Method for modeling respiratory system based on mixed model and electronic device

Abstract

A method for modelling a respiratory system based on a mixed model, comprising: constructing an initial respiratory system mechanical model based on a fractional calculus and double-exponential function mixed model; the initial respiratory system mechanical model characterised by an equation including terms for respiratory pressure at time t, respiratory system elasticity, respiratory volume at time t, Airway resistance, gas flow speed at time t, positive end expiratory pressure, constant coefficients, exponential parameters, fractional derivatives of the respiratory volume and double exponential terms. The method comprises acquiring measured data, wherein the measured data comprises a pressure value, a flow speed value and a respiratory volume value of the respiratory system collected in real time, then optimising the parameters and substituting the optimal exponential parameters into the initial respiratory system mechanical model to obtain an optimized respiratory system mechanical model.

Description

TECHNICAL FIELD [00011 The present disclosure relates to the technical field of respiratory system simulation, in particular to a method for modeling a respiratory system based on a mixed model and an electronic device. BACKGROUND

[0002] In the study of mechanical ventilation of a respiratory system, lung tissues have certain path-dependent viscoelasticity, heterogeneity and step response characteristics. Especially in a pressure control ventilation mode, the path-dependent viscoelasticity and heterogeneity are obvious, while in a volume control ventilation mode, the step response characteristic is obvious. It is difficult to describe and reflect the characteristics well by using a classical lumped parameter model based on differential equations. Research on these problems is conducive to deeply understanding the characteristics of the respiratory system and reducing the ventilation damage resulted from a ventilator. SUMMARY

[0003] In order to solve the above problems in the prior art, the present disclosure provides a method for modeling a respiratory system based on a mixed model and an electronic device.

[0004] In order to achieve the above objects, the present disclosure provides the following scheme.

[0005] A method for modeling a respiratory system based on a mixed mode includes:

[0006] constructing an initial respiratory system mechanical model based on a fractional calculus and double-exponential function mixed model;

[0007] acquiring measured data, where the measured data includes pressure value, flow speed value and respiratory volume value of a respiratory system collected in real time;

[0008] determining matrix-form data, where the matrix-form data is matrix data corresponding to a form of the fractional calculus and double-exponential function mixed model;

[0009] inputting the matrix-form data into the initial respiratory system mechanical model to obtain fitting results of various coefficients under a condition of specifying a set of initialization exponential parameters;

[0010] substituting the measured data into the initial respiratory system mechanical model on a basis of the fitting results of various coefficients, performing optimization iteration until a residual square or a root mean square error of an obtained initial respiratory system mechanical model is minimum, and determining the exponential parameters that minimize the residual square or the root mean square error of the obtained initial respiratory system mechanical model as optimal exponential parameters;

[0011] substituting the optimal exponential parameters into the initial respiratory system mechanical model to obtain an optimized respiratory system mechanical model.

[0012] In an embodiment, the determining matrix-form data includes:

[0013] obtaining a total number of fractional calculus terms and total number of double-exponential terms of the fractional calculus and double-exponential function mixed model according to the measured data under a condition of specifying a set of fractional order and exponential parameters;

[0014] collating the measured data into the matrix-form data based on the total number of fractional calculus terms and the total number of double-exponential terms.

[0015] In an embodiment, a particle swarm algorithm is used to carry out optimization iteration.

[0016] In an embodiment, the initial respiratory system mechanical model is:

[0017] P(t) = EV(t) + RV'(t) + ^2)^(7(0) + k2eea2VWV(t) - + + kmeeamV^V(t) + Po;

[0018] where P(t) is a respiratory pressure at time t, E is a respiratory system elasticity, V(t) is a respiratory volume at time t, R is an airway resistance, V'(t) is a gas flow speed at time t, PQ is a positive end expiratory pressure, {k^ k2,..., km} are constant coefficients of fractional calculus term and double-exponential term, {a1,a2,---,am} are exponential parameters, 2)^(7(0) is at -th fractional derivative of the respiratory volume 7(0, ee* is a double-exponential form with the natural base e as a base, and (7(0) is the a^-i-th fractional derivative of the respiratory volume V(0.

[0019] In an embodiment, the initial respiratory system mechanical model after simplified is:

[0020] P(t) = EV^ + RV'(t) + ^2)^(7(0) + / c2eea2lz(t)7(0 + Po.

