CN113674865B - Cardiovascular system data platform built-in processing method based on transient characteristics - Google Patents
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Abstract
The invention discloses a cardiovascular system data platform built-in processing method based on transient characteristics, which comprises the following steps: constructing a cardiovascular system blood flow transient equation considering dynamic friction and wall viscoelasticity; establishing a calculation grid, converting the hyperbolic partial differential equation set into a normal differential equation set according to a characteristic line method, and integrating to obtain a characteristic line equation; solving partial differentiation of the hysteresis strain of the vascular wall to time; introducing a Kagawa dynamic friction model and partial differentiation into a characteristic line equation; the calculation result is obtained and processed in consideration of the boundary conditions. The invention adopts the one-dimensional model to replace the existing three-dimensional CFD for modeling, breaks through the technical bottleneck that the existing cardiovascular system data platform is difficult to model by adopting the one-dimensional model, not only has simple modeling, strong universality and short simulation time, but also considers the dynamic friction effect and the viscoelastic effect of the vascular wall, is more in line with the actual situation, and improves the simulation precision of the platform.
Description
Technical Field
The invention belongs to the technical field of hydrodynamic numerical simulation calculation, relates to a cardiovascular system data platform, and in particular relates to a cardiovascular system data platform built-in processing method based on transient characteristics.
Background
The cardiovascular system is also called the "circulatory system" and is a closed system of pipes consisting of the heart and blood vessels. The heart undergoes rhythmic contraction and relaxation under the control of the nervous system, ensuring that blood circulates in a certain direction and thus can be regarded as a pump. Normally, heart pump blood is delivered through blood vessels to various parts of the whole body. The cardiovascular system data platform is used as a data integration and sharing center, not only needs to acquire various cardiovascular data, but also provides higher requirements for simulation calculation.
Modeling of the cardiovascular system of a human body is an important step for realizing simulation calculation of the cardiovascular system. The existing cardiovascular system data platform is based on three-dimensional CFD modeling to acquire the blood flow state of the whole system, and the method can realize the visualization of the blood flow of the cardiovascular system through calculation and acquire simulation calculation data. However, the three-dimensional CFD system has difficult modeling, poor universality and long calculation time, and needs to meet the calculation requirement through a large server, so that real-time simulation of large platform data is difficult to realize. The one-dimensional modeling method is a conventional calculation method in the field of engineering at present, and has the advantages of simple model, wide applicability and high calculation efficiency, and can realize real-time simulation of a system level. It should be noted that the one-dimensional modeling is a simplified version of the three-dimensional model, the problem of simplifying assumptions of the system must be fully considered, reasonable assumptions must be adopted for necessary information to make the simulation result accurate, and the existing cardiovascular system data platform cannot realize the problems.
Disclosure of Invention
The invention aims to: in order to overcome the defects in the prior art, the method for processing the cardiovascular system data platform built-in based on transient characteristics is provided, and the problems that an existing cardiovascular system data platform simulation model is complex, the data acquisition time is long and the like can be solved.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for processing a cardiovascular system data platform based on transient characteristics, comprising the following steps:
S1: constructing a cardiovascular system blood flow transient equation considering dynamic friction and wall viscoelasticity;
s2: establishing a calculation grid, converting a hyperbolic partial differential equation set (a cardiovascular system blood flow transient equation) into a normal differential equation set according to a characteristic line method, and integrating to obtain a characteristic line equation;
S3: solving partial differentiation of the hysteresis strain of the vascular wall to time;
S4: introducing a Kagawa dynamic friction model and partial differentiation into a characteristic line equation;
s5: and (3) considering the heart boundary condition, and obtaining and processing a calculation result according to the characteristic line equation processed in the step (S4).
Further, the cardiovascular system blood flow transient equation constructed in the step S1 is:
Wherein H is the pressure of the blood vessel wall; v is the average flow rate of blood in the vessel; epsilon r is the vascular wall hysteresis strain; a is the speed of sound waves in blood; g is gravity acceleration; x is the distance along the axis of the vessel; t is time; d is the inner diameter of the vessel wall; ρ is the blood density; τ w is the vessel wall shear stress, τ w＝τs+τu,τs and τ u represent steady state and dynamic friction, respectively.
Further, the system of ordinary differential equations in the step S2 is specifically:
Where τ w＝τu+τu＝ρfV|V|/8+τu, f is the darcy-vessbach coefficient, when f is a fixed value, it is a steady state friction, when f=f q, it is a quasi-steady state friction, and f q is a quasi-steady state friction coefficient.
Further, in the step S2, the normal differential equation set is integrated along the positive and negative characteristic lines to obtain a characteristic line equation:
Wherein H P、HA、HB is the blood pressure of P, A, B points respectively; q P、QA、QB is the blood flow at P, A, B points, respectively; η is an integral approximation control coefficient, η=0.5 to 1; Δt is the calculation time step.
