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

Abstract

The invention discloses a magnetic resonance imaging simulating method for irrelevant movement in a myocardial microcirculation perfusion voxel, and belongs to the field of magnetic resonance imaging computer simulating. The method solves the problems that an in vivo experiment qualitative evaluation method cannot precisely quantize the detection effect, and a traditional simulating experiment quantitative evaluation method is large in evaluation difficulty, high in evaluation cost and long in evaluation period. The simulating method comprises the steps that firstly, a network avoidance algorithm, a boundary avoidance algorithm and a fluid branch constraint algorithm are utilized for building a virtual myocardial microcirculation network model; secondly, a blood perfusion model in a blood vessel and a water molecule diffusion movement model outside the blood vessel are built; thirdly, on the basis of the diffusion magnetic resonance imaging principle, an IVIM MRI mechanism is simulated, and a magnetic resonance fading signal is generated; fourthly, nonlinear fitting is performed on the fading signal, and the simulating detection result of the myocardial microcirculation perfusion model is obtained. The method can provide the reliable simulation quantitative evaluation conclusion.

Description

Irrelevant motion nuclear magnetic resonance emulation mode in Myocardial Microcirculation perfusion voxel

Technical field

The invention belongs to nuclear magnetic resonance Computer Simulation field.

Background technology

Myocardial Microcirculation is the blood circulation between arteriole, blood capillary and venule, is that myocardial cell enters with blood The important place of row mass exchange.Myocardial Microcirculation perfusion abnormality can cause the clinical symptoms such as corresponding myocardial ischemia, serious threat Human health.(the Intra-voxel Incoherent Motion Magnetic of irrelevant motion nuclear magnetic resonance in voxel Resonance Imaging, IVIM MRI) technology is the most emerging a kind of microcirculatory perfusion imaging means, is in diffusion Developing in weighted magnetic resonance imaging technical foundation, its principle is to utilize to flow to random blood perfusion at diffusion-sensitive ladder The serious incoherent physical phenomenon of proton group phase place under degree effect, generates many b value (decay factor) magnetic resonance deamplification, and The microcirculatory perfusion information such as volumetric blood mark and blood flow rate are obtained eventually from deamplification.Owing to IVIM MRI technique has Without developer and resolution advantages of higher, the most actively attempting being applied to Myocardial Microcirculation perfusion Clinical detection, wherein, the assessment of Detection results is particularly important.

Imaging technique Detection results appraisal procedure includes experiment made on the living qualitative evaluation and emulation experiment qualitative assessment.Live body is real Testing qualitative evaluation is in the case of indefinite tested biological tissue real physiological parameter, only by by biological tissue imaging results With the physiological parameter comparison in this tissue universal meaning, the Detection results of rough estimate imaging technique.Owing to experiment made on the living is qualitative Assessment cannot precise quantification Detection results, so needing to combine with emulation experiment qualitative assessment, could obtain comprehensive, reliable Assessment result.Traditional emulation experiment qualitative assessment first to make can the artificial physical of imitated biological tissue's physiological feature, then By the error between statistics solid imaging result and substance parameter, obtain the qualitative assessment conclusion of Detection results.But, due to The physiological structure of Myocardial Microcirculation is extremely complex, so the manufacture difficulty of artificial physical will substantially increase.Meanwhile, make preferably Artificial physical needs accurate process equipment and complicated processing technology, and this will dramatically increase assessed cost and assessment cycle.Base In above-mentioned reason, it is only capable of the most both at home and abroad irrigating IVIM by experiment made on the living qualitative evaluation method rough estimate Myocardial Microcirculation The Detection results of MRI.Owing to lacking the assessment result of precise quantification, seriously hinder IVIM MRI technique and examine at Myocardial Microcirculation Clinical practice in terms of survey.

Summary of the invention

The invention aims to solve experiment made on the living qualitative evaluation method can not precise quantification testing result, Yi Jichuan The emulation experiment quantitative evaluating method assessment difficulty of system is big, and assessed cost is high, the problem of assessment cycle length, and it is micro-to propose cardiac muscle Irrelevant motion nuclear magnetic resonance emulation mode in circumfusion voxel.