[0021] In an embodiment, when values of the respiratory system at n time points are collected, the matrix-form data includes n-dimensional air pressure vector and a data matrix with n rows and m+3 columns.

[0022] An electronic device, includes:

[0023] a memory, in which a computer program is stored;

[0024] a processor, connected with the memory and configured to call and execute the computer program to implement the method for modeling the respiratory system based on the mixed model provided above.

[0025] In an embodiment, the memory is a computer-readable storage medium.

[0026] According to a specific embodiment provided by the present disclosure, the present disclosure provides the following technical effects.

[0027] According to the method, a fractional calculus term and a double-exponential function term are used for mechanical modeling of the respiratory system, and an optimized mechanical model of the respiratory system is obtained through optimization iteration, so that the path-dependent viscoelasticity, heterogeneity and step response characteristics of the respiratory system can be reflected. It is easier to obtain a better fitting degree compared with the classical respiratory mechanics (single-compartment) model. Moreover, the data acquisition of the present disclosure does not require a specific respiratory mode, which is more conducive to deeply understanding the characteristics of the respiratory system and reducing the ventilation damage resulted from a ventilator. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to explain the embodiments of the present disclosure or the technical schemes in the prior art more clearly, the drawings that need to be used in the embodiments will be briefly introduced hereinafter. Obviously, the drawings in the following description are only some embodiments of the present disclosure. For those skilled in the art, other drawings can be obtained according to these drawings without creative labor.

[0029] FIG. 1 is a flowchart of a method for modeling a respiratory system based on a mixed model according to the present disclosure.

[0030] FIG. 2 is a schematic diagram showing comparison results of simulated data and measured data of different models according to the present disclosure. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] The technical schemes in the embodiments of the present disclosure will be clearly and completely described with reference to the drawings in the embodiments of the present disclosure hereinafter. Obviously, the described embodiments are only some embodiments of the present disclosure, rather than all of the embodiments. Based on the embodiment of the present disclosure, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present disclosure.

[0032] The purpose of the present disclosure is to provide a method for modeling a respiratory system based on a mixed model and an electronic device, which reflects a better fitting degree than the classical model when using the measured data, and is capable of being suitable for describing the path-dependent viscoelasticity, heterogeneity and step response characteristics of the respiratory system at the same time, thus facilitating deeply understanding the characteristics of the respiratory system and reducing the ventilation damage resulted from a ventilator.

[0033] In order to make the above objects, features and advantages of the present disclosure more obvious and understandable, the present disclosure will be explained in further detail with reference to the drawings and detailed description hereinafter.

[0034] As shown in FIG. 1, the method for modeling the respiratory system based on the mixed model according to the present disclosure includes the following steps.

[0035] Step 100: an initial respiratory system mechanical model is constructed based on a fractional calculus and double-exponential function mixed model; where a general form of the initial respiratory system mechanical model is:

[0036] P(t) = EV(t) + RV\t) + k^^V^) + k2eea2V^V(t) - + km_^m~^V(tS) + kmeeamVWV(t) + Po;

[0037] where P(t) is the respiratory pressure at time t, E is the respiratory system elasticity, V(t) is the respiratory volume at time t, R is the airway resistance, V'(0 is the gas flow speed at timet, PQ is the positive end expiratory pressure, and {k^, k2,..., km} are constant coefficients of fractional calculus term and double-exponential term. {alt a2, •••, am} are exponential parameters, such as 1 .6, 8 .5, etc. 2)^(7(0) is the at-th fractional derivative of the respiratory volume F(0, which may be a p-th derivative with p of a non-integer such as 1 .51 and 6.37. 2)^^(100) is the am_1 -th fractional derivative of the respiratory volume. ee* is a double-exponential form with the natural base e as the base. is a double-exponential form with as an exponential and the natural base e as the base. a2 is the coefficient to be estimated in the exponential parameter. For example, c represents that the uppermost right corner e2 is first calculated, that is, the square of the natural base e is about 7.389, and then e7 j89 is calculated.

[0038] In practical application, it can be simplified to reflect the path-dependent viscoelasticity, heterogeneity and step response characteristics of the respiratory system by using a few fractional calculus terms and double-exponential terms (generally, the number of several double-exponential terms is the same as that of step jumps in the respiratory volume). Based on this, the initial respiratory system mechanical model after simplification is as follows:

[0039] P(t) = FK(t) + RV\t) +            + / c2ee"2       + Po

[0040] Step 101: measured data is acquired. For example, for the initial respiratory system mechanical model with m fractional calculus terms and double-exponential terms (including three terms EV(t), RV'(t) and PQ, that is, m+3 terms in total), data such as the pressure value, the flow speed value and the respiratory volume value of the respiratory system can be collected in real time as measured data.

