CN109846500A - A method and apparatus for determining fractional coronary flow reserve - Google Patents
A method and apparatus for determining fractional coronary flow reserve Download PDFInfo
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Abstract
本申请实施例公开了一种确定冠状动脉血流储备分数的方法、装置及计算机可读存储介质，所述方法包括：获取冠状动脉的图像信息，从所述冠状动脉的图像信息中获取冠状动脉病变的特征参数；基于所述冠状动脉病变的特征参数确定冠状动脉病变的修正参数；基于所述修正参数对流动控制方程进行修正，得到修正后的流动控制方程；求解所述修正后的流动控制方程，得到所述冠状动脉内部的血压值；基于所述冠状动脉内部的血压值和第一血压值，得到所述冠状动脉的血流储备分数FFR。
The embodiments of the present application disclose a method, a device, and a computer-readable storage medium for determining a coronary blood flow reserve fraction. The method includes: acquiring image information of a coronary artery, and acquiring a coronary artery from the image information of the coronary artery characteristic parameters of the lesions; determining the correction parameters of the coronary lesions based on the characteristic parameters of the coronary lesions; modifying the flow control equation based on the correction parameters to obtain the corrected flow control equation; solving the corrected flow control Equation, the blood pressure value inside the coronary artery is obtained; based on the blood pressure value inside the coronary artery and the first blood pressure value, the blood flow reserve fraction FFR of the coronary artery is obtained.
Description
Technical field
This application involves biomedical engineering technology more particularly to a kind of sides of determining coronary flow reserve score
Method, device and computer can storage mediums.
Background technique
The data of 2018 " Chinese cardiovascular disease report " show, existing 2.9 hundred million people of cardiovascular patient in China, wherein being preced with
13,000,000 people of cardiaopath, and disease incidence, still in lasting ascent stage, the medical expense of patients with coronary heart disease has become China
Great public health burden.Coronary heart disease, which refers mainly to lumen of vessels stenosis or occlusion caused by coronary atherosclerosis, leads to cardiac muscle
Hypoxic-ischemic, necrosis, and then cause angina pectoris, myocardial infarction and even die suddenly, it is a kind of high-incidence disease for perplexing the world mankind.Cause
How this, efficiently and accurately assess coronary ischemia, and the effectively treatment of intervention in time is the long-term research focus of medical field.
Coronary artery computed tomography angiography (Computer Tomography is used at present
Angiography, CTA) and invasive coronarography (Invasive Coronary Angiography, ICA) inspection be to examine
The conventional method of disconnected coronary heart disease, but myocardial ischemia is a kind of states of physiologic function, with hemadostewnosis, supply myocardium size, micro- follow
Ring status etc. is all closely related, can not only reflect the state of myocardial ischemia comprehensively by hemadostewnosis.Research shows that according to hat
Shape arteriarctia judges myocardial ischemia, and to diagnosis of coronary heart disease, there are 28% false positives and 13% false negative.
Nowadays clinically assessing " goldstandard " of myocardial ischemia caused by hemadostewnosis is coronary flow reserve score
(Fractional Flow Reserve, FFR), FFR refer under coronary artery microcirculation maximum congestive state that there are narrow diseases
Blood vessel can be obtained maximum blood flow when change, can be obtained the ratio of maximum blood flow with blood vessel under normal condition.It is coronal
Resistance under arterial microcirculation congestive state is negligible, according to Hydrodynamics Theory it is found that the blood flow of cardiac muscular tissue with
Perfusion pressure is proportional.Therefore FFR can be obtained by the ratio calculation of the pressure and narrow upstream pressure of stenotic lesion far downstream end.
But FFR inspection is needed using expensive operation consumptive material Pressure wire, and operating time is long, and operation has damage lesion vessels
Risk, need the microcirculation dilator injected also to there is certain side effect, many reasons all limit it clinically
Application.
