CN104021301A - 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 magnetic resonance imaging emulation mode in Myocardial Microcirculation perfusion voxel

Technical field

The invention belongs to magnetic resonance imaging Computer Simulation field.

Background technology

Myocardial Microcirculation is the blood circulation between arteriole, capillary and veinlet, is the important place that cardiac muscle cell and blood carry out mass exchange.Myocardial Microcirculation perfusion abnormality can cause the clinical symptoms such as corresponding myocardial ischemia, serious threat human health.Irrelevant motion magnetic resonance imaging (Intra-voxel Incoherent Motion Magnetic Resonance Imaging in voxel, IVIM MRI) technology is emerging in recent years a kind of microcirculatory perfusion imaging means, on diffusion-weighted mr imaging technique basis, develop, its principle is to utilize to flow to the serious incoherent physical phenomenon of random blood perfusion proton group phase place under diffusion-sensitive gradient effect, generate many b values (decay factor) magnetic resonance deamplification, and finally from deamplification, obtain the microcirculatory perfusion information such as volumetric blood mark and blood flow rate.Because IVIM MRI technology has without developer and resolution advantages of higher, actively attempt being applied at present the clinical detection of Myocardial Microcirculation perfusion both at home and abroad, wherein, the assessment that detects effect is particularly important.

Imaging technique detects effect evaluation method and comprises experiment made on the living qualitative evaluation and emulation experiment qualitative assessment.Experiment made on the living qualitative evaluation is the in the situation that of the true physiological parameter of indefinite tested biological tissue, only by the physiological parameter in biological tissue imaging results and this tissue universal significance is compared, and the detection effect of guestimate imaging technique.Because experiment made on the living qualitative evaluation cannot detect effect by precise quantification, so need to combine with emulation experiment qualitative assessment, could obtain comprehensive, reliable assessment result.Traditional emulation experiment qualitative assessment first will be made artificial physical that can imitated biological tissue's physiological characteristic, then by the error between statistics solid imaging result and substance parameter, obtains detecting the qualitative assessment conclusion of effect.But, because the physiological structure of Myocardial Microcirculation is very complicated, so the manufacture difficulty of artificial physical will obviously increase.Meanwhile, making desirable artificial physical needs accurate process equipment and complicated manufacture craft, and this will significantly increase assessed cost and assessment cycle.For these reasons, at present both at home and abroad only can be by the detection effect of experiment made on the living qualitative evaluation method guestimate Myocardial Microcirculation perfusion IVIM MRI.Owing to lacking the assessment result of precise quantification, seriously hinder the clinical practice of IVIM MRI technology in Myocardial Microcirculation context of detection.

Summary of the invention

The object of the invention is can not precise quantification testing result in order to solve experiment made on the living qualitative evaluation method, and traditional emulation experiment quantitative evaluating method assessment difficulty is large, assessed cost is high, the problem that assessment cycle is long, and irrelevant motion magnetic resonance imaging emulation mode in Myocardial Microcirculation perfusion voxel has been proposed.

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

One, Adoption Network is dodged equation (1) and is made the vessel segment that will generate towards function f ₁(x) be the direction growth of minimum value;

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

Its network is dodged the terminal that the middle x of equation (1) represents the vessel segment axis that will generate, x _nthe barycenter that represents to have generated vessel segment, N represents to generate the hop count of blood vessel, β _vrepresent attenuation coefficient, U _nrepresent to 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 section blood vessel having generated, L _nrepresent the length of the n section blood vessel having generated;

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

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

The terminal that the middle x of equation (3) represents the vessel segment axis that will generate, x are dodged in its border _brepresent that x is at borderline projection, β _brepresent attenuation coefficient, U _bweights are dodged, U in expression 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 to dodge weights;

Adopt optimum branching angle equation (5) 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, r ₁represent the radius of subsegment a, r ₂represent the radius of subsegment b, r ₀represent the radius of parent segment, based on θ ₁set up the fluid branch equation of constraint (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 equation of constraint (6) _lrepresent that fluid branch equation of constraint is dodged equation (1) with respect to network and the weight of equation (3) in final Myocardial Microcirculation network modelling equation, β are dodged in border ₃represent inhibiting factor, v represents the direction vector of parent segment, x _pthe starting point of the vessel segment axis that expression will generate;

