Cardiovascular system-blood pump coupling modeling method and coupling working state analysis method

Abstract

The present disclosure discloses a cardiovascular system-blood pump coupling modeling method and a coupling working state analysis method, the cardiovascular system-blood pump coupling modeling method comprising: constructing a blood pump unsteady working hysteresis response model; constructing a cardiovascular system-blood pump coupling model structure diagram taking into account the unsteady response of the impeller machine; and constructing a cardiovascular system-blood pump coupling model taking into account the unsteady response of the impeller machine according to the blood pump unsteady working hysteresis response model and the cardiovascular system-blood pump coupling model structure diagram. The technical solution provided by the present disclosure can obtain relatively reliable coupling working characteristics, greatly facilitate the analysis of the cardiovascular system-blood pump coupling working characteristics, lay a foundation for the unsteady optimization design of the blood pump, and have important significance for reducing adverse reactions under the blood pump coupling working state.

Description

Technical Field

[0001] This disclosure belongs to the field of cardiovascular system analysis, and in particular relates to a cardiovascular system-blood pump coupling modeling method and a coupling working state analysis method. Background Technology

[0002] Numerical models of the cardiovascular system are all based on the Windkessel model, proposed in 1899 by the German physiologist Otto Frank. This model simplifies the cardiovascular system into a system consisting of the heart (pump), the aorta (elastic arterial lumen), and peripheral damping, expressed using a circuit model. This simplification greatly facilitates the relatively simple and intuitive simulation and observation of the cardiovascular system's operation.

[0003] Research in the 1970s mainly focused on simulating the relationship between the left ventricular elasticity coefficient (PV) and modeling values ​​for different pathological states. The basic relationship was described as an elastic model of the left ventricular elasticity coefficient changing over time: P(t) = E(t)(V(t) - V). d This model laid the foundation for heart research.

[0004] Building on this, many classic three-element Windkessel models emerged in the 1990s. Researchers such as Knierbein, Ferrari, and Stergiopulos used some 0-dimensional or 1-dimensional assumptions to simulate blood flow in various chambers: using fully developed tube flow to replace blood flow in the blood vessels, using damping to represent the relationship between pressure rise and flow rate inside the blood vessels, using bulk modulus to express the relationship between pressure rise and volume in the elastic cavity, and using capacitance to represent the elasticity inside the artery.

[0005] Following this, Stergiopulos et al. further incorporated the inertia of blood flow into the concept of inductance, forming a four-element Windkessel model. Among the typical three-element and four-element Windkessel models, the four-element model forms the basic framework for various current cardiovascular system models. As medical understanding of the human circulatory system deepened, in 1998, a reflex model in which exercise, etc., excites the carotid sinus and affects heart rate was also incorporated into cardiovascular system models. To meet the needs of observing and simulating different chambers, more complex multi-elastic chamber models began to develop. Different chambers in the cardiovascular system were simulated as different four-element Windkessel model units, connected in series to form cardiovascular system models of varying forms and complexities. The research of Baloa and Vollkron et al. demonstrated that by adjusting peripheral, left ventricular elasticity, heart rate, and other state parameters, cardiovascular system models could simulate different clinical pathological states, laying a solid foundation for later modeling of blood pump / cardiovascular system coupled systems.

[0006] With the development of blood pumps, it is realized that blood pumps can interact with the cardiovascular system and cause complex changes in the human blood circulation. Therefore, a blood pump model is also added to the modeling of the cardiovascular system to form a blood pump / cardiovascular system coupling model. In such a model, the flow pressure rise relationship (P-Q curve) of the steady operation of the blood pump is usually used to express the blood pump as a voltage source or a current source to observe the influence of the blood pump on the blood circulation system. In 1999, Zhou et al. used a relationship among flow Q, pressure rise ΔP and rotational speed ω to describe the working state of an implanted ventricular assist system (IVAS) blood pump. The blood pump branch was regarded as a voltage source, but the inertia of the blood flow in the blood pump branch was not reflected in this expression. In 2002, Vandenberghe et al. incorporated the inertia of the blood pump branch in the form of an inductor and thereby studied the cardiovascular system response characteristics when the Medos Microdiagonal pump generated backflow.

[0007] However, no matter how detailed the disassembly of each chamber and blood vessel in the cardiovascular system is, the current cardiovascular system-blood pump coupling model only considers the characteristics of the fluid resistance in the pump that causes changes in the flow rate, without considering the unsteady characteristics of the continuous fluid impeller pump itself and the unsteady hysteresis effect under the pulsatile boundary condition. The neglect of this effect not only cannot predict the working point performance of the blood pump under the pulsatile boundary condition, but also may further affect the prediction of blood pressure and other parameters in the cardiovascular system. SUMMARY

[0008] The present disclosure aims to at least partially solve one of the technical problems in the related art. To this end, a cardiovascular system-blood pump coupling modeling method and an unsteady coupling working state analysis method are proposed, which can directly obtain relatively reliable coupling working characteristics through zero-dimensional numerical simulation, greatly facilitating the analysis of the cardiovascular system-blood pump coupling working characteristics, laying a foundation for the unsteady optimization design of the blood pump, and having important significance for reducing adverse reactions under the coupling working state of the blood pump.

