CN114113227B - Measurement system and measurement method - Google Patents

Measurement system and measurement method Download PDF

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CN114113227B
CN114113227B CN202111383660.9A CN202111383660A CN114113227B CN 114113227 B CN114113227 B CN 114113227B CN 202111383660 A CN202111383660 A CN 202111383660A CN 114113227 B CN114113227 B CN 114113227B
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CN114113227A (en
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姚佳烽
万建芬
杨璐
刘凯
朱芸
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Jiangsu Jilun Medical Intelligent Technology Co ltd
Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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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

Measurement system and measurement method
Technical Field
The invention relates to a method for combining measurement and data processing, in particular to an accurate measurement method for electrical characteristics in the embryo development process.
Background
Since single cells are the smallest structural and functional unit of living tissue, detection of the developmental process of an embryo is of great importance for revealing the life's mysterious, research of drug responses.
However, conventional detection methods such as: single cell sequencing, gene editing techniques are complex and expensive. Bioimpedance spectroscopy (Bioimpedance Spectroscopy, BIS) has been widely used in industry, biology and medicine as a non-invasive, non-labeled, non-radiative, novel technique.
The bioimpedance spectroscopy method can quantitatively judge the type, size and number (one-dimensional information) of cells, and is also widely applied. Such as:
reference 1: JP2011050765a provides a method and apparatus for performing 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 fat content of the body part.
Reference 2: WO2005027717A2 provides a method and apparatus for bioimpedance analysis. The data obtained by bioimpedance spectroscopy (BIS) and MRI on the lower leg of the subject demonstrate that correlation can be improved compared to single frequency analysis at 50kHz and analysis using the conventional Cole-Cole model.
However, the detection accuracy of the bioimpedance spectrum is often affected by the position variation of the object to be detected, and thus, the electrical characteristic parameters of the cells in the development process cannot be accurately extracted by directly using the measurement data of the bioimpedance spectrum.
Disclosure of Invention
The invention aims to solve the problem of low detection precision of the existing bioimpedance spectroscopy method and provides a measurement system and a measurement method.
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;
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.
Further, the position measurement system adopts an electron microscope.
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;
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.
Further, for the first step, a mathematical model between the position of the cell in the sensor and the impedance is obtained through numerical simulation, which specifically includes:
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:
further, step two recorded 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
Further, the fourth step specifically 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: magnitude or mode generalized element of front factor, normal phase element after stripping frequency, generally taking value (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;
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 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:
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 better individuals in each generation can be transmitted to the next generation with a higher probability, and additionally setting 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 time the GA algorithm 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.
The technical scheme of the invention has the advantages that:
1) The first invention point of the present application is that: the phenomenon of "the cell location in the sensor is different, the measured impedance is different" was found. Based on this phenomenon, to study the impedance of different cells or cells at different stages, it is necessary to remove the effect of the actually measured impedance from the position.
Based on this problem, the inventors found through a large number of experiments that the relationship between the position of the cell in the sensor and the impedance satisfies the following equation:
accordingly, steps one and three are provided to eliminate the above-mentioned position influence.
2) The second invention point of the present application is that: the method can be used for measuring the electrical characteristic parameters of the cells; the method has good application prospect for researching drug reaction.
Drawings
The invention is described in further detail below in connection with the embodiments in the drawings, but is not to be construed as limiting the invention in any way.
Fig. 1 is a flow chart of a measurement method of the present application.
Detailed Description
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 the technical scheme of the invention, and all technical schemes formed by adopting equivalent substitution or equivalent transformation fall within the scope of the invention.
Embodiment 1: integral frame design for accurate measurement method]
The present invention is further described with reference to fig. 1.
An accurate measurement method of electrical characteristics in embryo development process comprises the following steps:
step one, obtaining a characteristic relation between a cell position and impedance: obtaining a numerical value between the cell position and the impedance through numerical simulation;
fitting and constructing a mathematical model between impedance and cell position by using a polynomial;
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: and (3) 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, carrying out corresponding correction on the impedance obtained in the second step, thereby avoiding the influence of the position factors on the impedance and realizing high-precision measurement.
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.
For the above measurement method, a measurement system is also provided in the first embodiment, and the composition and function of the measurement system are shown in table 1.