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

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

Two, simulation blood perfusion, the displacement of calculating hydrone directed flow in blood vessel by hydrone directed flow displacement equation (8), the displacement equation of hydrone directed flow is:

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

The diffusion motion of simulated blood vessel free surface moisture, calculates the size of water diffusion displacement by water diffusion displacement mould value expression (9), water diffusion displacement mould value expression (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 mould value expression (9), Δ x represents the displacement size of hydrone single step walking, m represents diffusion space dimension, and τ represents single step travel time, and D represents hydrone free diffusing coefficient, q represents the random number between (0,1);

The diffusion sense of displacement that calculates hydrone by water diffusion sense of displacement expression formula (10), water diffusion sense of displacement expression formula (10) is:

In its water diffusion sense of displacement expression formula (10) represent the projection of water diffusion displacement unit vector on cartesian coordinate system x axle, y axle, z axle, θ represents to spread the angle of sense of displacement and z axle positive dirction, and φ represents to spread the projection of displacement in xOy plane and the angle of x axle positive dirction;

Three, based on the mobile displacement of hydrone in diffusion Principle of Magnetic Resonance Imaging and step 2 and water diffusion displacement, calculate the phase dispersion being caused by hydrone displacement, the phase dispersion formula (11) being caused by hydrone displacement is:

In the phase dispersion formula (11) that it is caused by hydrone displacement represent the phase dispersion value that i hydrone j walking is walked to cause, γ represents the gyromagnetic ratio of proton, represent diffusion-sensitive gradient, δ represents the diffusion-sensitive gradient duration, represent the displacement that i hydrone j walking is walked;

Under the effect of bipolar gradient pulse spin-echo sequence, the time interval of setting bipolar gradient pulse is Δ, hydrone single step walking (comprise and flowing and the diffusion) time is τ, hydrone walking step number k=Δ/τ (12), closing after bipolar gradient pulse, the phase dispersion that the displacement of hydrone i causes is that in delta time, the phase dispersion sum that displacement produces is walked in each walking of hydrone i, and the expression formula that the phase dispersion sum of displacement generation is walked in each walking of hydrone i is then according to diffusion Principle of Magnetic Resonance Imaging, the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause is:

Wherein S represents the magnetic resonance signal under diffusion-sensitive gradient effect, S ₀represent not apply the magnetic resonance signal of diffusion-sensitive gradient, the number of hydrone in n representation unit voxel;

By magnetic resonance signal decay expression formula in IVIM MRI can obtain with the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause:

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

Four, the magnetic resonance signal attenuation type (14) that in the expression formula (13) of phase dispersion sum that displacement produces and unit voxel, all hydrone phase dispersions cause is walked in the phase dispersion formula (11) based on being caused by hydrone displacement, each walking of hydrone i, calculates difference be worth corresponding magnetic resonance deamplification S/S ₀thereby, obtain a series of S/S ₀discrete value, the then expression formula based on b (17), calculates different be worth corresponding b value, thereby obtain the discrete value of a series of b, based on acquired S/S ₀with the discrete value of b, finally magnetic resonance signal decay expression formula (15) is carried out to nonlinear fitting, obtain the IVIM MRI emulation testing result of Myocardial Microcirculation perfusion model.

The present invention is geometry and the topological structure based on true heart microcirculation network first, utilizes network to dodge algorithm, algorithm and fluid branch bounding algorithm are dodged in border, in conjunction with the powerful arithmetic capability of computing machine, set up virtual Myocardial Microcirculation network model; Then, based on the histology knowledge of microcirculation of the heart perfusion, set up blood perfusion model in blood vessel, based on Monte Carlo method, set up the sub-diffusion motion model of blood vessel free surface moisture, and then set up Myocardial Microcirculation perfusion model; Simulation with I VIMMRI mechanism in computing machine again, calculates the magnetic resonance deamplification corresponding to diffusion-sensitive gradient of different amplitudes; Finally, to deamplification nonlinear fitting, obtain the IVIM MRI computer simulation experiment testing result of Myocardial Microcirculation perfusion model.And calculate the error between each parameter in testing result and Myocardial Microcirculation perfusion model, realize thus the qualitative assessment to IVIM MRI technology for detection effect.

