CN107045075A - A kind of characterizing method of the cell physical state based on porous media model - Google Patents
A kind of characterizing method of the cell physical state based on porous media model Download PDFInfo
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Abstract
The present invention provides a kind of characterizing method of the cell physical state based on porous media model.In order to obtain above-mentioned characterizing method, need to obtain Young's Moduli based on porous media model first, wherein, the acquisition methods of Young's Moduli include：S1. the loading force time graph based on cell surface to be measured, obtains the loading force and compression distance when cell to be measured is region infinity in the time；S2. it is the loading force and compression distance when region is infinitely great in the time based on cell to be measured, the Young's modulus for obtaining cell to be measured is calculated using Hertz model.The method that the present invention is provided can be efficiently solved measures the problem of result difference that Young's modulus and the different compression distances present in cell rigidity obtain from being measured under different loading speeds is big according to Hertz model using conventional method, and the reason for difference occurs in conventional method measurement is reasonably explained, and accurately characterize the mesoporous elastic property of cell and cell physical state.
Description
Technical field
The present invention relates to cell characterization technical field, more particularly, to a kind of cell thing based on porous media model
The characterizing method of reason state.
Background technology
The method of existing description cyto-mechanics state mainly has firm using Young's modulus sign cell based on Hertz model
Degree, is characterized using relaxation modulus based on Theory of Viscoelasticity with apparent viscosity to cell, and based on porous medium theory
To calculate cytoplasmic diffusion coefficient.
The method that Young's Moduli is calculated using Hertz model mainly uses AFM to carry out cell
Indentation test gathers power-distance Curve of cell, is fitted for probe of different shapes using different formula.
For tapered probe, cell is carried out in indentation test, such as Fig. 1 shown in (a), having using tapered probe：
For spherical probes, cell is carried out in indentation test, such as Fig. 1 shown in (b), having using tapered probe：
Wherein, F is loading force, and E is Young's modulus, and v is Poisson's ratio,It is half angle of release of tapered probe, R is spherical probes
Radius, δ is compression distance.
The method that viscosity and rigidity are calculated using viscoelastic model is first to allow probe certain with certain speed press-in cell
Compression distance, be then allowed to settle the regular hour, force curve a relaxation can occur with time of repose.By by pine
The force curve in relaxation stage is fitted with equation below：
Wherein, ERIt is relaxation modulus, τσAnd τsIt is the Relaxation time constant of load and deformation respectively, apparent viscosity can root
Calculated according to following formula：
μ=ER(τσ-τε)
The power that AFM probe is applied to cell can pass through：
F=S × Δ × k
To calculate, wherein, S is the susceptibility of probe, and Δ is the change of deflection values, and k is the force constant of probe.
The method for measuring cellular invasion coefficient using porous media model also mainly uses the curve in loose stage to carry out
Fitting.Fit equation is as follows：
For tapered probe, have：
α=(2/ π) δ tan θ
For spherical probes, have：
Wherein, D is diffusion coefficient, and α is effective contact area.
The method of the physical state of traditional sign cell whether has it from model hypothesis or in data acquisition
Deficiency.On model hypothesis, cell is assumed to be a Homogeneous Elastic Solid by Hertz model, and viscoelastic model regards cell as
It is complete viscoelastic body, cell is assumed to be a single porous media system by porous media model.And these are assumed not
Meet the state of cell in itself.In data acquisition, Hertz model has two always, and one is survey under different compression distances
The value of the Young's modulus measured has a larger difference, and two be to measure obtained value under different loading speeds also to have larger difference.This
Outside, conventional a variety of models, are all used as sign cyto-mechanics only with one or two kinds of physical parameters based on the model
The main standard of state, and cell interior, due to its complexity, its physical state is described by one or two kinds of parameters may be simultaneously
Needs can not be met, and the state of its description also has certain one-sidedness, residing for description cell that can not be accurate or perfect
Physiological status.
The content of the invention
(1) technical problem to be solved
The technical problem to be solved in the present invention is how to reduce to obtain under different compression distances and different loading speeds
Difference between obtained Young's modulus value.
(2) technical scheme
In order to solve the above problems, the invention provides a kind of acquisition methods of Young's Moduli, including：
S1. the loading force-time curve based on cell surface to be measured, obtains cell to be measured when the time is infinitely great for region
Loading force and compression distance；
S2. it is the loading force and compression distance when region is infinitely great in the time based on cell to be measured, utilizes Hertz model meter
Calculate the Young's modulus for obtaining cell to be measured.
