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

Cardiovascular system realistic model based on lumped parameter

Technical field

The present invention relates to a kind of cardiovascular system realistic model based on lumped parameter.

Background technology

Cardiovascular system is the piping system of a sealing, is one of of paramount importance system in person's physiological processes.The Simulation Calculation of cardiovascular system, can reflect the relation between human body physiological characteristics parameter, Hemodynamics variable and cardiophony parameter, can also embody function and the state of each ingredient of heart.By the research of the realistic model to cardiovascular system, can provide a kind of feasible theoretical foundation for normal or ill hear sounds mechanism of production, and cardiovascular system realistic model is the physiological function of study heart and the good instrument of research cardiac auscultation.

Summary of the invention

The object of the invention is to propose a kind of cardiovascular system realistic model based on lumped parameter, utilize cardiovascular system realistic model to remove to analyze the normal and improper cardiovascular status of ventricular atrial blood volume, atrial ventricle's pressure, blood flow volume and sign.The present invention is based on the relevant rudimentary theory of fluid mechanics and electrical network, set up a kind of cardiovascular system realistic model based on lumped parameter.This cardiovascular system realistic model is divided into three submodels: body cyclic submodule type, pulmonary circulation submodel and heart submodel.Selective analysis body cyclic submodule type and heart submodel, provide systolic pressure, diastolic pressure, the blood flow parameters such as ejection fraction and simulation waveform figure, and hear sounds mechanism of production is analyzed.Then expand on this basis, pulmonary circulation, blood vessel, coupled wall etc. are increased, make it form a closed closed circuit, form cardiovascular system realistic model, utilize State-Variable Analysis Method to set up the mathematic(al) representation of this model, and carry out analog simulation, draw the simulation results such as ventricular atrial blood volume, atrial ventricle's pressure, blood flow volume, and can utilize this model emulation hypertension morbid state and heart failure pathologic condition.

The technical scheme that realizes the object of the invention is: the cardiovascular system realistic model based on lumped parameter, comprise the pulmonary valve between body cyclic submodule type, pulmonary circulation submodel, heart submodel, 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, coupled wall in the middle of atrium dextrum, four chambers of right ventricle and ventricle, is characterized in that:

In described heart submodel, atrium sinistrum, left ventricle, the free wall of atrium dextrum, right ventricle all with first pressure transducer, the second pressure transducer of series connection successively, 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, the bicuspid valve between atrium sinistrum and left ventricle represents with the inductance, resistance and the Bernoulli Jacob's impedance that are connected between the resistance terminal of atrium sinistrum and the resistance terminal of left ventricle successively; 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.

Described pulmonary circulation submodel is by pulmonary artery, pulmonary vein and PC cascade composition, pulmonary artery, pulmonary vein and PC are by two pulmonary circulation branch road compositions in parallel, 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, the second branch road electric capacity and the second branch road pressure transducer composition that route is connected successively propped up in the second pulmonary circulation, and the first pulmonary circulation branch road of pulmonary artery, pulmonary vein and PC is connected successively; 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.

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, wherein electric capacity represents the compliance of blood, resistance represents blood flow viscous resistance, inductance represents blood flow inertia, the first body circulation branch road of the first body circulation branch road of sustainer, artery, the first body circulation branch road of capillary, vein and venacaval the first body circulation branch road successively the first connection.

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, and Bernoulli Jacob's impedance Bpv represents the dynamic resistance of blood flow viscosity;

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

Cardiovascular system modeling is a complex process, and for model is tallied with the actual situation as much as possible, structure cardiovascular system realistic model should be followed following principle:

(1) consistency principle: refer to that the parameter or the simulation waveform that obtain by model are consistent with parameter or the waveform of actual measurement as far as possible.

(2) soluble principle: refer to that the cardiovascular system realistic model of design can explain the generation mechanism of cardiovascular physiological mechanism and hear sounds, and can represent physiological cardio-vascular parameters by state variable, can study by the variation tendency of observer state variable the physiological status of heart.