[0009] To achieve the above-mentioned purpose, the present disclosure provides a cardiovascular system-blood pump coupling modeling method, comprising:

[0010] A cardiovascular system-blood pump coupling modeling method, comprising:

[0011] constructing a blood pump unsteady working hysteresis response model;

[0012] constructing a cardiovascular system-blood pump coupling model structure diagram taking into account the unsteady response of the impeller machine;

[0013] Based on the blood pump unsteady operation hysteresis response model and the cardiovascular system-blood pump coupling model structure diagram, a cardiovascular system-blood pump coupling model incorporating the impeller unsteady response is constructed.

[0014] In a preferred embodiment, the process of constructing the blood pump unsteady hysteresis response model includes:

[0015] Based on the unsteady working principle of the compressor system and the comparison of the similarities and differences between the blood pump system and the compressor system, the principle of the blood pump coupled unsteady working is derived as the blood pump system responding to the local "instability" caused by changes in boundary conditions. The principle of the blood pump coupled unsteady working is expressed by the first-order response equation of the impeller unsteady response.

[0016] Based on the first-order response equation of the unsteady response of the impeller and the unsteady coupling working principle of the blood pump, the hysteresis response model of the unsteady operation of the blood pump is constructed.

[0017] In a preferred embodiment, the hysteresis response model of the blood pump during unsteady operation is as follows:

[0018]

[0019] Where τ is the response time constant, I ST I is the steady-state volumetric flow rate per unit time at the operating point of the pump's steady-state characteristic curve. TR This refers to the transient volumetric flow rate per unit time through the pump during coupled operation.

[0020] In a preferred embodiment, the construction of the cardiovascular system-blood pump coupling model structure that incorporates the unsteady response of the impeller includes:

[0021] When the cardiovascular system-blood pump coupling is working, the simplified route of blood flow is: left ventricle - blood pump / aortic valve - aorta - peripheral circulation - left atrium - mitral valve - left ventricle;

[0022] The flow of blood in blood vessels is modeled using the fully developed pipe flow hypothesis, and the proportional relationship between the pressure rise and volumetric flow rate inside the blood vessel is established. The proportionality coefficient is modeled as resistance in the circuit.

[0023] The volumetric flow rate per unit time is analogous to electric current; pressure is analogous to voltage; the relationship between the pressure rise and volume of an elastic cavity is expressed by the bulk modulus, and the proportionality coefficient is the capacitance.

[0024] Analyze the fluid control volume to obtain the proportional relationship between pressure and the rate of change of volumetric flow rate per unit time, and abstract the proportionality coefficient as inertia;

[0025] The series and parallel connections between various electrical analog components are determined based on the flow control system analysis.

[0026] In a preferred embodiment, according to the blood pump unsteady operation hysteresis response model and the cardiovascular system-blood pump coupling model structure diagram, the cardiovascular system-blood pump coupling model of impeller machine unsteady response is constructed by the following steps:

[0027] The coupling operation control differential equation set is derived without considering the blood pump unsteady operation hysteresis response model,

[0028]

[0029] In the formula, I represents volumetric flow rate per unit time, P represents blood static pressure, R represents resistance, C represents capacitance, L represents inductance, t represents time, and E represents elasticity; in the subscript, LV represents left ventricle, MV represents mitral valve, AV represents aortic valve, LA represents left atrium, AO represents aorta, A represents artery, C represents combination, S represents periphery, TR represents transient state during coupling operation, and ST represents steady state at a steady-state characteristic line operating point.

[0030] The control equation of the blood pump branch that needs to be added after considering the unsteady response of the impeller machine is as follows:

[0031]

[0032] In the formula, I represents volumetric flow rate per unit time, P represents blood static pressure, R represents resistance, L represents inductance, t represents time, and τ represents response time constant; in the subscript, LV represents left ventricle, AO represents aorta, s represents periphery, TR represents transient state during coupling operation, and ST represents steady state at a steady-state characteristic line operating point.

[0033] A cardiovascular system-blood pump coupling operation state analysis method, comprising the cardiovascular system-blood pump coupling model constructed by the cardiovascular system-blood pump coupling modeling method, and obtaining the unsteady operation characteristics of the cardiovascular system and the blood pump in the coupling operation state.

[0034] In a preferred embodiment, the method further comprises: comparing the unsteady operation characteristics of the cardiovascular system and the blood pump in the coupling operation state with the operation characteristics of the blood pump and the cardiovascular system obtained by the existing cardiovascular system-blood pump coupling model without considering the unsteady response of the impeller machine.