Preferably, S1 is specially：
Based on deformation-time graph of cell surface AFM probe to be measured, cell surface to be measured is obtained using viscoelastic model
Loading force-time curve, it is the loading force and compression distance when region is infinitely great in the time to obtain cell to be measured.
Preferably, in the acquisition of the deformation-time graph, data collection steps include：Withdraw of the needle section, stand section, it is near
Pin section and slack strand.
Preferably, the data collection steps are specially：
S11. according to the force curve of cell to be measured, estimation obtains the position of probe and cells contacting point to be measured, is estimated with described
Location is set to contact point, and probe is lifted and is placed in the first height, is designated as withdraw of the needle section, the time value and AFM probe of collection withdraw of the needle section
Deflection changing values；
S12. probe is stood in first height, is designated as standing section, collection stands the time value and AFM probe of section
Deflection changing values；
S13. make probe decline the first distance with First Speed, so as to obtain the first compression distance in cell surface, be designated as
Nearly pin section, gathers the time value and AFM probe Deflection changing values of nearly pin section；
S14. keep probe constant in first compression distance, record the relaxation behavior of probe, be designated as slack strand, gather
The time value and AFM probe Deflection changing values of slack strand.
Preferably, the data collection steps also include：
Using S11-S14 as a cycle, multiple cycles are repeated.
Preferably, the First Speed is at least 10 μm/s.
According to an aspect of the present invention, a kind of characterizing method of cell physical state is additionally provided, including：Use Young
Modulus, apparent viscosity and diffusion coefficient comprehensive characterization cell physical state；Wherein, the Young's modulus is to use above-mentioned cell poplar
The measuring method of family name's modulus is obtained.
Preferably, the apparent viscosity is the song of slack strand described in the measuring method based on above-mentioned Young's Moduli
Line, acquisition is fitted using viscoelastic model.
Preferably, the diffusion coefficient is the song of slack strand described in the measuring method based on above-mentioned Young's Moduli
Line, acquisition is fitted using porous media model.
Preferably, the characterizing method also includes：Use comprehensive porosity combination Young's modulus, apparent viscosity and diffusion system
Number synthesis characterizes cell physical state；Wherein, the comprehensive porosity is calculated using single bore diameter porous MEDIUM THEORY and obtained.
According to an aspect of the present invention, the acquisition methods of a kind of mesoporous elasticity of cell or rigidity are additionally provided, including：Make
Young's Moduli is obtained with the acquisition methods of Young's Moduli described in preceding claim, to characterize the mesoporous elasticity of cell
Or rigidity.
Method proposed by the present invention can be efficiently solved using conventional method according to conspicuous based on porous media model
Hereby model measurement Young's modulus and the different compression distances present in cell rigidity are obtained from measurement under different loading speeds
The problem of result difference is big, and reasonably explain the reason for difference occurs in conventional method measurement；Cell characterization proposed by the present invention
Method solves traditional insufficient and incomplete problem, root described using various physical models present in cell physical state
According to multilevel multiphase porous medium theory, the more deep essence for disclosing intracellular mechanical behavior, more comprehensively more comprehensive description
The physical state of cell interior.It is also multilevel multiphase porous media based on tissue, method of the invention goes for tissue
Or biomimetic material, it is applied to clinical medicine, it would be possible to help scientific worker to see clearly the reason for disease occurs and right
The diagnosis and treatment of disease.
Brief description of the drawings
Fig. 1 carries out the schematic diagram of indentation test for tapered probe (a), spherical probes (b) in the prior art to cell respectively；
Fig. 2 is the overview flow chart according to the acquisition methods of Young's Moduli in embodiment of the present invention；
Fig. 3 is according to the curve that z is changed over time to distance in a cycle experiment in a preferred embodiment of the invention
Scheme (a), Deflection with curve map (b) from z to distance change and Deflection time history plots；
Fig. 4 is what is obtained according to measured by a preferred embodiment of the invention using the method for conventional method and the present invention
The curve map that 3T3 Young's Modulis value changes with compression distance；
Fig. 5 is what is obtained according to measured by a preferred embodiment of the invention using the method for conventional method and the present invention
The curve map that DC Young's Modulis value changes with loading speed.