(3) can control principle: refer to that one or several parameter by changing model can simulate the healthy or ill situation of cardiovascular system, and the relation that Study system parameters changes with hear sounds changes and cardio-vascular parameters changes.

Beneficial effect: understanding, the prevention and treatment of diseases of the characteristic of Research on Cardiovascular system to angiocardiopathy genesis mechanism has important meaning.The cardiovascular system realistic model that the present invention proposes lumped parameter has met three required cardinal rules of tectonic model, some minutias of cardiovascular system are embodied, for the mechanism of production analysis of cardiechema signals is had laid a good foundation, also for the research of angiocardiopathy provides a kind of new way.

Brief description of the drawings

The block diagram of the cardiovascular system realistic model of Fig. 1 based on lumped parameter;

Fig. 2 heart submodel;

Fig. 3 body cyclic submodule type;

Vascular pattern in Fig. 4 pulmonary circulation;

The cardiovascular system realistic model of Fig. 5 based on lumped parameter.

Embodiment

First design respectively body cyclic submodule type, pulmonary circulation submodel and heart submodel according to the principle of structure cardiovascular system realistic model, as shown in accompanying drawing 2,3,4; Then according to the volume of blood flow of flow through direction and the each section of blood vessel of blood flow in the cardiac cycle, the circulation of heart, body is connected with pulmonary circulation, obtains cardiovascular system realistic model based on lumped parameter as shown in Figure 5.

The block diagram of the cardiovascular system realistic model based on lumped parameter as shown in Figure 1.

As shown in Figure 5, cardiovascular system realistic model based on lumped parameter, comprise the pulmonary valve between body cyclic submodule type, pulmonary circulation submodel, heart submodel, 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, the coupled wall in the middle of atrium dextrum, four chambers of right ventricle and ventricle.

1. heart submodel

As shown in Figure 2, atrium dextrum by the first pressure transducer Pit connecting successively, the second pressure transducer Ppc, time become elastance era and resistance sra forms, the first pressure transducer Pit represents to press in thorax, the second pressure transducer Ppc represents paracardiac pressure, in time, becomes elastance era and represents atrium sinistrum free wall, and resistance sra characterizes blood flow viscous resistance.

Right ventricle by the first pressure transducer Pit connecting successively, the second pressure transducer Ppc, time become elastance erv and resistance srv forms, the first pressure transducer Pit represents to press in thorax, the second pressure transducer Ppc represents paracardiac pressure, in time, becomes elastance erv and represents atrium dextrum free wall, and resistance srv characterizes blood flow viscous resistance.

Atrium sinistrum by the first pressure transducer Pit connecting successively, the second pressure transducer Ppc, time become elastance ela and resistance sla forms, the first pressure transducer Pit represents to press in thorax, the second pressure transducer Ppc represents paracardiac pressure, in time, becomes elastance ela and represents atrium sinistrum free wall, and resistance sla characterizes blood flow viscous resistance.

Left ventricle by the first pressure transducer Pit connecting successively, the second pressure transducer Ppc, time become elastance erv and resistance srv forms, the first pressure transducer Pit represents to press in thorax, the second pressure transducer Ppc represents paracardiac pressure, in time, becomes elastance elv and represents left ventricular free wall, and resistance slv characterizes blood flow viscous resistance.

Pulmonary valve between right ventricle and pulmonary circulation submodel input end represents with resistance R pv, Bernoulli Jacob's impedance Bpv and the inductance L pv of series connection successively, wherein, resistance R pv represents the resistance of blood flow of pulmonary valve, inductance L pv represents the inertial effect of blood in pulmonary valve, and Bernoulli Jacob's impedance Bpv represents the dynamic resistance of blood flow viscosity;

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

The major impetus of heart is from periodicity diastole and the contractile motion of heart, heart submodel is by five parts (Ventricular free wall, coupled wall in the middle of left and right atrium free wall and ventricle) carry out Equivalent Modeling, periodicity diastole and the contractile motion of heart are described, it is equivalently represented that the time-varying characteristics of free ventricular wall become elastance during with one, 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 ventricle, changing this coefficient is E _rva, E _rvbbe used for representing right ventricle, E _lva, E _lvbvalue as shown in table 1.F _lbe a scale factor, while being used for describing ventricle, become the nonlinear characteristic between elastance and vascular capacitance, F _lcan be described by following formula:

F _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, can be become v _rv.

