CN104050857A - Cardiovascular system simulation model based on lumped parameters - Google Patents

Abstract

The invention provides a cardiovascular system simulation model based on lumped parameters. The cardiovascular system simulation model comprises a systemic circulation sub-model, a pulmonary circulation sub-model, a heart sub-model, a pulmonary valve and an aortic valve. In the heart sub-model, the free wall of the left atrium, the free wall of the ventriculus sinister, the free wall of the right atrium and the free wall of the ventriculus dexter are respectively represented by a first pressure sensor, a second pressure sensor, a time varying elastance device and a resistor, wherein the first pressure sensor, the second pressure sensor, the time varying elastance device and the resistor are sequentially connected in series. The elasticity of the coupling wall between the ventriculus sinister and the ventriculus dexter is represented by a capacitor. The mitral valve between the left atrium and the ventriculus sinister is represented by an inductor, a resistor and a Bernoulli impedor, wherein the inductor, the resistor and the Bernoulli impedor are sequentially connected between the resistance end of the left atrium and the resistance end of the ventriculus dexter in series. The tricuspid valve between the right atrium and the ventriculus dexter is represented by a Bernoulli impedor, a resistor and an inductor, wherein the Bernoulli impedor, the resistor and the inductor are sequentially connected between the resistance end of the right atrium and the resistance end of the ventriculus dexter in series. The model conforms to the basic principle of model construction, reflects the detail feature of a cardiovascular system, and establishes a foundation for mechanism analysis of heart sound signals.

Description

Translated fromChinese

基于集总参数的心血管系统仿真模型Simulation Model of Cardiovascular System Based on Lumped Parameters

技术领域technical field

本发明涉及一种基于集总参数的心血管系统仿真模型。 The invention relates to a simulation model of a cardiovascular system based on lumped parameters. the

背景技术Background technique

心血管系统是一个封闭的管道系统，是人体生理过程中最为重要的系统之一。心血管系统的仿真计算模型，能够反映出人体生理特征参数、血液动力学变量以及心音听诊参数之间的关系，还能体现出心脏各个组成部分的功能和状态。通过对心血管系统的仿真模型的研究，可以为正常或病态的心音产生机理提供了一种可行的理论依据,并且心血管系统仿真模型是学习心脏的生理机能和研究心脏听诊的很好的工具。 The cardiovascular system is a closed pipeline system and one of the most important systems in the physiological process of the human body. The simulation calculation model of the cardiovascular system can reflect the relationship between the physiological characteristic parameters of the human body, hemodynamic variables and heart sound auscultation parameters, and can also reflect the function and state of each component of the heart. Through the study of the simulation model of the cardiovascular system, a feasible theoretical basis can be provided for the mechanism of normal or pathological heart sounds, and the simulation model of the cardiovascular system is a good tool for studying the physiological functions of the heart and studying heart auscultation . the

发明内容Contents of the invention

本发明的目的是提出一种基于集总参数的心血管系统仿真模型，利用心血管系统仿真模型去分析心室心房血容量、心房心室压力、动脉血流量和表征正常和非正常心血管状态。本发明基于流体力学与电气网络的相关基础理论，建立一种基于集总参数的心血管系统仿真模型。该心血管系统仿真模型分为三个子模型：体循环子模型、肺循环子模型及心脏子模型。重点分析了体循环子模型和心脏子模型，给出收缩压，舒张压，射血分数等血流参数和仿真波形图，并对心音产生机理进行了分析。然后在此基础上进行扩展，增加了肺循环、血管、耦合壁等，使其形成一个闭合的循环回路，构成了心血管系统仿真模型，利用状态变量分析法建立该模型的数学表达式，并进行模拟仿真，得出心室心房血容量、心房心室压力、动脉血流量等仿真结果，并且可以利用该模型仿真高血压病态和心衰病态状况。 The purpose of the present invention is to propose a cardiovascular system simulation model based on lumped parameters, using the cardiovascular system simulation model to analyze ventricular and atrial blood volume, atrium and ventricular pressure, arterial blood flow and characterize normal and abnormal cardiovascular conditions. The invention establishes a simulation model of the cardiovascular system based on lumped parameters based on the relevant basic theories of fluid mechanics and electrical network. The cardiovascular system simulation model is divided into three sub-models: systemic circulation sub-model, pulmonary circulation sub-model and heart sub-model. The systemic circulation sub-model and the heart sub-model are analyzed emphatically, blood flow parameters such as systolic blood pressure, diastolic blood pressure and ejection fraction and simulation waveform diagrams are given, and the mechanism of heart sound generation is analyzed. Then expand on this basis, add pulmonary circulation, blood vessels, coupling wall, etc., to form a closed loop, and constitute a simulation model of the cardiovascular system, use the state variable analysis method to establish the mathematical expression of the model, and carry out The simulation can obtain the simulation results of ventricular and atrial blood volume, atrial and ventricular pressure, arterial blood flow, etc., and the model can be used to simulate the pathological conditions of hypertension and heart failure. the

实现本发明目的的技术方案是：基于集总参数的心血管系统仿真模型，包括体循环子模型、肺循环子模型、心脏子模型、右心室和肺循环子模型之间的肺动脉瓣，以及左心室和体循环子模型之间的主动脉瓣，其中心脏子模型包括左心房、左心室，右心房、右心室四个腔室和心室中间的耦合壁，其特征是： The technical solution for realizing the object of the present invention is: the cardiovascular system simulation model based on lumped parameters, including the pulmonary valve between the systemic circulation sub-model, the pulmonary circulation sub-model, the heart sub-model, the right ventricle and the pulmonary circulation sub-model, and the left ventricle and the systemic circulation The aortic valve between the sub-models, wherein the heart sub-model includes the left atrium, left ventricle, right atrium, right ventricle and the coupling wall in the middle of the ventricle, which is characterized by:

所述心脏子模型中，左心房、左心室，右心房、右心室的游离壁均用依次串联的第一压力传感器、第二压力传感器、时变倒电容和电阻表示，心室中间的耦合壁的弹性用电容表示，其中，第一压力传感器端接地，电阻端为输出端，左心房和左心室之间的二尖瓣用依次串联在左心房的电阻端和左心室的电阻端之间的电感、电阻和伯努利阻抗表示；右心房和右心室之间的三尖瓣用依次串联在右心房的电阻端和右心室的电阻端之间的伯努利阻抗、电阻和电感表示，其中，第一压力传感器表示胸廓内压，第二压力传感器表示心包压，时变倒电容表示心肌的弹性系数，电阻表征血流粘性阻力，电感表示血流惯性，伯努利阻抗表示血流粘性的动态阻力。 In the heart sub-model, the free walls of the left atrium, left ventricle, right atrium, and right ventricle are all represented by the first pressure sensor, the second pressure sensor, time-varying inverted capacitance and resistance connected in series, and the coupling wall in the middle of the ventricle Elasticity is represented by capacitance, wherein the first pressure sensor end is grounded, the resistance end is the output end, and the mitral valve between the left atrium and the left ventricle is connected in series with the inductance between the resistance end of the left atrium and the resistance end of the left ventricle. , resistance and Bernoulli impedance; the tricuspid valve between the right atrium and the right ventricle is represented by Bernoulli impedance, resistance and inductance connected in series between the resistance end of the right atrium and the resistance end of the right ventricle, where, The first pressure sensor represents the intrathoracic pressure, the second pressure sensor represents the pericardial pressure, the time-varying inverted capacitance represents the elastic coefficient of the myocardium, the resistance represents the viscous resistance of blood flow, the inductance represents the inertia of blood flow, and the Bernoulli impedance represents the dynamics of blood flow viscosity resistance. the

