell and the pressing force (F) of the probe, the pressing position of the probe is determined. calculating the relationship between the deformation amount (d) of the cell at and the pressing force (F) of the probe;
Using the actually measured values obtained by associating the measured deformation amount of the cell with the pressing force of the probe, and the calculated value calculated by the model formula, the variance value (Δ _T ) of the fitting error is obtained by the probe calculating a shape parameter that is the minimum value for the parameter R related to the tip radius of
creating at least one of a stress distribution and an elastic value distribution of the cell to be measured using the minimum shape parameter;
generating at least one of a stress distribution map and an elasticity value distribution map of the nucleus of the cell under measurement and around the nucleus based on at least one of the created stress distribution and elasticity distribution of the cell under measurement;
program to run the A method for determining shape parameters of an atomic force microscope probe for analyzing elastic properties of cells, comprising:
a step of acquiring an actual measurement value that associates the amount of deformation of the cell with the pressing force of the probe obtained when the probe is pressed against the measurement point (x, y) on the surface of the cell to be measured; ,
A calculated value by a model formula that associates the deformation amount of the cell with the pressing force of the probe is calculated for a plurality of obtained measured values that associate the deformation amount of the cell with the pressing force of the probe. a computing step;
a fitting error calculation step of obtaining a fitting error (Δ _x,y ) between the measured value and the calculated value;
a minimum value calculation step of calculating a minimum fitting error (Δ _{x, y} ^min ) with the tip radius R of the probe as a parameter R ;
a minimum value determination step of determining whether the minimum fitting error (Δ _{x, y} ^min ) calculated in the minimum value calculation step is the minimum value for a parameter R related to the tip radius of the probe ;
a step of changing the contact stress parameter of the model formula when it is determined that the minimum value is not the minimum value in the minimum value determination step;
a contact stress parameter setting step of setting the contact stress parameter of the initial value or the contact stress parameter updated in the minimum value determination step in the step of calculating the fitting error;
If the minimum value _{determination} step determines that the minimum ^value a sending step;
repeating the step of obtaining the measured value to the step of sending the minimum fitting error of the single measurement point for all measurement points of the cell to be measured;
a fitting error variance value calculation step of obtaining a fitting error variance value (Δ _T ) for all measurement points of a cell to be measured;
a fitting error variance minimum value determining unit computing step for determining whether the fitting error variance (Δ _T ) computed in the fitting error variance computing step is the minimum value for a parameter R;
If it is determined in the step of determining the minimum value of the matching error variance that the variance of the matching error (Δ _T ) is not the minimum value, the step of sending the variance of the matching error Δ _T to the step of calculating the residual. and,
a residual calculation step of changing the parameter of the tip radius R of the probe tip using the variance value ΔT of the fitting error _by the Monte Carlo method and sending it to the contact stress parameter setting step;
and determining the parameter R for which the dispersion value (Δ _T ) of the fitting error is determined to be the minimum value as the shape parameter of the probe in the step of determining the minimum value of the fitting error variance value. The shape parameter of the probe of the atomic force microscope is the tip radius R, and the formula representing the tip radius R is
Here, R is the tip radius of the probe, a, b, c, r are the fitting parameters, z is the height direction coordinate of the cell, ∂z/∂x is the x-axis tilt of the cell, ∂z/∂y is the slope of the cell in the y-axis direction, and d is the amount of depression at the location of the cell pressed by the probe,
9. A method for determining shape parameters of a probe according to claim 8. The model formula is
Here, F is the pressing force of the probe, R is the tip radius of the probe, d is the amount of depression of the cell at the position where the probe is pressed, σ is the membrane stress of the cell, ν is the Poisson's ratio of the cell, and E is the thickness of the cell. is the elastic modulus,
10. A method for determining shape parameters of a probe according to claim 8 or 9. The contact stress parameter of the model formula includes the elastic modulus E of the cell and the membrane stress σ of the cell, and the formula for obtaining the fitting error (Δ _{x, y} ) is
Here, the calculated pressing force F _l ^cal uses the pressing force F _l of the Hertz+membrane stress model, and the actually measured pressing force F _l ^Exp uses the depression amount d as a parameter.