In Myocardial Microcirculation of the present invention perfusion voxel, irrelevant motion nuclear magnetic resonance emulation mode follows these steps to realize:

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

$f_1\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{{\left|\right|x-x_n\left|\right|}^{{\mathrm{\β}}_v}}---\left(1\right)$

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

$U_n=R_n^2\×L_n---\left(2\right)$

Its U_nR in expression formula (2)_nRepresent the radius of the n-th section of blood vessel generated, L_nN-th section of blood vessel that expression has generated Length；

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:

$f_2\left(x\right)=\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{{\left|\right|x-x_b\left|\right|}^{{\mathrm{\β}}_b}}---\left(3\right)$

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

$U_b=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{U}_n---\left(4\right)$

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；

${\mathrm{\θ}}_1={\cos }^{-1}\left[\frac{\frac{1}{r_0^4}+\frac{r_1^4}{{(r_1^4+r_2^4)}^2}+\frac{r_2^4}{{(r_1^4+r_2^4)}^2}}{\frac{2r_1^2}{{(r_1^4+r_2^4)}^2{r}_0^2}}\right]---\left(5\right)$

θ in its optimum branching angle equation (5)₁Represent the angle of subsegment a and parent segment, r₁Represent the radius of subsegment a, r₂Table Show the radius of subsegment b, r₀Represent the radius of parent segment, based on θ₁Set up the fluid branch constraint equation (6) of subsegment a；

$f_3\left(x\right)=-U_l{\left(\right|(x-x_p)\·v-\cos {\mathrm{\θ}}_1\left|\right)}^{{\mathrm{\β}}_3}---\left(6\right)$

U in its fluid branch constraint equation (6)_lRepresent fluid branch constraint equation relative to network dodge equation (1) and The equation (3) weight in final Myocardial Microcirculation network modelling equation, β are dodged in border₃Representing inhibitive factor, v represents female The direction vector of section, 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 cardiac muscle micro- Recirculating network modeling (7), the expression formula of Myocardial Microcirculation network modelling equation (7) is:

$f\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{{\left|\right|x-x_n\left|\right|}^{{\mathrm{\β}}_v}}+\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{{\left|\right|x-x_b\left|\right|}^{{\mathrm{\β}}_b}}-U_l{\left(\right|(x-x_p)\·v-\cos \mathrm{\θ}\left|\right)}^{{\mathrm{\β}}_3}---\left(7\right);$

Two, simulation blood perfusion, calculates Ink vessel transfusing hydrone directed flow by hydrone directed flow displacement equation (8) Displacement, 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 vessels axis The Peak Flow Rate at place, r represents the hydrone distance to vessels axis, and R represents that vessel radius, τ represent single step travel time；

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

$\mathrm{\Δx}=\sqrt{2\mathrm{mD\τ}}(2/\sqrt{\mathrm{\π}}\underset{0}{\overset{2q-1}{\∫}}{e}^{-x^2}\mathrm{dx})---\left(9\right)$

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 dimension, τ represents 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 position is calculated by water diffusion direction of displacement expression formula (10) Moving direction expression formula (10) is:

In its water diffusion direction of displacement expression formula (10)Represent that water diffusion displacement unit vector exists Projection in cartesian 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 i-th hydrone jth walking is walked to cause Phase dispersion value, γ represents the gyromagnetic ratio of proton,Representing diffusion sensitising gradient, δ represents the diffusion sensitising gradient persistent period,Represent 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, moisture Sub-single step walking (including flowing and the diffusion) time is τ, then hydrone walking step number k=Δ/τ (12) is closing bipolar gradient After pulse, the phase dispersion that the displacement of hydrone i causes be in delta time each walking of hydrone i walk phase place that displacement produces from Dissipating sum, each walking of hydrone i is walked the expression formula of the phase dispersion sum that displacement produces and isThen depend on According to diffusion magnetic resonance image-forming principle, the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause For:

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

By magnetic resonance signal decay expression formula in IVIM MRIAnd list The magnetic resonance signal attenuation type (14) that in the voxel of position, 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, In bipolar gradient pulse spin-echo sequence, the expression formula of b is:

Four, walk what displacement produced based on the phase dispersion formula (11) caused by hydrone displacement, each walking of hydrone i The magnetic resonance signal attenuation type that in the expression formula (13) of phase dispersion sum and unit voxel, all hydrone phase dispersions cause (14), difference is calculatedThe magnetic resonance deamplification S/S that value is corresponding₀, thus obtain a series of S/S₀Centrifugal pump, be then based on The expression formula (17) of b, calculates differenceThe b value that value is corresponding, thus obtain the centrifugal pump of a series of b, based on acquired S/S₀ With the centrifugal pump of b, finally magnetic resonance signal decay expression formula (15) is carried out nonlinear fitting, it is thus achieved that Myocardial Microcirculation perfusion mould The IVIM MRI of type emulates testing result.

