CN109920549A - A kind of lumped parameter model personalized method based on improvement simulated annealing optimization algorithm - Google Patents
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Abstract
A kind of lumped parameter model personalized method based on improvement simulated annealing optimization algorithm, belongs to combinatorial optimization algorithm field.The physiology Wave data of this method acquisition human body；Blood circulation system structure and physiological parameter building based on human body are suitable for the blood circulation system lumped parameter model of common people；Using collected physiology Wave data as target, sensitivity analysis is carried out to the parameter in lumped parameter model, is determined to the biggish sensitive parameter of object effects；Optimization is iterated to the sensitive parameter in lumped parameter model using the root-mean-square error between the calculated simulation waveform of physiology Wave data and lumped parameter model of acquisition as objective function based on improved simulated annealing optimization algorithm；When objective function is less than tolerance, it is believed that optimum results reach acceptable optimal solution, terminate optimization, export optimal solution.The present invention realizes the personalization of lumped parameter model parameter value.
Description
Technical field
The invention belongs to combinatorial optimization algorithm fields, are related to a kind of based on the lumped parameter for improving simulated annealing optimization algorithm
Model personalized method.
Background technique
Hemodynamics Numerical Simulation is a kind of common, effective analogy method, commonly used in illustrating blood in medical treatment
Rule, physiological significance and the relationship with disease of flowing.And lumped parameter model is one of common haemodynamics number
It is worth model, it is compared blood circulation of human body system with circuit element, and the physiological parameter or physiological property of human body can be anti-by it
It mirrors and.Wherein resistance is used to simulate the viscosity resistance and vascular wall resistance of blood flow, and capacitor is suitable for simulated blood vessel wall
Ying Xing, inductance are used to simulate the inertial flow of blood, and diode makes one-way blood flow in part-structure for simulating valve.
The model is based on circuit Kirchhoff law, describes circuit conditions with differential-algebraic equation group.
Numerous research is by blood in the blood circulation system of the numerical simulation calculation result of lumped parameter model and human body
Flow behavior relatively after, discovery has many aspects to be consistent, it was demonstrated that the validity of the model.Either study entire blood circulation system
The haemodynamics of system, or boundary condition, lumped parameter mould are provided for the three-dimensional blood vessel numbered analog simulation of local fine
Type can play its effect well, complete to calculate.Therefore, lumped parameter model has in haemodynamics numerical simulation
Significant effect and important meaning.However since everyone physiological parameter is different, haemodynamics simulation result
Should be different, if the model using identical parameters is emulated, calculated result can not reflect each one itself it is true
Situation, it is difficult to convincing.Most researchers are carrying out haemodynamics to Different Individual using lumped parameter model at present
It is most of to be all based on the method for manually adjusting parameter although having used personalizing parameters when emulation.And this will cause largely
The repeated work of very complicated and inefficiency causes time and human resources when model is complex or data volume is larger
Waste.A kind of method of quick, specific lumped parameter model individualising parameters is provided for personalized haemodynamics
Numbered analog simulation work has great importance, and has certain valence for personalized medical diagnosis on disease, therapeutic strategy research
Value.
Summary of the invention
The present invention provides a kind of based on the lumped parameter model personalized method for improving simulated annealing optimization algorithm, realizes
For the personalization of parameter in Different Individual blood circulation system lumped parameter model.Based on improvement simulated annealing optimization algorithm
Lumped parameter model personalized method includes: the physiology Wave data for acquiring human body, including aortic pressure, cardiac output, neck move
Arteries and veins flow and four limbs pressure waveform；Blood circulation system structure and physiological parameter building based on human body are suitable for the blood of common people
Fluid circulation lumped parameter model；Using collected physiology Wave data as target, to the parameter in lumped parameter model into
Row sensitivity analysis is determined to the biggish sensitive parameter of object effects；Based on improved simulated annealing optimization algorithm, by acquisition
Root-mean-square error between physiology Wave data and calculated simulation waveform is as objective function, in lumped parameter model
Sensitive parameter is iterated optimization；When objective function is less than tolerance, it is believed that optimum results reach acceptable optimal solution, terminate
Optimization exports optimal solution.