[0035] The beneficial effects of the present disclosure are: compared with the conventional method, the present disclosure increases the unsteady response of the impeller machine in principle to simulate the hysteresis response characteristics of the blood pump in the coupled working state, so that the working characteristics of the blood pump and the cardiovascular system in the coupled state can be more accurately simulated. The method described in the present disclosure only needs to increase the response time constant of the input blood pump to complete the simulation, and this response time constant is closely related to the blood pump speed, which shows that this method is simple and easy to implement. Moreover, before this, the working characteristics of the blood pump in the coupled state can only be obtained by experiment and three-dimensional numerical simulation, and by using the modeling method proposed in the present disclosure, more reliable coupled working characteristics can be directly obtained through zero-dimensional numerical simulation, so that the analysis of the cardiovascular system-blood pump coupled working characteristics is greatly facilitated, which lays a foundation for the unsteady optimization design of the blood pump, and has important significance for reducing the adverse reactions of the blood pump in the coupled working state.

[0036] Additional aspects and advantages of the present disclosure will be given in the following description section, some of which will become apparent from the following description, or will be understood through practice of the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only some embodiments of the present disclosure, and other drawings can also be obtained according to the structures shown in the drawings without creative labor for those skilled in the art.

[0038] Figure 1 is the overall flow chart of the cardiovascular system-blood pump coupling modeling method of the embodiment of the present disclosure;

[0039] Figure 2 is the logic block diagram of the cardiovascular system-blood pump coupling modeling method of the embodiment of the present disclosure;

[0040] Figure 3 is the cardiovascular system-blood pump coupling model schematic diagram of the cardiovascular system-blood pump coupling modeling method of the embodiment of the present disclosure;

[0041] Figure 4 is the cardiovascular system-blood pump coupling model structure diagram of the cardiovascular system-blood pump coupling modeling method of the embodiment of the present disclosure, which takes into account the unsteady response of the impeller machine;

[0042] Figure 5 is the blood pump unsteady working hysteresis response principle diagram of the cardiovascular system-blood pump coupling modeling method of the embodiment of the present disclosure;

[0043] Figure 6is a pump steady-state characteristic fitting state diagram of a cardiovascular system-blood pump coupling modeling method of an embodiment of the present disclosure;

[0044] Figure 7 is a left ventricle, aorta pressure pulsation condition diagram in a cycle of a cardiovascular system-blood pump coupling modeling method of an embodiment of the present disclosure;

[0045] Figure 8 is a comparison diagram of pump steady-state characteristics, blood pump unsteady working characteristics, and pump working characteristics of a cardiovascular system-blood pump coupling modeling method of an embodiment of the present disclosure;

[0046] Figure 9 is a left ventricle, aorta pressure pulsation gap change over time diagram of a cardiovascular system-blood pump coupling modeling method of an embodiment of the present disclosure compared with an existing method.

[0047] The implementation, functional features and advantages of the present disclosure will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0048] The embodiments of the present disclosure are described in detail below, and examples of the embodiments are shown in the accompanying drawings, in which the same or similar notations represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present disclosure, and cannot be understood as a limitation of the present disclosure, and all other embodiments obtained by those skilled in the art without creative labor on the basis of the embodiments in the present disclosure are within the scope of protection of the present disclosure.

[0049] Please refer to the accompanying drawings Figures 1-9 A cardiovascular system-blood pump coupling modeling method taking into account the unsteady response of an impeller machine, the specific steps of which are as follows:

[0050] Step 1: According to the first-order response equation of the unsteady response of the impeller machine and the unsteady coupling working principle of the blood pump, the corresponding blood pump unsteady working hysteresis response model is established,

[0051] That is, the product of the change rate of the unit time transient volume flow over time and the response coefficient is the difference between the unit time transient volume flow and the unit time steady-state volume flow.

[0052] Step 2: Based on the cardiovascular system-blood pump coupling working electrical analog modeling method, a cardiovascular system-blood pump coupling model structure diagram taking into account the unsteady response of the impeller machine is made;

[0053] In the electrical analogy modeling method, the unit time volume flow rate is analogous to the electric current; the pressure is analogous to the voltage; the chamber elasticity is analogous to the inverse of the capacitance; the proportional relationship between the pressure and the unit time volume flow rate is derived from the fully developed pipe flow, and the proportional coefficient is abstracted as the resistance; the proportional relationship between the pressure and the unit time volume flow rate change rate is analyzed from the fluid control body according to Newton's second law, and the proportional coefficient is abstracted as the inertia; the series and parallel relationship between the various electrical analogy components is analyzed according to the pipe flow control body; the left ventricle is analogous to the periodically variable capacitance with the time period variable elasticity; the blood pump is analogous to the voltage source, and the electric currents before and after the blood pump are equal, which are the unit time transient volume flow rates.

