CN114113227B - Measurement system and measurement method - Google Patents

Abstract

The application relates to a measurement system and a measurement method, and the technical key points are as follows: firstly, obtaining a characteristic relation between cell position variation and impedance in a simulation mode, and establishing a mathematical model between the cell position variation and the impedance; secondly, correcting the impedance data according to the mathematical model so as to eliminate the influence of the position on the impedance and improve the measurement accuracy; and finally, extracting the electrical characteristics of the biological embryo through an impedance spectrum equivalent circuit automatic fitting algorithm. The measurement system and the measurement method provided by the application have important significance for researching drug reaction and cell development.

Description

A measurement system and measurement method

Technical field

The invention relates to a method that combines measurement and data processing, and in particular, to a method for accurately measuring electrical properties during embryonic development.

Background technique

Since single cells are the smallest structural and functional units of living tissue, detecting the development process of embryos is of extremely important significance for revealing the mysteries of life and studying drug responses.

However, conventional detection methods such as single-cell sequencing and gene editing technology are complex and expensive. Bioimpedance Spectroscopy (BIS), as a new label-free, radiation-free, non-invasive technology, has been widely used in industry, biology and medicine.

The bioimpedance spectroscopy method can quantitatively determine the type, size and number of cells (one-dimensional information), and its application is also widespread. like:

Reference 1: JP2011050765A provides a method and equipment for bioimpedance analysis. In some embodiments, an equivalent circuit frequency response model is provided that provides improved correlation with MRI data. The frequency response model takes into account body composition, including the fat composition of body parts.

Reference 2: WO2005027717A2 provides a method and device for bioimpedance analysis. Data obtained from bioimpedance spectroscopy (BIS) and MRI of subjects' calves illustrate improved correlations compared to single-frequency analysis at 50 kHz and analysis using the conventional Cole-Cole model.

However, the detection accuracy of bioimpedance spectroscopy is often affected by changes in the position of the measured object. Therefore, it is impossible to accurately extract the electrical characteristic parameters of cells during development by directly using the measurement data of bioimpedance spectroscopy.

Contents of the invention

The purpose of the present invention is to solve the problem of low detection accuracy of existing bioimpedance spectroscopy methods and provide a measurement system and a measurement method.

A measurement system, which includes: a sensor, a position measurement system, a numerical simulation system, a position correction system, and an electrical characteristic parameter extraction system;

The sensor is used to measure the impedance of cells;

The position measurement system is used to measure the position of cells in the sensor;

The numerical simulation system is used to obtain the characteristic relationship between cell position and impedance;

The position correction system is used to obtain the impedance after position correction;

The electrical characteristic parameter extraction system is used to extract electrical characteristic parameters using a bioimpedance spectrum equivalent circuit self-fitting algorithm.

Further, the position measurement system uses an electron microscope.

A measurement method including the following steps:

Step 1: Obtain the characteristic relationship between cell position and impedance: obtain several values between cell position and impedance through numerical simulation; use polynomials to fit and construct a mathematical model between impedance and cell position;

Step 2: Measure the impedance of the cell in the sensor and observe the coordinate position of the cell through an electron microscope;

Step three, position correction: Based on the mathematical model between the impedance obtained in step one and the cell position and the coordinate position of the cell recorded in step two, the impedance obtained in step two is corrected accordingly;

Step 4: Based on the corrected data in Step 3, use the bioimpedance spectrum equivalent circuit self-fitting algorithm to extract electrical characteristic parameters.

Furthermore, for step one, numerical simulation is used to obtain the mathematical model between the position and impedance of cells in the sensor, specifically including:

S1-1, mesh the simulation area;

S1-2, randomly select any one of the positions as the center coordinate position of the embryo, its coordinates are expressed as (x _c , y _c ), the frequency f is any frequency f _b , and the measured impedance value is expressed as Z _bc ;

The center coordinates select j group, and the frequency selects n group;

Then, record the impedance value matrix Z:

Record position matrix X:

S1-3, solve matrix A:

A＝ZX ^-1

in:

Further, step two records the actual position of the embryo in the sensor as (x _p , y _p ), the recorded frequency is f _g and the impedance is Z _g ; then the impedance converted to the reference position (x _r , y _r ) is Z ' _g :

Further, step four specifically includes the following sub-steps:

S4-1, construct an equivalent circuit model based on the Gene Expression Algorithm (GEP):

Set the function symbol of GEP to {"S", "P"};