In order to achieve the above objectives, the present invention is achieved through the following technical solutions:
Based on the lumped parameter model personalized method for improving simulated annealing optimization algorithm, method includes the following steps:
Step A1: acquisition the actual physiology Wave data of human body, including aortic pressure, cardiac output, Volume of blood foow and
Four limbs pressure waveform；
Step A2: blood circulation system structure and physiological parameter building based on human body are suitable for the blood circulation of common people
System lumped parameter model；
Step A3: using collected actual physiology Wave data as target, to the ginseng in step A2 lumped parameter model
Number carries out sensitivity analysis, determines to the biggish sensitive parameter of object effects；
Step A4: by the actual physiology Wave data of acquisition and the calculated simulation waveform data of lumped parameter model it
Between root-mean-square error as optimization objective function, using improved simulated annealing optimization algorithm, in lumped parameter model
Sensitive parameter be iterated optimization；
Step A5: when objective function is less than tolerance, it is believed that optimum results reach acceptable optimal solution, terminate optimization,
Export optimal solution.
As the further technical solution of the present invention, feature described in step A1, the physiological wave figurate number including acquiring human body
According to wherein the pressure waveform of aortic root is clinically difficult to non-invasively be collected, and the arteria brachialis of upper arm is apart from aorta
Root is not far and pressure waveform at this is easy pressure instead aortic pressure that is collected, therefore can using arteria brachialis.
As the further technical solution of the present invention, feature described in step A2, the blood including being suitable for common people is followed
Loop system lumped parameter model are as follows: the knot of the anatomical structure design lumped parameter model based on normal human blood's circulatory system
The parameter of model is adjusted to that the physiology waveform of common people can be calculated based on the physiological parameter of common people, but needed not be by structure
Personalized Wave data (such as aortic pressure is 80-120mmHg).
As the further technical solution of the present invention, feature described in step A3, including determine the judgement of sensitive parameter according to
According to are as follows: the single each parameter adjusted in lumped parameter model observes it and changes the influence for optimization aim, if working as Parameters variation
When 30%, the shape feature of any 5% or more physiology Wave data Change in Mean or physiology waveform changes in optimization aim
Become, it is when being considered as waveform significant change occurs that the root-mean-square error between the waveform of variation front and back, which is greater than the 5% of waveform mean value,
Think that the parameter is sensitive parameter.
As the further technical solution of the present invention, improved simulated annealing optimization algorithm is used described in step A4, it is right
Sensitive parameter in lumped parameter model be iterated the method for optimization the following steps are included:
Step B1: using each sensitive parameter in step A3 as the initial parameter of optimization；
Step B2: setting needs the search range of Optimal Parameters；
Step B3: it sets the initial temperature T of simulated annealing, the cooling factor, parameter growth/reduction maximum step-length, hold
The parameters such as difference and the termination condition of Optimized Iterative；
Step B4: using improved parameter regulation mode, and loop iteration executes optimization.Traditional simulated annealing optimization algorithm
In every suboptimization, the growth/reduction at random in search range of the parameter of optimization, and by by each parameter optimization in the present invention
The calculated simulation waveform data of model are compared with clinical acquisitions Wave data afterwards, the parameter that will need to optimize according to comparison result
Increased or reduced by assigned direction in search range.If emulation pressure be lower than actual goal pressure, improve resistance and
Voltage source pressure；If the flow of emulation is lower than actual target blood flow, resistance is reduced；If the pressure waveform pulse pressure difference of emulation
Less than the pulse pressure difference of goal pressure waveform, then capacitor is reduced；If the systole phase duration of the cardiac output waveform of emulation is less than target
The systole phase duration of cardiac output waveform, then increase inductance；
Step B5: each parameter for updating front and back is substituted into carry out objective function in lumped parameter model (simulated program) respectively
Calculating, new and old calculated result twice, parameter it is updated solution f (s ') if be less than update before solution f (s), receiving work as
Preceding solution is updated solution, otherwise with probability e-(f(s’)-f(s))/TReceive current solution, the solution is the calculating knot of objective function
Fruit；
Step B6: when meeting termination condition, terminate optimization, otherwise return to step B4.
The beneficial effect of the present invention compared with the prior art is:
The present invention gives it is a kind of quickly, the specific lumped parameter model personalization side based on modified-immune algorithm
Method simplifies the process that lumped parameter model parameter is adjusted for each one, has saved the beam worker that haemodynamics emulates early period
Make the time, have great importance for personalized Hemodynamics Numerical Simulation simulation work, for personalized disease
Diagnosis, therapeutic strategy research have certain value.