[0054] Step three: according to the coupling working control equation and the blood pump unsteady working hysteresis response model, a cardiovascular system-blood pump coupling model considering the unsteady response of the impeller machine is derived and established, and the control equation set is listed;

[0055] According to the blood pump unsteady working hysteresis response model obtained in step one and the blood pump branch in the model structure diagram obtained in step two, the differential equations are listed, and the blood pump branch differential control equation considering the unsteady response of the impeller machine is derived by simultaneous derivation; according to the other branch differential equations obtained in step two; the cardiovascular system-blood pump coupling model controlled by seven differential equations is obtained by simultaneous derivation;

[0056] Step four: adjusting the initial value and time step, etc., the coupling simulation is carried out;

[0057] In the matlab software, the classical fourth-order Runge-Kutta method is used to solve the differential equation set composed of the above seven equations.

[0058] Step five: cardiovascular system-blood pump unsteady coupling working state analysis;

[0059] According to the simulation results obtained in step four, the result analysis is carried out, and the unsteady working characteristics of the cardiovascular system and the blood pump in the coupling working state are obtained.

[0060] In the specific implementation process, in step one, the method for establishing the blood pump unsteady working hysteresis response model according to the first-order response equation of the impeller machine unsteady response and the blood pump unsteady coupling working principle is as follows:

[0061] Firstly, the unsteady working principle of the compressor system and the first-order response equation of the impeller machine unsteady response are analyzed, and then the principle of the blood pump coupling unsteady working is derived.

[0062] 1) Unsteady working principle of the compressor system:

[0063] In Greitzer model describing compressor unsteady response, compressor system constitutes a typical "inertia (inlet and outlet pipe) - mass (air tank) - damping (throttle valve)" system; when reducing compressor through-flow, the generated pressure rise will gradually increase, but when it approaches the critical point, further reducing the flow will make the compressor operating point jump into the stall characteristic, since the stall occurs, the stall cell in the blade rotates around the shaft and gradually develops completely, i.e. from "unstable" transient state to "stable" steady state, it needs a certain response time, therefore, the unsteady response of the impeller is generated.

[0064] 2) First-order response equation of impeller unsteady response:

[0065] For compressor transient pressure rise, the product of time constant τ and the rate of change of transient pressure rise is selected to describe the process from transient pressure rise P c to steady-state pressure rise P css , which is calculated by the following formula:

[0066]

[0067] Where P c is the compressor transient pressure rise (unit: pascal, Pa), P css is the compressor steady-state pressure rise described on the compressor steady-state characteristic line (unit: pascal, Pa), τ is the response time constant (unit: second, s), which is defined as:

[0068]

[0069] Where N is the rotor speed, r is the average rotor radius (unit: meter, m), U is the average rotor speed (unit: meter per second: m / s), since:

[0070] U = ω·r

[0071] Where ω is the angular velocity (unit: radian per second, rad / s), so the response time constant τ can be calculated by the following formula:

[0072] τ = N·T P

[0073] Where T P is the rotor period (unit: second, s).

[0074] 3) Coupling unsteady working principle of blood pump:

[0075] By analogy, the working condition of coupling compressor system and blood pump in cardiovascular system can be found that they have something in common: both the impeller and the blood pump are modeled as "discs", and the flow through the "discs" is incompressible fluid.

[0076] At the same time, there are also obvious differences between them: the internal cavity of blood pump is smaller, the flow medium is blood (often modeled as incompressible fluid), the cavity effect is weaker, and the forced pressure fluctuation of left ventricle exists at the inlet; while in the compressor system model, the working medium is air, which will express its compressibility at the plenum cavity, forming a significant cavity effect, and the inlet pressure is constant.

[0077] However, as a turbomachinery, the basic characteristics of blood pump will not change, so the analysis of the coupling unsteady working principle of blood pump is as follows:

[0078] When the blood pump is coupled to work, the forced pressure fluctuation of the left ventricle at the inlet is considered as "instability". Like the compressor, the blood pump also needs time to respond to the "instability" of the system, which is manifested as the time required for the unit time transient volume flow rate I TR (Units: milliliters per second, ml / s) through the blood pump to reach the unit time steady-state volume flow rate I ST (Units: milliliters per second, ml / s) determined by the inlet and outlet pressure boundary conditions. Therefore, the rate of change of the unit time transient volume flow rate through the blood pump with time is the product of the rate of change of the unit time transient volume flow rate with time and the response time constant τ ST -I TR .

[0079] 4) Blood pump unsteady working delay response model:

[0080] The established blood pump unsteady working delay response model is expressed as:

[0081]

[0082] Where τ is the response time constant, which is defined in the same way as the time constant in the Greitzer model, that is:

[0083]

[0084] Where the rotor speed N varies with different pump types, etc.