Based on commonly used electrical components in bioimpedance spectrum equivalent circuits, set the terminal symbols of GEP to {"R", "C", "L", "CPE", "Z_w"};

Among them, "S" represents the series relationship, "P" represents the parallel relationship, "R" represents the resistance element, "C" represents the capacitance element, "L" represents the inductance element, "CPE" represents the constant phase element, and "Z_w" represents the diffusion impedance. , the impedance expression corresponding to the terminal symbol is as follows:

Z _L =jwL

t＝h(n-1)+1

l＝t+h

In the formula:

Z_c means: capacitive reactance, unit: Ω;

ω represents: angular frequency, unit is rad/s;

C represents: capacitance value, unit: c;

Z _L means: inductive reactance, unit: Ω;

Z _ω represents: diffusion impedance, unit: Ω;

Y represents: the modulus of Warburg admittance, the specific value is within the range of (0,1), and the unit is dimensionless;

Z _CPE means: constant phase impedance, unit: Ω;

Y ₀ represents: the size or modulus of the pre-factor and constant-phase components after stripping off the frequency, generally taking the value (0,1)

n represents: power index, the value is in the range of [-1,1];

t means: tail length, dimensionless;

h means: head length, dimensionless;

l represents: the total length of the GEP gene, dimensionless;

L means: inductance, unit: H;

j imaginary unit;

According to the GEP individual composition principle, you first need to set the head length h and n according to your needs, then the individual length can be known at this time;

S4-2, form an equivalent circuit model through GEP encoding and decoding methods. The parent node of the child node is the functional symbol, which corresponds to the combination relationship of electrical components:

Based on the equivalent circuit model established by GEP, the bioimpedance spectrum is fitted by genetic algorithm:

First, GA initializes the electrical characteristic parameter population and the maximum number of iterations based on the electrical components contained in the equivalent circuit model;

Secondly, the GA selection probability P _s is set to ensure that the better individuals in each generation can be inherited to the next generation with a greater probability. In addition, the crossover probability P _c and mutation probability P _m are set to generate new individuals to avoid solving the problem. The set falls into a local optimum, thereby ensuring that each GA algorithm can ensure that the current equivalent circuit can achieve the best fitness;

Thirdly, the individuals who obtain the best fitness from GA are fed back to GEP for the optimization of equivalent circuits;

Finally, through GEP optimization and GA calculation and fitting, the best equivalent circuit and its corresponding electrical parameters can be obtained, and then the electrical characteristic parameters contained in the bioimpedance spectrum can be obtained.

The advantages of the technical solution of the present invention are mainly reflected in:

1) The first invention of this application is the discovery of the phenomenon that "different cell positions in the sensor result in different measured impedances." Based on this phenomenon, if you want to study the impedance of different cells or cells at different stages, you need to remove the influence of position from the actual measured impedance.

Based on this problem, the inventor found through a large number of experiments that the relationship between the position of cells in the sensor and the impedance satisfies the following formula:

Based on this, steps one and three are proposed to eliminate the above-mentioned location effects.

2) The second invention of this application is that this application can be used to measure the electrical characteristic parameters of cells; the method of this application has good application prospects for studying drug responses.

Description of the drawings

The present invention will be further described in detail below with reference to the embodiments in the drawings, but this does not constitute any limitation on the present invention.

Figure 1 is a flow chart of the measurement method of the present application.

Detailed ways

The objects, advantages and features of the present invention will be explained by the following non-limiting description of preferred embodiments. These embodiments are only typical examples of applying the technical solutions of the present invention. Any technical solutions formed by adopting equivalent substitutions or equivalent transformations fall within the scope of protection claimed by the present invention.

[Example 1: Overall framework design of accurate measurement method]

The precise measurement method and a measurement system of the present application will be further described below with reference to Figure 1.

A method for accurately measuring electrical properties during embryonic development, including the following steps:

Step 1: Obtain the characteristic relationship between cell position and impedance: obtain the value between cell position and impedance through numerical simulation;

Use polynomials to fit and construct a mathematical model between impedance and cell position;

Step 2: Measure the impedance of the cell in the sensor and observe the coordinate position of the cell through an electron microscope;

Step three, position correction: Based on the mathematical model between the impedance obtained in step one and the cell position and the coordinate position of the cell recorded in step two, the impedance obtained in step two is corrected accordingly to avoid the influence of position factors on the impedance and achieve High-precision measurement.

Step 4: Based on the corrected data in Step 3, use the bioimpedance spectrum equivalent circuit self-fitting algorithm to extract electrical characteristic parameters.

