CN104021301B

CN104021301B - Magnetic resonance imaging simulating method for irrelevant movement in myocardial microcirculation perfusion voxel

Info

Publication number: CN104021301B
Application number: CN201410273349.2A
Authority: CN
Inventors: 刘宛予; 郐子翔; 黄建平; 朱跃敏
Original assignee: Harbin Institute of Technology Shenzhen
Current assignee: Harbin Institute of Technology Shenzhen
Priority date: 2014-06-18
Filing date: 2014-06-18
Publication date: 2017-01-11
Anticipated expiration: 2034-06-18
Also published as: CN104021301A

Abstract

A magnetic resonance imaging simulation method for incoherent motion in myocardial microcirculation perfusion voxel, the invention belongs to the field of computer simulation of magnetic resonance imaging, it aims to solve the inability to accurately quantify the detection effect of the qualitative evaluation method of the in vivo experiment, and the difficulty of evaluating the quantitative evaluation method of the traditional simulation experiment Large scale, high evaluation cost, and long evaluation period. Simulation method: 1. Establish a virtual myocardial microcirculation network model by using network avoidance algorithm, boundary avoidance algorithm and fluid branch constraint algorithm; 2. Establish blood perfusion model in blood vessel and water molecule diffusion model outside blood vessel; The principle of resonance imaging simulates the mechanism of IVIM MRI to generate magnetic resonance attenuation signals; 4. Non-linear fitting of the attenuation signals obtains the simulation detection results of the myocardial microcirculation perfusion model. The method of the invention can provide reliable simulation quantitative evaluation conclusions.

Description

Intravoxel incoherent motion MRI simulation method for myocardial microcirculation perfusion

技术领域technical field

本发明属于磁共振成像计算机仿真领域。The invention belongs to the field of magnetic resonance imaging computer simulation.

背景技术Background technique

心肌微循环是微动脉、毛细血管和小静脉之间的血液循环，是心肌细胞与血液进行物质交换的重要场所。心肌微循环灌注异常会引发相应心肌缺血等临床症状，严重威胁人类健康。体素内不相干运动磁共振成像(Intra-voxel Incoherent Motion MagneticResonance Imaging，IVIM MRI)技术是近年来新兴的一种微循环灌注成像手段，是在扩散加权磁共振成像技术基础上发展而来的，其原理是利用流向随机的灌注血液在扩散敏感梯度作用下质子群相位严重不相干的物理现象，生成多b值(衰减因子)磁共振衰减信号，并最终从衰减信号中获得血液容积分数和血流速度等微循环灌注信息。由于IVIM MRI技术具有无需显像剂以及分辨率高等优点，目前国内外正在积极尝试将其应用于心肌微循环灌注的临床检测，其中，检测效果的评估尤为重要。Myocardial microcirculation is the blood circulation between arterioles, capillaries and venules, and is an important place for material exchange between myocardial cells and blood. Abnormal myocardial microcirculation perfusion can cause corresponding clinical symptoms such as myocardial ischemia, which seriously threatens human health. Intra-voxel Incoherent Motion Magnetic Resonance Imaging (IVIM MRI) technology is an emerging microcirculation perfusion imaging method in recent years, which is developed on the basis of diffusion-weighted MRI technology. The principle is to use the physical phenomenon that the phase of the proton group is seriously incoherent under the action of the diffusion-sensitive gradient of perfused blood in a random direction to generate multiple b-value (attenuation factors) magnetic resonance attenuation signals, and finally obtain the blood volume fraction and blood volume fraction from the attenuation signals. Microcirculation perfusion information such as flow velocity. Because IVIM MRI technology has the advantages of no imaging agent and high resolution, it is currently being actively tried to be applied to the clinical detection of myocardial microcirculation perfusion at home and abroad, and the evaluation of the detection effect is particularly important.

成像技术检测效果评估方法包括活体实验定性评估和仿真实验定量评估。活体实验定性评估是在不明确被测活体组织真实生理参数的情况下，仅通过将活体组织成像结果与该组织普遍意义上的生理参数比对，粗略估计成像技术的检测效果。由于活体实验定性评估无法精确量化检测效果，所以需要与仿真实验定量评估相结合，才能获得全面、可靠的评估结论。传统的仿真实验定量评估先要制作能够模拟生物组织生理特征的仿真实体，再通过统计实体成像结果与实体参数之间的误差，得到检测效果的定量评估结论。然而，由于心肌微循环的生理结构极为复杂，所以仿真实体的制作难度将明显增加。同时，制作理想的仿真实体需要精密的加工设备和复杂的制作工艺，这将显著增加评估成本和评估周期。基于上述原因，目前国内外仅能通过活体实验定性评估方法粗略估计心肌微循环灌注IVIMMRI的检测效果。由于缺乏精确量化的评估结论，严重阻碍了IVIM MRI技术在心肌微循环检测方面的临床应用。The detection effect evaluation methods of imaging technology include qualitative evaluation of in vivo experiments and quantitative evaluation of simulation experiments. The qualitative evaluation of in vivo experiments is to roughly estimate the detection effect of imaging technology by comparing the imaging results of in vivo tissue with the general physiological parameters of the tissue under the condition that the real physiological parameters of the measured living tissue are not clear. Since the qualitative evaluation of the in vivo experiment cannot accurately quantify the detection effect, it needs to be combined with the quantitative evaluation of the simulation experiment to obtain a comprehensive and reliable evaluation conclusion. In the quantitative evaluation of traditional simulation experiments, it is necessary to first create a simulation entity that can simulate the physiological characteristics of biological tissues, and then obtain a quantitative evaluation conclusion of the detection effect by counting the errors between the imaging results of the entity and the entity parameters. However, due to the extremely complex physiological structure of myocardial microcirculation, the difficulty of making the simulation entity will increase significantly. At the same time, making an ideal simulation entity requires sophisticated processing equipment and complex manufacturing techniques, which will significantly increase the evaluation cost and evaluation cycle. Based on the above reasons, the detection effect of IVIMMRI on myocardial microcirculation perfusion can only be roughly estimated by qualitative evaluation methods in vivo experiments at home and abroad. The clinical application of IVIM MRI technology in the detection of myocardial microcirculation is seriously hindered by the lack of accurate and quantitative assessment conclusions.