[0085] The symbols in the formula are as follows:

[0086] I ST - Unit time steady-state volume flow rate at the working point of pump steady-state characteristic line (unit: milliliters per second, ml / s);

[0087] I TR - Unit time transient volume flow rate through the pump when working (unit: milliliters per second, ml / s).

[0088] ​In step two, the "cardiovascular system-blood pump coupling working electrical analog modeling method" is used to make a cardiovascular system-blood pump coupling model structure diagram considering the unsteady response of the impeller machine. The method is as follows:

[0089] When the cardiovascular system-blood pump coupling works, the blood flow path is simplified as "left ventricle-blood pump / aortic valve-aorta-peripheral circulation-left atrium-mitral valve-left ventricle". The model schematic diagram is shown in the following figure Figure 3 .

[0090] Based on the cardiovascular system-blood pump coupling working electrical analog modeling method, the Poiseuille flow assumption is used to model the blood flow in the blood vessel, the pressure rise and volume flow ratio relationship in the blood vessel is established, and the proportional coefficient is modeled as a resistor in the circuit; the unit time volume flow is analogous to the electric current; the pressure is analogous to the voltage; the pressure rise and volume ratio relationship of the elastic cavity is expressed by the bulk modulus, and the proportional coefficient is analogous to the capacitance in the circuit; the proportional relationship between the pressure and the unit time volume flow rate change rate is obtained by analyzing the fluid control body according to Newton's second law, and the proportional coefficient is abstracted as inertia; the series and parallel relationship between each electrical analog component is determined according to the pipe flow control body analysis; the left ventricle is analogous to a periodic variable capacitor with a variable elasticity over time; the blood pump is analogous to a voltage source, and the current before and after the blood pump is equal, which is the unit time transient volume flow; the specific circuit structure schematic diagram is shown in the following figure Figure 4 .

[0091] The main difference from the existing model is that the unit time volume flow through the blood pump is no longer the unit time steady-state volume flow I ST at the steady-state characteristic line working point of the pump, but the unit time transient volume flow I TR ; this indicates that when the transient response occurs, the working point determined by the pump pressure rise and the transient flow is not on the pump steady-state characteristic line, as shown in the following figure Figure 5 .

[0092] The symbols in the figure are as follows:

[0093] I - unit time volume flow (unit: milliliter per second, ml / s); P - blood static pressure (unit: millimeters of mercury, mmHg); R - resistance (unit: millimeters of mercury multiplied by seconds per milliliter, mmHg·s / ml); C - capacitance (unit: milliliters per millimeter of mercury, ml / mmHg); L - inductance (unit: millimeters of mercury multiplied by seconds squared per milliliter, mmHg·s 2 / ml); t - time (unit: seconds, s); E - elasticity (unit: millimeters of mercury per milliliter, mmHg / ml); D - ideal diode.

[0094] In the figure, the specific meanings of the subscripts are as follows:

[0095] LV - left ventricle, MV - mitral valve, AV - aortic valve, LA - left atrium, AO - aorta, A - artery, C - combination, S - peripheral, TR - transient during coupling, ST - steady state at steady state characteristic line operating point, IN - inlet conduit, LVAD - blood pump, OUT - outlet conduit.

[0096] where C(t) and E(t) exist inverse relationship:

[0097] C(t) = 1 / E(t),

[0098] The calculation formula of elasticity is:

[0099]

[0100] where E max is the maximum elasticity of left ventricle, E min is the minimum elasticity of left ventricle, and the unit is: millimeters of mercury per milliliter, mmHg / ml, is a coefficient function describing the change of elasticity with time, and the calculation formula is:

[0101]

[0102] where t n is the ratio of elapsed time t to maximum time interval T max (unit: seconds, s), and the calculation formula is:

[0103]

[0104] The calculation formula of maximum time interval T max is:

[0105] T max = 0.2 + 0.15T c ,

[0106] where T c is the cardiac cycle (unit: seconds, s), and its relationship with heart rate HR (unit: beats per minute, beats / min) is:

[0107] T c = 60 / HR.

[0108] The method for establishing the cardiovascular system-blood pump coupling model considering the unsteady response of the impeller machine according to the coupling work control equation and the blood pump unsteady work delay response model described in step three is as follows:

[0109] 1) Coupling work control equation:

[0110] According to Kirchhoff's theorem, and the derived voltage and current relations at each branch and node, the control differential equations are obtained as:

[0111]

[0112] where fun(x) represents the function:

[0113]

[0114] x has no explicit physical meaning, and only represents a variable;

[0115] where P ST (I ST ) is the "pressure rise - unit time volume flow" function relation of the steady-state characteristic line of the pump at a specific rotational speed state. According to different pumps, the steady-state pressure rise P ST is written as a function of the steady-state flow rate I ST , rotational speed n (unit: revolutions per minute, r / min) or angular velocity ω (unit: radians per second, rad / s):

[0116] P ST = f(I ST , n), or P ST = f(I ST , ω),

[0117] where f represents a function;

[0118] or directly divided into different rotational speeds, and written as a steady-state flow rate I ST n polynomial form:

[0119] P ST = a1(I ST ) n +a2(I ST ) n-1 +…+a n-1 (I ST ) 1 +a n

[0120] where a1, …, a n are coefficients.