In view of the above measurement method, Embodiment 1 also proposes a measurement system, whose composition and function are shown in Table 1.

Table 1

For step four, the bioimpedance spectrum equivalent circuit self-fitting algorithm is used to extract electrical characteristics; the automatic fitting algorithm is a hybrid algorithm that combines genetic expression algorithm and genetic algorithm, in which the genetic expression algorithm realizes biological For the construction of the equivalent circuit of the impedance spectrum, the genetic algorithm realizes the fitting of the bioimpedance spectrum and the calculation of the electrical parameters based on the constructed equivalent circuit model.

[Embodiment 2: Specific work of the numerical simulation system]

The specific work of the numerical simulation system corresponds to the work of step one.

For step one, numerical simulation is used to obtain the mathematical model between the position and impedance of cells in the sensor, specifically including:

S1-1, mesh the simulation area;

S1-2, randomly select any one of the positions as the central coordinate position of the embryo, its coordinates are expressed as (x _c , y _c ), the frequency f is any frequency f _b , and the measured impedance value is expressed as Z _bc ;

The center coordinates select j group, and the frequency selects n group;

Then, record the impedance value matrix Z:

Record position matrix X:

S1-3, solve matrix A:

The above matrix is expressed by the following formula: Z=A·X

It can be seen that: A=ZX ^-1 (that is, each value in the matrix A can be solved)

in,

S1-4, establish impedance and cell position to fit and establish a corresponding mathematical model:

[Embodiment 3: Specific work of the position correction system]

For the method of Embodiment 1, one of the difficult problems is "how to perform position correction". Specifically, this problem is that during the actual measurement process, the embryo will change, causing the embryo to be in different positions of the sensor; and When the embryo is in different positions of the sensor, the measured impedance is different, so it is difficult to evaluate the effect.

That is to say, the actual coordinate position (x _p , y _p ) of the embryo in the sensor must be different every time it is measured, and the impedance values measured at different coordinate positions need to be converted to the same coordinate position (reference position (x _r , y _r )), which can avoid the influence of position factors on impedance and obtain high-precision measurement results.

For this problem, proceed as follows:

The steps of the calibration process are as follows:

Step 2 records the actual position of the embryo in the sensor as (x _p , y _p ), the recorded frequency is f _g and the impedance is Z _g ;

Then the impedance converted to the reference position (x _r , y _r ) is Z' _g :

[Example 4: Extracting electrical characteristics using bioimpedance spectrum equivalent circuit self-fitting algorithm]

For the method of Embodiment 1, one of the difficult problems is "how to use the bioimpedance spectrum equivalent circuit self-fitting algorithm to extract electrical characteristics." For step three, use the bioimpedance spectrum equivalent circuit self-fitting algorithm. Extract electrical characteristic parameters; the automatic fitting algorithm is a hybrid algorithm that combines genetic expression algorithm and genetic algorithm. The genetic expression algorithm realizes the construction of bioimpedance spectrum equivalent circuit, and the genetic algorithm is based on the constructed equivalent circuit. The effective circuit realizes the fitting of bioimpedance spectrum and the extraction of electrical characteristic parameters. Specifically, it includes the following steps:

S4-1, construct an equivalent circuit model based on the Gene Expression Algorithm (GEP):

Set the function symbol of GEP to {"S", "P"};

Based on commonly used electrical components in bioimpedance spectrum equivalent circuits, set the terminal symbols of GEP to {"R", "C", "L", "CPE", "Z_w"};

Among them, "S" represents the series relationship, "P" represents the parallel relationship, "R" represents the resistance element, "C" represents the capacitance element, "L" represents the inductance element, "CPE" represents the constant phase element, and "Z_w" represents the diffusion impedance. , the impedance expression corresponding to the terminal symbol is shown in (2)-(6).

Z _L =jwL

t＝h(n-1)+1

l＝t+h

Z_c means: capacitive reactance, unit: Ω;

ω represents: angular frequency, unit is rad/s;

C represents: capacitance value, unit: c;

Z _L means: inductive reactance, unit: Ω;

Z _ω represents: diffusion impedance, unit: Ω;

Y represents: the modulus of Warburg admittance, the specific value is within the range of (0,1), and the unit is dimensionless;

Z _CPE means: constant phase impedance, unit: Ω;

Y ₀ represents: the size or modulus of the pre-factor and constant-phase components after stripping off the frequency, generally taking the value (0,1)

n represents: power index, the value is in the range of [-1,1];

t means: tail length, dimensionless;

h means: head length, dimensionless;

l represents: the total length of the GEP gene, dimensionless;

L means: inductance, unit: H;

j imaginary unit;

According to the GEP individual composition principle, the head length h and n need to be set first according to the researcher's own needs. At this time, the individual length can be known by formula (8).