发明内容Contents of the invention

本发明的目的是为了解决活体实验定性评估方法不能精确量化检测结果，以及传统的仿真实验定量评估方法评估难度大，评估成本高，评估周期长的问题，而提出了心肌微循环灌注体素内不相干运动磁共振成像仿真方法。The purpose of the present invention is to solve the problems that the qualitative evaluation method of the in vivo experiment cannot accurately quantify the detection results, and the traditional quantitative evaluation method of the simulation experiment is difficult to evaluate, the evaluation cost is high, and the evaluation period is long. Simulation methods for incoherent motion magnetic resonance imaging.

本发明心肌微循环灌注体素内不相干运动磁共振成像仿真方法按下列步骤实现：The MRI simulation method of incoherent motion in the myocardial microcirculation perfusion voxel of the present invention is realized according to the following steps:

一、采用网络避让方程(1)使将要生成的血管段朝向函数f₁(x)为最小值的方向生长；1. Use the network avoidance equation (1) to make the blood vessel segment to be generated grow towards the direction where the function f ₁ (x) is the minimum value;

${f f}_{11} ((x x)) = = {Σ Σ}_{n no = = 11}^{N N} \frac{{U u}_{n no}}{{| | | | x x - - {x x}_{n no} | | | |}^{{β β}_{v v}}} - - - - - - ((11))$

其网络避让方程(1)中x表示将要生成的血管段轴线的终点，x_n表示已生成血管段的质心，N表示已生成血管的段数，β_v表示衰减系数，U_n表示避让权值，U_n的表达式为：In its network avoidance equation (1), x represents the end point of the axis of the blood vessel segment to be generated, x _n represents the centroid of the generated blood vessel segment, N represents the number of generated blood vessel segments, β _v represents the attenuation coefficient, U _n represents the avoidance weight, The expression of U _n is:

${U u}_{n no} = = {R R}_{n no}^{22} \times \times {L L}_{n no} - - - - - - ((22))$

其U_n表达式(2)中R_n表示已生成的第n段血管的半径，L_n表示已生成的第n段血管的长度；In its U _n expression (2), R _n represents the radius of the nth section blood vessel that has been generated, and L _n represents the length of the nth section blood vessel that has been generated;

采用边界避让方程(3)避免将要生成的血管段冲出组织边界，边界避让方程为：The boundary avoidance equation (3) is used to avoid the blood vessel segment to be generated from rushing out of the tissue boundary, and the boundary avoidance equation is:

${f f}_{22} ((x x)) = = {Σ Σ}_{b b = = 11}^{66} \frac{{U u}_{b b}}{{| | | | x x - - {x x}_{b b} | | | |}^{{β β}_{b b}}} - - - - - - ((33))$

其边界避让方程(3)中x表示将要生成的血管段轴线的终点，x_b表示x在边界上的投影，β_b表示衰减系数，U_b表示边界避让权值，U_b的表达式为：In the boundary avoidance equation (3), x represents the end point of the axis of the blood vessel segment to be generated, x _b represents the projection of x on the boundary, β _b represents the attenuation coefficient, U _b represents the boundary avoidance weight, and the expression of U _b is:

${U u}_{b b} = = \frac{11}{N N} {Σ Σ}_{n no = = 11}^{N N} {U u}_{n no} - - - - - - ((44))$

其U_b表达式(4)中U_n表示避让权值；In its U _b expression (4), U _n represents avoidance weight;

采用最优分枝角度方程(5)计算子段与母段的夹角；Using optimal branch angle equation (5) to calculate the angle between the child section and the parent section;

${θ θ}_{11} = = {cos cos}^{- - 11} [[\frac{\frac{11}{{r r}_{00}^{44}} + + \frac{{r r}_{11}^{44}}{{(({r r}_{11}^{44} + + {r r}_{22}^{44}))}^{22}} + + \frac{{r r}_{22}^{44}}{{(({r r}_{11}^{44} + + {r r}_{22}^{44}))}^{22}}}{\frac{22 {r r}_{11}^{22}}{{(({r r}_{11}^{44} + + {r r}_{22}^{44}))}^{22} {r r}_{00}^{22}}}]] - - - - - - ((55))$

其最优分枝角度方程(5)中θ₁表示子段a与母段的夹角，r₁表示子段a的半径，r₂表示子段b的半径，r₀表示母段的半径，基于θ₁建立子段a的流体分支约束方程(6)；In its optimal branching angle equation (5), θ ₁ represents the angle between the sub-section a and the parent section, r ₁ represents the radius of the sub-section a, r ₂ represents the radius of the sub-section b, and r ₀ represents the radius of the parent section, Establish the fluid branch constraint equation (6) of subsection a based on θ ₁ ;

${f f}_{33} ((x x)) = = - - {U u}_{l l} {((| | ((x x - - {x x}_{p p})) \cdot \cdot v v - - cos cos {θ θ}_{11} | |))}^{{β β}_{33}} - - - - - - ((66))$

其流体分支约束方程(6)中U_l表示流体分支约束方程相对于网络避让方程(1)和边界避让方程(3)在最终的心肌微循环网络建模方程中的权重，β₃表示抑制因子，v表示母段的方向矢量，x_p表示将要生成的血管段轴线的起点；In its fluid branch constraint equation (6), U1 represents the weight of the fluid branch constraint equation relative to the network avoidance equation ( ₁ ) and the boundary avoidance equation ( ₃ ) in the final myocardial microcirculation network modeling equation, and β3 represents the inhibitory factor , v represents the direction vector of the parent segment, x _p represents the starting point of the axis of the vessel segment to be generated;

将网络避让方程(1)、边界避让方程(3)和流体分支约束方程(6)加和，建立心肌微循环网络建模方程(7)，心肌微循环网络建模方程(7)的表达式为：Add the network avoidance equation (1), the boundary avoidance equation (3) and the fluid branch constraint equation (6) to establish the myocardial microcirculation network modeling equation (7), and the expression of the myocardial microcirculation network modeling equation (7) for:

$f f ((x x)) = = {Σ Σ}_{n no = = 11}^{N N} \frac{{U u}_{n no}}{{| | | | x x - - {x x}_{n no} | | | |}^{{β β}_{v v}}} + + {Σ Σ}_{b b = = 11}^{66} \frac{{U u}_{b b}}{{| | | | x x - - {x x}_{b b} | | | |}^{{β β}_{b b}}} - - {U u}_{l l} {((| | ((x x - - {x x}_{p p})) \cdot \cdot v v - - cos cos θ θ | |))}^{{β β}_{33}} - - - - - - ((77));;$

二、模拟血流灌注，通过水分子定向流动位移方程(8)计算血管内水分子定向流动的位移，水分子定向流动的位移方程为：2. To simulate blood perfusion, calculate the displacement of the directional flow of water molecules in the blood vessel through the displacement equation (8) of the directional flow of water molecules. The displacement equation of the directional flow of water molecules is:

其水分子定向流动的位移方程(8)中Δp表示水分子流动位移，表示血管轴线处的最大流速，r表示水分子到血管轴线的距离，R表示血管半径，τ表示单步行走时间；In the displacement equation (8) of the directional flow of water molecules, Δp represents the flow displacement of water molecules, Indicates the maximum flow velocity at the axis of the vessel, r indicates the distance from the water molecule to the axis of the vessel, R indicates the radius of the vessel, and τ indicates the single-step walking time;

模拟血管外水分子的扩散运动，通过水分子扩散位移模值表达式(9)计算水分子扩散位移的大小，水分子扩散位移模值表达式(9)为：Simulate the diffusion movement of water molecules outside the blood vessel, and calculate the size of the water molecule diffusion displacement through the water molecule diffusion displacement modulus expression (9). The water molecule diffusion displacement modulus expression (9) is:

$Δx Δx = = \sqrt{22 mDτ mDτ} ((22 / / \sqrt{π π} {&Integral; &Integral;}_{00}^{22 q q - - 11} {e e}^{- - {x x}^{22}} dx dx)) - - - - - - ((99))$

其水分子扩散位移模值表达式(9)中Δx表示水分子单步行走的位移大小，m表示扩散空间维数，τ表示单步行走时间，D表示水分子自由扩散系数，q表示(0,1)之间的随机数；In the water molecule diffusion displacement modulus expression (9), Δx represents the displacement of water molecules in a single step, m represents the dimension of the diffusion space, τ represents the time of a single step, D represents the free diffusion coefficient of water molecules, and q represents (0 , a random number between 1);

通过水分子扩散位移方向表达式(10)计算水分子的扩散位移方向，水分子扩散位移方向表达式(10)为：Calculate the diffusion displacement direction of water molecules through the expression (10) of the diffusion displacement direction of water molecules, and the expression (10) of the diffusion displacement direction of water molecules is:

其水分子扩散位移方向表达式(10)中表示水分子扩散位移单位矢量在笛卡尔坐标系x轴、y轴、z轴上的投影，θ表示扩散位移方向与z轴正方向的夹角，φ表示扩散位移在xOy平面上的投影与x轴正方向的夹角；Its water molecule diffusion displacement direction expression (10) Indicates the projection of the water molecule diffusion displacement unit vector on the x-axis, y-axis and z-axis of the Cartesian coordinate system, θ represents the angle between the diffusion displacement direction and the positive direction of the z-axis, and φ represents the projection of the diffusion displacement on the xOy plane and x The included angle in the positive direction of the axis;

三、基于扩散磁共振成像原理以及步骤二中水分子流动位移和水分子扩散位移，计算由水分子位移导致的相位离散，由水分子位移导致的相位离散公式(11)为：3. Based on the principle of diffusion magnetic resonance imaging and the water molecule flow displacement and water molecule diffusion displacement in step 2, calculate the phase dispersion caused by the water molecule displacement. The phase dispersion formula (11) caused by the water molecule displacement is:

其由水分子位移导致的相位离散公式(11)中表示第i个水分子第j步行走导致的相位离散值，γ表示氢核的旋磁比，表示扩散敏感梯度，δ表示扩散敏感梯度持续时间，表示第i个水分子第j步行走的位移；In the phase dispersion formula (11) caused by the displacement of water molecules Indicates the phase dispersion value caused by the i-th water molecule walking in the j-th step, γ indicates the gyromagnetic ratio of the hydrogen nucleus, represents the diffusion-sensitive gradient, δ represents the duration of the diffusion-sensitive gradient, Indicates the displacement of the i-th water molecule in the j-th step;

在双极梯度脉冲自旋回波序列作用下，设定双极梯度脉冲的时间间隔为Δ，水分子单步行走(包括流动和扩散)时间为τ，则水分子行走步数k＝Δ/τ(12)，在关闭双极梯度脉冲后，水分子i的位移导致的相位离散为Δ时间内水分子i每一步行走位移产生的相位离散之和，水分子i每一步行走位移产生的相位离散之和的表达式为然后依据扩散磁共振成像原理，单位体素内所有水分子相位离散引起的磁共振信号衰减式(14)为：Under the action of the bipolar gradient pulse spin-echo sequence, set the time interval of the bipolar gradient pulse as Δ, and the single-step walking (including flow and diffusion) time of water molecules as τ, then the number of walking steps of water molecules k=Δ/τ (12), after the bipolar gradient pulse is turned off, the phase dispersion caused by the displacement of water molecule i is the sum of the phase dispersion produced by each walking displacement of water molecule i within Δ time, and the phase dispersion produced by each walking displacement of water molecule i The expression of the sum is Then, according to the principle of diffusion magnetic resonance imaging, the magnetic resonance signal attenuation formula (14) caused by the phase dispersion of all water molecules in a unit voxel is:

其中S表示扩散敏感梯度作用下的磁共振信号，S₀表示未施加扩散敏感梯度的磁共振信号，n表示单位体素内水分子的个数；Where S represents the magnetic resonance signal under the action of the diffusion sensitive gradient, S ₀ represents the magnetic resonance signal without the diffusion sensitive gradient, and n represents the number of water molecules in the unit voxel;

由IVIM MRI中磁共振信号衰减表达式和单位体素内所有水分子相位离散引起的磁共振信号衰减式(14)可得：The expression of magnetic resonance signal attenuation in IVIM MRI And the magnetic resonance signal attenuation formula (14) caused by the phase dispersion of all water molecules in a unit voxel can be obtained:

其中f表示血液容积分数，D表示扩散系数，D^*表示伪扩散系数，b表示衰减因子，在双极梯度脉冲自旋回波序列中，b的表达式为：where f represents the blood volume fraction, D represents the diffusion coefficient, D ^* represents the pseudo-diffusion coefficient, and b represents the attenuation factor. In the bipolar gradient pulsed spin-echo sequence, the expression of b is:

四、基于由水分子位移导致的相位离散公式(11)、水分子i每一步行走位移产生的相位离散之和的表达式(13)和单位体素内所有水分子相位离散引起的磁共振信号衰减式(14)，计算不同值对应的磁共振衰减信号S/S₀，从而获得一系列S/S₀的离散值，然后基于b的表达式(17)，计算不同值对应的b值，从而获得一系列b的离散值，基于已获得的S/S₀和b的离散值，最后对磁共振信号衰减表达式(15)进行非线性拟合，获得心肌微循环灌注模型的IVIM MRI仿真检测结果。4. Based on the phase dispersion formula (11) caused by the displacement of water molecules, the expression (13) of the sum of the phase dispersion produced by each step of water molecule i’s displacement and the magnetic resonance signal caused by the phase dispersion of all water molecules in a unit voxel Attenuation formula (14), the calculation is different value corresponding to the magnetic resonance attenuation signal S/S ₀ , so as to obtain a series of discrete values of S/S ₀ , and then based on the expression (17) of b, calculate the different value corresponding to the value of b, so as to obtain a series of discrete values of b, based on the obtained discrete values of S/S ₀ and b, and finally perform nonlinear fitting on the magnetic resonance signal attenuation expression (15) to obtain myocardial microcirculation IVIM MRI simulation test results of the perfusion model.

本发明首先基于真实心脏微循环网络的几何和拓扑结构，利用网络避让算法、边界避让算法及流体分支约束算法，结合计算机强大的运算能力，建立虚拟心肌微循环网络模型；然后，基于心脏微循环灌注的组织学知识，建立血管内血流灌注模型，基于蒙特卡洛法，建立血管外水分子扩散运动模型，进而建立心肌微循环灌注模型；再在计算机中模拟IVIMMRI机制，计算不同幅值的扩散敏感梯度对应的磁共振衰减信号；最后对衰减信号非线性拟合，获得心肌微循环灌注模型的IVIM MRI计算机仿真实验检测结果。并计算检测结果与心肌微循环灌注模型中各参数之间的误差，由此实现对IVIM MRI技术检测效果的定量评估。Firstly, based on the geometric and topological structure of the real cardiac microcirculation network, the present invention uses the network avoidance algorithm, boundary avoidance algorithm and fluid branch constraint algorithm, combined with the powerful computing power of the computer, to establish a virtual myocardial microcirculation network model; then, based on the cardiac microcirculation Based on the histological knowledge of perfusion, establish the intravascular blood perfusion model, based on the Monte Carlo method, establish the extravascular water molecule diffusion model, and then establish the myocardial microcirculation perfusion model; then simulate the IVIMMRI mechanism in the computer to calculate the different amplitude The magnetic resonance attenuation signal corresponding to the diffusion-sensitive gradient; finally, the attenuation signal is nonlinearly fitted to obtain the IVIM MRI computer simulation test results of the myocardial microcirculation perfusion model. And calculate the error between the detection result and each parameter in the myocardial microcirculation perfusion model, thereby realizing the quantitative evaluation of the detection effect of IVIM MRI technology.

本发明心肌微循环灌注体素内不相干运动磁共振成像仿真方法包含以下有益效果：The MRI simulation method of incoherent motion within the myocardial microcirculation perfusion voxel of the present invention includes the following beneficial effects:

(1)为心肌微循环灌注的IVIM MRI检测效果提供可靠的仿真定量评估结论，促进其临床应用；(1) Provide reliable simulation and quantitative evaluation conclusions for the IVIM MRI detection effect of myocardial microcirculation perfusion, and promote its clinical application;

(2)利用网络避让算法、边界避让算法及流体分支约束算法，结合计算机强大的运算能力，建立虚拟单位体素心肌微循环网络模型，无需考虑仿真实体的制作难度，并且能够最大程度地逼近心肌微循环网络真实的生理结构。(2) Using the network avoidance algorithm, the boundary avoidance algorithm and the fluid branch constraint algorithm, combined with the powerful computing power of the computer, a virtual unit voxel myocardial microcirculation network model is established, without considering the difficulty of making the simulation entity, and it can approximate the myocardium to the greatest extent The real physiological structure of the microcirculatory network.

(3)在计算机中建立虚拟心肌微循环网络模型，无需精密的加工设备和复杂的制作工艺，相比传统的仿真实验评估方法，显著降低评估成本，缩短评估周期。(3) Establishing a virtual myocardial microcirculation network model in the computer does not require sophisticated processing equipment and complicated manufacturing techniques. Compared with traditional simulation experiment evaluation methods, the evaluation cost is significantly reduced and the evaluation cycle is shortened.

(4)由于建立心肌微循环灌注模型及模拟IVIM MRI机制均在计算机中进行，所以能够连续调整模型参数和成像参数(δ、Δ)，得到丰富的误差统计数据，相比只能获得少量误差统计数据的传统仿真实验定量评估方法，评估结果的准确性显著提高。(4) Since the establishment of the myocardial microcirculation perfusion model and the simulation of the IVIM MRI mechanism are carried out in the computer, the model parameters and imaging parameters can be continuously adjusted ( δ, Δ), to obtain rich error statistics, compared with the traditional quantitative evaluation method of simulation experiments that can only obtain a small amount of error statistics, the accuracy of the evaluation results is significantly improved.