Then coronary artery FFRCTATechnology is come into being, coronary artery FFRCTATechnology is the CT angiography based on patient
Image realizes the reconstructing three-dimensional model of coronary artery, and the method for recycling numerical simulation realizes fluid force coronarius
Emulation is learned, coronary artery pathological changes proximal part and remote pressure value are obtained by simulation calculation, so that noninvasive acquisition patient is coronal
The FFR value of artery.In FFRCTAIn technology, the quality of coronary artery reconstructing three-dimensional model and hydrodynamics method boundary condition
Setting is to influence two principal elements of calculated result accuracy.
And in Coronary Artery Disease Intervention Treatment, diffusivity lesion accounts for about 20%, and has increased trend year by year.Diffusivity lesion
It is typically more complicated, and there is its exclusive feature: it is irregular etc. to be frequently accompanied by angulation, calcification, distortion, eccentricity, runner.And
These irregular factors of calcification, eccentricity and runner are difficult to reappear by three-dimensionalreconstruction, and the missing of these information will limit generally
The applicability of Fluid Mechanics Computation (Computational Fluid Dynamics, CFD) method, while these complex characteristics
The difficulty of clinical diagnosis is increased, so clinically usually directlying adopt more conservative interventional therapy means, is traced it to its cause exactly
Because there is no efficient, the targetedly diagnostic method of reply diffusivity lesion at present.
Summary of the invention
In order to solve the above technical problems, the embodiment of the present application is intended to provide a kind of determining coronary flow reserve score
Method, apparatus and computer readable storage medium can especially be directed to this kind of complex lesions of diffusivity lesion, carry out personalized essence
True FFR is calculated.
The technical solution of the application is achieved in that
In a first aspect, providing a kind of method of determining coronary flow reserve score, which comprises
Image information coronarius is obtained, the spy of coronary artery pathological changes is obtained from the image information coronarius
Levy parameter；
The corrected parameter of coronary artery pathological changes is determined based on the characteristic parameter of the coronary artery pathological changes；
Fluid Control Equation is modified based on the corrected parameter, obtains revised Fluid Control Equation；
The revised Fluid Control Equation is solved, the pressure value inside the coronary artery is obtained；
Based on the pressure value and the first pressure value inside the coronary artery, the blood flow reserve coronarius point is obtained
Number FFR.
Second aspect, it is described the embodiment of the present application also provides a kind of device of determining coronary flow reserve score
Device includes:
Image processing module is obtained from the image information coronarius for obtaining image information coronarius
Take the characteristic parameter of coronary artery pathological changes；
Correction module, for determining that the amendment of coronary artery pathological changes is joined based on the characteristic parameter of the coronary artery pathological changes
Number；Fluid Control Equation is modified based on the corrected parameter, obtains revised Fluid Control Equation；
Computing module obtains the blood pressure inside the coronary artery for solving the revised Fluid Control Equation
Value；Based on the pressure value and the first pressure value inside the coronary artery, the blood flow reserve score coronarius is obtained
FFR。
The third aspect, the embodiment of the present application also provides another device for determining coronary flow reserve score, institutes
Device is stated to include: processor and be configured to store the memory for the computer program that can be run on a processor,
Wherein, when the processor is configured to run the computer program, the step of any one of aforementioned the method is executed
Suddenly.
Fourth aspect provides a kind of computer readable storage medium, is stored thereon with computer program, wherein the meter
The step of preceding method is realized when calculation machine program is executed by processor.
By adopting the above technical scheme, after coronary artery pathological changes, without intrusive Operations Research, but the coronal of individual is utilized
The characteristic parameter of arterial disease is obtained personalized corrected parameter, and then is repaired using corrected parameter to Fluid Control Equation
Just, make influence of the complexity to blood flow that coronary artery pathological changes are emerged from hydrodynamics method, to make up using general
CFD approach inevitable information loss when calculating the FFR of complicated coronary lesion, reduces the calculating error of FFR.