Further, the step S3 specifically includes:
Solving partial differentiation of the hysteresis strain of the vascular wall to time t, and knowing by a generalized K-V model:
Where ε r (t) is a function of ε r time; alpha is poisson's ratio; e is the thickness of the vessel wall; h (t) is a function of time of the pressure H; j (t) is the creep compliance over time t, t being a differential variable; converting the integral into a sum function, i.e.
Wherein N is the total number of integral segments; epsilon rk (t) is the kth segment value of epsilon r (t); j k and τ k are corresponding viscoelastic mechanical model parameters;
according to a convolution derivative formula, the above derivative is obtained:
I.e.
According to the element conversion method and the fractional integration, the higher-order infinitely small term is omitted, and the method can be obtainedIs a first order approximation solution of (a):
In the method, in the process of the invention,
CO_A3＝CO_A1·CO_A2 (14)
CO_A4＝CO_A1(1-CO_A2) (15)
Bringing equation (11) into equation (10) yields:
Further, the step S4 specifically includes:
For the Kagawa dynamic friction model:
In the method, in the process of the invention,
Wherein, the coefficient mi＝(1;1.16725;2.20064;3.92861;6.78788;11.6761;20.0612;34.4541;59.1642;101.59);ni＝(26.3744;72.8033;187.424;536.626;1570.6;4618.13;13601.1;40082.5;118153;348316);ν is the hemodynamic viscosity;
by taking equations (16) and (17) into the feature line equation, there is
In the method, in the process of the invention,
Let b=a/gA, r=fa Δt/2gDA 2, there is
BA＝B+ηR|QA| (23)
BB＝B+ηR|QB| (25)
At the time of programming, for unified writing, the following parameters can be added:
HP＝CP-BPQP (27)
HP＝CM+BMQP (28)
In the method, in the process of the invention,
Thus, the first and second substrates are bonded together,
Further, the step S5 specifically includes:
approximating the heart boundary as: a pump boundary and a pressurized container boundary;
For the pump boundary:
HP＝HS+QP(a1+a2QP) (32)
wherein H S is a flow breaking head, a1, a2 is a characteristic curve constant;
For a pressurized container boundary, H P is a fixed value;
the boundary conditions are combined to obtain the pressure and flow rate at the boundary.
The invention improves the existing cardiovascular system data platform, combines the correlation between the heart pump blood pressure and the ejection fraction according to the one-dimensional flow assumption of blood in the cardiovascular system, considers the viscoelasticity effect and the friction effect of blood vessels, establishes the one-dimensional cardiovascular system blood flow model for calculating the data such as the heart pump blood pressure, the ejection fraction and the like when the cardiovascular system blood flows, can solve the problems of complex simulation model, long data acquisition time and the like of the existing cardiovascular system data platform, and has important theoretical significance and practical application value for realizing the simulation of the cardiovascular system large data platform.
The beneficial effects are that: compared with the prior art, the invention improves the built-in algorithm of the cardiovascular system data platform, and has the following advantages:
1. The cardiovascular system data platform provided by the invention adopts a one-dimensional model to replace the existing three-dimensional CFD for modeling, breaks through the technical bottleneck that the existing cardiovascular system data platform is difficult to model by adopting the one-dimensional model, and has the advantages of simplicity in modeling, strong universality and short simulation time.
2. The built-in algorithm of the cardiovascular system data platform considers the dynamic friction effect and the viscoelasticity effect of the vascular wall, is more in line with the actual situation, and improves the simulation precision of the platform.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a computational grid along the vessel axis;
FIG. 3 is a graph of aortic blood volume experiments versus simulations;
fig. 4 is a graph of ventricular pressure experiments versus simulations.
Detailed Description
The present application is further illustrated in the accompanying drawings and detailed description which are to be understood as being merely illustrative of the application and not limiting of its scope, and various modifications of the application, which are equivalent to those skilled in the art upon reading the application, will fall within the scope of the application as defined in the appended claims.
The invention provides a cardiovascular system data platform built-in processing method based on transient characteristics, as shown in figure 1, comprising the following steps:
S1: constructing a cardiovascular system blood flow transient equation considering dynamic friction and wall viscoelasticity;
Wherein H is the pressure of the blood vessel wall; v is the average flow rate of blood in the vessel; epsilon r is the vascular wall hysteresis strain; a is the speed of sound waves in blood; g is gravity acceleration; x is the distance along the axis of the vessel; t is time; d is the inner diameter of the vessel wall; ρ is the blood density; τ w is the vessel wall shear stress, τ w＝τs+τu,τs and τ u represent steady state and dynamic friction, respectively.