Atrium sinistrum free wall time to become the account form of elastance ela as follows:

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 _rabbe used for representing atrium dextrum, τ _lac, τ _larrepresent respectively lasting time and the lasting time of diastole in systole phase in the cardiac cycle, E _laa, E _labvalue in table 1.

In addition, in the time of heart modeling, also need to consider the interaction between left and right ventricles, because in fact left and right ventricles is not independently to work, between them, carry out transmission of pressure and then interact by coupled wall (being the barrier film between ventricle), the diastole and the contractile motion that form ventricular cycle, the expression formula of this model is as follows:

$P_{\mathrm{lv}}=E_s\·\frac{\mathrm{elv}}{\mathrm{elv}+E_s}\·v_{\mathrm{lv}}+\frac{\mathrm{elv}}{\mathrm{elv}+E_s}\·P_{\mathrm{rv}}---\left(4\right)$

$P_{\mathrm{rv}}=E_s\·\frac{\mathrm{erv}}{\mathrm{erv}+E_s}\·v_{\mathrm{lv}}+\frac{\mathrm{erv}}{\mathrm{erv}+E_s}\·P_{\mathrm{lv}}---\left(5\right)$

Wherein Es represents the elasticity of coupled wall, is a constant.Plv, Prv represents respectively the pressure of left and right ventricles, elv, erv represent left and right ventricles time become elastance, vlv, vrv represents respectively the capacity of left and right ventricles.In the time setting up compartment model, also need to consider the viscous resistance of chamber free wall to blood flow, on circuit model, the resistance (sla, sra, slv, srv) of connecting respectively on chamber elastance, can characterize blood flow viscous resistance.

Parameter value in table 1 heart submodel

E lva	E lvb	E laa	E lab	E rva	E rvb	E raa	E rab	τ lac	τ lar	τ rac	τ rar
												1.43	0.03	0.07	0.09	0.26	0.022	0.04	0.06	0.4	0.05	0.4	0.05
E lva	E lvb	E laa	E lab	E rva	E rvb	E raa	E rvb	τ lac	τ lar	τ rac	τ rar
												1.43	0.03	0.07	0.09	0.26	0.022	0.04	0.06	0.4	0.05	0.4	0.05

Valvular effect is to stop blood flow in the blood vessel blood flow of heart or the ventricle atrium of flowing backwards go back to of flowing backwards go back to, generally, simulates the Kai Heguan of valve by the unidirectional general character of ideal diode, simulates the viscous resistance of valve with resistance.For nonlinear characteristic and the blood flow of discussion heart valve mouth and the relation in valve aperture of multianalysis valve, can represent valve with three elements: B is (based on bernoulli principle for Bernoulli Jacob's impedance, can represent with the Bernoulli equation of having simplified, pressure is the product of speed, and speed is calculated by the cross-sectional area of pressure gradient and valve); Blood flow inertia L (inertia of reflection blood flow); Viscous resistance R.

Above-mentioned atrium, ventricle and valve model are coupled according to the physiological structure of heart, the heart submodel just having formed, as shown in Figure 2.This model comprised atrium sinistrum (by sla, ela, ppc, pit forms), and atrium dextrum (by sra, era, ppc, pit form), left ventricle (by slv, elv, ppc, pit forms), right ventricle is (by srv, erv, ppc, pit form) and tricuspid valve (by Lmv, Rmv, Bmv forms), aortic valve is (by Rav, Bav, Lav forms), mitral valve is (by Btv, Rtv, Ltv forms), cusps of pulmonary valve is (by Rpv, Bpv, Lpv forms), ppc represents paracardiac pressure, in pit thorax, presses and represents.The function of paracardiac pressure is to exert pressure to ventricle, is exponential relationship with the capacity of whole heart, and heart volume comprises vascular capacitance, atrium capacity and pericardium capacity.Vascular capacitance and atrium capacity change in time, and pericardium capacity value is 30ml.In thorax, pressing is a constant, and value is 5mmHg.