Detailed description of the invention
Fig. 1 is the method schematic diagram 1 that coronary flow reserve score is determined in the embodiment of the present application；
Fig. 2 is the CTA image schematic diagram of the embodiment of the present application cardiac；
Fig. 3 is the 3-D image schematic diagram of the embodiment of the present application cardiac image；
Fig. 4 is aorta and 3-D image schematic diagram coronarius in the embodiment of the present application；
Fig. 5 is CPR image schematic diagram coronarius in the embodiment of the present application；
Fig. 6 is the grid image schematic diagram of arteria coroaria sinistra in the embodiment of the present application；
Fig. 7 is in the embodiment of the present application based on general FFRCTAFFR distribution signal in the arteria coroaria sinistra that method obtains
Figure；
The FFR distribution schematic diagram in revised arteria coroaria sinistra in Fig. 8 the embodiment of the present application；
Fig. 9 is the flow diagram 2 that FFR determines method in the embodiment of the present application；
Figure 10 is the composed structure schematic diagram 1 that the device of coronary flow reserve score is determined in the embodiment of the present application；
Figure 11 is the composed structure schematic diagram 2 that the device of coronary flow reserve score is determined in the embodiment of the present application.
Specific embodiment
The characteristics of in order to more fully hereinafter understand the embodiment of the present application and technology contents, with reference to the accompanying drawing to this Shen
Please the realization of embodiment be described in detail, appended attached drawing purposes of discussion only for reference is not used to limit the embodiment of the present application.
Embodiment one
As shown in Figure 1, the method for determining coronary flow reserve score specifically includes:
Step 101: obtaining image information coronarius, obtain coronary artery pathological changes from image information coronarius
Characteristic parameter；
Step 102: the corrected parameter of coronary artery pathological changes is determined based on the characteristic parameter of coronary artery pathological changes；
Step 103: Fluid Control Equation being modified based on corrected parameter, obtains revised Fluid Control Equation；
Step 104: solving revised Fluid Control Equation, obtain the pressure value inside coronary artery；
Step 105: based on the pressure value and the first pressure value inside coronary artery, obtaining blood flow reserve coronarius point
Number FFR.
Here, the executing subject of step 101 to step 105 can be the place of determining coronary flow reserve score device
Manage device.
Here, FFR refers under coronary artery maximum congestive state that there are blood vessels when stenotic lesion can be obtained maximum blood
Blood vessel can be obtained the ratio of maximum blood flow when under flow, with normal condition, can be equivalent to most in clinical medicine application
Mean pressure (P in narrow remote end coronary artery under big congestive stated) and coronary artery oral area AoMP (Pa) ratio
Value.
Here, image information coronarius be can characterize coronary artery pathological changes feature meet Digital imaging in medicine and
Communicate the two dimensional image, three-dimensional of (Digital Imaging and Communications in Medicine, DICOM) specification
The image of image or other forms, such as: CTA image.
In practical application, step 101 can also include: according to image information acquisition coronarius three-dimensional coronarius
Image；3-D image coronarius can be used for further generating the CFD model for calculating.Here, CFD model is for solving
Revised Fluid Control Equation, CFD model can be threedimensional model, dimensionality reduction model (such as one-dimensional or POD dimensionality reduction model)
And approximate simplified model.
Here, Fluid Control Equation can be the Navier Stokes equation (N-S in conventional computational fluid Mechanics Calculation
Equation), it is also possible to calculate the fluid flowing controlling party of used simplification or deformation when dimensionality reduction model or approximate simplified model
Journey.
Here, the method for obtaining image information coronarius can specifically include: the image information of heart be obtained, from the heart
Image information coronarius is obtained in dirty image information.
Illustratively, the computed tomography angiography CTA image information of heart is obtained；CTA figure based on heart
As the 3-D image of signal reconstruct heart, the 3-D image of heart is obtained；The three of cardiac muscle are isolated from the 3-D image of heart
Tie up image and 3-D image coronarius；Based on the 3-D image and 3-D image coronarius of cardiac muscle, calculate coronal dynamic
The outlet impedance of arteries and veins；Wherein, outlet impedance coronarius is for solving revised Fluid Control Equation.