[0121] 2) Cardiovascular system-blood pump coupling model considering the unsteady response of the impeller:

[0122] According to the unsteady working delay response model of the blood pump, if it is directly and coupled with the working control equation group above to solve, two differential equations will appear, and I ST cannot be solved, so two The differential equations are derived from the differential equations of the cardiovascular system and the blood pump, and one of them is transformed into The results of the derivation are as follows:

[0123]

[0124] where L = L IN + L OUT ; R = R IN + R OUT ;

[0125] Therefore, the cardiovascular system-blood pump coupling model taking into account the unsteady response of the impeller machine is established by the following seven differential equations:

[0126]

[0127]

[0128] In steps four and five, the "adjusting initial values and time steps, etc., and performing coupling simulation; cardiovascular system-blood pump unsteady coupling working state analysis" is described, and the establishment method is as follows:

[0129] According to the clinical data, the pathological parameters of the cardiovascular system are set, such as the left ventricular elasticity E max , the size of E min , and the size of the heart rate HR;

[0130] According to the blood pump, the steady-state characteristic line of the blood pump is set, that is, the P ST (I ST ) function relationship is changed;

[0131] Reasonable initial values and time steps that have been verified to be independent of time steps are set;

[0132] The classical fourth-order Runge-Kutta method is used in the matlab software to solve the above-mentioned seven equations consisting of a differential equation group (i.e., a cardiovascular system-blood pump coupling model taking into account the unsteady response of the impeller machine);

[0133] The method is represented as:

[0134]

[0135] Wherein, the initial value may affect the convergence of the result, and therefore the simulation result obtained from the existing cardiovascular system-blood pump coupling model without taking into account the unsteady response of the impeller machine is used for initial value setting; the simulation result needs to be stable before being extracted, so as to ensure that the analyzed result is under the boundary condition of periodic pulsation.

[0136] Thus, the unsteady working characteristics of the blood pump under the coupling working state, i.e., P ST (ITR ) relationship;

[0137] P LV , P LA , P AO , P A , I C parameters over time, and calculates other parameters such as mean arterial pressure (MAP) and the like, analyzes the change over time, and obtains the unsteady working characteristics of the cardiovascular system in the coupled working state.

[0138] The unsteady working characteristics of the blood pump and the cardiovascular system in the coupled working state obtained by simulating the method of the present disclosure are compared with the working characteristics of the blood pump and the cardiovascular system obtained by the existing cardiovascular system-blood pump coupling model without considering the unsteady response of the impeller machine. The results can show the influence of the unsteady response of the impeller machine on the coupled working of the cardiovascular system-blood pump.

[0139] Compared with the prior art, the cardiovascular system-blood pump coupling modeling method considering the unsteady response of the impeller machine increases the unsteady response of the impeller machine in principle to simulate the hysteresis response characteristics of the blood pump in the coupled working state, so that the working characteristics of the blood pump and the cardiovascular system in the coupled state can be more accurately simulated. The method of the present disclosure only needs to increase the response time constant of the input blood pump to complete the simulation, and this response time constant is closely related to the blood pump speed, which embodies the simplicity and ease of implementation of the method. Moreover, before this, the working characteristics of the blood pump in the coupled state can only be obtained by experiment and three-dimensional numerical simulation. By using the modeling method proposed in the present disclosure, more reliable coupled working characteristics can be directly obtained through zero-dimensional numerical simulation, thus greatly facilitating the analysis of the cardiovascular system-blood pump coupled working characteristics, laying a foundation for the unsteady optimization design of the blood pump, and having important significance for reducing the adverse reactions of the blood pump in the coupled working state.

[0140] The key technologies and difficulties in the cardiovascular system-blood pump coupling modeling method considering the unsteady response of the impeller machine are as follows:

[0141] 1) Analogy and correlation of the unsteady response of the compressor system and the unsteady response of the blood pump,

[0142] In the compressor system model, the inlet and outlet boundary conditions are stable and unchanging, and the instability disturbance is caused by the sudden increase and decrease of the internal separation pressure rise; while in the cardiovascular system-blood pump unsteady coupling model, the disturbance source is the pressure forced vibration caused by the residual heart pulse at the inlet. Although the disturbance sources are different, the "delayed response" of the impeller in these two models does not change in nature. In the compressor system model, the principle of the delayed response of the impeller is that near the instability boundary, the impeller needs time to respond to "instability". Therefore, by analogy, the principle of the unsteady delayed response of the blood pump is that when the residual heart pulse causes sudden changes in the pressure at the inlet and outlet of the blood pump, the flow in the pump cannot change instantaneously, resulting in a delayed response. The present disclosure establishes a blood pump unsteady working delayed response model by analogy with the compressor system.