Embodiment
With reference to the accompanying drawings and examples, the embodiment to the present invention is described in further detail.Implement below
Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
The acquisition methods for the Young's Moduli that the present invention is provided, as shown in Fig. 2 including：
S1. the loading force-time curve based on cell surface to be measured, obtains cell to be measured when the time is infinitely great for region
Loading force and compression distance；
S2. it is the loading force and compression distance when region is infinitely great in the time based on cell to be measured, utilizes Hertz model meter
Calculate the Young's modulus for obtaining cell to be measured.
The present invention obtains the Young's modulus of cell based on porous media model, it is contemplated that utilize traditional Hertz model method
The effect for the intracellular liquid phase that measurement Young's modulus is not considered.In the method for traditional measurement Young's modulus, only will
Cell is processed as pure elastomer, is situated between for calculating the compression distance of Young's modulus and the data of loading force equivalent to us with porous
Matter model calculate when relaxation curve in t=0 data.And if by cell carry out porous media model processing, due to liquid
The presence of phase, in t=0, intracellular liquid is not redistributed also mutually, and the also non-complete stability of integrality of cell gets off,
Therefore, measured obtained Young's modulus is highly susceptible to the influence of compression distance and loading speed.And it is bent if choosing relaxation
Value in line during t=∞, intracellular liquid has mutually been redistributed completely, and the integrality of cell has reached one completely
Stable state, now, it is possible to exclude the different behaviors in different compression distances from liquid phase under loading speed and cause to do
Disturb, therefore with certain superiority and higher accuracy.
When based on being loading force under the infinity ∞ of region with compression distance in unorthodox method using t being 0 in the time
Loading force and compression distance, calculate obtained Young's modulus value using Hertz model more accurate, reduce in different press-ins
Difference between the Young's modulus value acquired under depth and different loading speeds.
Wherein, compression distance refers to compression distance of the probe on the surface of cell to be measured.
Hertz model is Hertz model commonly used in the art, generally main to utilize atomic force microscope probe to thin
Born of the same parents carry out indentation test collection cell force-displacement curve and AFM probe deformation-time (also referred to as Deflection-t, or
The Deflection- times) curve.
It can be fitted, for tapered probe, be visited using taper using different formula for probe of different shapes
Indentation test is carried out for cell, in such as Fig. 1 shown in (a), is had：
For spherical probes, cell is carried out in indentation test, such as Fig. 1 shown in (b), having using tapered probe：
Wherein, F is loading force, and E is Young's modulus, and v is Poisson's ratio,It is half angle of release of tapered probe, R is spherical probes
Radius, δ is compression distance.
In embodiments of the present invention, obtained loading force and compression distance are substituted into above-mentioned model, it is possible to
Obtain the Young's modulus of cell.
In a preferred embodiment of the invention, used is spherical probes, and diameter is usually 10 μm.Art technology
Personnel can according to actual needs and the known advantage and disadvantage of each probe select different type or various sizes of probe.
In a preferred embodiment of the invention, in order to obtain more accurate loading force and compression distance, S1 is specific
For：
Based on deformation-time graph of cell surface AFM probe to be measured, cell surface to be measured is obtained using viscoelastic model
Loading force-time curve, it is the loading force and compression distance when region is infinitely great in the time to obtain cell to be measured.
Wherein, when probe is along testee apparent motion, the reaction force of measured surface deforms upon probe.Use
During AFM probe, it can go to obtain the loading of cell surface to be measured by deformation-time graph of cell surface AFM probe to be measured
Force-time curve.
Wherein, according to deformation-time (Deflection-t) curve of AFM probe, in viscoelastic model, AFM probe
The power applied to cell can pass through：
F=S × Δ × k
To calculate the curve for obtaining loading force-time (F-t), wherein, S is the susceptibility of probe, and Δ is deflection
The change of value, k is the force constant of probe.
In order that data are more accurate and obtain other characterization values, in a preferred embodiment of the invention, in deformation
In the acquisition of Deflection- times t change curve, as shown in figure 3, data collection steps include：The withdraw of the needle section, stand section,
Nearly pin section and slack strand.