For periodicity diastole and the contractile motion of ventricle, conventionally also adopt pressure-volume curve to carry out directviewing description, the pressure-volume curve relation of ventricle can be expressed as:

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

Wherein, p (t) represents the pressure of ventricle, and over time, Vd represents ventricular contraction tension-free ventricular volume in latter stage to the blood volume of V (t) expression ventricle, and E (t) becomes Elastic Function while being one.On physiological significance, E (t) represents myocardium elasticity coefficient.E (t) becomes elastance while being also called as, be equivalent to the inverse of electric capacity in corresponding circuit model.E (t) is mainly made up of two parts: ventricle by dynamic elasticity Ep, be a constant, represent the passive stretching of cardiac muscle when ventricular filling, value is 0.06mmHg/ml; The active elasticity E of ventricle _a(t), represent the active shrinkability of ventricle, E _a(t) can be tried to achieve by following formula:

E _A(t)=E _max×E _n(t _n) (7)

Wherein: normalized function: $E_n\left(t_n\right)=1.5532\×\frac{{\left(\frac{t_n}{0.7}\right)}^{1.8}}{1+{\left(\frac{t_n}{0.7}\right)}^{1.8}}\×\frac{1}{1+{\left(\frac{t_n}{1.1735}\right)}^{21.8}},$ The normalization time: e _maxbe the active elastic maximum of ventricle, HR represents heart rate.

2. body circulation and pulmonary circulation submodel

When body cyclic submodule type as shown in Figure 3.Body cyclic submodule type is made up of sustainer, artery, capillary, vein and vena cave, and sustainer represents with sustainer capacitor C ao, sustainer the first resistance Sao, sustainer inductance L ao and the sustainer second resistance R ao of series connection successively.Artery represents with two branch roads in parallel, and the first artery tributaries is composed in series by the first artery resistance Sart and the first artery capacitor C art, and the second artery tributaries is composed in series by the second artery inductance L art and the second artery tributaries resistance R art.Capillary represents with two branch roads in parallel, the first capillary props up route the first capillary resistance Scap and the first capillary capacitor C cap is composed in series, and the second capillary props up route the second capillary inductance L cap and the second capillary resistance R cap is composed in series.Vein represents with two branch roads in parallel, and first venous branch route the first vein resistance Sven and the first vein capacitor C ven are composed in series, and second venous branch route the second vein inductance L ven and the second vein resistance R ven are composed in series.Vena cave represents with two branch roads in parallel, and the first vena cave props up route the first vena cave resistance Sve and the first vena cave capacitor C ve is composed in series, and the second vena cave props up route the second vena cave inductance L ve and the second vena cave resistance R ve is composed in series.

This model used time change elastance is simulated the active contraction of ventricle, use electric capacity Cao, inductance L ao, resistance R ao, capacitor C art and resistance R 1 represent arterial system, capacitor C ao, and Cart represents respectively the compliance of arterial system medium vessels, inductance L ao is used for characterizing the inertial effect of the lump blood in sustainer, and resistance R 1 represents peripheral resistance.Blood flow flows out from ventricle, flows into arterial system through aorta petal, enters lung through peripheral resistance, and capacitor C r represents the lump compliance of lung and venous system.

As shown in Figure 4, pulmonary circulation is made up of pulmonary artery, pulmonary vein and PC, and pulmonary circulation submodel can be regarded as by the cascade of multistage blood vessel and forms, and blood vessel can represent with elastic cavity model, forms vascular pattern, as schemes as shown in the of attached 4.Every grade of blood vessel is by two pulmonary circulation branch road compositions in parallel.

In pulmonary artery, the first branch road resistance R puv and the first branch road inductance L puv composition that route is connected successively propped up in the first pulmonary circulation, and the second branch road resistance Spua, the second branch road electric capacity Epua and the second branch road pressure transducer Pit composition that route is connected successively propped up in the second pulmonary circulation.