S2: establishing a computational grid along the axial direction of the blood vessel as shown in fig. 2;
converting the hyperbolic partial differential equation set into a normal differential equation set according to a characteristic line method:
Where τ w＝τu+τu＝ρfV|V|/8+τu, f is the darcy-vessbach coefficient, when f is a fixed value, it is a steady state friction, when f=f q, it is a quasi-steady state friction, and f q is a quasi-steady state friction coefficient.
And integrating the normal differential equation set along positive and negative characteristic lines to obtain a characteristic line equation:
Wherein H P、HA、HB is the blood pressure of P, A, B points respectively; q P、QA、QB is the blood flow at P, A, B points, respectively; η is an integral approximation control coefficient, η=0.5 to 1; Δt is the calculation time step.
S3: solving partial differentiation of the hysteresis strain of the vascular wall with respect to time:
Solving partial differentiation of the hysteresis strain of the vascular wall to time t, and knowing by a generalized K-V model:
Where ε r (t) is a function of ε r time; alpha is poisson's ratio; e is the thickness of the vessel wall; h (t) is a function of time of the pressure H; j (t) is the creep compliance over time t, t being a differential variable; converting the integral into a sum function, i.e.
Wherein N is the total number of integral segments; epsilon rk (t) is the kth segment value of epsilon r (t); j k and τ k are corresponding viscoelastic mechanical model parameters;
according to a convolution derivative formula, the above derivative is obtained:
I.e.
According to the element conversion method and the fractional integration, the higher-order infinitely small term is omitted, and the method can be obtainedIs a first order approximation solution of (a):
In the method, in the process of the invention,
CO_A3＝CO_A1·CO_A2 (14)
CO_A4＝CO_A1(1-CO_A2) (15)
Bringing equation (11) into equation (10) yields:
S4: introducing a Kagawa dynamic friction model and partial differentiation into a characteristic line equation;
For the Kagawa dynamic friction model:
In the method, in the process of the invention,
Wherein, the coefficient mi＝(1;1.16725;2.20064;3.92861;6.78788;11.6761;20.0612;34.4541;59.1642;101.59);ni＝(26.3744;72.8033;187.424;536.626;1570.6;4618.13;13601.1;40082.5;118153;348316);ν is the hemodynamic viscosity;
by taking equations (16) and (17) into the feature line equation, there is
In the method, in the process of the invention,
Let b=a/gA, r=fa Δt/2gDA 2, there is
BA＝B+ηR|QA| (23)
BB＝B+ηR|QB| (25)
At the time of programming, for unified writing, the following parameters can be added:
HP＝CP-BPQP (27)
HP＝CM+BMQP (28)
In the method, in the process of the invention,
Thus, the first and second substrates are bonded together,
S5: considering the heart boundary condition, according to the characteristic line equation processed in the step S4, obtaining and processing a calculation result:
approximating the heart boundary as: a pump boundary and a pressurized container boundary;
For the pump boundary:
HP＝HS+QP(a1+a2QP) (32)
wherein H S is a flow breaking head, a1, a2 is a characteristic curve constant;
For a pressurized container boundary, H P is a fixed value;
the boundary conditions are combined to obtain the pressure and flow rate at the boundary.
In order to verify the use effect of the built-in model of the cardiovascular system data platform provided by the invention, the verification is performed by using the existing experimental data, and the main experimental parameters are as follows: the heart rate was 70 times/min, and the single shot blood volume was 802ml, aortic systolic pressure 1205mmHg, diastolic pressure 805mmHg, pulmonary systolic pressure 252mmHg, and diastolic pressure 81.5mmHg. The experimental and simulated comparison results are shown in fig. 3 and 4.
Fig. 3 shows experimental and simulated contrast plots of aortic blood volume over time. From fig. 3, the simulation result is well matched with the experimental result, and the model can well simulate the change of the aortic blood volume and the maximum and minimum flow values. Fig. 4 shows an experimental versus simulated comparison of ventricular pressure over time. As can be seen from fig. 4, the simulation result of the model is substantially identical to the actual ventricular pressure variation result, and the model can accurately reflect the pressure peak value in each period of the ventricle. For both fig. 3 and fig. 4, there is some degree of phase shift in the pressure and flow simulation results compared to the experiment, which may be due to inaccuracy in the simulated wave velocity but more accurate overall simulation results.