所述肺循环子模型由肺动脉，肺静脉以及肺毛细血管级联组成，肺动脉、肺静脉和肺毛细血管均由两条并联的肺循环支路组成，第一肺循环支路由依次串联的第一支路电阻和第一支路电感组成，第二肺循环支路由依次串联的第二支路电阻、第二支路电容和第二支路压力传感器组成，肺动脉、肺静脉和肺毛细血管的第一肺循环支路依次连接；其中，第一支路电阻表示血液流动产生的阻力，第一支路电感表示血流的惯性，第二支路电阻表示弹性腔的内部阻力，第二支路电容表示血管的顺应性，第二支路压力传感器表示胸内压。 The pulmonary circulation sub-model is composed of pulmonary artery, pulmonary vein and pulmonary capillary cascade. The pulmonary artery, pulmonary vein and pulmonary capillary are all composed of two parallel pulmonary circulation branches. The second branch of the pulmonary circulation is composed of the resistance of the second branch, the capacitance of the second branch and the pressure sensor of the second branch in series, and the first branch of the pulmonary circulation of the pulmonary artery, pulmonary vein and pulmonary capillary are connected in sequence; Among them, the first branch resistance represents the resistance generated by blood flow, the first branch inductance represents the inertia of blood flow, the second branch resistance represents the internal resistance of the elastic cavity, the second branch capacitance represents the compliance of blood vessels, and the second branch A branch pressure transducer indicates intrathoracic pressure. the

所述体循环子模型由主动脉、动脉、毛细血管、静脉和腔静脉组成，主动脉用依次串联的主动脉电容、主动脉第一电阻、主动脉电感和主动脉第二电阻表示，动脉、毛细血管、静脉和腔静脉均用两条并联的体循环支路表示，第一体循环支路由第一血管电阻和第一血管电容串联组成，第二体循环支路由第二血管电感和第二血管电阻串联组成，其中电容表示血液的顺应性，电阻表示血流粘性阻力，电感表示血流惯性；主动脉、动脉的第一体循环支路、毛细血管的第一体循环支路、静脉的第一体循环支路和腔静脉的第一体循环支路依次首位连接。 The systemic circulation sub-model is composed of aorta, artery, capillary, vein and vena cava. Blood vessels, veins, and vena cava are represented by two parallel systemic circulation branches. The first systemic circulation branch is composed of the first vascular resistance and the first vascular capacitance in series, and the second systemic circulation branch is composed of the second vascular inductance and the second vascular resistance in series. Composition, where the capacitance represents the compliance of blood, the resistance represents the viscous resistance of blood flow, and the inductance represents the inertia of blood flow; the aorta, the first systemic circulation branch of arteries, the first systemic circulation branch of capillaries, and the first body circulation of veins The circulatory branch and the first systemic branch of the vena cava are connected first in turn. the

所述右心室和肺循环子模型输入端之间的肺动脉瓣用依次串联的电阻、伯努利阻抗和电感表示，其中，电阻表示肺动脉瓣的血流阻力，电感表示肺动脉瓣中血液的惯性效应，伯努利阻抗Bpv表示血流粘性的动态阻力； The pulmonary valve between the right ventricle and the input end of the pulmonary circulation sub-model is represented by serially connected resistance, Bernoulli impedance and inductance, wherein the resistance represents the blood flow resistance of the pulmonary valve, and the inductance represents the inertial effect of blood in the pulmonary valve, Bernoulli impedance Bpv represents the dynamic resistance of blood flow viscosity;

所述左心室和体循环子模型输入端之间的主动脉瓣用依次串联的电阻、伯努利阻抗和电感，电阻表示主动脉瓣的血流阻力，电感表示主动脉瓣中血液的惯性效应，伯努利阻抗Bav表示血流粘性的动态阻力。 The aortic valve between the left ventricle and the input end of the systemic circulation sub-model uses resistance, Bernoulli impedance and inductance in series in sequence, the resistance represents the blood flow resistance of the aortic valve, and the inductance represents the inertial effect of blood in the aortic valve, The Bernoulli impedance Bav represents the dynamic resistance of blood flow viscosity. the

心血管系统建模是一个复杂过程，为了使模型尽可能的符合实际情况，构造心血管系统仿真模型应遵循如下原则： Cardiovascular system modeling is a complex process. In order to make the model as realistic as possible, the following principles should be followed in constructing a cardiovascular system simulation model:

(1)一致性原则：是指通过模型所得到的参数或仿真波形尽可能与实测的参数或波形相一致。 (1) Consistency principle: It means that the parameters or simulation waveforms obtained through the model are as consistent as possible with the measured parameters or waveforms. the

(2)可解释原则：是指设计的心血管系统仿真模型可以解释心血管的生理机制以及心音的产生机制，并且能用状态变量来表示生理学上的心血管参数，可以通过观测状态变量的变化趋势来研究心脏的生理状态。 (2) Interpretable principle: It means that the designed cardiovascular system simulation model can explain the physiological mechanism of cardiovascular system and the mechanism of heart sound generation, and can use state variables to represent physiological cardiovascular parameters, which can be observed by observing the changes of state variables trends to study the physiological state of the heart. the

(3)可控制原则：是指通过改变模型的一个或几个参数能够模拟出心血管系统的健康或者病态的情形，以及研究系统各个参数变化与心音变化以及心血管参数变化的关系。 (3) Controllable principle: It means that by changing one or several parameters of the model, it is possible to simulate the healthy or sick state of the cardiovascular system, and to study the relationship between the changes of various parameters of the system, the changes of heart sounds and the changes of cardiovascular parameters. the

有益效果：研究心血管系统的特性对心血管疾病发生机理的认识、疾病的预防和治疗有重要的意义。本发明提出集总参数的心血管系统仿真模型满足了构造模型所需的三个基本原则,体现了心血管系统的一些细节特征,为心音信号的产生机理分析奠定了良好的基础，也为心 血管疾病的研究提供了一种新途径。 Beneficial effects: the study of the characteristics of the cardiovascular system is of great significance to the understanding of the mechanism of cardiovascular diseases, the prevention and treatment of diseases. The cardiovascular system simulation model with lumped parameters proposed by the present invention satisfies the three basic principles required for constructing the model, embodies some detailed features of the cardiovascular system, and lays a good foundation for the analysis of the generation mechanism of the heart sound signal, and also provides a basis for the heart sound signal generation mechanism analysis. Vascular disease research offers a new avenue. the

附图说明Description of drawings

图1基于集总参数的心血管系统仿真模型的框图； Figure 1 is a block diagram of a cardiovascular system simulation model based on lumped parameters;

图2心脏子模型； Figure 2 heart sub-model;

图3体循环子模型； Figure 3 systemic circulation sub-model;

图4肺循环中的血管模型； Fig. 4 Vascular model in pulmonary circulation;

图5基于集总参数的心血管系统仿真模型。 Fig. 5 Simulation model of cardiovascular system based on lumped parameters. the