In PC, the first branch road resistance R puc and the first branch road inductance L puc composition that route is connected successively propped up in the first pulmonary circulation, and the second branch road resistance Spuc, the second branch road electric capacity Epuc and the second branch road pressure transducer Pit composition that route is connected successively propped up in the second pulmonary circulation.

In pulmonary vein, the first branch road resistance R puv and the first branch road inductance L puv composition that route is connected successively propped up in the first pulmonary circulation, and the second branch road resistance Spuv, the second branch road electric capacity Epuv and the second branch road pressure transducer Pit composition that route is connected successively propped up in the second pulmonary circulation.

Pulmonary artery, PC and pulmonary venous the first pulmonary circulation branch road are connected successively; Wherein, the first branch road resistance R pua, Rpuc, Rpuv represents the resistance that blood flow produces, the first branch road inductance L pua, Lpuc, Lpuv represents the inertia of blood flow, the second branch road resistance Spua, Spuc, Spuv represents the internal drag of elastic cavity, the second branch road electric capacity Epua, Epuc, Epuv represents the compliance of blood vessel.

According to Kirchhoff's law, can list the circuit expressions formula of pulmonary circulation medium vessels model:

Wherein, P _inrepresent the input blood pressure of this section of blood vessel, P _outrepresent the output blood pressure of this section of blood vessel, q _inrepresent to flow into the volume of blood flow of this blood vessel, q _outrepresent to flow out the volume of blood flow of this blood vessel, P _epuarepresent E _puathe pressure differential at two ends.Because the compliance of actual cardiovascular system medium vessels has nonlinear characteristic, the compliance of blood vessel is not fixed entirely, can not all use constant electric capacity to represent, therefore the P-V relation of pulmonary circulation medium vessels is as follows:

p＝E ₀·θ ^v/2.Z (II)

Wherein E ₀represent that blood volume is the elastance of 0 o'clock, Z is voluminosity constant, the blood volume of each section of blood vessel in the corresponding pulmonary circulation of v, and P represents the blood pressure of blood vessel, changes E ₀can characterize the different blood vessel of lung, E with the value of Z ₀be labeled in cardiovascular system realistic model with the value of Z.Pulmonary circulation submodel is mainly made up of pulmonary arterial vascular, PC, pulmonary vein blood vessel, and the vascular pattern cascade shown in available 3 sections of accompanying drawings 4 forms.

3. cardiovascular system realistic model

According to the volume of blood flow of flow through direction and the each section of blood vessel of blood flow in the cardiac cycle, heart, body circulation are connected with pulmonary circulation, the cardiovascular system realistic model based on lumped parameter as shown in Figure 5.

As can be seen from Figure, in body circulation, blood flow is from left ventricle elv, and slv flows out, the sustainer Cao that flows through, Sao, Lao, Rao, artery Sart, Cart, Lart, Rart, the cardiovascular Scap of hair, Ccap, Lcap, Rcap, vein Sven, Cven, Lven, Rven, vena cave Sve, Cve, Lve, Rve finally flows into atrium dextrum era, sra.In pulmonary circulation, blood flow is from right ventricle erv, and srv flows out, the pulmonary artery Epua that flows through, and Spua, Rpua, Lpua, PC Spuc, Epuc, Rpuc, Lpuc, pulmonary vein Spuv, Epuv, Rpuv, Lpuv flows into atrium sinistrum ela, sla.This cardiovascular realistic model is followed the principle that the submodel volume of blood flow of flowing through equals to flow out submodel volume of blood flow and is coupled, in heart submodel, not only consider VA self cyclical movement, also consider the interaction between ventricle, and respectively body circulation and pulmonary circulation submodel are specialized to artery, vein, three parts such as capillary.Make the physiological mechanism of the reflection cardiovascular system that this model can be more detailed by these means, relatively approach the physiological structure of cardiovascular system, be convenient to understand intuitively the principle of work of cardiovascular system.

The cardiac cycle of heart, using ventricular contraction as the mark starting, can produce four hear sounds each cardiac cycle, and general equal what can hear is the first and second hear sounds.Explain the generation principle of hear sounds below with cardiovascular system realistic model.