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

(1) provide reliable emulation qualitative assessment conclusion for the IVIM MRI of Myocardial Microcirculation perfusion detects effect, promote its clinical practice;

(2) utilize network to dodge algorithm, algorithm and fluid branch bounding algorithm are dodged in border, in conjunction with the powerful arithmetic capability of computing machine, set up virtual unit bodies element Myocardial Microcirculation network model, without the manufacture difficulty of considering artificial physical, and can farthest approach the real physiological structure of Myocardial Microcirculation network.

(3) in computing machine, set up virtual Myocardial Microcirculation network model, without accurate process equipment and complicated manufacture craft, compare traditional emulation experiment appraisal procedure, significantly reduce assessed cost, shorten assessment cycle.

(4) owing to setting up Myocardial Microcirculation perfusion model and Simulation with I VIM MRI mechanism is all carried out in computing machine, thus can continuous setup model parameter and imaging parameters ( δ, Δ), obtain abundant error statistics data, compare the traditional simulation experiment quantitative evaluating method that can only obtain a small amount of error statistics data, the accuracy of assessment result significantly improves.

Brief description of the drawings

Fig. 1 is the process flow diagram of irrelevant motion magnetic resonance imaging emulation mode in Myocardial Microcirculation perfusion voxel;

Fig. 2 is the geometric representation that in step 1, network is dodged 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 1,1-subsegment a, 2-subsegment b, 3-parent segment;

Fig. 5 is the Laminar flow diagram of blood flow in step 2 Myocardial microcirculation network;

Fig. 6 is that in step 2, single hydrone spreads schematic diagram at t1 within the t2 time period;

Fig. 7 is 500 × 500 × 500 μ m that embodiment mono-sets up ³virtual Myocardial Microcirculation network model figure in voxel;

Fig. 8 is that embodiment mono-is in difference the lower corresponding S/S of value ₀the nonlinear fitting curve of value and b value and Levenberg – Marquardt.

Embodiment

Embodiment one: in present embodiment Myocardial Microcirculation perfusion voxel, irrelevant motion magnetic resonance imaging emulation mode follows these steps to realize:

One, Adoption Network is dodged equation (1) and is made the vessel segment that will generate towards function f ₁(x) be the direction growth of minimum value;

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

Its network is dodged the terminal that the middle x of equation (1) represents the vessel segment axis that will generate, x _nthe barycenter that represents to have generated vessel segment, N represents to generate the hop count of blood vessel, β _vrepresent attenuation coefficient, U _nrepresent to 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 section blood vessel having generated, L _nrepresent the length of the n section blood vessel having generated;

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

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

The terminal that the middle x of equation (3) represents the vessel segment axis that will generate, x are dodged in its border _brepresent that x is at borderline projection, β _brepresent attenuation coefficient, U _bweights are dodged, U in expression 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 to dodge weights;

Adopt optimum branching angle equation (5) 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, r ₁represent the radius of subsegment a, r ₂represent the radius of subsegment b, r ₀represent the radius of parent segment, based on θ ₁set up the fluid branch equation of constraint (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 equation of constraint (6) _lrepresent that fluid branch equation of constraint is dodged equation (1) with respect to network and the weight of equation (3) in final Myocardial Microcirculation network modelling equation, β are dodged in border ₃represent inhibiting factor, v represents the direction vector of parent segment, x _pthe starting point of the vessel segment axis that expression will generate;

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

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

Two, simulation blood perfusion, the displacement of calculating hydrone directed flow in blood vessel by hydrone directed flow displacement equation (8), the displacement equation of hydrone directed flow is:

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

The diffusion motion of simulated blood vessel free surface moisture, calculates the size of water diffusion displacement by water diffusion displacement mould value expression (9), water diffusion displacement mould value expression (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 mould value expression (9), Δ x represents the displacement size of hydrone single step walking, m represents diffusion space dimension, and τ represents single step travel time, and D represents hydrone free diffusing coefficient, q represents the random number between (0,1);

The diffusion sense of displacement that calculates hydrone by water diffusion sense of displacement expression formula (10), water diffusion sense of displacement expression formula (10) is:

In its water diffusion sense of displacement expression formula (10) represent the projection of water diffusion displacement unit vector on cartesian coordinate system x axle, y axle, z axle, θ represents to spread the angle of sense of displacement and z axle positive dirction, and φ represents to spread the projection of displacement in xOy plane and the angle of x axle positive dirction;