具体实施方式Detailed ways

首先按照构造心血管系统仿真模型的原则分别设计出体循环子模型、肺循环子模型及心脏子模型，如附图2、3、4所示；然后根据一个心动周期内血流的流经方向以及各段血管的血流量将心脏、体循环和肺循环进行连接，得到基于集总参数的心血管系统仿真模型如附图5所示。 First, according to the principle of constructing a cardiovascular system simulation model, respectively design the systemic circulation sub-model, the pulmonary circulation sub-model and the heart sub-model, as shown in Figures 2, 3 and 4; The blood flow of segmental blood vessels connects the heart, systemic circulation and pulmonary circulation, and a simulation model of the cardiovascular system based on lumped parameters is obtained, as shown in Figure 5. the

基于集总参数的心血管系统仿真模型的框图如附图1所示。 The block diagram of the cardiovascular system simulation model based on lumped parameters is shown in Fig. 1 . the

如图5所示，基于集总参数的心血管系统仿真模型，包括体循环子模型、肺循环子模型、心脏子模型、右心室和肺循环子模型之间的肺动脉瓣，以及左心室和体循环子模型之间的主动脉瓣，其中心脏子模型包括左心房、左心室，右心房、右心室四个腔室和心室中间的耦合壁。 As shown in Figure 5, the cardiovascular system simulation model based on lumped parameters includes the systemic circulation submodel, the pulmonary circulation submodel, the heart submodel, the pulmonary valve between the right ventricle and the pulmonary circulation submodel, and the left ventricle and the systemic circulation submodel. Between the aortic valve, the heart sub-model includes the left atrium, left ventricle, right atrium, right ventricle and the coupling wall in the middle of the ventricle. the

1.心脏子模型 1. Heart sub-model

如图2所示，右心房由依次串联的第一压力传感器Pit、第二压力传感器Ppc、时变倒电容era和电阻sra组成，第一压力传感器Pit表示胸廓内压，第二压力传感器Ppc表示心包压，时变倒电容era表示左心房游离壁，电阻sra表征血流粘性阻力。 As shown in Figure 2, the right atrium is composed of a first pressure sensor Pit, a second pressure sensor Ppc, a time-varying reciprocal capacitor era and a resistance sra connected in series in sequence. The first pressure sensor Pit represents the intrathoracic pressure, and the second pressure sensor Ppc represents Pericardial pressure, time-varying inverted capacitance era represents the free wall of the left atrium, and resistance sra represents the viscous resistance of blood flow. the

右心室由依次串联的第一压力传感器Pit、第二压力传感器Ppc、时变倒电容erv和电阻srv组成，第一压力传感器Pit表示胸廓内压，第二压力传感器Ppc表示心包压，时变倒电容erv表示右心房游离壁，电阻srv表征血流粘性阻力。 The right ventricle is composed of the first pressure sensor Pit, the second pressure sensor Ppc, the time-varying reciprocal capacitance erv and the resistance srv in series in sequence. The first pressure sensor Pit represents the intrathoracic pressure, and the second pressure sensor Ppc represents the pericardial pressure. The capacitance erv represents the free wall of the right atrium, and the resistance srv represents the viscous resistance of blood flow. the

左心房由依次串联的第一压力传感器Pit、第二压力传感器Ppc、时变倒电容ela和电阻sla组成，第一压力传感器Pit表示胸廓内压，第二压力传感器Ppc表示心包压，时变倒电容ela表示左心房游离壁，电阻sla表征血流粘性阻力。 The left atrium is composed of the first pressure sensor Pit, the second pressure sensor Ppc, the time-varying inverted capacitance ela and the resistance sla which are serially connected in sequence. The first pressure sensor Pit represents the intrathoracic pressure, and the second pressure sensor Ppc represents the pericardial pressure. The capacitance ela represents the free wall of the left atrium, and the resistance sla represents the viscous resistance of blood flow. the

左心室由依次串联的第一压力传感器Pit、第二压力传感器Ppc、时变倒电容erv和电阻srv组成，第一压力传感器Pit表示胸廓内压，第二压力传感器Ppc表示心包压，时变倒电容elv表示左心室游离壁，电阻slv表征血流粘性阻力。 The left ventricle is composed of the first pressure sensor Pit, the second pressure sensor Ppc, the time-varying reciprocal capacitance erv and the resistance srv in series in sequence. The first pressure sensor Pit represents the intrathoracic pressure, and the second pressure sensor Ppc represents the pericardial pressure. The capacitance elv represents the free wall of the left ventricle, and the resistance slv represents the viscous resistance of blood flow. the

右心室和肺循环子模型输入端之间的肺动脉瓣用依次串联的电阻Rpv、伯努利阻抗Bpv 和电感Lpv表示，其中，电阻Rpv表示肺动脉瓣的血流阻力，电感Lpv表示肺动脉瓣中血液的惯性效应，伯努利阻抗Bpv表示血流粘性的动态阻力； The pulmonary valve between the right ventricle and the input end of the pulmonary circulation sub-model is represented by a serial series resistance Rpv, Bernoulli impedance Bpv and inductance Lpv, wherein the resistance Rpv represents the blood flow resistance of the pulmonary valve, and the inductance Lpv represents the blood flow in the pulmonary valve Inertial effect, Bernoulli impedance Bpv represents the dynamic resistance of blood flow viscosity;

左心室和体循环子模型输入端之间的主动脉瓣用依次串联的电阻Rav、伯努利阻抗Bav和电感Lav表示，电阻Rav表示主动脉瓣的血流阻力，电感Lav表示主动脉瓣中血液的惯性效应，伯努利阻抗表示血流粘性的动态阻力。 The aortic valve between the left ventricle and the input end of the systemic circulation sub-model is represented by a series connection of resistance Rav, Bernoulli impedance Bav and inductance Lav. The resistance Rav represents the blood flow resistance of the aortic valve, and the inductance Lav represents the blood in the aortic valve. The inertial effect, Bernoulli impedance represents the dynamic resistance of blood flow viscosity. the

心脏的主要动力来自心脏的周期性舒张和收缩运动，心脏子模型按五部分(左、右心室游离壁，左、右心房游离壁以及心室中间的耦合壁)来进行等效建模，描述心脏的周期性舒张和收缩运动，心室游离壁的时变特性用一个时变倒电容来等效表示，左心室游离壁的时变倒电容elv的表达式如下： The main power of the heart comes from the periodic relaxation and contraction of the heart. The heart sub-model is equivalently modeled according to five parts (left and right ventricular free walls, left and right atrial free walls, and the coupling wall in the middle of the ventricle) to describe the heart The periodic diastolic and systolic movements of the ventricular free wall are equivalently represented by a time-varying reciprocal capacitance. The expression of the time-varying reciprocal capacitance elv of the left ventricular free wall is as follows:

其中t_ee表示收缩期心室压力达到峰值的时刻，取值为0.3s。E_lva，E_lvb表示心室时变倒电容的系数，改变该系数为E_rva，E_rvb用于表示右心室，E_lva，E_lvb的取值如表1所示。F_L是一个比例因子，用来描述心室时变倒电容与心室容量之间的非线性特性，F_L可由下式来描述： Among them, t_ee represents the moment when the systolic ventricular pressure reaches its peak value, and the value is 0.3s. E_lva and E_lvb represent the coefficients of ventricular time-varying reciprocal capacitance. Change the coefficients to E_rva and E_rvb to represent the right ventricle. The values of E_lva and E_lvb are shown in Table 1. F_L is a scaling factor used to describe the nonlinear characteristics between the time-varying capacitive capacity of the ventricle and the volume of the ventricle. F_L can be described by the following formula:

F_L=1-v_lv/v_max   (2) F_L =1-v_lv /v_max (2)

其中v_max是正常人的最大的心脏流体体积，900ml，v_lv是指左心室的容量，描述右心室时可将其变为v_rv。 Among them, v_max is the largest cardiac fluid volume of a normal person, 900ml, and v_lv refers to the capacity of the left ventricle, which can be changed to v_rv when describing the right ventricle.