附图说明Description of drawings

图1为心肌微循环灌注体素内不相干运动磁共振成像仿真方法的流程图；Fig. 1 is the flowchart of the magnetic resonance imaging simulation method of incoherent motion in the myocardial microcirculation perfusion voxel;

图2为步骤一中网络避让算法的几何示意图；Fig. 2 is the geometric diagram of the network avoidance algorithm in step one;

图3为将要生成的血管段轴线的终点在组织边界上的投影；Fig. 3 is the projection of the end point of the axis of the blood vessel segment to be generated on the tissue boundary;

图4为步骤一中流体分支约束算法的几何示意图，1—子段a，2—子段b，3—母段；Fig. 4 is a schematic diagram of the geometry of the fluid branch constraint algorithm in step 1, 1—subsection a, 2—subsection b, 3—parent section;

图5为步骤二中心肌微循环网络中血流的Laminar流示意图；Fig. 5 is the Laminar flow schematic diagram of the blood flow in the myocardial microcirculation network in step two;

图6为步骤二中单个水分子在t1到t2时间段内扩散示意图；Fig. 6 is a schematic diagram of the diffusion of a single water molecule in the time period from t1 to t2 in step 2;

图7为实施例一建立的500×500×500μm³体素内虚拟心肌微循环网络模型图；7 is a virtual myocardial microcirculation network model diagram in a 500×500×500 μm ³ voxel established in Example 1;

图8为实施例一在不同值下对应的S/S₀值和b值以及Levenberg–Marquardt的非线性拟合曲线。Fig. 8 is embodiment one in different The corresponding S/S ₀ value and b value under the value and the nonlinear fitting curve of Levenberg–Marquardt.

具体实施方式detailed description

具体实施方式一：本实施方式心肌微循环灌注体素内不相干运动磁共振成像仿真方法按下列步骤实现：Specific Embodiment 1: In this embodiment, the MRI simulation method of incoherent motion in the myocardial microcirculation perfusion voxel is implemented according to the following steps:

${f f}_{33} ((x x)) = = - - {U u}_{l l} {((| | ((x x - - {x x}_{p p})) \cdot &Center Dot; v v - - cos cos {θ θ}_{11} | |))}^{{β β}_{33}} - - - - - - ((66))$

$f f ((x x)) = = {Σ Σ}_{n no = = 11}^{N N} \frac{{U u}_{n no}}{{| | | | x x - - {x x}_{n no} | | | |}^{{β β}_{v v}}} + + {Σ Σ}_{b b = = 11}^{66} \frac{{U u}_{b b}}{{| | | | x x - - {x x}_{b b} | | | |}^{{β β}_{b b}}} - - {U u}_{l l} {((| | ((x x - - {x x}_{p p})) \cdot &Center Dot; v v - - cos cos θ θ | |))}^{{β β}_{33}} - - - - - - ((77));;$

本实施方式步骤一中利用网络避让算法，避免将要生成的血管段与已生成的血管相互交叠，同时促使将要生成的血管段向血管分布稀疏的空间延伸，网络避让算法中的β_v表示衰减系数，降低β_v可强化远处血管段对将要生成血管段的影响；边界避让算法中的β_b也表示衰减系数，降低β_b可强化远处边界对将要生成血管段的影响。步骤一建立虚拟心肌微循环网络模型时除了避免血管之间，血管与边界之间彼此交叠外，还要保证血管分支角度符合血液动力学。心肌微循环网络中血管通常以二叉树的形式产生新的分支，依据血液动力学，子段与母段的夹角应保证血液流经夹角时所受的粘性摩擦应力最小。因此采用最优分枝角度方程。流体分支约束方程中β₃表示抑制因子，β₃越大，对非最优分支角度的抑制越大，反之亦然。In the first step of this embodiment, the network avoidance algorithm is used to avoid the overlapping of the generated blood vessel segment and the generated blood vessel, and at the same time, to promote the extension of the to-be-generated blood vessel segment to the space where the distribution of blood vessels is sparse. The β _v in the network avoidance algorithm represents attenuation Coefficient, reducing β _v can strengthen the influence of distant vascular segments on the vascular segment to be generated; β _b in the boundary avoidance algorithm also represents the attenuation coefficient, reducing β _b can strengthen the influence of the distant boundary on the vascular segment to be generated. Step 1: When establishing a virtual myocardial microcirculation network model, in addition to avoiding overlapping between blood vessels and between blood vessels and boundaries, it is also necessary to ensure that the branching angles of blood vessels conform to hemodynamics. Blood vessels in the myocardial microcirculation network usually generate new branches in the form of a binary tree. According to hemodynamics, the angle between the subsection and the mother section should ensure that the viscous friction stress on the blood flowing through the angle is minimal. Therefore, the optimal branching angle equation is adopted. _In the fluid branching constraint equation, β3 represents the suppression factor, and the larger the β3, the greater the suppression of non _- optimal branching angles, and vice versa.

本实施方式步骤二模拟血流灌注等同于模拟大量水分子的定向流动。心肌微循环网络中的血流以Laminar流为主，即水分子沿着与血管轴平行的方向作平滑直线运动，流速在血管轴线处最大，近壁处最小，血管内水分子的平均流速与最大流速之比等于0.5。In step 2 of this embodiment, simulating blood perfusion is equivalent to simulating the directional flow of a large number of water molecules. The blood flow in the myocardial microcirculation network is dominated by Laminar flow, that is, the water molecules move smoothly and linearly along the direction parallel to the blood vessel axis. The flow velocity is the largest at the blood vessel axis and the smallest near the wall. The ratio of maximum flow rates is equal to 0.5.