[0041] Step 102: matrix-form data is determined, where the matrix-form data is the matrix data corresponding to the form of the fractional calculus and double-exponential function mixed model.

[0042] Specifically, according to the total number m of fractional calculus terms and double-exponential terms of the initial respiratory system mechanical model and their corresponding forms, as well as a set of specified fractional order and exponential parameters, the values of fractional calculus terms and double-exponential terms are obtained, which are then sorted into corresponding matrix-form data. In some embodiments, the total number of fractional calculus terms and double-exponential terms are obtained. Moreover, the matrix-form data is used as input data. That is, when am is specified, the value of the double-exponential term eeXmV^y eeamVmV(t) can be calculated correspondingly, and the same is true after the fractional calculus term is specified with a fixed fractional order. If values of the respiratory system are collected at n time points, for example, values of the respiratory system, i.e., respiratory mechanics data, are collected every few miliseconds over a period of time, the input data includes n-dimensional air pressure vector P and a data matrix X with n rows and m+3 columns. The air pressure vector P and the data matrix X are:

[0043] P = \ : v' V.1

[0044] X=\ v2 v‘ ym * N [00451 where V™ (the second column from the right of the data matrix X) is the value except the constant coefficient obtained by combining the double-exponential term, / =1, 2, and the same is true for other corresponding fractional calculus terms and double-exponential terms. If there is only one of the flow velocity value and the respiratory volume value limited by 5 sampling conditions, the other missing value can be obtained by using the same principle through appropriate numerical differentiation and numerical integration methods.

[0046] Step 103: the matrix-form data is input into the initial respiratory system mechanical model to obtain fitting results of various coefficients under the condition of specifying a set of initialization exponential parameters.

[0047] For example, for the initial respiratory system mechanical model with m fractional calculus terms and double-exponential terms, after a set of initial exponential parameters are specified, the fitting results of various coefficients can be obtained by carrying out matrix calculation according to the equation A = \XTX\ 'XTP, where Tis transposed.

[0048] Various coefficient vector A is as follows:

[0049] A =

[0050] The calculation method proposed in the above equation is derived from an extreme point where the partial derivative for each coefficient is 0 when the sum of squared residuals (SSR) is set as a minimum value.

[0051] Step 104: the measured data is substituted into the initial respiratory system mechanical model on the basis of the fitting results of various coefficients, optimization iteration is performed until a residual square or a root mean square error of the obtained initial respiratory system mechanical model is minimum, and the exponential parameters that minimize the residual square or the root mean square error of the obtained initial respiratory system mechanical model are determined as the optimal exponential parameters.

[0052] In the practical utilization process, after various coefficients of the specified fractional calculus term and the double-exponential model are obtained, the measured data can be substituted into the model to simulate and calculate the sum of squared residuals (SSR) and the root mean square error (RMSE) of corresponding model. In order to optimize and obtain the most appropriate series of exponential parameters {a^, a2, , am}, the present disclosure selects the particle swarm algorithm for iteration and optimization among various machine learning algorithms in consideration of computational efficiency. In genetic algorithms, simulated annealing and other similar algorithms, although the particle swarm algorithm may fall into a local optimal solution, the particle swarm algorithm converges faster and timeliness is more emphasized in practical application.

[0053] In the iteration and optimization process, parameters to be optimized is a series of exponential parameters {a1,a2, , am). After a set of exponential parameters is specified, the SSR / RMSE can be obtained based on all coefficients obtained in step 103. Various parameters can be continuously updated following the change trend of the SSR or the RMSE so as to minimize the SSR or RMSE. The following model better than the initial respiratory system mechanical model can be obtained after iteration and calculation.

[0054] In this process, the selection of machine learning algorithms is not the core of the present disclosure. After the same type of methods is replaced or changed, its overall framework still falls within the scope of protection of the present disclosure.

[0055] Step 105: the optimal exponential parameters are substituted into the initial respiratory system mechanical model to obtain an optimized respiratory system mechanical model.