[0143] 2) Based on the cardiovascular system-blood pump coupling working electric analogy modeling method, a cardiovascular system-blood pump coupling model considering the unsteady response of the impeller is established,

[0144] The present disclosure establishes a blood pump unsteady working delayed response model by analogy, and couples with the cardiovascular system model, develops a cardiovascular system-blood pump coupling modeling method considering the unsteady response of the impeller, uses seven differential equations to solve simultaneously, establishes a cardiovascular system-blood pump coupling model considering the unsteady response of the impeller, so that the unsteady working performance of the cardiovascular system and the blood pump under the coupling working state can be simulated more truly.

[0145] The present disclosure will be further described below in combination with the drawings and actual cases:

[0146] Based on the axial flow blood pump designed according to the present disclosure, the cardiovascular system-blood pump coupling working under a typical heart failure state is simulated and analyzed to verify the feasibility of the present disclosure by using the cardiovascular system-blood pump coupling modeling method considering the unsteady response of the impeller proposed in the present disclosure.

[0147] First, the simulation process is as follows:

[0148] Step 1: Pump characteristic line determination and parameter given

[0149] The verification object selected in this example is the axial flow pump designed according to the present disclosure. In the selection, according to the designed working state, a speed of 10000 revolutions per minute is selected as the fully supporting state. According to the experimental results, the pump steady-state characteristics are fitted by a fourth-degree polynomial, and the fitting accuracy r 2 >0.99, for details, please refer to Figure 6 .

[0150] The parameters of the cardiovascular system are set to be in a healthy heart state, and the heart rate is given as 120 beats per minute, as shown in the following table:

[0151] Table 1 Parameter setting of electro-analog cardiovascular system

[0152]

[0153]

[0154] Second step: bring each parameter into the cardiovascular system-blood pump coupling model taking into account the unsteady response of the impeller machine proposed in the present disclosure, and perform numerical simulation. Bring the above cardiovascular system setting parameters and polynomial fitting of pump steady state characteristics into the model control equation set composed of 7 differential equations:

[0155]

[0156] The designed value of time step is 0.1 ms, and the calculation is stable after 7 cycles. Data is extracted from the 8th cycle for result analysis.

[0157] Third step: analysis of the unsteady coupling working state of the cardiovascular system-blood pump,

[0158] The pressure pulsation of the left ventricle and the aorta in one cycle is shown in Figure 7 It can be seen that when the axial flow pump is fully assisted, the pressure of the aorta is about 110 mmHg, and there is a small pulsation. The pressure of the left ventricle pulsates between 10-100 mmHg.

[0159] In Figure 8 , the unsteady working characteristics of the blood pump calculated by the cardiovascular system-blood pump coupling model taking into account the unsteady response of the impeller machine simulated by the method of the present disclosure (taking into account the unsteady response), and the pump working characteristics calculated by the existing generally used cardiovascular system-blood pump coupling model only considering inertia without taking into account the unsteady response of the impeller machine (only taking into account inertia) are compared. The results show that the pump characteristic loop simulated by the existing coupling model (only taking into account inertia) almost completely coincides with the steady state characteristics (steady state), while the model established in the present disclosure after taking into account the unsteady response of the impeller machine (taking into account the unsteady response) can simulate the pump unsteady characteristics loop often occurring in clinical and numerical simulation.

[0160] The difference in left ventricular and aortic pressure pulsation simulated by different cardiovascular system-blood pump coupling models before and after taking into account the unsteady response of the impeller machine Figure 9 It can be seen in that after taking into account the unsteady response of the impeller machine using the method proposed in the present disclosure, the left ventricular and aortic pressure simulated by the cardiovascular system-blood pump coupling model also changes. The maximum value of the left ventricular pressure pulsation difference is about 2.2 mmHg, and the maximum value of the aortic pressure pulsation difference is about 0.5 mmHg. From the numerical change, the influence on the left ventricular pressure is greater than the influence on the aortic pressure.

[0161] Therefore, based on the above data analysis, the following conclusions can be drawn:

[0162] 1) After adding the blood pump unsteady working hysteresis response model proposed in the present disclosure, the cardiovascular system-blood pump coupling model can simulate the characteristic ring phenomenon generated by the blood pump under the boundary condition of residual heart pressure pulsation.

[0163] 2) After using the cardiovascular system-blood pump coupling model taking into account the unsteady response of the impeller machine proposed in the present disclosure, the pressure fluctuation simulation results of the left ventricle and the aorta will also change.

[0164] 3) The present disclosure can be used to preliminarily estimate the coupling unsteady characteristics of the blood pump and the cardiovascular system, and is helpful for the development of blood pump unsteady design optimization.

[0165] In the description of the present disclosure, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present disclosure. In the present description, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, the different embodiments or examples described in the present description and the features of the different embodiments or examples can be combined and combined by those skilled in the art without contradiction.