Detailed description of the invention
The present invention is based on the implementation flow charts of the lumped parameter model personalization algorithm of simulated annealing improved by Fig. 1
Blood circulation system lumped parameter model schematic diagram in Fig. 2 present invention
The lumped parameter model schematic diagram of Fig. 3 center pulmonary circulation of the present invention；
Enhanced simulated annealing optimizes the algorithm flow chart of parameter in lumped parameter model in Fig. 4 present invention
Lumped parameter model optimum results of Fig. 5 present invention for the physiology Wave data of clinical acquisitions an example individual；
Specific embodiment
The present invention is described in detail below with reference to specific embodiment and attached drawing.
Step A1: the physiology Wave data of clinical acquisitions human body, including aortic pressure, cardiac output, Volume of blood foow and
Four limbs pressure waveform；
Step A2: blood circulation system structure and physiological parameter building based on human body are suitable for the blood circulation of common people
System lumped parameter model；
Step A3: using collected physiological data as target, carrying out sensitivity analysis to the parameter in lumped parameter model,
It determines to the biggish sensitive parameter of object effects；
Step A4: by the root-mean-square error between the calculated simulation waveform of physiology waveform and lumped parameter model of acquisition
The sensitive parameter in lumped parameter model is carried out using improved simulated annealing optimization algorithm as the objective function of optimization
Iteration optimization；
Step A5: when objective function is less than tolerance, it is believed that optimum results reach acceptable optimal solution, terminate optimization,
Export optimal solution.
As the further technical solution of the present invention, feature described in step A1, the physiological wave figurate number including acquiring human body
According to wherein aortic pressure waveform uses the arteria brachialis pressure waveform pressure instead of upper arm.
As the further technical solution of the present invention, feature described in step A2, the blood including being suitable for common people is followed
Loop system lumped parameter model are as follows: the knot of the anatomical structure design lumped parameter model based on normal human blood's circulatory system
The parameter of model is adjusted to that the physiology Wave data of common people can be calculated based on the physiological parameter of common people by structure, but not
Must be personalized Wave data (such as make aortic pressure 80-120mmHg, cardiac output 5L/min by adjusting parameter,
Unilateral carotid flow is 10% i.e. 0.5L/min of cardiac output, and pressure is 70-120mmHg at ankle).The blood of foundation follows
Loop system lumped parameter model as shown in Fig. 2, cardiopulmonary therein circulation lumped parameter model as shown in Figure 3, model include one
A cardiopulmonary cycling element, 18 artery units, 19 intravenous units and 9 Peripheral Microcirculation units, wherein cardiopulmonary cycling element
Including atrium dextrum: resistance RRA, capacitor CRA, right ventricle: resistance RRV, variable capacitance CRV (t), lung: resistance RL, capacitor CL, electricity
Feel LL, atrium sinistrum: resistance RLA, capacitor CLA, left ventricle: resistance RLV, variable capacitance CLV (t), aortic root: resistance R0,
RA, capacitor C0, C1, CA, inductance L0, LA go back to the root of cardiac vein: resistance RV, inductance LV, and are present between atrial ventricle
The valve of diode simulation between left ventricle, aorta；The artery unit of unit A1-A18 expression blood circulation system；
The intravenous unit of V1-V18 expression blood circulation system；The Peripheral Microcirculation unit of P2-P16 expression blood circulation system.And it is each
Arteriovenous unit is made of a resistance R, a capacitor C and an inductance L, and Peripheral Microcirculation unit is by two resistance
Ra, Rv and a capacitor C composition (such as artery unit A1 consisting of RA1, CA1 and LA1).