In order to reduce data acquisition to measuring obtained Young's modulus under different compression distances and different loading speeds
Influence, in a preferred embodiment of the invention, preferably carrys out gathered data from following methods：
S11. according to the force curve of cell to be measured, estimation obtains the position of probe and cells contacting point to be measured, is estimated with described
Location is set to contact point, and probe is lifted and is placed in the first height, is designated as withdraw of the needle section, the time value and AFM probe of collection withdraw of the needle section
Deflection changing values；
S12. probe is stood in the first height, is designated as standing section, collection stands the time value and AFM probe of section
Deflection changing values；
S13. make probe decline the first distance with First Speed, so as to obtain the first compression distance in cell surface, be designated as
Nearly pin section, gathers the time value and AFM probe Deflection changing values of nearly pin section；
S14. keep probe constant in the first compression distance, record the relaxation behavior of probe, be designated as slack strand, collection relaxation
The time value and AFM probe Deflection changing values of section.
It is also possible to gather Z-direction distance value respectively in withdraw of the needle section, standing section, nearly pin section and slack strand, it can obtain
It is bent with Z-direction distance change (Deflection-Z to distance) that Z-direction distance changes over time (Z-direction distance-t) curve and deformation
Line, as shown in figure 3, can show whole experiment process under different presentations.
Wherein, in S11, a force curve is done on cell to be measured to estimate the position of contact point.With the estimation position
For contact point, probe is lifted and is placed in the first height d0。
, can be according to deformation in order to more accurately obtain the position of contact point in a preferred embodiment of the invention
With Z-direction distance change (Deflection-Z to distance) curve, the linearity range of curve and the separation of non-linear section are to estimate
Position, position is estimated as contact point using this, and probe is lifted and is placed in the first height d0。
In S12, section is being stood, probe a period of time is being stood into first height, the time can set as needed
Put.Response of the different cells to probe is possible to identical, it is also possible to different, and standing is in order that cell recovers normal shape for a moment
State, this time needs are adjusted according to specific experimental subjects and phenomenon.Usually several seconds.
In S13, in nearly pin section, First Speed can be arranged as required to, with least 10 μm/s speed in the present invention
Exemplified by be described in detail the present invention.Wherein, the second height is d1, compression distance is δ.
In the velocity interval value, the liquid in cell is not yet redistributed.
In S14, in slack strand, due to the redistribution of cell stream body phase, probe can show a time dependence
Relaxation, record probe relaxation behavior.
, can be by the first height d according to experiment needs0With first apart from d1Same or different value is set to, can be collected
Experimental data of the cell under same compression distance or different compression distances.
When the first height and the first distance value are set to identical, i.e. probe is lifted into the first height and then declined again and the
One height identical distance, while returning to normal condition by standing Procedure Cell, then position after decline and before lifting
Position be same position, i.e., the compression distance tested twice is also the same, you can collect cell deep in same press-in
Experimental data under degree.
In order to obtain more accurately data, data collection steps also include：S11-S14 is set to a cycle, repeated many
The individual cycle.
Wherein, " multiple " in the present invention refer to 2 or more than 2.
I.e. after the completion of the experiment in said one cycle, the experiment of next cycle can be and then carried out.
Present invention also offers a kind of acquisition methods of cell rigidity, including：Use the measurement of above-mentioned Young's Moduli
Method obtains Young's Moduli, so as to obtain the rigidity of cell.
Wherein, the rigidity of cell is corresponded with Young's Moduli, from the perspective of biology, is all used to indicate that
The soft or hard degree of cell.
Because the Young's modulus is inwardly measuring in porous media model, therefore the above method can be measured again
Obtained Young's modulus is referred to as the mesoporous elasticity of cell.
That is, present invention also offers a kind of mesoporous elastic characterizing method of cell, including：Use above-mentioned Young's Moduli
Acquisition methods obtain Young's Moduli to be measured, to characterize the mesoporous elasticity of cell.
Present invention also offers a kind of characterizing method of cell physical state, including：Using Young's modulus, apparent viscosity and
Diffusion coefficient comprehensive characterization cell physical state；Wherein, Young's modulus is to be obtained using the measuring method of above-mentioned Young's Moduli
.
In the characterizing method of the present invention, cell is considered as a multilevel multiphase porous media, it is false in traditional model
If on, cell is assumed to be a Homogeneous Elastic Solid by Hertz model, and viscoelastic model regards cell as complete viscoelastic body, many
Cell is assumed to be a single porous media system by hole dielectric model.And these hypothesis do not meet the shape of cell in itself
State.Cell is innovatively considered as a multilevel multiphase porous media by the state based on cell, the present invention in itself, uses the present invention
Measured obtained Young's modulus combination apparent viscosity and diffusion coefficient carry out comprehensive characterization cell physical state, wherein, use this
The Young's modulus that the method for invention is obtained can more reflect the state of cytoskeleton, the state relation of apparent viscosity then with cell liquid
Bigger, the diffusion coefficient comprehensive description active state of one cell interior compensate for conventional various models and carry out thing to cell
Manage the deficiency present in state representation.