The present invention is primarily based on geometry and the topological structure of true heart Microcirculatory failure, utilizes network to dodge algorithm, limit Boundary dodges algorithm and fluid branch bounding algorithm, in conjunction with the operational capability that computer is powerful, sets up virtual Myocardial Microcirculation network Model；Then, histology's knowledge based on microcirculation of the heart perfusion, set up Ink vessel transfusing blood perfusion model, based on Monte Carlo Method, sets up blood vessel free surface moisture diffusion motion model, and then sets up Myocardial Microcirculation perfusion model；Simulate the most in a computer IVIMMRI mechanism, calculates the magnetic resonance deamplification that the diffusion sensitising gradient of different amplitude is corresponding；Finally to deamplification non-thread Property matching, it is thus achieved that the IVIM MRI computer simulation experiment testing result of Myocardial Microcirculation perfusion model.And calculate testing result And error between each parameter in Myocardial Microcirculation perfusion model, is achieved in quantitatively commenting IVIM MRI technique Detection results Estimate.

In Myocardial Microcirculation of the present invention perfusion voxel, irrelevant motion nuclear magnetic resonance emulation mode comprises following useful effect Really:

(1) the IVIM MRI Detection results for Myocardial Microcirculation perfusion provides emulation qualitative assessment conclusion reliably, promotes Its clinical practice；

(2) utilize network to dodge algorithm, algorithm is dodged on border and fluid branch bounding algorithm, in conjunction with the fortune that computer is powerful Calculation ability, sets up virtual unit bodies wish flesh Microcirculatory failure model, it is not necessary to consider the manufacture difficulty of artificial physical, and can Farthest approach the real physiological structure of Myocardial Microcirculation network.

(3) virtual Myocardial Microcirculation network model is set up in a computer, it is not necessary to accurate process equipment and complicated system Make technique, compare traditional emulation experiment appraisal procedure, significantly reduce assessed cost, shorten assessment cycle.

(4) due to set up Myocardial Microcirculation perfusion model and simulation IVIM MRI machine system carry out the most in a computer, so Can adjust continuously model parameter and imaging parameters (δ, Δ), obtain the error statistics data enriched, compare and can only obtain less The traditional simulation experiment quantitative evaluating method of amount error statistics data, the accuracy of assessment result significantly improves.

Accompanying drawing explanation

Fig. 1 is the flow chart of irrelevant motion nuclear magnetic resonance emulation mode in Myocardial Microcirculation perfusion voxel；

Fig. 2 is the geometric representation that in step one, network dodges algorithm；

Fig. 3 is the projection in organizational boundary of the terminal of the vessel segment axis that will generate；

Fig. 4 is the geometric representation of fluid branch bounding algorithm in step one, 1 subsegment a, 2 subsegments b, 3 parent segments；

Fig. 5 is the Laminar flow diagram of blood flow in step 2 Myocardial Microcirculatory failure；

Fig. 6 be in step 2 single hydrone at t1 to t2 time period internal diffusion schematic diagram；

Fig. 7 is 500 × 500 × 500 μm that embodiment one is set up³Virtual Myocardial Microcirculation network model figure in voxel；

Fig. 8 is that embodiment one is in differenceThe lower corresponding S/S of value₀Value and b value and Levenberg Marquardt's is non- Linear fit curve.