As the further technical solution of the present invention, feature described in step A3, including determine the judgement of sensitive parameter according to
According to are as follows: the single each parameter adjusted in lumped parameter model observes it and changes the influence for optimization aim, if working as Parameters variation
When 30%, the shape feature of any 5% or more physiology Wave data Change in Mean or physiology waveform changes in optimization aim
Become, the root-mean-square error between the waveform of variation front and back is greater than the 5% of waveform mean value, when being considered as waveform generation significant change
Think that the parameter is sensitive parameter.The sensitive parameter for needing to optimize in the present invention has: R0, C0, L0, RA, CA, RA8, CA8, RA9,
CA9,RA10,CA10,RA11,CA11,RA12,CA12,RA13,CA13,RA14,CA14,RA15,CA15,RA16,CA16,
RA17, CA17, RA18, CA18, Ra2, Ra5, Ra6, Ra7, Ra9, Ra11, Ra13, Ra14, Ra16 and decision voltage source pressure
Parameter EmaxAnd Emin.Wherein parameter EmaxAnd EminApplied to being used to simulate left ventricular pressure in voltage source, to be entire blood
Fluid circulation provides energy source.By applying time-varying function E (t) on the variable capacitance CLV (t) in Fig. 3, voltage is controlled
The pressure in source.The function expression of E (t) are as follows:
E (t)=(Emax-Emin)·En(tn)+Emin
Wherein En(tn) expression formula are as follows:
Wherein tn=t/Tmax, TmaxExpression formula are as follows:
Tmax=0.4tc-0.05
Wherein tcFor personal personalized cardiac cycle.
As the further technical solution of the present invention, improved simulated annealing optimization algorithm flow is used described in step A4
Figure as shown in figure 4, to the sensitive parameter in lumped parameter model be iterated optimization method the following steps are included:
Step B1: using each sensitive parameter in step A3 as the initial parameter a (n) of optimization；
Step B2: the search range [0.1a (n), 2a (n)] of Optimal Parameters needed for setting, the upper limit are each initial parameter
200%, lower limit is the 10% of each initial parameter；
Step B3: the initial temperature T of simulated annealing is set as 100, cooling factor coolingFactor is 0.95, ginseng
The maximum step-length step of number growth/reduction is 10%, and tolerance Tolerance is the 5% of each optimization aim waveform mean value Ave, repeatedly
The termination condition of generation optimization is that new explanation (value of objective function) is less than tolerance；
Step B4: using improved parameter regulation mode, and loop iteration executes optimization.Based on improved simulated annealing optimization
Algorithm, by the calculated simulation waveform of model after each parameter optimization and clinical acquisitions waveform comparison, according to comparison result by need
The parameter to be optimized is increased or is reduced by assigned direction in search range.If the pressure U of emulation is lower than actual goal pressure
Ut, then resistance and voltage source pressure are improved；If the flow I of emulation is lower than actual target blood flow It, then resistance is reduced；If imitative
Genuine pressure waveform pulse pressure difference PP is less than the pulse pressure difference PP of goal pressure waveformt, then capacitor is reduced；If the cardiac output wave of emulation
The systole phase duration T of shapesLess than the systole phase duration T of target cardiac output waveformst, then increase inductance.Based on the above parameter tune
Section mode, when each iteration each sensitive parameter growth/reduction 0-10%, T=T × coolingFactor in search range；
Step B5: respectively by update front and back each parameter substitute into lumped parameter model (simulated function fitness ()) in into
The calculating of row objective function, new and old calculated result twice, updated solution f (s ') of parameter is if be less than the solution f before updating
(s), then receive current solution, otherwise with probability e-(f(s’)-f(s))/TReceive current solution；
Step B6: when meeting termination condition, terminate optimization, otherwise return to step B4.
It include: the physiology number for acquiring human body based on the lumped parameter model personalized method for improving simulated annealing optimization algorithm
According to, including cardiac output, Volume of blood foow and four limbs pressure waveform data；Blood circulation system structure and physiology based on human body
Parameter building is suitable for the blood circulation system lumped parameter model of common people；Using collected physiology Wave data as target,
Sensitivity analysis is carried out to the parameter in lumped parameter model, is determined to the biggish sensitive parameter of object effects；Based on improved
Simulated annealing optimization algorithm, using the root-mean-square error between the physiology Wave data of acquisition and calculated simulation waveform as mesh
Scalar functions are iterated optimization to the sensitive parameter in lumped parameter model；When objective function is less than tolerance, it is believed that optimization knot
Fruit reaches acceptable optimal solution, terminates optimization, exports optimal solution.To the collection of the physiology Wave data of clinical acquisitions an example individual
Middle parameter model optimum results are as shown in Figure 5.