左心房游离壁的时变倒电容ela的计算方式如下： The time-varying inverse capacitance ela of the left atrial free wall is calculated as follows:

其中t_ac表示心房开始收缩的时刻，取值为0.696s，t_ar表示心房开始舒张，取值为0.835s，t_r表示的是一个心动周期，取值为0.855s。E_laa，E_lab表示左心房倒电容的系数，改变该系数为E_raa，E_rab用于表示右心房，τ_lac，τ_lar分别表示一个心动周期内收缩期持续的时间以及舒张期持续的时间，E_laa，E_lab的取值见表1。 Among them, t_ac indicates the moment when the atrium begins to contract, and the value is 0.696s;_tar indicates that the atrium begins to relax, and the value is 0.835s; t_r indicates a cardiac cycle, and the value is 0.855s. E_laa , E_lab represent the coefficient of left atrial reciprocal capacitance, change the coefficient to E_raa , E_rab is used to represent the right atrium, τ_lac , τ_lar represent the duration of systole and diastole in a cardiac cycle, respectively , E_laa , and E_lab are shown in Table 1.

另外，在心脏建模时还需要考虑左右心室之间的相互作用，因为左右心室实际上并不是独立起作用，它们之间通过耦合壁(即心室之间的隔膜)来传递压力进而互相影响，形成心 室周期性的舒张和收缩运动，该模型的表达式如下： In addition, the interaction between the left and right ventricles needs to be considered when modeling the heart, because the left and right ventricles do not actually work independently, and they transmit pressure through the coupling wall (that is, the diaphragm between the ventricles) and then affect each other. Form the periodic diastolic and systolic motion of the ventricle, the expression of the model is as follows:

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>lv</span>lv</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>\frac{\mathrm{<span><span>elv</span>elv</span>}}{\mathrm{<span><span>elv</span>elv</span>}<span><span>+</span>+</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>lv</span>lv</span>}}<span><span>+</span>+</span>\frac{\mathrm{<span><span>elv</span>elv</span>}}{\mathrm{<span><span>elv</span>elv</span>}<span><span>+</span>+</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>rv</span>rv</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

${\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>rv</span>rv</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>\frac{\mathrm{<span><span>erv</span>erv</span>}}{\mathrm{<span><span>erv</span>erv</span>}<span><span>+</span>+</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>{\mathrm{<span><span>v</span>v</span>}}_{\mathrm{<span><span>lv</span>lv</span>}}<span><span>+</span>+</span>\frac{\mathrm{<span><span>erv</span>erv</span>}}{\mathrm{<span><span>erv</span>erv</span>}<span><span>+</span>+</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>s</span>the\; s</span>}}}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>lv</span>lv</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

其中Es表示耦合壁的弹性，是一个常数。Plv，Prv分别表示左右心室的压力，elv，erv表示左右心室的时变倒电容，vlv，vrv分别表示左右心室的容量。在建立房室模型时还需要考虑房室游离壁对血流的粘性阻力，在电路模型上，在房室倒电容上分别串联一个电阻(sla，sra，slv，srv)，可以表征血流粘性阻力。 where Es represents the elasticity of the coupling wall and is a constant. Plv, Prv represent the pressure of the left and right ventricle, elv, erv represent the time-varying capacitive capacity of the left and right ventricle, vlv, vrv represent the capacity of the left and right ventricle, respectively. When establishing the atrioventricular model, it is also necessary to consider the viscous resistance of the atrioventricular free wall to the blood flow. In the circuit model, a resistor (sla, sra, slv, srv) is connected in series with the atrioventricular reciprocal capacitance, which can represent the blood flow viscosity. resistance. the

表1心脏子模型中的参数值 Table 1 Parameter values in the heart submodel

E_lvaElvaE_lvbE_lvbE_laaE_laaE_labE_labE_rvaErvaE_rvbE_rvbE_raaE_raaE_rabE_rabτ_lacτ_lacτ_larτ_larτ_racτ_racτ_rarτ_rar1.431.430.030.030.070.070.090.090.260.260.0220.0220.040.040.060.060.40.40.050.050.40.40.050.05E_lvaElvaE_lvbE_lvbE_laaE_laaE_labE_labE_rvaErvaE_rvbE_rvbE_raaE_raaE_rvbE_rvbτ_lacτ_lacτ_larτ_larτ_racτ_racτ_rarτ_rar1.431.430.030.030.070.070.090.090.260.260.0220.0220.040.040.060.060.40.40.050.050.40.40.050.05

心脏瓣膜的作用是阻止血管中的血流倒流回心脏或者是心室的血流倒流回心房，一般情况下，用理想二极管的单向导通性来模拟瓣膜的开和关，用电阻来模拟瓣膜的粘性阻力。为了全面分析瓣膜的非线性特性以及探讨心脏瓣口的血流与瓣膜孔径的关系，可用三个元件来表示瓣膜：伯努利阻抗B(基于伯努利原理，可以用简化了的伯努利方程表示，压力为速率的乘积，速率由压力阶差和瓣膜的横截面积计算得到)；血流惯性L(反映血流的惯性)；粘性阻力R。 The function of the heart valve is to prevent the blood flow in the blood vessel from flowing back to the heart or the blood flow of the ventricle to flow back to the atrium. Generally, the unidirectional conductivity of the ideal diode is used to simulate the opening and closing of the valve, and the resistance is used to simulate the valve. viscous drag. In order to comprehensively analyze the nonlinear characteristics of the valve and explore the relationship between the blood flow of the heart valve and the valve aperture, three components can be used to represent the valve: Bernoulli impedance B (based on Bernoulli's principle, a simplified Bernoulli can be used The equation indicates that the pressure is the product of the velocity, which is calculated from the pressure gradient and the cross-sectional area of the valve); the flow inertia L (reflecting the inertia of the blood flow); the viscous resistance R. the