Claims (6)
1. The cardiovascular system data platform built-in processing method based on transient characteristics is characterized by comprising the following steps of:
S1: constructing a cardiovascular system blood flow transient equation considering dynamic friction and wall viscoelasticity;
S2: establishing a calculation grid, converting a cardiovascular system blood flow transient equation into a normal differential equation set according to a characteristic line method, and integrating to obtain a characteristic line equation;
S3: solving partial differentiation of the hysteresis strain of the vascular wall to time;
S4: introducing a Kagawa dynamic friction model and partial differentiation into a characteristic line equation;
s5: considering boundary conditions, and obtaining and processing a calculation result according to the characteristic line equation processed in the step S4;
the cardiovascular system blood flow transient equation constructed in the step S1 is as follows:
Wherein H is the pressure of the blood vessel wall; v is the average flow rate of blood in the vessel; epsilon r is the vascular wall hysteresis strain; a is the speed of sound waves in blood; g is gravity acceleration; x is the distance along the axis of the vessel; t is time; d is the inner diameter of the vessel wall; ρ is the blood density; τ w is the vessel wall shear stress, τ w＝τs+τu,τs and τ u represent steady state and dynamic friction, respectively.
2. The method for processing the cardiovascular system data platform according to claim 1, wherein the system of ordinary differential equations in step S2 is specifically:
Where τ w＝τs+τu＝ρfV|V|/8+τu, f is the darcy-vessbach coefficient, when f is a fixed value, it is a steady state friction, when f=f q, it is a quasi-steady state friction, and f q is a quasi-steady state friction coefficient.
3. The method for processing the cardiovascular system data platform according to claim 2, wherein in the step S2, the normal differential equation set is integrated along positive and negative characteristic lines to obtain characteristic line equations:
Wherein H P、HA、HB is the blood pressure of P, A, B points respectively; q P、QA、QB is the blood flow at P, A, B points, respectively; η is an integral approximation control coefficient, η=0.5 to 1; Δt is the calculation time step.
4. A method for processing a cardiovascular system data platform according to claim 3, wherein the step S3 specifically comprises:
Solving partial differentiation of the hysteresis strain of the vascular wall to time t, and knowing by a generalized K-V model:
Where ε r (t) is a function of ε r time; alpha is poisson's ratio; e is the thickness of the vessel wall; h (t) is a function of time of the pressure H; j (t) is the creep compliance over time t, t being a differential variable; converting the integral into a sum function, i.e.
Wherein N is the total number of integral segments; epsilon rk (t) is the kth segment value of epsilon r (t); j k and τ k are corresponding viscoelastic mechanical model parameters;
according to a convolution derivative formula, the above derivative is obtained:
I.e.
According to the element conversion method and the fractional integration, the higher-order infinitely small term is omitted, and the method can be obtainedIs a first order approximation solution of (a):
In the method, in the process of the invention,
CO_A3＝CO_A1·CO_A2 (14)
CO_A4＝CO_A1(1-CO_A2) (15)
Bringing equation (11) into equation (10) yields:
5. The method for processing the cardiovascular system data platform according to claim 4, wherein the step S4 specifically comprises:
For the Kagawa dynamic friction model:
In the method, in the process of the invention,
Wherein v is hemodynamic viscosity;
by taking equations (16) and (17) into the feature line equation, there is
In the method, in the process of the invention,
Let b=a/gA, r=fa Δt/2gDA 2, there is
BA＝B+ηR|QA| (23)
BB＝B+ηR|QB| (25)
At the time of programming, for unified writing, the following parameters are added:
HP＝CP-BPQP (27)
HP＝CM+BMQP (28)
In the method, in the process of the invention,
Thus, the first and second substrates are bonded together,
6. The method for processing the cardiovascular system data platform according to claim 5, wherein the step S5 specifically comprises:
Approximating the boundary as: a pump boundary and a pressurized container boundary;
For the pump boundary:
HP＝HS+QP(a1+a2QP) (32)
wherein H S is a flow breaking head, a1, a2 is a characteristic curve constant;
For a pressurized container boundary, H P is a fixed value;
the boundary conditions are combined to obtain the pressure and flow rate at the boundary.
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| 国外有压瞬变流研究进展;***;河海科技进展;第11卷(第2期);9-13 * |
| 工程管道与人体血管之比较分析;陈贵清;丁幼松;;唐山学院学报;20080720(第04期);45-48 * |
| 微血管自律运动的流体力学及血液粘弹性质的影响;郭仲三;应用数学和力学;19920215(第02期);59-65 * |
| 心血管内流场的高质量模拟实验研究（Ⅰ）──动态流体双折射测试原理与分析方法;孙永达等;实验力学;11(1);8-11 * |
| 心血管***多元数字计算机模型及其应用前景;白净;中国生物医学工程学报(第03期);51-55 * |
| 结合呼吸运动的改进型多分支心血管***建模与仿真;王末;王群;刘志文;;北京生物医学工程(第01期);47-52、113 * |
| 黏弹性输水管道中含气瞬变流压力衰减分析;Alberto Coccarelli;水利学报;第49卷(第3期);303-312 * |
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