Claims (9)
1. based on the lumped parameter model personalized method for improving simulated annealing optimization algorithm, which is characterized in that this method includes
Following steps:
Step A1: the acquisition actual physiology Wave data of human body, including aortic pressure, cardiac output, Volume of blood foow and four limbs
Pressure waveform；
Step A2: blood circulation system structure and physiological parameter building based on human body are suitable for the blood circulation system of common people
Lumped parameter model；
Step A3: using collected actual physiology Wave data as target, to the parameter in step A2 lumped parameter model into
Row sensitivity analysis is determined to the biggish sensitive parameter of object effects；
Step A4: will be between the calculated simulation waveform data of actual physiology Wave data and lumped parameter model of acquisition
Objective function of the root-mean-square error as optimization, using improved simulated annealing optimization algorithm, to quick in lumped parameter model
Sense parameter is iterated optimization；
Step A5: when objective function is less than tolerance, it is believed that optimum results reach acceptable optimal solution, terminate optimization, output
Optimal solution.
2. the lumped parameter model personalized method described in accordance with the claim 1 based on improvement simulated annealing optimization algorithm,
It is characterized in that, the physiology Wave data of human body is acquired in step A1, wherein the pressure waveform of aortic root is clinically difficult to
Non-invasively be collected, and the arteria brachialis of upper arm is not far apart from aortic root and pressure waveform at this be easy it is collected, therefore can
With the pressure instead aortic pressure of arteria brachialis.
3. the lumped parameter model personalized method described in accordance with the claim 1 based on improvement simulated annealing optimization algorithm,
It is characterized in that, the blood circulation system lumped parameter model of common people is used in step A2 are as follows: recycled based on normal human blood
The parameter of model, is adjusted to by the structure of the anatomical structure design lumped parameter model of system based on the physiological parameter of common people
The physiology waveform of common people can be calculated, but needs not be personalized Wave data.
4. the lumped parameter model personalized method described in accordance with the claim 1 based on improvement simulated annealing optimization algorithm,
It is characterized in that, the judgment basis of sensitive parameter is determined in step A3 are as follows: the single each parameter adjusted in lumped parameter model, observation
It changes the influence for optimization aim, if any physiology Wave data mean value becomes in optimization aim when Parameters variation 30%
The shape feature of 5% or more change or physiology waveform changes, and the root-mean-square error between the waveform of variation front and back is greater than waveform
When the 5% of mean value is considered as waveform generation significant change, i.e., it is believed that the parameter is sensitive parameter.
5. the lumped parameter model personalized method described in accordance with the claim 1 based on improvement simulated annealing optimization algorithm,
Be characterized in that, described in step A4 use improved simulated annealing optimization algorithm, to the sensitive parameter in lumped parameter model into
Row iteration optimization method the following steps are included:
Step B1: using each sensitive parameter in step A3 as the initial parameter of optimization；
Step B2: setting needs the search range of Optimal Parameters；
Step B3: set simulated annealing initial temperature T, cooling the factor, parameter growth/reduction maximum step-length, tolerance, with
And the parameters such as termination condition of Optimized Iterative；
Step B4: using improved parameter regulation mode, and loop iteration executes optimization, by by model meter after each parameter optimization
The simulation waveform data of calculating are compared with clinical acquisitions Wave data, according to comparison result by the parameter for needing to optimize in search model
Increased or reduced by assigned direction in enclosing；
Step B5: each parameter for updating front and back is substituted into lumped parameter model (simulated program) to the meter for carrying out objective function respectively
It calculates, new and old calculated result twice, updated solution f (s ') of parameter receives current solution if being less than the solution f (s) before updating
I.e. updated solution, otherwise with probability e-(f(s’)-f(s))/TReceive current solution, the solution is the calculated result of objective function；
Step B6: when meeting termination condition, terminate optimization, otherwise return to step B4.
6. the lumped parameter model personalized method according to claim 5 based on improvement simulated annealing optimization algorithm,
It is characterized in that,
Step B4: using improved parameter regulation mode, the method that loop iteration executes optimization, if the pressure of emulation is lower than practical
Goal pressure, then improve resistance and voltage source pressure；If the flow of emulation is lower than actual target blood flow, electricity is reduced
Resistance；If the pressure waveform pulse pressure difference of emulation is less than the pulse pressure difference of goal pressure waveform, capacitor is reduced；If the cardiac output of emulation
The systole phase duration of waveform is less than the systole phase duration of target cardiac output waveform, then increases inductance.