The CTA image of heart as shown in Fig. 2, the CTA image information reconfiguring heart based on heart 3-D image, according to
The second order greyscale image data of the CTA image of heart utilizes 3-D image reconstruction algorithm processes, obtains the 3 D stereo knot of heart
Structure data, and it is shown as the 3-D image with true feeling, as shown in Figure 3.
The 3-D image and 3-D image coronarius of cardiac muscle are isolated, from the 3-D image of heart in reconstruct
On cardiac three-dimensional image, it is corresponding that each branch of myocardium each section, aorta, coronary artery is isolated using the method for image recognition
3 d image data, as shown in figure 4, being just to pass through image recognition, cutting, the coronary artery three obtained based on region growing method
Dimensional data image, wherein the thicker blood vessel of top half is aorta, and the thinner branch vessel in lower half portion is coronary artery.
Correspondingly, step 101 can specifically include: obtaining curved surface weight coronarius from the CTA image information of heart
Build CPR image information；The characteristic parameter of coronary artery pathological changes is obtained from CPR image information coronarius.
Curve reestablishing CPR image information coronarius is obtained, from the CTA image information of heart for according to the two of CTA
Rank greyscale image data obtains projected image such as Fig. 5 institute of corresponding different perspectives coronarius by surface reconstruction algorithm
Show, also show the coordinate of two points in Fig. 5, index (index) information and pixel [R, G, B], wherein first point
[X, Y] is [317,105], and indexing is 1455, and [R, G, B] is [0.502,0.502,0.502]；[X, the Y] of second point be
[254,271], indexing is 1449, and [R, G, B] is [0.498,0.498,0.498].
The characteristic parameter of coronary artery pathological changes is obtained, from CPR image information coronarius for CPR coronarius
Image information is quantified, and obtains such as length of lesion, blood vessel diameter, a series of ginsengs such as patch sectional area by software measurement
Number, and convert and corresponding characteristic parameter is calculated.
Here, 3-D image and 3-D image coronarius based on cardiac muscle, calculate outlet impedance coronarius, wrap
Include: the 3-D image based on cardiac muscle calculates blood total flow coronarius；Based on 3-D image coronarius and coronal dynamic
The blood total flow of arteries and veins calculates the blood flow of at least one branch of coronary artery；Based at least one branch of coronary artery
Blood flow and third pressure value calculate the outlet impedance of at least one branch of coronary artery.
Illustratively, the 3-D image based on cardiac muscle, calculates blood total flow coronarius, comprising: according to cardiac muscle
3-D image determines the myocardial volume of left ventricle；According to the myocardial volume and cardiac texture of left ventricle, the cardiac muscle of left ventricle is obtained
Quality；Myocardial mass and blood flow coefficient of discharge based on left ventricle, obtain blood total flow coronarius.
Based on 3-D image coronarius and blood total flow coronarius, at least one branch of coronary artery is calculated
Blood flow, comprising: be based on 3-D image coronarius, obtain at least one branch inlet information of coronary artery；It is based on
At least one branch inlet information of coronary artery distributes blood total flow coronarius, obtain entering coronary artery at least one
The blood flow of branch.
In practical application, step 102 be can specifically include: the characteristic parameter based on coronary artery pathological changes is normal at least one
Number, determines the corrected parameter of coronary artery pathological changes.Illustratively, the characteristic parameter of coronary artery pathological changes includes at least: coronal dynamic
Arteries and veins diameter stenosis rate, length of lesion, coronary artery pathological changes minimum diameter and Volume Loss rate.
In practical application, step 103 be can specifically include: being based on corrected parameter, hemodynamics viscosity coronarius, is obtained
To the source item of Fluid Control Equation；Source item is added in Fluid Control Equation, revised Fluid Control Equation is obtained.
Blood is medically typically considered incompressible fluid, then its Fluid Control Equation (being herein N-S equation)
It can indicate are as follows:
WhereinFor blood flow velocity, t is the time, and ▽ is divergence (divergence), and ρ is density of blood, and p is pressure, and μ is
Hemodynamics viscosity (dynamic viscosity),For kinematic viscosity (kinematic viscosity), SiFor source item,
SiAdditional a kind of constraint condition when solving Fluid Control Equation can be considered as.