将上述的心房、心室以及瓣膜模型依据心脏的生理结构进行耦合，就形成了的心脏子模型，如附图2所示。该模型包括了左心房(由sla，ela，ppc，pit构成)，右心房(由sra，era，ppc，pit构成)、左心室(由slv，elv，ppc，pit构成)，右心室(由srv，erv，ppc，pit构成)以及三尖瓣膜(由Lmv，Rmv，Bmv构成)，主动脉瓣膜(由Rav，Bav，Lav构成)，二尖瓣膜(由Btv，Rtv，Ltv构成)，肺动脉瓣膜(由Rpv，Bpv，Lpv构成)，ppc表示心包压，pit胸廓内压表示。心包压的功能是给心室施加压力，与整个心脏的容量呈指数关系，心脏容量包括心室容量，心房容量以及心包容量。心室容量和心房容量随时间发生变化，心包容量取值为30ml。胸廓内压是一个常数，取值为5mmHg。 The above-mentioned atrium, ventricle and valve models are coupled according to the physiological structure of the heart to form a sub-model of the heart, as shown in Fig. 2 . The model includes left atrium (composed of sla, ela, ppc, pit), right atrium (composed of sra, era, ppc, pit), left ventricle (composed of slv, elv, ppc, pit), right ventricle (composed of srv, erv, ppc, pit) and tricuspid valve (consisting of Lmv, Rmv, Bmv), aortic valve (consisting of Rav, Bav, Lav), mitral valve (consisting of Btv, Rtv, Ltv), pulmonary artery Valve (composed of Rpv, Bpv, Lpv), ppc means pericardial pressure, and pit means intrathoracic pressure. The function of pericardial pressure is to exert pressure on the ventricles, which is exponentially related to the volume of the whole heart, which includes ventricular volume, atrial volume and pericardial volume. Ventricular volume and atrial volume change with time, and the value of pericardial volume is 30ml. The intrathoracic pressure is a constant value of 5mmHg. the

对于心室的周期性舒张和收缩运动，通常还采用压力-容积曲线来直观描述，心室的压力 -容积曲线关系可以表示为： For the periodic relaxation and contraction of the ventricle, the pressure-volume curve is usually used to describe it intuitively. The relationship between the pressure-volume curve of the ventricle can be expressed as:

P(t)=E(t)(V(t)-Vd)   (6) P(t)=E(t)(V(t)-Vd) (6)

其中，p(t)表示心室的压力，V(t)表示心室的血容量随时间的变化，Vd表示心室收缩末期无张力的心室容积，E(t)是一个时变弹性函数。在生理意义上，E(t)表示心肌的弹性系数。E(t)还被称为时变倒电容，在相应的电路模型中等价于电容的倒数。E(t)主要由两部分组成：心室的被动弹性Ep，是一个常数，表示心室充盈时心肌的被动拉伸，取值为0.06mmHg/ml；心室的主动弹性E_A(t)，表示心室的主动收缩性，E_A(t)可以由如下公式求得： Among them, p(t) represents the pressure of the ventricle, V(t) represents the change of the blood volume of the ventricle with time, Vd represents the volume of the ventricle without tension at the end of ventricular systole, and E(t) is a time-varying elastic function. In a physiological sense, E(t) represents the elastic coefficient of the myocardium. E(t) is also called time-varying inverse capacitance, which is equivalent to the reciprocal of capacitance in the corresponding circuit model. E(t) is mainly composed of two parts: the passive elasticity Ep of the ventricle, which is a constant, represents the passive stretching of the myocardium when the ventricle is filled, and the value is 0.06mmHg/ml; the active elasticity E_A (t) of the ventricle represents the The active contractility, E_A (t) can be obtained by the following formula:

E_A(t)=E_max×E_n(t_n)   (7) E_A (t)=E_max ×E_n (t_n ) (7)

其中：归一化函数：$E_n\left(t_n\right)=1.5532\&times;\frac{{\left(\frac{t_n}{0.7}\right)}^{1.8}}{1+{\left(\frac{t_n}{0.7}\right)}^{1.8}}\&times;\frac{1}{1+{\left(\frac{t_n}{1.1735}\right)}^{21.8}},$归一化时间：    E_max是心室的主动弹性最大值，HR表示心率。 Among them: the normalization function:${\mathrm{E.}}_{\mathrm{no}}\left(t_{\mathrm{no}}\right)=1.5532\&times;\frac{{\left(\frac{t_{\mathrm{no}}}{0.7}\right)}^{1.8}}{1+{\left(\frac{t_{\mathrm{no}}}{0.7}\right)}^{1.8}}\&times;\frac{1}{1+{\left(\frac{t_{\mathrm{no}}}{1.1735}\right)}^{21.8}},$ Normalized time: E_max is the maximum active elasticity of the ventricle, and HR is the heart rate.

2.体循环及肺循环子模型 2. Systemic circulation and pulmonary circulation sub-model

体循环子模型时如附图3所示。体循环子模型由主动脉、动脉、毛细血管、静脉和腔静脉组成，主动脉用依次串联的主动脉电容Cao、主动脉第一电阻Sao、主动脉电感Lao和主动脉第二电阻Rao表示。动脉用两条并联的支路表示，第一动脉支路由第一动脉电阻Sart和第一动脉电容Cart串联组成，第二动脉支路由第二动脉电感Lart和第二动脉支路电阻Rart串联组成。毛细血管用两条并联的支路表示，第一毛细血管支路由第一毛细血管电阻Scap和第一毛细血管电容Ccap串联组成，第二毛细血管支路由第二毛细血管电感Lcap和第二毛细血管电阻Rcap串联组成。静脉用两条并联的支路表示，第一静脉支路由第一静脉电阻Sven和第一静脉电容Cven串联组成，第二静脉支路由第二静脉电感Lven和第二静脉电阻Rven串联组成。腔静脉用两条并联的支路表示，第一腔静脉支路由第一腔静脉电阻Sve和第一腔静脉电容Cve串联组成，第二腔静脉支路由第二腔静脉电感Lve和第二腔静脉电阻Rve串联组成。 The systemic circulation sub-model is shown in Figure 3. The systemic circulation sub-model is composed of aorta, artery, capillary, vein, and vena cava. The aorta is represented by the aortic capacitance Cao, aortic first resistance Sao, aortic inductance Lao, and aortic second resistance Rao in series. The artery is represented by two parallel branches. The first arterial branch is composed of the first arterial resistance Sart and the first arterial capacitance Cart in series, and the second arterial branch is composed of the second arterial inductance Lart and the second arterial branch resistance Rart in series. The capillary is represented by two parallel branches, the first capillary branch is composed of the first capillary resistance Scap and the first capillary capacitance Ccap in series, and the second capillary branch is composed of the second capillary inductance Lcap and the second capillary Resistor Rcap is formed in series. The vein is represented by two parallel branches, the first vein branch is composed of the first vein resistance Sven and the first vein capacitance Cven in series, and the second vein branch is composed of the second vein inductance Lven and the second vein resistance Rven in series. The vena cava is represented by two parallel branches, the first vena cava branch is composed of the first vena cava resistance Sve and the first vena cava capacitance Cve in series, and the second vena cava branch is composed of the second vena cava inductance Lve and the second vena cava The resistance Rve is formed in series. the

该模型用时变倒电容来模拟心室的主动收缩作用，用电容Cao，电感Lao，电阻Rao，电容Cart和电阻R1来表示动脉系统，电容Cao，Cart分别表示动脉系统中血管的顺应性，电感Lao用来表征主动脉中的集总血液的惯性效应，电阻R1表示外周阻力。血流从心室流出，经过主动脉瓣流入动脉系统，经过外周阻力进入肺部，电容Cr表示肺部和静脉系统的集总顺应性。 The model uses time-varying inverse capacitance to simulate the active contraction of the ventricle. The arterial system is represented by capacitance Cao, inductance Lao, resistance Rao, capacitance Cart and resistance R1. Capacitance Cao and Cart represent the compliance of blood vessels in the arterial system, and inductance Lao Used to characterize the inertial effect of lumped blood in the aorta, resistance R1 represents peripheral resistance. Blood flows out of the ventricles, flows into the arterial system through the aortic valve, and enters the lungs through peripheral resistance. The capacitance Cr represents the lumped compliance of the lungs and the venous system. the