Detailed description of the invention

Detailed description of the invention one: irrelevant motion nuclear magnetic resonance emulation in present embodiment Myocardial Microcirculation perfusion voxel Method follows these steps to realize:

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

$f_1\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{{\left|\right|x-x_n\left|\right|}^{{\mathrm{\β}}_v}}---\left(1\right)$

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

$U_n=R_n^2\×L_n---\left(2\right)$

Its U_nR in expression formula (2)_nRepresent the radius of the n-th section of blood vessel generated, L_nN-th section of blood vessel that expression has generated Length；

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:

$f_2\left(x\right)=\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{{\left|\right|x-x_b\left|\right|}^{{\mathrm{\β}}_b}}---\left(3\right)$

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

$U_b=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{U}_n---\left(4\right)$

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；

${\mathrm{\θ}}_1={\cos }^{-1}\left[\frac{\frac{1}{r_0^4}+\frac{r_1^4}{{(r_1^4+r_2^4)}^2}+\frac{r_2^4}{{(r_1^4+r_2^4)}^2}}{\frac{2r_1^2}{{(r_1^4+r_2^4)}^2{r}_0^2}}\right]---\left(5\right)$

θ in its optimum branching angle equation (5)₁Represent the angle of subsegment a and parent segment, r₁Represent the radius of subsegment a, r₂Table Show the radius of subsegment b, r₀Represent the radius of parent segment, based on θ₁Set up the fluid branch constraint equation (6) of subsegment a；

$f_3\left(x\right)=-U_l{\left(\right|(x-x_p)\·v-\cos {\mathrm{\θ}}_1\left|\right)}^{{\mathrm{\β}}_3}---\left(6\right)$

U in its fluid branch constraint equation (6)_lRepresent fluid branch constraint equation relative to network dodge equation (1) and The equation (3) weight in final Myocardial Microcirculation network modelling equation, β are dodged in border₃Representing inhibitive factor, v represents female The direction vector of section, 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 cardiac muscle micro- Recirculating network modeling (7), the expression formula of Myocardial Microcirculation network modelling equation (7) is:

$f\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{{\left|\right|x-x_n\left|\right|}^{{\mathrm{\β}}_v}}+\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{{\left|\right|x-x_b\left|\right|}^{{\mathrm{\β}}_b}}-U_l{\left(\right|(x-x_p)\·v-\cos \mathrm{\θ}\left|\right)}^{{\mathrm{\β}}_3}---\left(7\right);$

Two, simulation blood perfusion, calculates Ink vessel transfusing hydrone directed flow by hydrone directed flow displacement equation (8) Displacement, 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 vessels axis The Peak Flow Rate at place, r represents the hydrone distance to vessels axis, and R represents that vessel radius, τ represent single step travel time；

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

$\mathrm{\Δx}=\sqrt{2\mathrm{mD\τ}}(2/\sqrt{\mathrm{\π}}\underset{0}{\overset{2q-1}{\∫}}{e}^{-x^2}\mathrm{dx})---\left(9\right)$

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 dimension, τ represents 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 position is calculated by water diffusion direction of displacement expression formula (10) Moving direction expression formula (10) is:

In its water diffusion direction of displacement expression formula (10)Represent that water diffusion displacement unit vector exists Projection in cartesian 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 i-th hydrone jth walking is walked to cause Phase dispersion value, γ represents the gyromagnetic ratio of proton,Representing diffusion sensitising gradient, δ represents the diffusion sensitising gradient persistent period,Represent 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, moisture Sub-single step walking (including flowing and the diffusion) time is τ, then hydrone walking step number k=Δ/τ (12) is closing bipolar gradient After pulse, the phase dispersion that the displacement of hydrone i causes be in delta time each walking of hydrone i walk phase place that displacement produces from Dissipating sum, each walking of hydrone i is walked the expression formula of the phase dispersion sum that displacement produces and isThen depend on According to diffusion magnetic resonance image-forming principle, the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause For:

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

By magnetic resonance signal decay expression formula in IVIM MRIAnd list The magnetic resonance signal attenuation type (14) that in the voxel of position, 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, In bipolar gradient pulse spin-echo sequence, the expression formula of b is:

Four, walk what displacement produced based on the phase dispersion formula (11) caused by hydrone displacement, each walking of hydrone i The magnetic resonance signal attenuation type that in the expression formula (13) of phase dispersion sum and unit voxel, all hydrone phase dispersions cause (14), difference is calculatedThe magnetic resonance deamplification S/S that value is corresponding₀, thus obtain a series of S/S₀Centrifugal pump, be then based on The expression formula (17) of b, calculates differenceThe b value that value is corresponding, thus obtain the centrifugal pump of a series of b, based on acquired S/S₀ With the centrifugal pump of b, finally magnetic resonance signal decay expression formula (15) is carried out nonlinear fitting, it is thus achieved that Myocardial Microcirculation perfusion mould The IVIM MRI of type emulates testing result.