Illustratively, when lesion occurs for coronary artery, such as diffusivity lesion, due to the Partial Feature of diffusivity lesion
It is difficult to reappear by three-dimensionalreconstruction coronarius, in order to make up the missing for the feature that these influence FFR, in Fluid Control Equation
It is middle to be introduced into additional source item as in amendment addition CFD calculating:
Wherein v is blood flow velocity, C1、C2It is constant.
Constant C in blood vessel laminar flow, in above formula2It can be considered 0, being then based on correction model that corrected parameter obtains (can
To be interpreted as source item) it can simplify are as follows:
Therefore, the pressure loss component of blood flow in all directions in CFD calculating are as follows:
Wherein, vjFor x, y, the velocity component on the direction z, Δ nx, Δ nyWith Δ nzIt is diffusivity lesion in x, y, the direction z
On length, corrected parameter C1For the relationship with diffusivity lesion characteristics parameter are as follows:
C1=A (DSa·Lb·MLDc·VLd)e+B(DSa·Lb·MLDc·VLd)+C
Wherein, A, B, C and a, b, c, d, e are to return to obtain constant by mathematical method, i.e., in the embodiment of the present application at least
One constant, DS are Coronary Artery Width stenosis rate, and L is diffusivity length of lesion, and MLD is coronary artery pathological changes minimum diameter,
VL is Volume Loss rate.Here, pass through corrected parameter C1Correction model is obtained, and is added to flowing for correction model as source item
In governing equation.
Here, Fluid Control Equation can be the Navier Stokes equation (N-S in conventional computational fluid Mechanics Calculation
Equation), it is also possible to calculate the fluid flowing controlling party of used simplification or deformation when dimensionality reduction model or approximate simplified model
Journey.Correction model as source item when being added in these Fluid Control Equations, according to the form of expression of specific governing equation, table
Existing form may also be slightly different.
Here, the diameter stenosis rate of diffusivity lesion, length, minimum diameter, Volume Loss rate are to pass through statistical method
The effective characteristic parameters filtered out can be obtained to the severity of comprehensive characterization diffusivity lesion according to these characteristic parameters
To personalized corrected parameter, and then correction model is obtained using corrected parameter, through correction model in hydrodynamics method
Embody influence of the complexity of diffusivity lesion to blood flow.
In practical application, step 104 be can specifically include: 3-D image coronarius being carried out region division, is obtained
Grid data coronarius；Using outlet impedance coronarius and the second pressure value, boundary condition is set；Based on coronal dynamic
The grid data and boundary condition of arteries and veins, solve revised Fluid Control Equation, obtain the pressure value inside coronary artery.This
In, the second pressure value can be identical as the first pressure value, for example, the first pressure value and the second pressure value are coronary artery entrance
Mean blood pressure value.
That is, at least the CFD model that can be used for calculating is generated based on grid data and boundary condition, in CFD model
It is upper to solve revised Fluid Control Equation.Here, CFD model can be threedimensional model, dimensionality reduction model (such as one-dimensional or POD
Dimensionality reduction model etc.) and approximate simplified model.For example, corresponding three-dimensional CFD model is established when grid data is three-dimensional, three
The revised Fluid Control Equation of Victoria C FD model solution；Corresponding one-dimensional CFD is established when using dimensionality reduction model such as one-dimensional model
Model solves revised Fluid Control Equation on one-dimensional CFD model.Solve using which kind of model and depends on practical feelings
The requirement that condition calculates CFD.
Illustratively, discrete region is carried out to 3-D image coronarius, obtains grid data coronarius, used
To utilize Numerical Methods Solve Fluid Control Equation on each grid, the blood of each net region of coronary artery is finally obtained
Liquid information of flow.Here, blood flow information includes at least the pressure value of each net region inside coronary artery.