如图4所示，肺循环由肺动脉、肺静脉以及肺毛细血管组成，肺循环子模型可以看作是由多段血管级联而成，血管可以用弹性腔模型来表示，形成血管模型，如图附4所示。每级血管均由两条并联的肺循环支路组成。 As shown in Figure 4, the pulmonary circulation is composed of the pulmonary artery, pulmonary vein, and pulmonary capillary. The sub-model of the pulmonary circulation can be regarded as a cascade of multiple blood vessels. The blood vessels can be represented by an elastic cavity model to form a blood vessel model, as shown in Figure 4. Show. Each level of blood vessels is composed of two parallel pulmonary circulation branches. the

肺动脉中，第一肺循环支路由依次串联的第一支路电阻Rpuv和第一支路电感Lpuv组成，第二肺循环支路由依次串联的第二支路电阻Spua、第二支路电容Epua和第二支路压力传感器Pit组成。 In the pulmonary artery, the first pulmonary circulation branch is composed of the first branch resistance Rpuv and the first branch inductance Lpuv in series, and the second pulmonary circulation branch is composed of the second branch resistance Spua, the second branch capacitance Epua and the second branch in series. The branch pressure sensor Pit is composed. the

肺毛细血管中，第一肺循环支路由依次串联的第一支路电阻Rpuc和第一支路电感Lpuc组成，第二肺循环支路由依次串联的第二支路电阻Spuc、第二支路电容Epuc和第二支路压力传感器Pit组成。 In the pulmonary capillaries, the first branch of the pulmonary circulation is composed of the first branch resistance Rpuc and the first branch inductance Lpuc in series, and the second pulmonary circulation branch is composed of the second branch resistance Spuc, the second branch capacitance Epuc and the The second branch pressure sensor Pit is composed. the

肺静脉中，第一肺循环支路由依次串联的第一支路电阻Rpuv和第一支路电感Lpuv组成，第二肺循环支路由依次串联的第二支路电阻Spuv、第二支路电容Epuv和第二支路压力传感器Pit组成。 In the pulmonary vein, the first pulmonary circulation branch is composed of the first branch resistance Rpuv and the first branch inductance Lpuv in series, and the second pulmonary circulation branch is composed of the second branch resistance Spuv, the second branch capacitance Epuv and the second branch in series. The branch pressure sensor Pit is composed. the

肺动脉、肺毛细血管和肺静脉的第一肺循环支路依次连接；其中，第一支路电阻Rpua,Rpuc,Rpuv表示血液流动产生的阻力，第一支路电感Lpua,Lpuc，Lpuv表示血流的惯性，第二支路电阻Spua，Spuc，Spuv表示弹性腔的内部阻力，第二支路电容Epua，Epuc，Epuv表示血管的顺应性。 The pulmonary artery, pulmonary capillary and the first pulmonary circulation branch of the pulmonary vein are connected in sequence; among them, the first branch resistance Rpua, Rpuc, Rpuv represent the resistance generated by blood flow, and the first branch inductance Lpua, Lpuc, Lpuv represent the inertia of blood flow , the second branch resistance Spua, Spuc, Spuv represent the internal resistance of the elastic cavity, and the second branch capacitance Epua, Epuc, Epuv represent the compliance of the blood vessel. the

根据基尔霍夫定律，可以列出肺循环中血管模型的电路表达式： According to Kirchhoff's laws, the circuit expression of the vascular model in the pulmonary circulation can be listed as:

其中，P_in表示该段血管的输入血压，P_out表示该段血管的输出血压，q_in表示流入该血管的血流量，q_out表示流出该血管的血流量，P_Epua表示E_pua两端的压力差。由于实际的心血管系统中血管的顺应性具有非线性特性，血管的顺应性并不全是固定的，不能都用常数电容来表示，因此肺循环中血管的P-V关系如下： Among them, P_in represents the input blood pressure of this segment of blood vessels, P_out represents the output blood pressure of this segment of blood vessels, q_in represents the blood flow flowing into this blood vessel, q_out represents the blood flow flowing out of this blood vessel, P_Epua represents the pressure at both ends of E_pua Difference. Since the compliance of blood vessels in the actual cardiovascular system has nonlinear characteristics, the compliance of blood vessels is not all fixed and cannot be represented by constant capacitance. Therefore, the PV relationship of blood vessels in the pulmonary circulation is as follows:

p＝E₀·θ^v/2.Z   (II) p＝E₀ ·θ^v /2.Z (II)

其中E₀表示血容量为0时的倒电容，Z是容积常数，v对应肺循环中各段血管的血容量，P表示血管的血压，改变E₀和Z的取值可以表征肺部不同的血管，E₀和Z的取值已标注在心血管系统仿真模型中。肺循环子模型主要由肺动脉血管、肺毛细血管、肺静脉血管组成，可用3段附图4所示的血管模型级联而成。 Among them, E₀ represents the reciprocal capacitance when the blood volume is 0, Z is the volume constant, v corresponds to the blood volume of each segment of the blood vessel in the pulmonary circulation, and P represents the blood pressure of the blood vessel. Changing the values of E₀ and Z can represent different blood vessels in the lungs , the values of E₀ and Z have been marked in the cardiovascular system simulation model. The pulmonary circulation sub-model is mainly composed of pulmonary arteries, pulmonary capillaries, and pulmonary veins, which can be formed by cascading the blood vessel models shown in Figure 4 of the three paragraphs.

3.心血管系统仿真模型 3. Cardiovascular system simulation model

根据一个心动周期内血流的流经方向以及各段血管的血流量将心脏、体循环和肺循环进 行连接，基于集总参数的心血管系统仿真模型如附图5所示。 The heart, systemic circulation and pulmonary circulation are connected according to the direction of blood flow in a cardiac cycle and the blood flow of each segment of blood vessels. The simulation model of the cardiovascular system based on lumped parameters is shown in Figure 5. the

由图可看出，体循环中，血流从左心室elv，slv流出，流经主动脉Cao，Sao，Lao，Rao、动脉Sart，Cart，Lart，Rart、毛心血管Scap，Ccap，Lcap，Rcap、静脉Sven，Cven，Lven，Rven、腔静脉Sve，Cve，Lve，Rve最后流入右心房era，sra。肺循环中血流从右心室erv，srv流出，流经肺动脉Epua，Spua，Rpua，Lpua、肺毛细血管Spuc，Epuc，Rpuc，Lpuc、肺静脉Spuv，Epuv，Rpuv，Lpuv流入左心房ela，sla。该心血管仿真模型遵循流经子模型血流量等于流出子模型血流量的原则将其进行耦合,在心脏子模型中，不仅考虑了心室心房的自身的周期性运动，还考虑到了心室之间的相互作用，并且分别把体循环和肺循环子模型具体化到了动脉，静脉，毛细血管等三个部分。通过这些手段使得该模型能够比较详细的反映心血管系统的生理机制，比较接近心血管系统的生理结构，便于直观地理解心血管系统的工作原理。 It can be seen from the figure that in the systemic circulation, blood flows out from the left ventricle elv, slv, and flows through the aorta Cao, Sao, Lao, Rao, arteries Sart, Cart, Lart, Rart, capillary vessels Scap, Ccap, Lcap, Rcap , Vein Sven, Cven, Lven, Rven, vena cava Sve, Cve, Lve, Rve finally flow into the right atrium era, sra. In the pulmonary circulation, blood flows out from the right ventricle erv, srv, flows through the pulmonary arteries Epua, Spua, Rpua, Lpua, pulmonary capillaries Spuc, Epuc, Rpuc, Lpuc, pulmonary veins Spuv, Epuv, Rpuv, Lpuv and flows into the left atrium ela, sla. The cardiovascular simulation model is coupled according to the principle that the blood flow through the sub-model is equal to the blood flow out of the sub-model. In the heart sub-model, not only the periodic motion of the ventricle and atrium is considered, but also the relationship between the ventricles is taken into account. Interaction, and the systemic circulation and pulmonary circulation sub-models are embodied in three parts: arteries, veins, and capillaries. Through these means, the model can reflect the physiological mechanism of the cardiovascular system in more detail, and is relatively close to the physiological structure of the cardiovascular system, which is convenient for intuitively understanding the working principle of the cardiovascular system. the