Present embodiment step one utilize network to dodge algorithm, it is to avoid the vessel segment that will generate and the blood vessel generated Mutually overlapping, promote the vessel segment that will generate to sparse spatially extended of vascularity simultaneously, network dodges the β in algorithm_v Represent attenuation quotient, reduce β_vThe vessel segment impact on vessel segment will be generated at a distance can be strengthened；The β in algorithm is dodged on border_bAlso Represent attenuation quotient, reduce β_bThe border impact on vessel segment will be generated at a distance can be strengthened.It is micro-that step one sets up virtual cardiac muscle Except avoiding between blood vessel during Cyclic Operation Network, outside overlapping each other between blood vessel and border, vessel branch angle to be ensured Meet hematodinamics.Myocardial Microcirculation network medium vessels generally produces new branch with the form of binary tree, moves according to blood Mechanics, it is minimum that subsegment and the angle of parent segment should ensure that blood flows through shear stress suffered during angle.Therefore optimum is used Crotch angle equation.β in fluid branch constraint equation₃Represent inhibitive factor, β₃The biggest, the suppression to non-optimal Branch Angle is got over Greatly, vice versa.

Present embodiment step 2 simulation blood perfusion is equal to the directed flow simulating large quantity of moisture.Myocardial Microcirculation Blood flow in network makees smooth linear motion, flow velocity based on Laminar stream, i.e. hydrone along the direction parallel with vessel axis Maximum at vessels axis, minimum at nearly wall, the mean flow rate of Ink vessel transfusing hydrone is equal to 0.5 with the ratio of Peak Flow Rate.

Detailed description of the invention two: subsegment b and parent segment in present embodiment step one unlike detailed description of the invention one Angle theta₂By following optimum branching angle Equation for Calculating:

${\mathrm{\θ}}_2={\cos }^{-1}\left[\frac{\frac{1}{r_0^4}+\frac{r_2^4}{{(r_1^4+r_2^4)}^2}+\frac{r_1^4}{{(r_1^4+r_2^4)}^2}}{\frac{2r_2^2}{{(r_1^4+r_2^4)}^2{r}_0^2}}\right].$

Detailed description of the invention three: present embodiment step 4 unlike detailed description of the invention one or two takes 15～20 DifferentValue.

Detailed description of the invention four: present embodiment step 4 unlike one of detailed description of the invention one to three utilizes Levenberg Marquardt (row literary composition Burger Ma Kuaerte) the algorithm expression formula (15) that decays magnetic resonance signal carries out non-thread Property matching.

Embodiment one: in 500 × 500 × 500 μm³Myocardial Microcirculation network model is set up in the voxel of size.Due to the heart The mass exchange that in flesh Microcirculatory failure, venule is not involved between myocardial cell, and the velocity of blood flow in venule is very Low, so IVIM MRI technique is insensitive to the blood flow in venule, thus the present embodiment is only set up and is comprised arteriole and capillary The Myocardial Microcirculation network model of blood vessel.Wherein, the data that define of arteriole and blood capillary select document " Coronary microvascular dysfunction”；Arteriole and the radius of blood capillary, length and hop count data select document " Morphometry of pig coronary arterial trees " and " Topology and dimensions of pig coronary capillary network”.Several random points are chosen, as arteriole and part blood capillary on voxel surface Pipe enters the starting point of voxel；

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

$f_1\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{{\left|\right|x-x_n\left|\right|}^{{\mathrm{\β}}_v}}---\left(1\right)$

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

$U_n=R_n^2\×L_n---\left(2\right)$

Its U_nR in expression formula (2)_nRepresent the radius of the n-th section of blood vessel generated, L_nN-th section of blood vessel that expression has generated Length；

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:

$f_2\left(x\right)=\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{{\left|\right|x-x_b\left|\right|}^{{\mathrm{\β}}_b}}---\left(3\right)$