7. the lumped parameter model personalized method according to claim 5 based on improvement simulated annealing optimization algorithm,
Be characterized in that, described in step A4 use improved simulated annealing optimization algorithm, to the sensitive parameter in lumped parameter model into
Row iteration optimization method the following steps are included:
Step B1: using each sensitive parameter in step A3 as the initial parameter a (n) of optimization；
Step B2: the search range [0.1a (n), 2a (n)] of Optimal Parameters needed for setting, the upper limit are the 200% of each initial parameter,
Lower limit is the 10% of each initial parameter；
Step B3: the initial temperature T of simulated annealing is set as 100, cooling factor coolingFactor is 0.95, and parameter increases
The maximum step-length step of length/reduction is 10%, and tolerance Tolerance is the 5% of each optimization aim waveform mean value Ave, and iteration is excellent
The termination condition of change is that new explanation (value of objective function) is less than tolerance；
Step B4: using improved parameter regulation mode, and loop iteration executes optimization.It is calculated based on improved simulated annealing optimization
Method, by the calculated simulation waveform of model after each parameter optimization and clinical acquisitions waveform comparison, according to comparison result by needs
The parameter of optimization is increased or is reduced by assigned direction in search range.If the pressure U of emulation is lower than actual goal pressure Ut,
Then improve resistance and voltage source pressure；If the flow I of emulation is lower than actual target blood flow It, then resistance is reduced；If emulation
Pressure waveform pulse pressure difference PP be less than goal pressure waveform pulse pressure difference PPt, then capacitor is reduced；If the cardiac output waveform of emulation
Systole phase duration TsLess than the systole phase duration T of target cardiac output waveformst, then increase inductance.Based on the above parameter regulation
Mode, when each iteration each sensitive parameter growth/reduction 0-10%, T=T × coolingFactor in search range；
Step B5: each parameter for updating front and back is substituted into carry out mesh in lumped parameter model (simulated function fitness ()) respectively
The calculating of scalar functions, new and old calculated result twice, parameter it is updated solution f (s ') if be less than update before solution f (s),
Receive current solution, otherwise with probability e-(f(s’)-f(s))/TReceive current solution；
Step B6: when meeting termination condition, terminate optimization, otherwise return to step B4.
8. the lumped parameter model personalized method described in accordance with the claim 1 based on improvement simulated annealing optimization algorithm,
It is characterized in that, blood circulation system lumped parameter model includes a cardiopulmonary cycling element, 18 artery units, 19 vein lists
Member and 9 Peripheral Microcirculation units, wherein cardiopulmonary cycling element includes atrium dextrum: resistance RRA, capacitor CRA, right ventricle: resistance
RRV, variable capacitance CRV (t), lung: resistance RL, capacitor CL, inductance LL, atrium sinistrum: resistance RLA, capacitor CLA, left ventricle: resistance
RLV, variable capacitance CLV (t), aortic root: resistance R0, RA, capacitor C0, C1, CA, inductance L0, LA return the root of cardiac vein
Portion: resistance RV, inductance LV, and be present between atrial ventricle between left ventricle, aorta diode simulation valve；
The artery unit of unit A1-A18 expression blood circulation system；The intravenous unit of V1-V18 expression blood circulation system；P2-P16
Indicate the Peripheral Microcirculation unit of blood circulation system；And each arteriovenous unit is by a resistance R, a capacitor C and one
Inductance L composition, and Peripheral Microcirculation unit is made of two resistance Ra, Rv and a capacitor C.
9. the lumped parameter model personalized method according to claim 8 based on improvement simulated annealing optimization algorithm,
It is characterized in that,
The sensitive parameter for needing to optimize has: R0, C0, L0, RA, CA, RA8, CA8, RA9, CA9, RA10, CA10, RA11, CA11,
RA12,CA12,RA13,CA13,RA14,CA14,RA15,CA15,RA16,CA16,RA17,CA17,RA18,CA18,Ra2,
Ra5, Ra6, Ra7, Ra9, Ra11, Ra13, Ra14, Ra16 and the parameter E for determining voltage source pressuremaxAnd Emin.Wherein parameter
EmaxAnd EminApplied to being used to simulate left ventricular pressure in voltage source, to provide energy source for entire blood circulation system；
By applying time-varying function E (t) on the variable capacitance CLV (t) in cardiopulmonary cycling element, the pressure of voltage source is controlled.E(t)
Function expression are as follows:
E (t)=(Emax-Emin)·En(tn)+Emin
Wherein En(tn) expression formula are as follows:
Wherein tn=t/Tmax, TmaxExpression formula are as follows:
Tmax=0.4tc-0.05
Wherein tcFor personal personalized cardiac cycle.
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