Three, based on the mobile displacement of hydrone in diffusion Principle of Magnetic Resonance Imaging and step 2 and water diffusion displacement, calculate the phase dispersion being caused by hydrone displacement, the phase dispersion formula (11) being caused by hydrone displacement is:

In the phase dispersion formula (11) that it is caused by hydrone displacement represent the phase dispersion value that i hydrone j walking is walked to cause, γ represents the gyromagnetic ratio of proton, represent diffusion-sensitive gradient, δ represents the diffusion-sensitive gradient duration, represent the displacement that i hydrone j walking is walked;

Under the effect of bipolar gradient pulse spin-echo sequence, the time interval of setting bipolar gradient pulse is Δ, hydrone single step walking (comprise and flowing and the diffusion) time is τ, hydrone walking step number k=Δ/τ (12), closing after bipolar gradient pulse, the phase dispersion that the displacement of hydrone i causes is that in delta time, the phase dispersion sum that displacement produces is walked in each walking of hydrone i, and the expression formula that the phase dispersion sum of displacement generation is walked in each walking of hydrone i is then according to diffusion Principle of Magnetic Resonance Imaging, the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause is:

Wherein S represents the magnetic resonance signal under diffusion-sensitive gradient effect, S ₀represent not apply the magnetic resonance signal of diffusion-sensitive gradient, the number of hydrone in n representation unit voxel;

By magnetic resonance signal decay expression formula in IVIM MRI can obtain with the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause:

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

Four, the magnetic resonance signal attenuation type (14) that in the expression formula (13) of phase dispersion sum that displacement produces and unit voxel, all hydrone phase dispersions cause is walked in the phase dispersion formula (11) based on being caused by hydrone displacement, each walking of hydrone i, calculates difference be worth corresponding magnetic resonance deamplification S/S ₀thereby, obtain a series of S/S ₀discrete value, the then expression formula based on b (17), calculates different be worth corresponding b value, thereby obtain the discrete value of a series of b, based on acquired S/S ₀with the discrete value of b, finally magnetic resonance signal decay expression formula (15) is carried out to nonlinear fitting, obtain the IVIM MRI emulation testing result of Myocardial Microcirculation perfusion model.

In present embodiment step 1, utilize network to dodge algorithm, avoid the vessel segment that will generate and the blood vessel having generated mutually overlapping, impel the vessel segment that will generate to extend to the sparse space of vascular distribution simultaneously, network is dodged the β in algorithm _vrepresent attenuation coefficient, reduce β _vcan strengthen distant place vessel segment to generating the impact of vessel segment; The β in algorithm is dodged on border _balso represent attenuation coefficient, reduce β _bcan strengthen border, distant place to generating the impact of vessel segment.When setting up virtual Myocardial Microcirculation network model, step 1 except avoiding between blood vessel, outside overlapping each other between blood vessel and border, also to ensure that vessel branch angle meets Hemodynamics.Myocardial Microcirculation network medium vessels produces new branch with the form of binary tree conventionally, and according to Hemodynamics, the angle of subsegment and parent segment should ensure blood flow suffered shear stress minimum in the time of angle.Therefore adopt optimum branching angle equation.β in fluid branch equation of constraint ₃represent inhibiting factor, β ₃larger, larger to the inhibition of non-optimum branching angle, vice versa.

Present embodiment step 2 simulation blood perfusion is equal to the directed flow of simulation large quantity of moisture.Blood flow in Myocardial Microcirculation network is taking Laminar stream as main, be that hydrone is made level and smooth rectilinear motion along the direction parallel with vessel axis, flow velocity is in vessels axis place maximum, nearly wall place minimum, and in blood vessel, the mean flow rate of hydrone and the ratio of Peak Flow Rate equal 0.5.

Embodiment two: the angle theta of what present embodiment was different from embodiment one is in step 1 subsegment b and parent segment ₂calculate by following optimum branching angle equation:

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

Embodiment three: step 4 that what present embodiment was different from embodiment one or two is get 15～20 different value.

Embodiment four: step 4 that what present embodiment was different from one of embodiment one to three is utilizes Levenberg – Marquardt (Lie Wenbaige – Ma Kuaerte) algorithm to carry out nonlinear fitting to the magnetic resonance signal expression formula (15) that decays.

