CN116796656B - Method for estimating lumped parameter respiratory system model parameters - Google Patents
Method for estimating lumped parameter respiratory system model parameters Download PDFInfo
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- CN116796656B CN116796656B CN202310553702.1A CN202310553702A CN116796656B CN 116796656 B CN116796656 B CN 116796656B CN 202310553702 A CN202310553702 A CN 202310553702A CN 116796656 B CN116796656 B CN 116796656B
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- 210000002345 respiratory system Anatomy 0.000 title claims abstract description 43
- 238000000034 method Methods 0.000 title claims abstract description 35
- 239000011159 matrix material Substances 0.000 claims description 15
- 230000029058 respiratory gaseous exchange Effects 0.000 claims description 12
- 230000001133 acceleration Effects 0.000 claims description 3
- 238000005070 sampling Methods 0.000 claims description 3
- 230000000241 respiratory effect Effects 0.000 abstract description 6
- 238000009423 ventilation Methods 0.000 abstract description 2
- 230000004069 differentiation Effects 0.000 description 8
- 238000004422 calculation algorithm Methods 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 4
- 238000007429 general method Methods 0.000 description 2
- 230000010354 integration Effects 0.000 description 2
- 238000005399 mechanical ventilation Methods 0.000 description 2
- 238000009795 derivation Methods 0.000 description 1
- 238000013213 extrapolation Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Abstract
The method is used for estimating the parameters of the lumped parameter respiratory system model, and based on the pressure value, the flow velocity value and the accumulated gas quantity of the respiratory circuit collected in real time in any ventilation mode, each parameter of the lumped parameter respiratory system model in any order can be estimated efficiently and simply according to the method.
Description
Technical Field
The present application relates to respiratory system models, and more particularly to a method for estimating lumped parameter respiratory system model parameters.
Background
In respiratory mechanical ventilation research, a non-lumped parameter respiratory system model can be asymptotically utilized by a finite-order lumped parameter model, and parameter estimation of the lumped parameter respiratory system model is an important link for researching respiratory system characteristics and applying medical intelligent mechanical ventilation. At present, a general method for efficiently and simply estimating various constant coefficient parameters of any lumped parameter respiratory system model is lacked.
Disclosure of Invention
In view of the above problems, the present application aims to provide a method for estimating parameters of a lumped parameter respiratory system model, which is used for estimating the parameters of the lumped parameter respiratory system model, and based on real-time acquisition of a pressure value, a flow velocity value and an accumulated gas volume of a respiratory circuit in any ventilation mode, each parameter of an arbitrary order lumped parameter respiratory system model can be estimated efficiently and simply according to the method provided in the present application.
The method of the present application for estimating lumped parameter respiratory system model parameters, wherein,
the lumped parameter respiratory system model is expressed as:
P＝a 0 V+a 1 V′+a 2 V″+…+a k V (k) +P 0 ；
wherein P is air pressure, V is the 1 st derivative of V' in the input total air formula, and represents the volume flow rate;v' is the 2 nd derivative of V and represents the airflow acceleration; v (V) (k) K-th derivative of V;
P 0 is the initial pressure in the respiratory system;
a 0 、a 1 、a 2 、…、a k coefficient parameters, a, of a lumped parameter respiratory system model 0 Is elastic; a, a 1 Is airway resistance; a, a 2 Is the inertial resistance coefficient;
using matricesObtaining fitting results of various coefficients;
wherein,m is the number of terms of the lumped parameter respiratory system model;
the matrix X is an n-row m-column matrix;
is an n-dimensional barometric pressure vector, which is composed of P values of n time sampling points of a breathing circuit.
Preferably, the numerical initial value of the derivative of V above 2 nd order is set to 0, and the k-th order derivative term value at the other timing t is calculated as follows:
where h is the time step.
Preferably, when the lumped parameter respiratory system model is a first order linear model, the lumped parameter respiratory system model is expressed as:
P＝a 0 V+a 1 V′+P 0 ；
wherein,
the method for estimating the parameters of the lumped parameter respiratory system model can be suitable for the lumped parameter respiratory system model of each order, is a general method, and can be used for conveniently and rapidly estimating the coefficient parameters.