[0056] Based on the above description, at present, there is no method to model the mechanics of the respiratory system by using the fractional calculus term and the double-exponential function term at the same time based on the measured data in any respiratory mode. The present disclosure provides a comprehensive mixed model that is feasible in actual measurement, which can reflect the path dependence viscoelasticity, heterogeneity and step response characteristics of the respiratory system. It is easier to obtain a better fitting degree compared with the classical respiratory mechanics (single-compartment) model.

[0057] The following examples illustrate the advantages of the method for modeling the respiratory system based on the mixed model according to the present disclosure.

[0058] In respiratory mechanics modeling, the classical single-compartment model is:

[0059] P = EV + RV +P0 (1)

[0060] Based on such traditional model, the calculation results are showed by supplementing the example of the mixed model containing a fractional calculus term and a double-exponential term, and the parameters of the following models [i.e. equation (2)] are estimated by using the method in the present disclosure:

[0061] P(t) = EV(t) + RV'(t) + + fc2ee“2mV(t) + Po (2)

[0062] In addition, the same data comparison is also performed on the model containing only the double-exponential term [i.e. equation (3)] and the model containing only the fractional calculus terms [i.e. equation (4)].

[0063] P(l) = EV(t) + RV (t) + aeeXVmV(t) + Po (3)

[0064] P(t) = EV(t) + RV (t) + + PQ (4)

[0065] The parameter estimation is based on the measured data of animal experiments (measured by Savina 300 ventilator of Draeger). The data of the pressure P (in unit of mbar), the flow velocity V (in unit of L / s) and the respiratory volume V (in unit of L) every 10ms are recorded as one row in chronological order (for the data, see caselVCACl.txt, and the data is intercepted for 150s).

[0066] Based on the example python+matlab code main.m (other *.py and *.m are python and matlab subfunctions called by the main code, and *.slx is the model file), the calculation results of three model parameters after reading the measured data are shown in Table 1.

[0067] Table 1: Parameter Estimation Result Table Of Each Model Type of models Estimated parameters and index results Single-compartment model E=27.4861, R=6.1912, P0=3.4041, BIC=-1352.4948, RMSE=7.7975, run_time=0.3069(s) model 2 [i.e. equation (2)] E=26.4259, R=6.0850, P0=3.4188, al=1.5112, al=10.6234, kl=0.0911, k2=1.0863e-10, BIC=-9608.386, RMSE=5.9140, run_time=374.3595(s) model 3 [i.e. equation (3)] E=25.7550, R=6.2159, a=9.6002e-08, x= 9.5421, P0=3.4504, BIC=-7665.8O15, RMSE= 6.3137, run_time= 297.01853(s) model 4 [i.e. equation (4)] E=27.6924, R=6.0834, kl=0.0778, al= 1.5351, P0=3.3860, BIC=-2218.1298, RMSE= 7.5709, run_time= 309.2401(s)

[0068] In Table 1, four decimal places are reserved, the RMSE is converted into the unit of milliliter, and run_time indicates running time (running on an ordinary PC with CPU i7-1165G7 @ 2.80GHz and a memory of 16GB).

[0069] It can be seen from the result that the mixed model proposed in the present disclosure is practical and effective, and with the best result among all models. And the mixed model has lower Bayesian Information Criterion (BIC) and lower Root Mean Square Error ( RMSE ) values. Further, the measured data and the flow fitting of equation (1) and equation (2) are shown in FIG. 2. FIG. 2 shows the results of 20 iterations of 20 particles, in which Measured Data indicates the measured data, model (1) indicates the classical single-compartment model, and mix model(2) indicates the better double-exponential model provided by the present disclosure. As can be seen from the results in FIG. 2, results of the mixed model are closer to the measured data.

[0070] Based on this, the calculation amount of the present disclosure is higher than that of the classical single-compartment model in the existing respiratory mechanics modeling. Correspondingly, more calculation amount is required to obtain a better fitting effect in the measured data, and the increased calculation amount is positively correlated to the number of parameters to be fitted.

[0071] Further, in the practical utilization process, based on the real-time acquisition of the pressure value, the flow velocity value and the respiratory volume of the respiratory system in any ventilation mode, a corresponding respiratory system mechanical model can be quickly obtained according to the method proposed in the present disclosure, including the most appropriate fractional order, exponential parameters and various coefficient parameters.