心脏的心动周期以心室收缩作为开始的标志，每一心动周期可产生四个心音，一般均能听到的是第一和第二心音。下面用心血管系统仿真模型解释心音的产生原理。 The cardiac cycle of the heart is marked by ventricular contraction, and each cardiac cycle can produce four heart sounds, generally the first and second heart sounds can be heard. The following uses the cardiovascular system simulation model to explain the principle of heart sound generation. the

第一心音发生在心室收缩期，持续时间约为0.1s，其音调较低，是心室开始收缩的标志。第一心音主要是由于心室肌收缩，由房室瓣关闭及相伴随的心室壁振动形成，此外主动脉瓣和肺动脉瓣开放，血液向大血管内流动，大血管壁的振动也与第一心音的产生有关。 The first heart sound occurs during ventricular systole, lasts about 0.1s, and has a low pitch, which is a sign of ventricular contraction. The first heart sound is mainly due to the contraction of the ventricular muscle, which is formed by the closure of the atrioventricular valve and the accompanying vibration of the ventricular wall. In addition, the aortic valve and the pulmonary valve are opened, blood flows into the large blood vessel, and the vibration of the large blood vessel wall is also related to the first sound. related to the production of heart sounds. the

从心血管系统仿真模型的结构中可以看出，心室部分和瓣膜部分电路模型中包含有电阻Rmv，电容elv和电感Lmv等器件，根据电路的基本原理，电路中含有这些元件时，当满足一定的条件，电路会发生电磁振荡。第一心音的产生主要是由于在房室压差的作用下，二尖瓣和三尖瓣关闭所引起的一系列机械振动造成的，机械振动和电路振荡的具有相似性，因此可以用电路的电磁振荡来比拟二尖瓣和三尖瓣的机械振动。当心室和瓣膜模型在房室压差的作用下发生振荡时，可获得二阶电路方程如下： From the structure of the cardiovascular system simulation model, it can be seen that the circuit models of the ventricular part and the valve part include devices such as resistor Rmv, capacitor elv and inductor Lmv. According to the basic principle of the circuit, when these components are included in the circuit, when certain condition, the circuit will undergo electromagnetic oscillation. The generation of the first heart sound is mainly due to a series of mechanical vibrations caused by the closure of the mitral and tricuspid valves under the action of the atrioventricular pressure difference. The mechanical vibration and the circuit oscillation are similar, so the circuit can be used The electromagnetic oscillations of the valve are compared to the mechanical vibrations of the mitral and tricuspid valves. When the ventricular and valve models oscillate under the action of the atrioventricular pressure difference, the second-order circuit equation can be obtained as follows:

上式中，△P表示左右心室的压力差，q表示产生振动时流经二尖瓣的血容量的变化，Lmv表示二尖瓣中血液的惯性效应，Rmv表示二尖瓣的血流阻力，elv表示心室的心肌弹性系数。心室和心房的压力差△P可以由心血管系统仿真模型求得，根据二阶微分方程的解法可求得该方程的特解以及通解，并且根据特征方程可知，在Rmv²＜4Lmv·θlv时，振荡频率为： In the above formula, △P represents the pressure difference between the left and right ventricles, q represents the change of blood volume flowing through the mitral valve when vibration occurs, Lmv represents the inertia effect of blood in the mitral valve, Rmv represents the blood flow resistance of the mitral valve, elv represents the myocardial elastic coefficient of the ventricle. The pressure difference △P between the ventricle and the atrium can be obtained by the simulation model of the cardiovascular system. According to the solution of the second-order differential equation, the special solution and the general solution of the equation can be obtained, and according to the characteristic equation, when Rmv² <4Lmv·θlv , the oscillation frequency is:

$\mathrm{<span><span>f</span>f</span>}<span><span>=</span>=</span>\frac{\sqrt{\mathrm{<span><span>Lmv</span>Lmv</span>}<span><span>\&CenterDot;</span>\&Center\; Dot;</span>\mathrm{<span><span>\&theta;lv</span>\&theta;lv</span>}<span><span>-</span>-</span>{\mathrm{<span><span>Rmv</span>Rmv</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>/</span>/</span>\mathrm{<span><span>4</span>4</span>}}{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>\&pi;Lmv</span>\&pi;Lmv</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

心房和心室的压力差作为一个驱动源，使得心室和瓣膜组成的电路模型产生电磁振荡，用该振荡波形来模拟第一心音。同理，右心室和三尖瓣组成的电路模型在右心房和右心室的激励下产生振荡，形成三尖瓣的振动波形。二尖瓣和三尖瓣的振动波形合成效果就形成了第一心音。 The pressure difference between the atrium and the ventricle is used as a driving source, so that the circuit model composed of the ventricle and the valve generates electromagnetic oscillation, and the oscillation waveform is used to simulate the first heart sound. Similarly, the circuit model composed of the right ventricle and the tricuspid valve oscillates under the excitation of the right atrium and the right ventricle, forming the vibration waveform of the tricuspid valve. The synthesis effect of the vibration waveform of the mitral and tricuspid valves forms the first heart sound. the

第二心音的产生过程：发生在心脏舒张期的开始，频率较高，持续时间较短(约0.08秒)。产生的原因是主动脉瓣和肺动脉瓣Bav，Lav，Rav，Btv，Bpv，Lpv，Rpv关闭，瓣膜互相撞击以及大动脉Cart,Sart,Lart,Rart中血液减速和室内压(Pra,Prv)迅速下降引起的振动。第二心音的产生可以类比第一心音的产生过程，由于心室的压力与动脉压的压力差使得瓣膜关闭，可用类似的电路模型对其进行建模。从心血管系统仿真模型中得出心脏舒张期的一些心血管参数作为第二心音产生的初始条件，进行电路仿真，可以得到第二心音的仿真波形。 The production process of the second heart sound: It occurs at the beginning of the diastolic period, with a higher frequency and a shorter duration (about 0.08 seconds). The cause is the closure of the aortic and pulmonary valves Bav, Lav, Rav, Btv, Bpv, Lpv, Rpv, the impact of the valves on each other and the deceleration of blood in the aorta Cart, Sart, Lart, Rart and the rapid drop in intraventricular pressure (Pra, Prv) caused vibration. The generation of the second heart sound can be compared to the generation process of the first heart sound. Because the pressure difference between the pressure of the ventricle and the arterial pressure causes the valve to close, it can be modeled with a similar circuit model. From the simulation model of the cardiovascular system, some cardiovascular parameters in the diastolic period are taken as the initial conditions for the generation of the second heart sound, and the simulation waveform of the second heart sound can be obtained by performing circuit simulation. the