Drawings
FIG. 1 is a comparison of the parameter estimation of the lumped parameter respiratory system model of equation 1 with the measured data respiration volume by the method of estimating the lumped parameter respiratory system model parameters of the present application;
FIG. 2 is a comparison of the parameter estimation of the lumped parameter respiratory system model of equation 2 with the measured data respiration volume by the method of estimating the lumped parameter respiratory system model parameters of the present application;
Detailed Description
The method for estimating the parameters of the lumped parameter respiratory system model is described in detail below with reference to the accompanying drawings.
1. Presetting the number m of lumped parameter respiratory system model items to be fitted and a corresponding form.
Taking m=5 as an example, i.e. there are 5 terms, the lumped parameter respiratory system model has the following form:
P＝a 0 V+a 1 V′+a 2 (V) 2 +a 3 (V′) 2 +P 0
wherein the relation between P air pressure and total input air volume V in the respiratory system is described, wherein V 'is the 1 st derivative of V, namely the air flow velocity, V' is the 2 nd derivative, namely the air flow acceleration, P 0 Is the initial pressure within the respiratory system. At this time a 0 I.e. the elasticity (or reciprocal of the compliance) in a typical breathing model, and a 1 Resistance to the airway, a 2 Is the inertial resistance coefficient.
For higher order system cases, the lumped parameter respiratory system model has the following form:
P＝a 0 V+a 1 V′+a 2 V″+…+a k V (k) +P 0
v in (k) Representing the k-th derivative.
The preset model can contain a i (V′) 2 、a j e V″ The principle of the constant coefficient nonlinear term estimation method is that the constant coefficient nonlinear term is obtained based on the fact that the coefficient partial derivative of each term is 0, and the fact that the corresponding term numerical sequence in the input matrix in the next step corresponds to the preset model term one by one is guaranteed.
2. And collecting the pressure value, the flow velocity value and the accumulated gas value of the breathing circuit in real time, and sorting the pressure value, the flow velocity value and the accumulated gas value into corresponding matrix form data according to the number m and the corresponding form of a preset model term and a numerical differentiation method to be used as algorithm input.
If the value of the acquired breathing circuit is n time points, the input data are n-dimensional barometric pressure vector P and n rows and m columns of data matrix X:
the medium-high order differential value can be obtained by a numerical differential method with proper precision, such as a three-point formula based on interpolation, a Simpson numerical differential formula or an extrapolation method. The numerical differentiation method of which accuracy is selected is not the key point of the algorithm, optionally, at the beginning and end of the respiratory cycle (differentiation end point), the numerical initial value of the higher-order differentiation (2 nd order derivative and above) in the above formula is optionally set to 0, and the numerical value of the kth order differentiation term at other time sequences t is as follows (midpoint formula):
where h is the time step.
If the flow rate value and the accumulated gas value are limited by the sampling condition, only one of the flow rate value and the accumulated gas value, the other missing value can be obtained by a proper value differentiation and value integration method.
3. And calculating according to the following matrix to obtain fitting results of various coefficients.
Wherein each coefficient vector a is as follows:
in the above formula, the m-dimensional A vector corresponds to each coefficient to be estimated and fitted, and only involves 2 matrix multiplications, 1 inversion and 1 matrix vector multiplication.
The algorithm method for estimating and fitting each constant coefficient parameter by the lumped parameter respiratory system model is derived based on the extreme point with each bias of 0.
In algorithm derivation, for a specified fitting target, for example, the sum of squares SSR (sum of squared residuals) of residuals or other similar important fitting indexes can be selected, when the fitting target takes the minimum value, the partial derivatives of all coefficients in the lumped model are 0, and at this time, all coefficients to be fitted can be solved by a series of 1-time equations. The nonlinear term pair coefficient bias is still the 1 st order term of the constant coefficient to be estimated, so the parameter estimation method is the same. For clearer presentation, the calculation mode of each coefficient can be further written as a matrix solving mode.