S4-2, the equivalent circuit model can be formed through GEP encoding (binary tree level in-order traversal) and decoding (binary tree post-order traversal). The parent node of the child node is the functional symbol, which corresponds to the combination relationship of electrical components.

Based on the equivalent circuit model established by GEP, the bioimpedance spectrum is fitted by genetic algorithm (GA):

First, GA initializes the electrical characteristic parameter population based on the electrical components contained in the equivalent circuit model, and the maximum number of iterations;

Secondly, the GA selection probability P _s is set to ensure that the better individuals in each generation can be inherited to the next generation with a greater probability. In addition, the crossover probability P _c and mutation probability P _m are set to generate new individuals to avoid solving the problem. The set falls into a local optimum, thus ensuring that each GA algorithm can ensure that the current equivalent circuit can achieve the best fitness ("best fit" with the bioimpedance spectrum)

Thirdly, the individuals who obtain the best fitness from GA are fed back to GEP for the optimization of equivalent circuits.

Finally, through GEP optimization and GA calculation and fitting, the best equivalent circuit and its corresponding electrical parameters can be obtained, and then the electrical characteristic parameters contained in the bioimpedance spectrum can be obtained.

In Figure 1: ③ Equivalent circuit fitting is the process of constructing an equivalent circuit by GEP, and the calculation of electrical parameters can be completed by fitting the bioimpedance spectrum with the GA algorithm.

This method has been successfully used by the applicant for equivalent circuit self-fitting of microparticle suspensions;

The applicant first measured 10μm polymethyl methacrylate (10PMMA), 10μm polystyrene magnetic microspheres (10μm Polystyrene Magnetic, 10PSM), 10μm, 20μm 30μm polystyrene (10μm, 20μm 30μm Polystyrene, 10PS). ,20PS,30PS) impedance data.

Secondly, the PMMA bioimpedance spectrum was fitted using the equivalent circuit self-fitting algorithm (the fitting accuracy was greater than 99%), and the bioimpedance spectra of the remaining four microparticle suspensions were fitted based on the PMMA equivalent circuit model. .

Finally, the particle diameter and particle type identification are shown based on the electrical characteristic parameters reflected by the equivalent circuit self-fitting algorithm.

The above-mentioned embodiments are preferred embodiments of the present invention. They are only used to facilitate the explanation of the present invention and are not intended to limit the present invention in any form. Anyone with ordinary knowledge in the relevant technical field can make any modifications without departing from the teachings of the present invention. Within the scope of the technical features of the present invention, equivalent embodiments that make partial changes or modifications using the technical content disclosed in the present invention, and do not deviate from the technical features of the present invention, still fall within the scope of the technical features of the present invention.

Claims (6)

1. A measurement system, comprising: the system comprises a sensor, a position measurement system, a numerical simulation system, a position correction system and an electrical characteristic parameter extraction system;

the sensor is used for measuring the impedance of the cells;

the position measurement system is used for measuring the position of the cells in the sensor;

the numerical simulation system is used for obtaining the characteristic relation between the cell position and the impedance; obtaining a mathematical model between the position of the cell in the sensor and the impedance through numerical simulation, wherein the mathematical model specifically comprises the following steps: s1-1, carrying out grid division on a simulation area; s1-2, randomly selecting any one position as the central coordinate position of the embryo, wherein the coordinate is expressed as (x) _c ，y _c ) The frequency f is an arbitrary frequency f _b And the measured impedance value is expressed as Z _bc The method comprises the steps of carrying out a first treatment on the surface of the Selecting j groups of center coordinates and n groups of frequencies; then, record impedance value matrix Z:

recording a position matrix X:

solving a matrix A:

A＝ZX ^-1

wherein:

fitting the impedance to the cell location creates a corresponding mathematical model:

the position correction system is used for obtaining impedance after position correction;

the electrical characteristic parameter extraction system is used for extracting electrical characteristic parameters by utilizing a bioelectrical impedance spectrum equivalent circuit self-fitting algorithm.