具体实施方式二：本实施方式与具体实施方式一不同的是步骤一中子段b与母段的夹角θ₂按如下最优分枝角度方程计算：Specific embodiment two: the difference between this embodiment and specific embodiment one is that the included angle θ ₂ of subsection b and parent section in step one is calculated according to the optimal branch angle equation as follows:

${θ θ}_{22} = = {cos cos}^{- - 11} [[\frac{\frac{11}{{r r}_{00}^{44}} + + \frac{{r r}_{22}^{44}}{{(({r r}_{11}^{44} + + {r r}_{22}^{44}))}^{22}} + + \frac{{r r}_{11}^{44}}{{(({r r}_{11}^{44} + + {r r}_{22}^{44}))}^{22}}}{\frac{22 {r r}_{22}^{22}}{{(({r r}_{11}^{44} + + {r r}_{22}^{44}))}^{22} {r r}_{00}^{22}}}]] . .$

具体实施方式三：本实施方式与具体实施方式一或二不同的是步骤四取15～20个不同的值。Specific implementation mode 3: The difference between this implementation mode and specific implementation mode 1 or 2 is that step 4 takes 15 to 20 different value.

具体实施方式四：本实施方式与具体实施方式一至三之一不同的是步骤四利用Levenberg–Marquardt(列文伯格–马夸尔特)算法对磁共振信号衰减表达式(15)进行非线性拟合。Specific embodiment four: the difference between this embodiment and one of the specific embodiments one to three is that step four uses the Levenberg–Marquardt (Levenberg–Marquardt) algorithm to perform nonlinearity on the magnetic resonance signal attenuation expression (15) fit.

实施例一：在500×500×500μm³大小的体素内建立心肌微循环网络模型。由于心肌微循环网络中小静脉不参与和心肌细胞之间的物质交换，并且小静脉中的血液流速很低，所以IVIM MRI技术对小静脉中的血流不敏感，因而本实施例只建立包含微动脉和毛细血管的心肌微循环网络模型。其中，微动脉和毛细血管的界定数据选用文献“Coronarymicrovascular dysfunction”；微动脉和毛细血管的半径、长度和段数数据选用文献“Morphometry of pig coronary arterial trees”和“Topology and dimensions of pigcoronary capillary network”。在体素表面选取若干个随机点，作为微动脉和部分毛细血管进入体素的起点；Embodiment 1: A myocardial microcirculation network model is established in a voxel with a size of 500×500×500 μm ³ . Since the venules in the myocardial microcirculation network do not participate in the material exchange with myocardial cells, and the blood flow rate in the venules is very low, IVIM MRI technology is not sensitive to the blood flow in the venules, so this embodiment only establishes Myocardial microcirculatory network model of arteries and capillaries. Among them, the definition data of arterioles and capillaries are selected from the literature "Coronarymicrovascular dysfunction"; the data of radius, length and segment number of arterioles and capillaries are selected from the literatures "Morphometry of pig coronary arterial trees" and "Topology and dimensions of pigcoronary capillary network". Select several random points on the surface of the voxel as the starting point of arterioles and some capillaries entering the voxel;

式(7)的β_v取2，β_b取2，β₃取1.5，U_l在生成微动脉血管段时等于U_b，在生成毛细血管段时等于40，循环执行式(7)建立心肌微循环网络模型，最终建成的心肌微循环网络模型中血液容积分数f(即体素内所有血管的容积和占体素容积的百分比)为14.45％；In formula (7), β _v takes 2, β _b takes 2, β ₃ takes 1.5, U _l is equal to U _b when generating arteriole segments, and is equal to 40 when generating capillary segments, and circularly execute formula (7) to establish myocardial Microcirculation network model, the blood volume fraction f (that is, the volume of all blood vessels in the voxel and the percentage of the voxel volume) in the finally built myocardial microcirculation network model is 14.45%;

二、在已建立的心肌微循环网络模型中模拟血流灌注，通过水分子定向流动位移方程(8)计算血管内水分子定向流动的位移，水分子定向流动的位移方程为：2. Simulate blood perfusion in the established myocardial microcirculation network model, and calculate the displacement of the directional flow of water molecules in the blood vessel through the displacement equation (8) of the directional flow of water molecules. The displacement equation of the directional flow of water molecules is:

其水分子定向流动的位移方程(8)中Δp表示水分子流动位移，表示血管轴线处的最大流速，r表示水分子到血管轴线的距离，R表示血管半径，τ表示单步行走时间，式(8)中，取1.0mm/s，其对应的伪扩散系数D^*为12.76×10^-3mm²/s，τ取1.0ms；In the displacement equation (8) of the directional flow of water molecules, Δp represents the flow displacement of water molecules, represents the maximum flow velocity at the axis of the blood vessel, r represents the distance from the water molecule to the axis of the blood vessel, R represents the radius of the blood vessel, and τ represents the single-step walking time. In formula (8), Take 1.0mm/s, the corresponding pseudo-diffusion coefficient D ^* is 12.76×10 ^-3 mm ² /s, τ takes 1.0ms;

在已建立的心肌微循环网络模型中模拟血管外水分子的扩散运动，通过水分子扩散位移模值表达式(9)计算水分子扩散位移的大小，水分子扩散位移模值表达式(9)为：In the established myocardial microcirculation network model, the diffusion movement of extravascular water molecules is simulated, and the size of the water molecule diffusion displacement is calculated by the water molecule diffusion displacement modulus expression (9), and the water molecule diffusion displacement modulus expression (9) for:

其水分子扩散位移模值表达式(9)中Δx表示水分子单步行走的位移大小，m表示扩散空间维数，τ表示单步行走时间，D表示水分子自由扩散系数，q表示(0,1)之间的随机数，本实施例式(9)中，D取1.0×10^-3mm²/s，m取3，τ取1.0ms；In the water molecule diffusion displacement modulus expression (9), Δx represents the displacement of water molecules in a single step, m represents the dimension of the diffusion space, τ represents the time of a single step, D represents the free diffusion coefficient of water molecules, and q represents (0 , 1) random number between, in the formula (9) of this embodiment, D takes 1.0×10 ^-3 mm ² /s, m takes 3, τ takes 1.0ms;