TABLE 1
For the fourth step, the electrical characteristics are extracted by utilizing a bioelectrical impedance spectrum equivalent circuit self-fitting algorithm; the automatic fitting algorithm is a mixed algorithm combining a genetic expression algorithm and a genetic algorithm, wherein the genetic expression algorithm realizes the construction of a bioelectrical impedance spectrum equivalent circuit, and the genetic algorithm realizes the fitting of the bioelectrical impedance spectrum and the calculation of electrical parameters based on the constructed equivalent circuit model.
Embodiment II: specific operation of a numerical simulation system]
The specific work of the numerical simulation system corresponds to the work of the first step.
For the first step, a mathematical model between the position of the cell in the sensor and the impedance is obtained through numerical simulation, and the method 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:
the above matrix is expressed by the following formula: z=a·x
It can be seen that: a=zx -1 (i.e., each value that can be solved into matrix A)
Wherein,
s1-4, building impedance and cell position fitting to build a corresponding mathematical model:
embodiment III: specific operation of the position correction system]
One of the difficulties with the method of embodiment one is "how to perform position correction", which is specifically that the embryo will change during the actual measurement process, so that the embryo will be at different positions of the sensor; while the impedance measured by the embryo is different when it is in different positions of the sensor, it is difficult to evaluate the effect.
I.e. the actual coordinate position (x p ,y p ) Are necessarily different, and it is necessary to convert impedance values measured at different coordinate positions into impedance values at the same coordinate position (reference position (x r ,y r ) And then comparing and analyzing, so that the influence of the position factors on the impedance can be avoided, and a high-precision measurement result can be obtained.
For this problem, the following process is performed:
the correction process comprises the following steps:
step two recorded the actual position of the embryo in the sensor as (x p ,y p ) The recorded frequency is f g Impedance is Z g
Then transition to the reference position (x r ,y r ) The impedance of (C) is Z' g
Embodiment IV: extracting electrical characteristics by using bioelectrical impedance spectrum equivalent circuit self-fitting algorithm]
One difficulty with the method of the first embodiment is how to extract the electrical characteristics with the bioelectrical impedance spectrum equivalent circuit self-fitting algorithm, and for the third step, the bioelectrical impedance spectrum equivalent circuit self-fitting algorithm is used to extract the electrical characteristic parameters; the automatic fitting algorithm is a mixed algorithm combining a genetic expression algorithm and a genetic algorithm, wherein the genetic expression algorithm realizes the construction of a bioelectrical impedance spectrum equivalent circuit, and the genetic algorithm realizes the fitting of the bioelectrical impedance spectrum and the extraction of electrical characteristic parameters based on the constructed equivalent circuit. Specifically, the method comprises the following 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 impedance expressions corresponding to the terminal symbols are shown in (2) to (6).
Z L =jwL
t=h(n-1)+1
l=t+h
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: magnitude or mode generalized element of front factor, normal phase element after stripping frequency, generally taking value (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, first, the head lengths h and n are required to be set according to the own needs of researchers, and then the individual lengths can be known by a formula (8).
S4-2, an equivalent circuit model can be formed by means of GEP coding (binary tree layer sequence traversal) and decoding (binary tree subsequent traversal), and father nodes of the child nodes are functional symbols, and the symbols correspond to the combination relation of the electrical elements.
An equivalent circuit model established based on GEP, and a biological impedance spectrum is fitted 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 better individuals in each generation can be transmitted to the next generation with a higher probability, and additionally setting the crossover probability P c Probability of variation P m For generating new individuals, avoiding solution sets from being trapped in local optima, thereby ensuring that each time the GA algorithm can ensure that the current equivalent circuit can achieve the best fitness (best fit with bioimpedance spectroscopy)
Again, the individual that the GA obtains the best fitness feedback to the GEP is used for optimization of the 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.
In fig. 1: (3) fitting of the equivalent circuit is the process of constructing the equivalent circuit by the GEP, and calculation of the electrical parameters can be completed by fitting the bioimpedance spectrum by the GA algorithm.
This method has been successfully used by applicant for the self-fitting of equivalent circuits of microparticle suspensions;
the applicant first measured impedance data for 10 μm polymethyl methacrylate (Poly Methyl Methacrylate,10 PMMA), 10 μm Polystyrene magnetic microspheres (10 μm m Polystyrene Magnetic,10 PSM), 10 μm,20 μm 30 μm Polystyrene (10 μm,20 μm 30 μm Polystyrene,10ps,20ps,30 ps).
And secondly, fitting of PMMA bioimpedance spectrums (fitting accuracy is more than 99%) is achieved by using an equivalent circuit self-fitting algorithm, and bioimpedance spectrums of the other four microparticle suspensions are fitted based on an equivalent circuit model of PMMA.
Finally, the particle diameter and the identification of the particle type are displayed according to the electrical characteristic parameters reflected by the equivalent circuit self-fitting algorithm.
The above examples are provided for convenience of description of the present invention and are not to be construed as limiting the invention in any way, and any person skilled in the art will make partial changes or modifications to the invention by using the disclosed technical content without departing from the technical features of the 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.
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