First heart sound occurs in ventricular systole, and the duration is about 0.1s, and its tone is lower, is that ventricle starts the mark shrinking.First heart sound is mainly because ventricular muscles is shunk, and is closed and the ventricle wall vibration of accompanying forms by atrioventricular valve, and aorta petal and pulmonary valve are open in addition, and blood is to mobile in trunk, and the vibration of trunk wall is also relevant with the generation of first heart sound.

From the structure of cardiovascular system realistic model, can find out, in ventricle part and valve partial circuit model, include resistance R mv, the devices such as electric capacity elv and inductance L mv, according to the ultimate principle of circuit, while containing these elements in circuit, when meeting some requirements, can there is electromagnetic oscillation in circuit.The generation of first heart sound is mainly due under the effect at chamber pressure reduction, the caused a series of mechanical vibration of bicuspid valve and TC cause, mechanical vibration and circuit oscillation there is similarity, therefore can be with the electromagnetic oscillation of circuit compare bicuspid valve and tricuspid mechanical vibration.In the time that vibration occurs under the effect of chamber pressure reduction for ventricle and valve model, can obtain second-order circuit equation as follows:

In above formula, △ P represents the pressure differential of left and right ventricles, and q represents to produce the flow through variation of mitral blood volume of when vibration, and Lmv represents the inertial effect of blood in bicuspid valve, and Rmv represents mitral resistance of blood flow, and elv represents the elasticity of heart coefficient of ventricle.The pressure differential △ P in ventricle and atrium can be tried to achieve by cardiovascular system realistic model, can try to achieve particular solution and the general solution of this equation according to the solution of second order differential equation, and known according to secular equation, at Rmv ²when < 4Lmv θ lv, oscillation frequency is:

$f=\frac{\sqrt{\mathrm{Lmv}\&CenterDot;\mathrm{\&theta;lv}-{\mathrm{Rmv}}^2}/4}{2\mathrm{\&pi;Lmv}}---\left(13\right)$

The pressure differential of atrium and ventricle is as a drive source, makes the circuit model of ventricle and valve composition produce electromagnetic oscillation, simulates first heart sound with this waveform.In like manner, the circuit model of right ventricle and tricuspid valve composition produces vibration under the excitation of atrium dextrum and right ventricle, forms tricuspid vibrational waveform.Bicuspid valve and tricuspid vibrational waveform synthetic effect have just formed first heart sound.

The production process of second heart sound: occur in the beginning of diastole, frequency is higher, the duration shorter (approximately 0.08 second).The reason producing is aorta petal and pulmonary valve Bav, Lav, and Rav, Btv, Bpv, Lpv, Rpv closes, and valve clashes into mutually and main artery Cart, Sart, Lart, the vibration that in Rart, blood slows down and intraventricular pressure (Pra, Prv) declines and causes rapidly.The generation of second heart sound can analogy first heart sound production process, because the pressure of ventricle and the pressure differential of angiosthenia are closed valve, available similar circuit model carries out modeling to it.From cardiovascular system realistic model, show that some cardio-vascular parameters of diastole, as the starting condition of second heart sound generation, carry out circuit simulation, can obtain the simulation waveform of second heart sound.

The production process of third heart sound and fourth heart sound can be regarded as at ventricular filling period, the volume of blood flow of chamber and the gradient of volume of blood flow produce, the frequency of the third and fourth hear sounds and amplitude and ventricle elv, the elasticity of heart coefficient of erv and ventricle are relevant to the viscous resistance (slv, srv) of blood flow.

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 _lva E _lvb E _laa E _lab E _rva E _rvb E _raa E _rab τ _lac τ _lar τ _rac τ _rar 1.43 0.03 0.07 0.09 0.26 0.022 0.04 0.06 0.4 0.05 0.4 0.05 E _lva E _lvb E _laa E _lab E _rva E _rvb E _raa E _rvb τ _lac τ _lar τ _rac τ _rar 1.43 0.03 0.07 0.09 0.26 0.022 0.04 0.06 0.4 0.05 0.4 0.05