Solving each order coefficient by taking extremum bias as 0 for fitting target is characterized by the method, the change of the form of the arithmetic writing method still belongs to the category of the method, for example, the matrix solving form is disassembled into the following estimation mode of each order coefficient (1-order linear model P=a 0 V+a 1 V′+P 0 Equivalent arithmetic is taken as an example)：
In the process of preparing input data, the selection of numerical differentiation and numerical integration methods with different accuracies is not the core of the method, and the whole framework of the same type of method after replacement and change still belongs to the category of the method.
Next, by using the method of the present application, the lumped parameter respiratory system models of formulas 1 and 2 are estimated separately and compared with the actually measured respiratory amount.
P＝a 0 V+a 1 V′+a 2 V″+a 3 ln(V+1)+P 0 (1)
The parameter estimation is based on animal experimental measured data (obtained by actual measurement of a Delge Savina 300 ventilator), and data of pressure P (unit mbar), flow velocity V' (unit L/s) and respiration volume V (unit L) of each 10 milliseconds in time sequence are recorded as one line (data see data. Txt, 150 seconds data are intercepted).
For the nonlinear equation of formula 1, V "and the corresponding value obtained using the numerical differentiation method, ln (v+1) is substituted into the value of V, and is sorted into the following numerical matrix form in each order as input.
Then, p0= 3.47632212, a0= 57.29251258, a1= 7.17413342, a2= 4.47134159 and a3= -36.22221325 in the formula 1 are calculated by using the method proposed by the patent. Corresponding to the model represented by equation 1, the correlation coefficient 0.7891 between the calculated breathing amount (dotted line) and the measured breathing amount (solid line) is substituted into the parameter calculation, as shown in fig. 1.
P＝a 0 V+a 1 V′+a 2 V″+P 0 (2)
For equation 2, the matrix input data matrix can be obtained based on the measured data, and p0= 3.39674027, a0= 26.11755376, a1= 7.17137465, a2= 0.08733642 can be obtained using the calculation method of this patent. The correlation coefficient between the calculated breathing amount (dotted line) and the measured breathing amount (solid line) of the corresponding model (2) is 0.9970 (the preset model 2 in the example is more consistent with the measured data characteristic than the model 1), as shown in fig. 2.
By using the method, various constant coefficient parameters of any lumped respiratory system model can be estimated, the calculation is efficient and simple, and the data acquisition does not require a specific respiratory mode.
Unless defined otherwise, all technical and/or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The materials, methods, and examples mentioned in this application are illustrative only and not intended to be limiting.
Although the present invention has been described in connection with specific embodiments thereof, those skilled in the art will appreciate that various substitutions, modifications and changes may be made without departing from the spirit of the invention.
Claims (2)
1. A method for estimating lumped parameter respiratory system model parameters, wherein,
the lumped parameter respiratory system model is expressed as:
P＝a 0 V+a 1 V′+a 2 V″+…+a k V (k) +P 0 ；
wherein P is air pressure, V is total input air quantity, V' is 1-order derivative of V, and the flow rate of the air is represented; v' is the 2 nd derivative of V, representing the airflow acceleration; v (V) (k) K-th derivative of V;
P 0 is the initial pressure in the respiratory system;
a 0 、a 1 、a 2 、...、a k coefficient parameters, a, of a lumped parameter respiratory system model 0 Is elastic; a, a 1 Is airway resistance; a, a 2 Is the inertial resistance coefficient;
using matricesObtaining fitting results of various coefficients;
wherein,m is the number of terms of the lumped parameter respiratory system model;
the matrix X is an n-row m-column matrix;
is an n-dimensional barometric pressure vector, which is composed of P values of n time sampling points of a breathing circuit;
the initial value of the derivative of V above 2 th order is set to 0, and the value of the kth order derivative term at the other time t is calculated as follows:
where h is the time step.
2. The method of estimating lumped parameter respiratory system model parameters as recited in claim 1 wherein:
when the lumped parameter respiratory system model is a first order linear model, the lumped parameter respiratory system model is expressed as:
P＝a 0 V+a 1 V′+P 0 ；
wherein,
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