Embodiment mono-: at 500 × 500 × 500 μ m ³in the voxel of size, set up Myocardial Microcirculation network model.Because veinlet in Myocardial Microcirculation network does not participate in the mass exchange between cardiac muscle cell, and the velocity of blood flow in veinlet is very low, so IVIM MRI technology is insensitive to the blood flow in veinlet, thereby the present embodiment is only set up the Myocardial Microcirculation network model that comprises arteriole and capillary.Wherein, the data that define of arteriole and capillary are selected document " Coronary microvascular dysfunction "; Radius, length and the hop count data of arteriole and capillary are selected document " Morphometry of pig coronary arterial trees " and " Topology and dimensions of pig coronary capillary network ".Choose several random points on voxel surface, the starting point that enters voxel as arteriole and part capillary;

One, Adoption Network is dodged equation (1) and is made the vessel segment that will generate towards function f ₁(x) be the direction growth of minimum value;

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

Its network is dodged the terminal that the middle x of equation (1) represents the vessel segment axis that will generate, x _nthe barycenter that represents to have generated vessel segment, N represents to generate the hop count of blood vessel, β _vrepresent attenuation coefficient, U _nrepresent to 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 section blood vessel having generated, L _nrepresent the length of the n section blood vessel having generated;

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

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

The terminal that the middle x of equation (3) represents the vessel segment axis that will generate, x are dodged in its border _brepresent that x is at borderline projection, β _brepresent attenuation coefficient, U _bweights are dodged, U in expression 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 to dodge weights;

Adopt optimum branching angle equation (5) 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, r ₁represent the radius of subsegment a, r ₂represent the radius of subsegment b, r ₀represent the radius of parent segment, based on θ ₁set up the fluid branch equation of constraint (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 equation of constraint (6) _lrepresent that fluid branch equation of constraint is dodged equation (1) with respect to network and the weight of equation (3) in final Myocardial Microcirculation network modelling equation, β are dodged in border ₃represent inhibiting factor, v represents the direction vector of parent segment, x _pthe starting point of the vessel segment axis that expression will generate;

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

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

The β of formula (7) _vget 2, β _bget 2, β ₃get 1.5, U _lin the time generating arteriole vessel segment, equal U _bin the time generating blood capillary pipeline section, equal 40, circulation execution formula (7) is set up Myocardial Microcirculation network model, and volumetric blood mark f in the Myocardial Microcirculation network model finally building up (being the volume of all blood vessels in voxel and the number percent that accounts for voxel volume) is 14.45%;

Two, in the Myocardial Microcirculation network model of having set up, simulate blood perfusion, calculate the displacement of hydrone directed flow in blood vessel by hydrone directed flow displacement equation (8), the displacement equation of hydrone directed flow is:

In the displacement equation (8) of its hydrone directed flow, Δ p represents the hydrone displacement of flowing, the Peak Flow Rate that represents vessels axis place, r represents the distance of hydrone to vessels axis, and R represents vessel radius, and τ represents single step travel time, in formula (8), get 1.0mm/s, the pseudo-diffusion coefficient D of its correspondence ^*be 12.76 × 10 ^-3mm ²/ s, τ gets 1.0ms;

The diffusion motion of simulated blood vessel free surface moisture in the Myocardial Microcirculation network model of having set up, the size of calculating water diffusion displacement by water diffusion displacement mould value expression (9), water diffusion displacement mould value expression (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 mould value expression (9), Δ x represents the displacement size of hydrone single step walking, m represents diffusion space dimension, τ represents single step travel time, D represents hydrone free diffusing coefficient, q represents (0,1) random number between, in the present embodiment formula (9), D gets 1.0 × 10 ^-3mm ²/ s, m gets 3, τ and gets 1.0ms;

The diffusion sense of displacement that calculates hydrone by water diffusion sense of displacement expression formula (10), water diffusion sense of displacement expression formula (10) is:

In its water diffusion sense of displacement expression formula (10) represent the projection of water diffusion displacement unit vector on cartesian coordinate system x axle, y axle, z axle, θ represents to spread the angle of sense of displacement and z axle positive dirction, and φ represents to spread the projection of displacement in xOy plane and the angle of x axle positive dirction;