第三心音和第四心音的产生过程可以看成是在心室充盈期，房室的血流量以及血流量的梯度产生的，第三和第四心音的频率和幅值与心室elv，erv的心肌弹性系数和心室对血流的粘性阻力(slv,srv)有关。 The generation process of the third heart sound and the fourth heart sound can be regarded as the generation of the atrioventricular blood flow and the gradient of the blood flow during the ventricular filling period. The frequency and amplitude of the third and fourth heart sounds are related to the myocardium of the ventricle elv and erv The modulus of elasticity is related to the viscous resistance of the ventricle to blood flow (slv, srv). the

Claims (7)

1. the cardiovascular system realistic model based on lumped parameter, comprise body cyclic submodule type, pulmonary circulation submodel, heart submodel, pulmonary valve between right ventricle and pulmonary circulation submodel, and aorta petal between left ventricle and body cyclic submodule type, its cardiac submodel comprises atrium sinistrum, left ventricle, atrium dextrum, coupled wall in the middle of four chambers of right ventricle and ventricle, it is characterized in that: in described heart submodel, atrium sinistrum, left ventricle, atrium dextrum, the free wall of right ventricle is all with first pressure transducer of connecting successively, the second pressure transducer, time become elastance and resistance represents, the elasticity of the coupled wall in the middle of ventricle represents with electric capacity, wherein, the first pressure transducer end ground connection, resistance terminal is output terminal, bicuspid valve between atrium sinistrum and left ventricle is with being connected on successively the inductance between the resistance terminal of atrium sinistrum and the resistance terminal of left ventricle, resistance and Bernoulli Jacob's impedance represent, tricuspid valve between atrium dextrum and right ventricle represents with the Bernoulli Jacob's impedance, resistance and the inductance that are connected between the resistance terminal of atrium dextrum and the resistance terminal of right ventricle successively, wherein, the first pressure transducer represents to press in thorax, the second pressure transducer represents paracardiac pressure, in time, becomes elastance and represents myocardium elasticity coefficient, resistance characterization blood flow viscous resistance, inductance represents blood flow inertia, Bernoulli Jacob's impedance represents the dynamic resistance of blood flow viscosity.

2. the cardiovascular system realistic model based on lumped parameter according to claim 1, it is characterized in that, described pulmonary circulation submodel is by pulmonary artery, pulmonary vein and PC cascade composition, pulmonary artery, PC and pulmonary vein are by two pulmonary circulation branch road compositions in parallel, wherein, the first branch road resistance and the first branch road inductance composition that route is connected successively propped up in the first pulmonary circulation, the second branch road resistance that route is connected is successively propped up in the second pulmonary circulation, the second branch road electric capacity and the second branch road pressure transducer composition, pulmonary artery, PC is connected with pulmonary venous the second pulmonary circulation branch road successively head and the tail, wherein, the first branch road resistance represents the resistance that blood flow produces, and the first branch road inductance represents the inertia of blood flow, and the second branch road resistance represents the internal drag of elastic cavity, and the second branch road electric capacity represents the compliance of blood vessel, and the second branch road pressure transducer represents intrathoracic pressure.

3. the cardiovascular system realistic model based on lumped parameter according to claim 1, it is characterized in that, described body cyclic submodule type is by sustainer, artery, capillary, vein and vena cave composition, the sustainer electric capacity of connecting successively for sustainer, sustainer the first resistance, sustainer inductance and sustainer the second resistance represent, artery, capillary, vein and vena cave all represent with two body circulation branch roads in parallel, first body circulation route the first blood vessel resistance and the first blood vessel capacitances in series composition, second body circulation route the second blood vessel inductance and the second blood vessel resistance are composed in series, sustainer and artery, capillary, vein and venacaval the second body circulation branch road successively the first connection, wherein electric capacity represents the compliance of blood, resistance represents blood flow viscous resistance, inductance represents blood flow inertia.

4. the cardiovascular system realistic model based on lumped parameter according to claim 1, it is characterized in that, pulmonary valve between described right ventricle and pulmonary circulation submodel input end represents with resistance, Bernoulli Jacob's impedance and the inductance of series connection successively, wherein, resistance represents the resistance of blood flow of pulmonary valve, inductance represents the inertial effect of blood in pulmonary valve, the dynamic resistance of blood flow viscosity;

Aorta petal between described left ventricle and body cyclic submodule type input end represents with resistance, Bernoulli Jacob's impedance and the inductance of series connection successively, resistance represents the resistance of blood flow of aorta petal, inductance represents the inertial effect of blood in aorta petal, and Bernoulli Jacob's impedance represents the dynamic resistance of blood flow viscosity.

5. the cardiovascular system realistic model based on lumped parameter according to claim 1, is characterized in that, left ventricular free wall time to become the expression formula of elastance elv as follows:

Wherein t_eerepresent that systole phase ventricular pressure reaches the moment of peak value, value is 0.3s, E_lva, E_lvbthe coefficient that becomes elastance while representing left ventricle, changing this coefficient is E_rva, E_rvbrepresent the coefficient of right ventricle elastance, for calculate right ventricle free wall time become elastance erv, F_lbe a scale factor, while being used for describing ventricle, become the nonlinear characteristic between elastance and vascular capacitance, F_ldescribed by following formula:

K_L=1-v_lv/v_max (2)

Wherein v_maxnormal person's maximum heart fluid volume 900ml, v_lvrefer to the capacity of left ventricle, while describing right ventricle, become v_rv;

Described atrium free wall time to become the account form of elastance as follows, when the ela of atrium sinistrum, become elastance into:

Wherein t_acrepresent that atrium starts the moment of shrinking, value is 0.696s, t_arrepresent that atrium starts diastole, value is 0.835s, t_rwhat represent is a cardiac cycle, and value is 0.855s, E_laa, E_labthe coefficient that represents atrium sinistrum elastance, changing this coefficient is E_raa, E_rabrepresent the coefficient of atrium dextrum elastance, for calculate atrium dextrum free wall time become elastance era, τ_lac, τ_larrepresent respectively lasting time and the lasting time of diastole in atrium sinistrum systole phase in the cardiac cycle, τ_rac, τ_rarrepresent respectively lasting time and the lasting time of diastole in atrium dextrum systole phase in the cardiac cycle.

6. the cardiovascular system realistic model based on lumped parameter according to claim 1, is characterized in that, the expression formula of described cardiac module is as follows:

Wherein Es represents the elasticity of coupled wall, is a constant, Plv, Prv represents respectively the pressure of left and right ventricles, vlv, vrv represents respectively the capacity of left and right ventricles, elv, erv represent left and right ventricles time become elastance.

7. the cardiovascular system realistic model based on lumped parameter according to claim 1, is characterized in that, the parameter value in described heart submodel is as following table:

E_lvaE_lvbE_laaE_labE_rvaE_rvbE_raaE_rabτ_lacτ_larτ_racτ_rar1.430.030.070.090.260.0220.040.060.40.050.40.05E_lvaE_lvbE_laaE_labE_rvaE_rvbE_raaE_rvbτ_lacτ_larτ_racτ_rar1.430.030.070.090.260.0220.040.060.40.050.40.05