In order to more accurately reflect the state of cell liquid, apparent viscosity is the measurement side of the Young's Moduli according to the present invention
The curve of slack strand in method, acquisition is fitted using viscoelastic model.
In order to more accurately reflect the active state of cell interior, diffusion coefficient is the Young's Moduli according to the present invention
The curve of slack strand in measuring method, acquisition is fitted using porous media model.
The curve of above-mentioned slack sections is the slack sections curve in deformation-time (Deflection-t) curve of cell, then
Power-time (F-t) curve for obtaining the slack sections curve is calculated according to F=S × Δ × k, viscoelastic model progress is utilized respectively
Fitting is obtained cell apparent viscosity value and the diffusion coefficient for obtaining cell is fitted using porous media model.
Whole deformation-time (Deflection-t) curve of cell can also be calculated according to F=S × Δ × k and obtained
Corresponding power-time (F-t) curve, further according to the curve of wherein slack strand, is utilized respectively viscoelastic model and is fitted acquisition
Cell apparent viscosity value and the diffusion coefficient that acquisition cell is fitted using porous media model.
Wherein, it is method common in this area to be fitted using viscoelastic model and obtain cell apparent viscosity value,
In a preferred embodiment of the invention, it is specially：
By the way that the F-t curves of slack sections are fitted with equation below：
Wherein, ERIt is relaxation modulus, τσAnd τsIt is the Relaxation time constant of load and deformation respectively, apparent viscosity can root
Calculated according to following formula：
μ=ER(τσ-τε)
Wherein, it is method common in this area to be fitted using porous media model and obtain the diffusion coefficient of cell,
In a preferred embodiment of the invention, it is specially：
By the way that the F-t curves of slack sections are fitted with equation below：
For the spherical probes in a preferred embodiment of the invention, have：
Wherein, D is diffusion coefficient, and α is effective contact area.
Diffusion coefficient D value can be obtained from above formula.
In porous media, in order to more comprehensively reflect the physical state of cell, generally also need to using comprehensive hole
Degree combines Young's modulus, apparent viscosity and diffusion coefficient and comes together to characterize cell physical state.
In the present invention, comprehensive porosity can be calculated using single bore diameter porous MEDIUM THEORY and obtained, i.e. Young mould
Amount, apparent viscosity, diffusion coefficient and pore size have following relation：
Wherein, ξ is pore size, characterizes comprehensive porosity；D is diffusion coefficient；α is effective contact area；E is Young mould
Amount.
In one preferred embodiment, because the different most probables of intracellular porous media structure are embodied in its pattern
In feature, therefore two kinds of larger cell 3T3 cells of two kinds of varying topographies and DC cells are taken as experimental subjects.Wherein, 3T3
Cell is big and thin, and DC cells are small and thick.
3T3 cells and DC cells are measured using the method for the present invention, as shown in figure 4, having obtained being directed to 3T3 cells
The Young's modulus value obtained under different compression distances using the method for conventional method and the present invention, as shown in figure 5, having obtained pin
The Young's modulus value obtained to DC cells under different loading speeds using the method for conventional method and the present invention.
It can be drawn from figure, using the method for the present invention under different compression distances and different loading velocities
Under, the difference very little of Young's Moduli, different from the use of the value obtained by conventional method.
The rigidity value, apparent viscous of the obtained 3T3 cells of characterizing method and DC cells using the present invention is given in table 1
Angle value, diffusion coefficient and comprehensive porosity.
The cell parameters value that table 1 is obtained with the characterizing method of the present invention
From table 1 it follows that for different cells, its various physical characteristic has obvious difference, and difference size
Differ, therefore, alone a certain physical quantity is possible and insufficient, it is necessary to which comprehensive this four kinds of parameters are total to come the state for characterizing cell
With being described, physical state that can more comprehensively with accurately description cell.