Three, based on the mobile displacement of hydrone in diffusion Principle of Magnetic Resonance Imaging and step 2 and water diffusion displacement, calculate the phase dispersion being caused by hydrone displacement, the phase dispersion formula (11) being caused by hydrone displacement is:

In the phase dispersion formula (11) that it is caused by hydrone displacement represent the phase dispersion value that i hydrone j walking is walked to cause, γ represents the gyromagnetic ratio of proton, represent diffusion-sensitive gradient, δ represents the diffusion-sensitive gradient duration, represent the displacement that i hydrone j walking is walked;

Under the effect of bipolar gradient pulse spin-echo sequence, the time interval of setting bipolar gradient pulse is Δ, hydrone single step walking (comprise and flowing and the diffusion) time is τ, hydrone walking step number k=Δ/τ (12), closing after bipolar gradient pulse, the phase dispersion that the displacement of hydrone i causes is that in delta time, the phase dispersion sum that displacement produces is walked in each walking of hydrone i, and the expression formula that the phase dispersion sum of displacement generation is walked in each walking of hydrone i is then according to diffusion Principle of Magnetic Resonance Imaging, the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause is:

Wherein S represents the magnetic resonance signal under diffusion-sensitive gradient effect, S ₀represent not apply the magnetic resonance signal of diffusion-sensitive gradient, the number of hydrone in n representation unit voxel;

By magnetic resonance signal decay expression formula in IVIM MRI can obtain with the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause:

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

Four, the magnetic resonance signal attenuation type (14) that the expression formula (13) of phase dispersion sum that displacement produces and the interior all hydrone phase dispersions of unit voxel cause is walked in the phase dispersion formula (11) based on being caused by hydrone displacement, each walking of hydrone i, make the time interval Δ of bipolar gradient pulse equal 50.0ms, diffusion-sensitive gradient duration δ equals 2.0ms equal respectively 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 magnetic resonance deamplification S/S ₀, and based on formula (17), calculate b value, and then, based on the S/S obtaining ₀with the discrete value of b, utilize Levenberg – Marquardt method to formula (15) nonlinear fitting, finally obtain the IVIM MRI emulation testing result of Myocardial Microcirculation perfusion model, result is: f=15.52%, D=0.85 × 10 ^-3mm ²/ s, D ^*=9.82 × 10 ^-3mm ²/ s.

With reference in step 1 to three, the parameter of Myocardial Microcirculation perfusion model, f=14.45%, D=1.0 × 10 ^-3mm ²/ s, D ^*=12.76 × 10 ^-3mm ²/ s, the error that can obtain between testing result and the each parameter of Myocardial Microcirculation perfusion model is: | Δ f|=1.07%, | D|=0.15 × 10 ^-3mm ²/ s, | Δ D ^*|=2.94 × 10 ^-3mm ²/ s.

Change Myocardial Microcirculation perfusion model parameter d and imaging parameters Δ, δ and direction, can obtain the more error statistics data of horn of plenty, for the detection effect of Myocardial Microcirculation perfusion IVIM MRI provides emulation qualitative assessment conclusion more reliably.

Claims (4)

1. irrelevant motion magnetic resonance imaging emulation mode in Myocardial Microcirculation perfusion voxel, it is characterized in that following these steps to realizing:

One, Adoption Network is dodged equation (1) and is made the vessel segment that will generate towards function f ₁(x) be the direction growth of minimum value;

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

Its network is dodged the terminal that the middle x of equation (1) represents the vessel segment axis that will generate, x _nthe barycenter that represents to have generated vessel segment, N represents to generate the hop count of blood vessel, β _vrepresent attenuation coefficient, U _nrepresent to 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 section blood vessel having generated, L _nrepresent the length of the n section blood vessel having generated;

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

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

The terminal that the middle x of equation (3) represents the vessel segment axis that will generate, x are dodged in its border _brepresent that x is at borderline projection, β _brepresent attenuation coefficient, U _bweights are dodged, U in expression 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 to dodge weights;