11. The method for determining shape parameters of a probe according to claim 10. An analysis system for determining shape parameters of an atomic force microscope probe for analyzing elastic properties of cells,
An actual measurement value obtained by associating the amount of deformation of the cell with the pressing force of the probe obtained when the probe is pressed against the measurement point (x, y) on the surface of the cell to be measured. an acquisition unit;
A calculated value by a model formula that associates the deformation amount of the cell with the pressing force of the probe is calculated for a plurality of obtained measured values that associate the deformation amount of the cell with the pressing force of the probe. a calculated value calculation unit for calculation;
a matching error calculation unit for obtaining a matching error (Δ _x,y ) between the measured value and the calculated value;
a minimum value calculator that calculates a minimum fitting error (Δ _{x, y} ^min ) with the tip radius R of the probe as a parameter R ;
a minimum value determination unit that determines whether the minimum fitting error (Δ _{x, y} ^min ) calculated by the minimum value calculation unit is the minimum value for a parameter R related to the tip radius of the probe ;
a unit for changing the contact stress parameter of the model formula when the minimum value determination unit determines that the value is not the minimum value;
a contact stress parameter setting unit for setting the contact stress parameter of the initial value or the contact stress parameter updated by the minimum value determination unit to the fitting error computing unit;
If ^the minimum value _{determination} unit determines that the minimum value a sending department;
an overall measurement point management unit that repeats the process from the actual value acquisition unit to the transmission unit of the minimum matching error of the single measurement point for all measurement points of the cell to be measured;
a fitting error variance value calculation unit that obtains a fitting error variance value (Δ _T ) for all measurement points of a cell to be measured;
a fitting error variance minimum value determining unit computing unit that determines whether the matching error variance (Δ _T ) computed by the fitting error variance computing unit is the minimum value for a parameter R;
If the variance value (Δ _T ) of the matching error is determined not to be the minimum value in the minimum value determining unit of the matching error variance value calculating unit, the variance value _ΔT of the matching error is sent to the residual calculating unit. and,
a residual error calculation unit that changes the parameter of the tip radius R of the probe using the Monte Carlo method using the dispersion value _ΔT of the fitting error and sends it to the contact stress parameter setting unit;
and determining, as a shape parameter of the probe, a parameter R for which the dispersion value (Δ _T ) of the fitting error has been determined to be the minimum value by the minimum fitting error variance value determining unit computing unit. A program for causing a computer to execute a method for determining shape parameters of a probe of an atomic force microscope for analyzing elastic properties of cells, comprising:
a step of acquiring an actual measurement value that associates the amount of deformation of the cell with the pressing force of the probe obtained when the probe is pressed against the measurement point (x, y) on the surface of the cell to be measured; ,
A calculated value by a model formula that associates the deformation amount of the cell with the pressing force of the probe is calculated for a plurality of obtained measured values that associate the deformation amount of the cell with the pressing force of the probe. a computing step;
a fitting error calculation step of obtaining a fitting error (Δ _x,y ) between the measured value and the calculated value;
a minimum value calculation step of calculating a minimum fitting error (Δ _{x, y} ^min ) with the tip radius R of the probe as a parameter R ;
a minimum value determination step of determining whether the minimum fitting error (Δ _{x, y} ^min ) calculated in the minimum value calculation step is the minimum value for a parameter R related to the tip radius of the probe ;
a step of changing the contact stress parameter of the model formula when it is determined that the minimum value is not the minimum value in the minimum value determination step;
a contact stress parameter setting step of setting the contact stress parameter of the initial value or the contact stress parameter updated in the minimum value determination step in the step of calculating the fitting error;
If the minimum value _{determination} step determines that the minimum ^value a sending step;
repeating the step of obtaining the measured value to the step of sending the minimum fitting error of the single measurement point for all measurement points of the cell to be measured;
a fitting error variance value calculation step of obtaining a fitting error variance value (Δ _T ) for all measurement points of a cell to be measured;
a fitting error variance minimum value determining unit computing step for determining whether the fitting error variance (Δ _T ) computed in the fitting error variance computing step is the minimum value for a parameter R;
If it is determined in the step of determining the minimum value of the matching error variance that the variance of the matching error (Δ _T ) is not the minimum value, the step of sending the variance of the matching error Δ _T to the step of calculating the residual. and,
a residual calculation step of changing the parameter of the tip radius R of the probe tip using the variance value ΔT of the fitting error _by the Monte Carlo method and sending it to the contact stress parameter setting step;
and determining, as a shape parameter of the probe, a parameter R for which the dispersion value (Δ _T ) of the fitting error is determined to be the minimum value in the step of determining the minimum value of the fitting error variance value. program for.