The present invention is based on multilevel multiphase porous medium theory, it is contemplated that the presence of intracellular fluid phase, it is proposed that utilize
The method that Hertz model obtains the new gathered data of Young's Moduli and rigidity, is perfectly solved one in conventional method
The cell rigidity directly existed is easily pressed into depth and the influence of loading speed the two problems, also discloses traditional vacation from side
If deficiency.Meanwhile, the present invention, which is proposed, uses diffusion coefficient, Young's modulus, and apparent viscosity and comprehensive porosity are retouched to integrate
The method for stating cell physical state, the liveness that they may respectively with cell entirety, the state of cytoskeleton, cell liquid status
And cell interior design feature is relevant.If this set system is applied in clinical medicine, potentially contribute to a variety of diseases
Disease is understood, Clinics and Practices, it is also possible to provide a new criterion for the physiological status of cell.
Finally, method of the invention is only preferably embodiment, is not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements made etc. should be included in the protection of the present invention
Within the scope of.
Claims (10)
1. a kind of acquisition methods of Young's Moduli, including：
S1. the loading force-time curve based on cell surface to be measured, obtains adding when cell to be measured is region infinity in the time
Carry power and compression distance；
S2. it is the loading force and compression distance when region is infinitely great in the time based on cell to be measured, is calculated using Hertz model
To the Young's modulus of cell to be measured.
2. acquisition methods of Young's Moduli according to claim 1, it is characterised in that S1 is specially：
Based on deformation-time graph of cell surface AFM probe to be measured, adding for cell surface to be measured is obtained using viscoelastic model
Force-time curve is carried, it is the loading force and compression distance when region is infinitely great in the time to obtain cell to be measured.
3. acquisition methods of Young's Moduli according to claim 2, it is characterised in that in the deformation-time graph
Acquisition in, data collection steps include：Withdraw of the needle section, standing section, nearly pin section and slack strand.
4. acquisition methods of Young's Moduli according to claim 3, it is characterised in that the data collection steps are specific
For：
S11. according to the force curve of cell to be measured, estimation obtains the position of probe and cells contacting point to be measured, with the estimation position
Contact point is set to, probe is lifted and is placed in the first height, withdraw of the needle section, the time value and AFM probe of collection withdraw of the needle section is designated as
Deflection changing values；
S12. probe is stood in first height, is designated as standing section, collection stands the time value and AFM probe of section
Deflection changing values；
S13. make probe decline the first distance with First Speed, so as to obtain the first compression distance in cell surface, be designated as nearly pin
Section, gathers the time value and AFM probe Deflection changing values of nearly pin section；
S14. keep probe constant in first compression distance, record the relaxation behavior of probe, be designated as slack strand, collection relaxation
The time value and AFM probe Deflection changing values of section.
5. acquisition methods of Young's Moduli according to claim 4, it is characterised in that the data collection steps are also wrapped
Include：
Using S11-S14 as a cycle, multiple cycles are repeated.
6. the acquisition methods of Young's Moduli according to claim 4 or 5, it is characterised in that the First Speed is at least
For 10 μm/s.
7. a kind of characterizing method of cell physical state, including：Use Young's modulus, apparent viscosity and diffusion coefficient comprehensive characterization
Cell physical state；Wherein, the Young's modulus is the measurement that usage right requires Young's Moduli any one of 1-6
Method is obtained.
8. the characterizing method of cell physical state according to claim 7, it is characterised in that the apparent viscosity is based on power
Profit requires the curve of slack strand described in the measuring method of Young's Moduli any one of 3-6, utilizes viscoelastic model
It is fitted acquisition；
And/or,
The diffusion coefficient is based on relaxation described in the measuring method of Young's Moduli any one of claim 3-6
The curve of section, acquisition is fitted using porous media model.
9. the characterizing method of cell physical state according to claim 7 or 8, it is characterised in that also include：Use comprehensive hole
Porosity combination Young's modulus, apparent viscosity and diffusion coefficient comprehensive characterization cell physical state；Wherein, the comprehensive porosity profit
Calculated and obtained with single bore diameter porous MEDIUM THEORY.
10. the characterizing method of a kind of mesoporous elasticity of cell or rigidity, including：Usage right requires cell any one of 1-6
The acquisition methods of Young's modulus obtain Young's Moduli, to characterize the mesoporous elasticity or rigidity of cell.
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| CN114112808B (en) * | 2021-11-05 | 2024-02-20 | 国家纳米科学中心 | Characterization method of cytoplasmic mechanical properties |
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