四、基于由水分子位移导致的相位离散公式(11)、水分子i每一步行走位移产生的相位离散之和的表达式(13)和单位体素内所有水分子相位离散引起的磁共振信号衰减式(14)，令双极梯度脉冲的时间间隔Δ等于50.0ms，扩散敏感梯度持续时间δ等于2.0ms，分别等于0、0.005、0.008、0.010、0.012、0.015、0.018、0.020、0.030、0.050、0.070、0.100、0.130、0.150、0.160、0.190、0.200、0.220、0.240(T/m)，计算磁共振衰减信号S/S₀，并基于式(17)，计算b值，然后，基于获得的S/S₀和b的离散值，利用Levenberg–Marquardt法对式(15)非线性拟合，最终获得心肌微循环灌注模型的IVIM MRI仿真检测结果，结果为：f＝15.52％，D＝0.85×10^-3mm²/s，D^*＝9.82×10^-3mm²/s。4. Based on the phase dispersion formula (11) caused by the displacement of water molecules, the expression (13) of the sum of the phase dispersion produced by each step of water molecule i’s displacement and the magnetic resonance signal caused by the phase dispersion of all water molecules in a unit voxel Attenuation formula (14), the time interval Δ of the bipolar gradient pulse is equal to 50.0ms, and the duration of the diffusion-sensitive gradient δ is equal to 2.0ms, Respectively equal to 0, 0.005, 0.008, 0.010, 0.012, 0.015, 0.018, 0.020, 0.030, 0.050, 0.070, 0.100, 0.130, 0.150, 0.160, 0.190, 0.200, 0.220, 0.240 (T/m), calculate the magnetic resonance attenuation signal S/S ₀ , and calculate b value based on formula (17), then, based on the obtained discrete values of S/S ₀ and b, use the Levenberg–Marquardt method to nonlinearly fit formula (15), and finally obtain myocardial micro The IVIM MRI simulation test results of the circulatory perfusion model are: f = 15.52%, D = 0.85×10 ^-3 mm ² /s, D ^* = 9.82×10 ^-3 mm ² /s.

参照步骤一至三中，心肌微循环灌注模型的参数，f＝14.45％，D＝1.0×10^-3mm²/s，D^*＝12.76×10^-3mm²/s，可得检测结果与心肌微循环灌注模型各参数之间的误差为：|Δf|＝1.07％，|D|＝0.15×10^-3mm²/s，|ΔD^*|＝2.94×10^-3mm²/s。Referring to the parameters of the myocardial microcirculation perfusion model in steps 1 to 3, f=14.45%, D=1.0×10 ^-3 mm ² /s, D ^* =12.76×10 ^-3 mm ² /s, and the test results and myocardial The errors among the parameters of the microcirculation perfusion model were: |Δf|=1.07%, |D|=0.15×10 ^-3 mm ² /s, |ΔD ^* |=2.94×10 ^-3 mm ² /s.

改变心肌微循环灌注模型参数D以及成像参数Δ、δ和的方向，能够获得更为丰富的误差统计数据，为心肌微循环灌注IVIM MRI的检测效果提供更加可靠的仿真定量评估结论。Change the parameters of the myocardial microcirculation perfusion model D and the imaging parameters Δ, δ and In this direction, more abundant error statistical data can be obtained, and more reliable simulation quantitative evaluation conclusions can be provided for the detection effect of myocardial microcirculation perfusion IVIM MRI.

Claims

1. irrelevant motion nuclear magnetic resonance emulation mode in Myocardial Microcirculation perfusion voxel, it is characterised in that be to follow these steps to Realize:

One, use network to dodge vessel segment that equation (1) makes to generate is towards function f₁X () is the direction growth of minima；

f_{1} (x) = Σ_{n = 1}^{N} \frac{U_{n}}{| | x - x_{n} | |^{β_{v}}} - - - (1)

Its network is dodged x in equation (1) and is represented the terminal of the vessel segment axis that will generate, x_nRepresent the matter having generated vessel segment The heart, N represents the hop count generating blood vessel, β_vRepresent attenuation quotient, U_nRepresent and dodge weights, U_nExpression formula be:

U_{n} = R_{n}^{2} \times L_{n} - - - (2)

Its U_nR in expression formula (2)_nRepresent the radius of the n-th section of blood vessel generated, L_nRepresent the length of the n-th section of blood vessel generated Degree；

Using border to dodge equation (3) avoids the vessel segment that will generate to go out organizational boundary, and border is dodged equation and is:

f_{2} (x) = Σ_{b = 1}^{6} \frac{U_{b}}{| | x - x_{b} | |^{β_{b}}} - - - (3)

Its border is dodged x in equation (3) and is represented the terminal of the vessel segment axis that will generate, x_bX is in borderline projection in expression, β_bRepresent attenuation quotient, U_bRepresent that weights, U are dodged in border_bExpression formula be:

U_{b} = \frac{1}{N} Σ_{n = 1}^{N} U_{n} - - - (4)

Its U_bU in expression formula (4)_nRepresent and dodge weights；

Optimum branching angle equation (5) is used to calculate the angle of subsegment and parent segment；

θ_{1} = \cos^{- 1} [\frac{\frac{1}{r_{0}^{4}} + \frac{r_{1}^{4}}{{(r_{1}^{4} + r_{2}^{4})}^{2}} + \frac{r_{2}^{4}}{{(r_{1}^{4} + r_{2}^{4})}^{2}}}{\frac{2 r_{1}^{2}}{{(r_{1}^{4} + r_{2}^{4})}^{2} r_{0}^{2}}}] - - - (5)

θ in its optimum branching angle equation (5)₁Represent the angle of subsegment a and parent segment, r₁Represent the radius of subsegment a, r₂Represent son The radius of section b, r₀Represent the radius of parent segment, based on θ₁Set up the fluid branch constraint equation (6) of subsegment a；

f_{3} (x) = - U_{l} {(| (x - x_{p}) \cdot v - {cosθ}_{1} |)}^{β_{3}} - - - (6)