[0166] The above is only the preferred embodiment of the present disclosure, and does not limit the patent scope of the present disclosure, and any equivalent structural transformation made by using the content of the present disclosure specification and drawings, or directly / indirectly applied in other related technical fields is included in the patent protection scope of the present disclosure.

Claims

1. A method of cardiovascular system-blood pump coupling modeling, characterized by, The application relates to a blood pump unsteady working hysteresis response model, a cardiovascular system-blood pump coupling model structure diagram considering the unsteady response of a turbomachine, and a cardiovascular system-blood pump coupling model considering the unsteady response of a turbomachine. The application relates to a blood pump unsteady working hysteresis response model, a cardiovascular system-blood pump coupling model structure diagram considering the unsteady response of a turbomachine, and a cardiovascular system-blood pump coupling model considering the unsteady response of a turbomachine. The process of constructing the blood pump unsteady working hysteresis response model comprises the following steps: According to the unsteady working principle of a compressor system and the similarities and differences between the blood pump system and the compressor system, the principle of blood pump coupling unsteady working is derived, that is, the blood pump system responds to the local "instability" of the boundary condition change, and the principle of blood pump coupling unsteady working is expressed by using a first-order response equation of the unsteady response of a turbomachine; According to the first-order response equation of the unsteady response of a turbomachine and the principle of blood pump unsteady coupling working, the blood pump unsteady working hysteresis response model is constructed. The blood pump unsteady working hysteresis response model is as follows: The process of constructing the cardiovascular system-blood pump coupling model structure diagram considering the unsteady response of a turbomachine comprises the following steps: When the cardiovascular system-blood pump coupling works, the blood flow path is simplified as: left ventricle-blood pump / aortic valve-aorta-peripheral circulation-left atrium-mitral valve-left ventricle; where τ is the response time constant, I ST is the steady state volumetric flow rate per unit time at the pump steady state characteristic line operating point, I TR is the transient volumetric flow rate per unit time through the pump when coupled in operation; The fully developed pipe flow assumption is adopted to model the blood flow in the blood vessel, the proportional relationship between the pressure rise and the volume flow rate in the blood vessel is established, and the proportional coefficient is modeled as a resistor in the circuit; The unit time volume flow rate is analogous to the electric current; the pressure is analogous to the voltage; the volume modulus is used to express the volume-pressure proportional relationship of the elastic cavity, and the proportional coefficient is the capacitance; The proportional relationship between the pressure and the unit time volume flow rate change rate of the fluid control body is analyzed, and the proportional coefficient is abstracted as the inertia; According to the pipe flow control body, the series-parallel relationship among the electric analog components is judged. According to the blood pump unsteady working hysteresis response model and the cardiovascular system-blood pump coupling model structure diagram, the cardiovascular system-blood pump coupling model considering the unsteady response of a turbomachine is constructed. The coupling working control differential equation group without considering the blood pump unsteady working hysteresis response model is obtained, 2. The cardiovascular system-blood pump coupling modeling method of claim 1, wherein, Wherein, the symbols: I is the unit time volume flow rate, P is the blood static pressure, R is the resistor, C is the capacitor, L is the inductor, t is the time, and E is the elasticity; the subscripts: LV is the left ventricle, MV is the mitral valve, AV is the aortic valve, LA is the left atrium, AO is the aorta, A is the artery, C is the combination, S is the periphery, TR is the transient state during coupling working, and ST is the steady state at the steady state characteristic line working point; The control equation of the blood pump branch that needs to be added after considering the unsteady response of a turbomachine is as follows: Wherein, the symbols: I is the unit time volume flow rate, P is the blood static pressure, R is the resistor, L is the inductor, t is the time, and tau is the response time constant; the subscripts: LV is the left ventricle, AO is the aorta, S is the periphery, TR is the transient state during coupling working, and ST is the steady state at the steady state characteristic line working point. The application relates to a blood pump unsteady working hysteresis response model, a cardiovascular system-blood pump coupling model structure diagram considering the unsteady response of a turbomachine, and a cardiovascular system-blood pump coupling model considering the unsteady response of a turbomachine. ​ 3. Cardiovascular system - blood pump coupling working state analysis method, characterized by, ​ The cardiovascular system-blood pump coupling model constructed according to the cardiovascular system-blood pump coupling modeling method of any one of claims 1-2 obtains the unsteady working characteristics of the cardiovascular system and the blood pump in the coupling working state.

4. The cardiovascular system-blood pump coupling working state analysis method according to claim 3, characterized in that, The method further comprises: comparing the unsteady working characteristics of the cardiovascular system and the blood pump in the coupling working state with the working characteristics of the blood pump and the cardiovascular system obtained by an existing cardiovascular system-blood pump coupling model without taking into account the unsteady response of the impeller machine.

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