[0072] Further, the present disclosure further provides an electronic device. The electronic device includes a memory and a processor. The processor is connected with the memory.

[0073] A computer program is stored in the memory. The processor is configured to call and execute the computer program to implement the method for modeling the respiratory system based on the mixed model provided above.

[0074] In addition, the computer program in the above-mentioned memory can be stored in a computer-readable storage medium when being implemented in the form of software functional units and sold or used as an independent product. Based on this understanding, the technical scheme of the present disclosure, or the part that contributes to the prior art, or the part of the technical scheme can be embodied in the form of a software product. The software product is stored in a storage medium and include several instructions to cause a computer device (such as a personal computer, a server or a network device) to execute all or part of the steps of the method described in various embodiments of the present disclosure. The above-mentioned storage medium includes various media that can store program codes, such as: a USB flash disk, a mobile hard disk drive, a read-only memory, a random access memory, a magnetic disk or an optical disk.

[0075] In this specification, various embodiments are described in a progressive way. The differences between each embodiment and other embodiments are highlighted, and the same and similar parts of various embodiments can be referred to each other. Since the system provided in the embodiment corresponds to the method provided in the embodiment, the system is described simply. Refer to the description of the method for the relevant points.

[0076] In the present disclosure, specific examples are applied to illustrate the principle and implementation of the present disclosure, and the explanations of the above embodiments are only used to help understand the method and core ideas of the present disclosure. At the same time, according to the idea of the present disclosure, there will be some changes in the specific implementation and application scope for those skilled in the art. To sum up, the contents of the specification should not be construed as limiting the present disclosure.

Claims

1. A method for modeling a respiratory system based on a mixed model, comprising:constructing an initial respiratory system mechanical model based on a fractional calculus and double-exponential function mixed model; the initial respiratory system mechanical model is:P(t) = EV(t) + RV'(t) + k^^V^) + k2eea2VWV(t) - + +kmeeamV^V(t) + Po; where P(t) is a respiratory pressure at time t, E is a respiratory system elasticity, V(t) is a respiratory volume at time t, R is an airway resistance, E'(t) is a gas flow speed at time t, Po is a positive end expiratory pressure, (k^ k2,...,km} are constant coefficients of fractional calculus term and double-exponential term, {a1,a2,-",otm} are exponential parameters, is a,-th fractional derivative of the respiratory volumeV(t), ee* is a double-exponential form with natural base e as a base, and isffm-t-th fractional derivative of the respiratory volume V(t);acquiring measured data, wherein the measured data comprises a pressure value, a flow speed value and a respiratory volume value of the respiratory system collected in real time;determining matrix-form data, wherein the matrix-form data is matrix data corresponding to a form of the fractional calculus and double-exponential function mixed model;inputting the matrix-form data into the initial respiratory system mechanical model to obtain fitting results of respective coefficients under a condition of specifying a set of initialization exponential parameters;substituting the measured data into the initial respiratory system mechanical model on a basis of the fitting results of respective coefficients for optimization iteration until a residual square or a root mean square error of an obtained initial respiratory system mechanical model is minimum, and determining the exponential parameters that minimize the residual square or the root mean square error of the obtained initial respiratory system mechanical model as optimal exponential parameters:substituting the optimal exponential parameters into the initial respiratory system mechanical model to obtain an optimized respiratory system mechanical model.

2. The method according to claim 1, wherein the determining matrix-form data comprises:obtaining a value of fractional calculus terms and value of double-exponential terms of the fractional calculus and double-exponential function mixed model according to the measured data under a condition of specifying a set of fractional order and exponential parameters;collating the measured data into the matrix-form data based on the value of fractional 11calculus terms and the value of double-exponential terms.

3. The method according to claim 1, wherein a particle swarm algorithm is used to carry out optimization iteration.

4. The method of according to claim 1, wherein the initial respiratory system mechanical model after simplification is:P(t) = EV(t) + RV'(t) + k^^V^ + k2eea2V^V(t~) + PQ.

5. The method according to claim 1, wherein when values of the respiratory system are collected at n time points, the matrix-form data comprises n-dimensional air pressure vector and a data matrix with n rows and m+3 columns.

6. An electronic device, comprising:a memory, in which a computer program is stored;a processor, connected with the memory and configured to call and execute the computer program to implement the method according to any one of claims 1 to 5.

7. The electronic device according to claim 6, wherein the memory is a computer-readable storage medium.13

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