U in its fluid branch constraint equation (6)_lRepresent that fluid branch constraint equation dodges equation (1) relative to network and border is kept away Allow the equation (3) weight in final Myocardial Microcirculation network modelling equation, β₃Representing inhibitive factor, v represents the side of parent segment To vector, x_pThe starting point of the vessel segment axis that expression will generate；

Network is dodged equation (1), equation (3) is dodged on border and fluid branch constraint equation (6) add and, set up Myocardial Microcirculation Network modelling equation (7), the expression formula of Myocardial Microcirculation network modelling equation (7) is:

f (x) = Σ_{n = 1}^{N} \frac{U_{n}}{| | x - x_{n} | |^{β_{v}}} + Σ_{b = 1}^{6} \frac{U_{b}}{| | x - x_{b} | |^{β_{b}}} - U_{l} {(| (x - x_{p}) \cdot v - c o s θ |)}^{β_{3}} - - - (7);

Two, simulation blood perfusion, calculates the position of Ink vessel transfusing hydrone directed flow by hydrone directed flow displacement equation (8) Moving, the displacement equation of hydrone directed flow is:

In the displacement equation (8) of its hydrone directed flow, Δ p represents hydrone flowing displacement,Represent at vessels axis Peak Flow Rate, r represents the hydrone distance to vessels axis, and R represents that vessel radius, τ represent hydrone single step travel time；

The diffusion motion of simulated blood vessel free surface moisture, calculates water diffusion by water diffusion displacement modulus value expression formula (9) The size of displacement, water diffusion displacement modulus value expression formula (9) is:

Δ x = \sqrt{2 m D τ} (2 / \sqrt{π} {&Integral;}_{0}^{2 q - 1} e^{- x^{2}} d x) - - - (9)

In its water diffusion displacement modulus value expression formula (9), Δ x represents the displacement size that hydrone single step is walked, and m represents diffusion Space dimensionality, τ represents hydrone single step travel time, and D represents hydrone free diffusing coefficient, and it is random that q represents between (0,1) Number；

The diffusion direction of displacement of hydrone, water diffusion displacement side is calculated by water diffusion direction of displacement expression formula (10) To expression formula (10) it is:

In its water diffusion direction of displacement expression formula (10)Represent that water diffusion displacement unit vector is at flute card Projection in you coordinate system x-axis, y-axis, z-axis, θ represents the angle of diffusion direction of displacement and z-axis positive direction, and φ represents diffusion displacement Projection in xOy plane and the angle of x-axis positive direction；

Three, based on hydrone flowing displacement and water diffusion displacement in diffusion magnetic resonance image-forming principle and step 2, calculate The phase dispersion caused by hydrone displacement, hydrone displacement the phase dispersion formula (11) caused is:

In the phase dispersion formula (11) that it is caused by hydrone displacementRepresent that the phase caused is walked in i-th hydrone jth walking Position centrifugal pump, γ represents the gyromagnetic ratio of proton,Representing diffusion sensitising gradient, δ represents the diffusion sensitising gradient persistent period,Table Show the displacement that i-th hydrone jth walking is walked；

Under bipolar gradient pulse spin-echo sequence effect, set the time interval of bipolar gradient pulse as Δ, hydrone list Foot walking time is τ, then hydrone walking step number k=Δ/τ (12), after closing bipolar gradient pulse, and the displacement of hydrone i The phase dispersion caused is the phase dispersion sum that each walking of hydrone i walks that displacement produces in delta time, each step of hydrone i The expression formula of the phase dispersion sum that walking displacement produces isThen according to diffusion magnetic resonance image-forming principle, The magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause is:

Magnetic resonance signal under wherein S represents diffusion sensitising gradient effect, S₀Represent the magnetic resonance letter not applying diffusion sensitising gradient Number, the number of hydrone in n representation unit voxel；

By magnetic resonance signal decay expression formula in IVIM MRIWith unit voxel The magnetic resonance signal attenuation type (14) that interior all hydrone phase dispersions cause can obtain:

Wherein f represents volumetric blood mark, and D represents diffusion coefficient, D^*Representing pseudo-diffusion coefficient, b represents decay factor, bipolar In gradient pulse spin-echo sequence, the expression formula of b is:

Four, walk, based on the phase dispersion formula (11) caused by hydrone displacement, each walking of hydrone i, the phase place that displacement produces The magnetic resonance signal attenuation type (14) that in the expression formula (13) of discrete sum and unit voxel, all hydrone phase dispersions cause, Calculate differenceThe magnetic resonance deamplification S/S that value is corresponding₀, thus obtain a series of S/S₀Centrifugal pump, be then based on the table of b Reach formula (17), calculate differenceThe b value that value is corresponding, thus obtain the centrifugal pump of a series of b, based on acquired S/S₀With b's Centrifugal pump, finally carries out nonlinear fitting to magnetic resonance signal decay expression formula (15), it is thus achieved that Myocardial Microcirculation perfusion model IVIM MRI emulates testing result.

Irrelevant motion nuclear magnetic resonance emulation mode in Myocardial Microcirculation the most according to claim 1 perfusion voxel, its It is characterised by subsegment b and the angle theta of parent segment in step one₂By following optimum branching angle Equation for Calculating:

θ_{2} = \cos^{- 1} [\frac{\frac{1}{r_{0}^{4}} + \frac{r_{2}^{4}}{{(r_{1}^{4} + r_{2}^{4})}^{2}} + \frac{r_{1}^{4}}{{(r_{1}^{4} + r_{2}^{4})}^{2}}}{\frac{2 r_{2}^{2}}{{(r_{1}^{4} + r_{2}^{4})}^{2} r_{0}^{2}}}] .

Irrelevant motion nuclear magnetic resonance emulation mode in Myocardial Microcirculation the most according to claim 1 perfusion voxel, its Be characterised by step 4 take 15～20 differentValue.

Irrelevant motion nuclear magnetic resonance emulation mode in Myocardial Microcirculation the most according to claim 1 perfusion voxel, its It is characterised by that step 4 utilizes the Levenberg Marquardt algorithm expression formula (15) that decays magnetic resonance signal to carry out non-linear Matching.