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

$U_b=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{U}_n---\left(4\right)$

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；

${\mathrm{\θ}}_1={\cos }^{-1}\left[\frac{\frac{1}{r_0^4}+\frac{r_1^4}{{(r_1^4+r_2^4)}^2}+\frac{r_2^4}{{(r_1^4+r_2^4)}^2}}{\frac{2r_1^2}{{(r_1^4+r_2^4)}^2{r}_0^2}}\right]---\left(5\right)$

θ in its optimum branching angle equation (5)₁Represent the angle of subsegment a and parent segment, r₁Represent the radius of subsegment a, r₂Table Show the radius of subsegment b, r₀Represent the radius of parent segment, based on θ₁Set up the fluid branch constraint equation (6) of subsegment a；

$f_3\left(x\right)=-U_l{\left(\right|(x-x_p)\·v-\cos {\mathrm{\θ}}_1\left|\right)}^{{\mathrm{\β}}_3}---\left(6\right)$

U in its fluid branch constraint equation (6)_lRepresent fluid branch constraint equation relative to network dodge equation (1) and The equation (3) weight in final Myocardial Microcirculation network modelling equation, β are dodged in border₃Representing inhibitive factor, v represents female The direction vector of section, 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 cardiac muscle micro- Recirculating network modeling (7), the expression formula of Myocardial Microcirculation network modelling equation (7) is:

$f\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{{\left|\right|x-x_n\left|\right|}^{{\mathrm{\β}}_v}}+\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{{\left|\right|x-x_b\left|\right|}^{{\mathrm{\β}}_b}}-U_l{\left(\right|(x-x_p)\·v-\cos \mathrm{\θ}\left|\right)}^{{\mathrm{\β}}_3}---\left(7\right);$

The β of formula (7)_vTake 2, β_bTake 2, β₃Take 1.5, U_lWhen generating arteriole vessel segment equal to U_b, generating blood capillary Equal to 40 during section, circulation execution formula (7) sets up Myocardial Microcirculation network model, in the Myocardial Microcirculation network model finally built up Volumetric blood mark f (i.e. the volume of all blood vessels and the percentage ratio accounting for voxel volume in voxel) is 14.45%；

Two, in the Myocardial Microcirculation network model set up, blood perfusion is simulated, by hydrone directed flow displacement Equation (8) calculates the displacement of Ink vessel transfusing hydrone directed flow, and 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 vessels axis The Peak Flow Rate at place, r represents the hydrone distance to vessels axis, and R represents that vessel radius, τ represent single step travel time, formula (8) in,Take 1.0mm/s, the pseudo-diffusion coefficient D of its correspondence^*It is 12.76 × 10^-3mm²/ s, τ take 1.0ms；

In the Myocardial Microcirculation network model set up, the diffusion motion of simulated blood vessel free surface moisture, is expanded by hydrone Dissipating displacement modulus value expression formula (9) and calculate the size of water diffusion displacement, water diffusion displacement modulus value expression formula (9) is:

$\mathrm{\Δx}=\sqrt{2\mathrm{mD\τ}}(2/\sqrt{\mathrm{\π}}\underset{0}{\overset{2q-1}{\∫}}{e}^{-x^2}\mathrm{dx})---\left(9\right)$

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 dimension, τ represents single step travel time, and D represents hydrone free diffusing coefficient, and it is random that q represents between (0,1) Number, in the present embodiment formula (9), D takes 1.0 × 10^-3mm²/ s, m take 3, and τ takes 1.0ms；

The diffusion direction of displacement of hydrone, water diffusion position is calculated by water diffusion direction of displacement expression formula (10) Moving direction expression formula (10) is:

In its water diffusion direction of displacement expression formula (10)Represent that water diffusion displacement unit vector exists Projection in cartesian 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 i-th hydrone jth walking is walked to cause Phase dispersion value, γ represents the gyromagnetic ratio of proton,Representing diffusion sensitising gradient, δ represents the diffusion sensitising gradient persistent period,Represent 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, moisture Sub-single step walking (including flowing and the diffusion) time is τ, then hydrone walking step number k=Δ/τ (12) is closing bipolar gradient After pulse, the phase dispersion that the displacement of hydrone i causes be in delta time each walking of hydrone i walk phase place that displacement produces from Dissipating sum, each walking of hydrone i is walked the expression formula of the phase dispersion sum that displacement produces and isThen depend on According to diffusion magnetic resonance image-forming principle, the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause For:

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

By magnetic resonance signal decay expression formula in IVIM MRIAnd list The magnetic resonance signal attenuation type (14) that in the voxel of position, 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, In bipolar gradient pulse spin-echo sequence, the expression formula of b is:

Four, walk what displacement produced based on the phase dispersion formula (11) caused by hydrone displacement, each walking of hydrone i The magnetic resonance signal attenuation type that in the expression formula (13) of phase dispersion sum and unit voxel, all hydrone phase dispersions cause (14), the time interval Δ of bipolar gradient pulse is made to be equal to 2.0ms equal to 50.0ms, diffusion sensitising gradient persistent period δ, 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), calculates magnetic resonance deamplification S/S₀, and based on Formula (17), calculates b value, then, based on the S/S obtained₀With the centrifugal pump of b, utilize Levenberg Marquardt method to formula (15) nonlinear fitting, the final IVIM MRI obtaining Myocardial Microcirculation perfusion model emulates testing result, and result is: f= 15.52%, D=0.85 × 10^-3mm²/ s, D^*=9.82 × 10^-3mm²/s。

With reference to step one in three, the parameter of Myocardial Microcirculation perfusion model, f=14.45%, D=1.0 × 10^-3mm²/ S, D^*=12.76 × 10^-3mm²/ s, the error that can obtain between testing result and each parameter of Myocardial Microcirculation perfusion model is: | Δ f |=1.07%, | D |=0.15 × 10^-3mm²/ s, | Δ D^*|=2.94 × 10^-3mm²/s。

Change Myocardial Microcirculation perfusion model parameterD and imaging parameters Δ, δ andDirection, it is possible to obtain more The error statistics data of horn of plenty, the emulation relatively reliable for the Detection results offer of Myocardial Microcirculation perfusion IVIM MRI is quantitative Assessment result.

Claims (4)

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；

$f_1\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{\left|\right|x-x_n|{|}^{{\mathrm{\β}}_v}}---\left(1\right)$

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:

$U_n=R_n^2\×L_n---\left(2\right)$

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:

$f_2\left(x\right)=\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{\left|\right|x-x_b|{|}^{{\mathrm{\β}}_b}}---\left(3\right)$

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:

$U_b=\frac{1}{N}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{U}_n---\left(4\right)$

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；

${\mathrm{\θ}}_1={\cos }^{-1}\[\frac{\frac{1}{r_0^4}+\frac{r_1^4}{{(r_1^4+r_2^4)}^2}+\frac{r_2^4}{{(r_1^4+r_2^4)}^2}}{\frac{2r_1^2}{{(r_1^4+r_2^4)}^2{r}_0^2}}\]---\left(5\right)$

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；

$f_3\left(x\right)=-U_l{\left(\right|\left(x-x_p\right)\·v-{\mathrm{cos\θ}}_1\left|\right)}^{{\mathrm{\β}}_3}---\left(6\right)$

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:

$f\left(x\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{U_n}{\left|\right|x-x_n|{|}^{{\mathrm{\β}}_v}}+\underset{b=1}{\overset{6}{\mathrm{\Σ}}}\frac{U_b}{\left|\right|x-x_b|{|}^{{\mathrm{\β}}_b}}-U_l{\left(\right|\left(x-x_p\right)\·v-cos\mathrm{\θ}\left|\right)}^{{\mathrm{\β}}_3}---\left(7\right);$

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:

$\mathrm{\Δ}x=\sqrt{2mD\mathrm{\τ}}(2/\sqrt{\mathrm{\π}}\underset{0}{\overset{2q-1}{\∫}}{e}^{-x^2}dx)---\left(9\right)$

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:

${\mathrm{\θ}}_2={\cos }^{-1}\[\frac{\frac{1}{r_0^4}+\frac{r_2^4}{{(r_1^4+r_2^4)}^2}+\frac{r_1^4}{{(r_1^4+r_2^4)}^2}}{\frac{2r_2^2}{{(r_1^4+r_2^4)}^2{r}_0^2}}\].$

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.