Adopt optimum branching angle equation (5) 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, r ₁represent the radius of subsegment a, r ₂represent the radius of subsegment b, r ₀represent the radius of parent segment, based on θ ₁set up the fluid branch equation of constraint (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 equation of constraint (6) _lrepresent that fluid branch equation of constraint is dodged equation (1) with respect to network and the weight of equation (3) in final Myocardial Microcirculation network modelling equation, β are dodged in border ₃represent inhibiting factor, v represents the direction vector of parent segment, x _pthe starting point of the vessel segment axis that expression will generate;

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

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

Two, simulation blood perfusion, the displacement of calculating hydrone directed flow in blood vessel by hydrone directed flow displacement equation (8), the displacement equation of hydrone directed flow is:

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

The diffusion motion of simulated blood vessel free surface moisture, calculates the size of water diffusion displacement by water diffusion displacement mould value expression (9), water diffusion displacement mould value expression (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 mould value expression (9), Δ x represents the displacement size of hydrone single step walking, m represents diffusion space dimension, and τ represents single step travel time, and D represents hydrone free diffusing coefficient, q represents the random number between (0,1);

The diffusion sense of displacement that calculates hydrone by water diffusion sense of displacement expression formula (10), water diffusion sense of displacement expression formula (10) is:

In its water diffusion sense of displacement expression formula (10) represent the projection of water diffusion displacement unit vector on cartesian coordinate system x axle, y axle, z axle, θ represents to spread the angle of sense of displacement and z axle positive dirction, and φ represents to spread the projection of displacement in xOy plane and the angle of x axle positive dirction;

Three, based on the mobile displacement of hydrone in diffusion Principle of Magnetic Resonance Imaging and step 2 and water diffusion displacement, calculate the phase dispersion being caused by hydrone displacement, the phase dispersion formula (11) being caused by hydrone displacement is:

In the phase dispersion formula (11) that it is caused by hydrone displacement represent the phase dispersion value that i hydrone j walking is walked to cause, γ represents the gyromagnetic ratio of proton, represent diffusion-sensitive gradient, δ represents the diffusion-sensitive gradient duration, represent the displacement that i hydrone j walking is walked;

Under the effect of bipolar gradient pulse spin-echo sequence, the time interval of setting bipolar gradient pulse is Δ, hydrone single step travel time is τ, hydrone walking step number k=Δ/τ (12), closing after bipolar gradient pulse, the phase dispersion that the displacement of hydrone i causes is that in delta time, the phase dispersion sum that displacement produces is walked in each walking of hydrone i, and the expression formula that the phase dispersion sum of displacement generation is walked in each walking of hydrone i is then according to diffusion Principle of Magnetic Resonance Imaging, the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause is:

Wherein S represents the magnetic resonance signal under diffusion-sensitive gradient effect, S ₀represent not apply the magnetic resonance signal of diffusion-sensitive gradient, the number of hydrone in n representation unit voxel;

By magnetic resonance signal decay expression formula in IVIM MRI can obtain with the magnetic resonance signal attenuation type (14) that in unit voxel, all hydrone phase dispersions cause:

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

Four, the magnetic resonance signal attenuation type (14) that in the expression formula (13) of phase dispersion sum that displacement produces and unit voxel, all hydrone phase dispersions cause is walked in the phase dispersion formula (11) based on being caused by hydrone displacement, each walking of hydrone i, calculates difference be worth corresponding magnetic resonance deamplification S/S ₀thereby, obtain a series of S/S ₀discrete value, the then expression formula based on b (17), calculates different be worth corresponding b value, thereby obtain the discrete value of a series of b, based on acquired S/S ₀with the discrete value of b, finally magnetic resonance signal decay expression formula (15) is carried out to nonlinear fitting, obtain the IVIM MRI emulation testing result of Myocardial Microcirculation perfusion model.

2. irrelevant motion magnetic resonance imaging emulation mode in Myocardial Microcirculation according to claim 1 perfusion voxel, is characterized in that the angle theta of subsegment b and parent segment in step 1 ₂calculate by following optimum branching angle equation:

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

3. irrelevant motion magnetic resonance imaging emulation mode in Myocardial Microcirculation according to claim 1 perfusion voxel, it is characterized in that step 4 get 15～20 different value.

4. irrelevant motion magnetic resonance imaging emulation mode in Myocardial Microcirculation according to claim 1 perfusion voxel, is characterized in that step 4 utilizes Levenberg – Marquardt algorithm to carry out nonlinear fitting to the magnetic resonance signal expression formula (15) that decays.