2. A measuring system according to claim 1, wherein the position measuring system employs an electron microscope.

3. A method of measurement comprising the steps of:

step one, obtaining a characteristic relation between a cell position and impedance: obtaining a plurality of numerical values between the cell positions and the impedance through numerical simulation; fitting and constructing a mathematical model between impedance and cell position by using a polynomial;

obtaining a mathematical model between the position of the cell in the sensor and the impedance through numerical simulation, wherein the mathematical model specifically comprises the following steps:

s1-1, carrying out grid division on a simulation area;

s1-2, randomly selecting any one position as the central coordinate position of the embryo, wherein the coordinate is expressed as (x) _c ，y _c ) The frequency f is an arbitrary frequency f _b And the measured impedance value is expressed as Z _bc ；

Selecting j groups of center coordinates and n groups of frequencies;

then, record impedance value matrix Z:

recording a position matrix X:

s1-3, solving a matrix A:

A＝ZX ^-1

wherein:

s1-4, fitting impedance and cell position to establish a corresponding mathematical model:

measuring the impedance of the cell in the sensor, and observing the coordinate position of the cell by an electron microscope;

step three, position correction: according to the mathematical model between the impedance obtained in the first step and the cell position and the coordinate position of the cell recorded in the second step, correspondingly correcting the impedance obtained in the second step;

and step four, according to the corrected data in the step three, the extraction of the electrical characteristic parameters is realized by using a bioelectrical impedance spectrum equivalent circuit self-fitting algorithm.

4. A method according to claim 3, wherein step two records the actual position of the embryo in the sensor as (x _p ,y _p ) The recorded frequency is f _g Impedance is Z _g The method comprises the steps of carrying out a first treatment on the surface of the Then transition to the reference position (x _r ,y _r ) The impedance of (C) is Z' _g ：

5. A measuring method according to claim 3, characterized in that step four, in particular, comprises the following sub-steps:

s4-1, constructing an equivalent circuit model according to a gene expression algorithm GEP:

setting the function symbol of GEP as { "S", "P" };

based on the commonly used electrical components of the bioelectrical impedance spectrum equivalent circuit, the terminal symbol of the GEP is set as { "R", "C", "L", "CPE", "Z_w" };

wherein "S" represents a series relationship, "P" represents a parallel relationship, "R" represents a resistive element, "C" represents a capacitive element, "L" represents an inductive element, "CPE" represents a normal phase element, "z_w" represents a diffusion impedance, and an impedance expression corresponding to a termination symbol is as follows:

Z _L ＝jwL

t＝h(n-1)+1

l＝t+h

wherein:

z_c represents: the capacitive reactance is as follows: omega;

ω represents: angular frequency in rad/s;

c represents: capacitance in units of: c, performing operation;

Z _L the representation is: the unit of the inductance is: omega;

Z _ω the representation is: diffusion resistance in units of: omega;

y represents: modulus of Warburg admittance, specific value is in the range of (0, 1), and unit is dimensionless;

Z _CPE the representation is: constant phase impedance in units of: omega;

Y ₀ the representation is: the magnitude of the front factor after the normal phase element is stripped off the frequency or the generalized element is molded, and the value is (0, 1);

n represents: the exponentiation, the value is within the range of [ -1,1 ];

t represents: tail length, dimensionless;

h represents: the head length is dimensionless;

l represents: the total length of the GEP gene is dimensionless;

l represents: the inductance is as follows: h is formed;

j imaginary units;

according to the GEP individual composition principle, the head lengths h and n are firstly required to be set according to the requirements, and then the individual lengths can be known.

6. The method of claim 5, wherein step four further comprises the sub-steps of: s4-2, forming an equivalent circuit model through a GEP coding and decoding mode, wherein father nodes of the child nodes are functional symbols, and the functional symbols correspond to the combination relation of the electric elements:

an equivalent circuit model established based on GEP is used for fitting a bioimpedance spectrum through a genetic algorithm GA:

firstly, initializing an electrical characteristic parameter population by GA according to electrical elements contained in an equivalent circuit model, and maximizing the iteration number;

next, GA selection probability P is set _s For ensuring that the preferred individuals in each generation are able to be inherited to the next generation with a greater probability, andsetting the crossover probability P _c Probability of variation P _m The method is used for generating new individuals, and solving and trapping are prevented from being in local optimum, so that each GA can ensure that the current equivalent circuit can obtain the optimum fitness;

thirdly, feeding back the optimal fitness obtained by the GA to an individual of the GEP for optimizing an equivalent circuit;

finally, the optimal equivalent circuit and the corresponding electrical parameters thereof can be obtained through GEP optimization and GA calculation fitting, and further the electrical characteristic parameters contained in the bioimpedance spectrum can be obtained.