Due to the complexity of Coronary Artery Structure, tetrahedral grid is generallyd use, boundary layer uses prism grid, divides net
Arteria coroaria sinistra 3-D image is as shown in Figure 6 after lattice.
Here, the second pressure value is coronary artery entrance mean arterial blood pressure, herein as coronary artery entrance side
Boundary's condition, each artery of coronary artery export impedance RiFor as export boundary condition, diffusivity lesion correction model is as source item
Fluid Control Equation is added:
Using Numerical Methods Solve Fluid Control Equation group, the flow field parameter information of coronary artery everywhere can be obtained, this
Place concerns the pressure value P of coronary artery everywhereCAi。
In practical application, since FFR value can be approximately equal to coronary artery stenosis remote pressure PdIt is pressed with coronary artery proximal end
Power PaThe ratio between (i.e. first pressure value), therefore, FFR value coronarius are as follows:
Work as PCAiIt takes in lesion with remote, P can be equivalent tod, the FFR value obtained at this time is the FFR in general medicine meaning
Value.For example, PCAiTake apart from lesion locations with the pressure value inside the coronary artery at the remote position 2-3cm.
Due to there is complicated diffusivity lesion in coronary artery, using general FFRCTAMethod (does not use diffusivity lesion
Correction model), the arteria coroaria sinistra FFR value grayscale image being calculated obtains as shown in fig. 7, diffusivity lesion correction model is added
Arteria coroaria sinistra FFR value grayscale image as shown in figure 8, in Fig. 7 and Fig. 8 the left side be determine FFR value scale, arteria coroaria sinistra is not
The size of FFR value is represented with position shade, the deeper FFR value that represents of color is smaller, and lesion harm is more serious；Color more shallow generation
Table FFR value is bigger, and the lesion extent of injury is lighter.The method that FFR is determined provided by the embodiment of the present application, can be according to coronary artery
The specific features parameter of lesion obtains personalized corrected parameter, Lai Xiuzheng Fluid Control Equation, to improve blood flow flow field
Computational accuracy reduces the error as caused by the complexity of individual difference and diffusivity lesion, and then improves the calculating essence of FFR
Degree.Comparing Fig. 7 and Fig. 8 can be seen that the FFR value obtained using diffusivity lesion correction model, than not using diffusivity lesion to repair
The FFR value that positive model obtains is smaller, closer to true value.Introducing diffusivity lesion correction model can more precisely be deposited
In the coronary artery FFR numerical value of diffusivity lesion, and then strong help is provided for clinical diagnosis.
By adopting the above technical scheme, after coronary artery pathological changes, without intrusive Operations Research, but the coronal of individual is utilized
The characteristic parameter of arterial disease is obtained personalized corrected parameter, and then is repaired using corrected parameter to Fluid Control Equation
Just, make influence of the complexity to blood flow that coronary artery pathological changes are emerged from hydrodynamics method, to make up using general
CFD approach inevitable information loss when calculating the FFR of complicated coronary lesion, reduces the calculating error of FFR.
Embodiment two
In order to further embody the technical solution of the application, on the basis of the embodiment of the present application one, carry out into one
Step for example, as shown in figure 9, determine coronary flow reserve fractal methods specifically include:
Step 901: obtaining the computed tomography angiography CTA image information of heart；
Step 902: the 3-D image of the CTA image information reconfiguring heart based on heart obtains the 3-D image of heart；From
The 3-D image and 3-D image coronarius of cardiac muscle are isolated in the 3-D image of heart；
Specifically, utilizing 3-D image reconstruction algorithm processes according to the second order greyscale image data of the CTA image of heart, obtain
To the three-dimensional structure data of heart, and it is shown as the 3-D image with true feeling, as shown in Figure 4；Using image recognition
Method isolates the corresponding 3-D image number of each branch of myocardium each section, aorta, coronary artery from the 3-D image of heart
According to.
Step 903: 3-D image and 3-D image coronarius based on cardiac muscle calculate outlet resistance coronarius
It is anti-；
Specifically, the 3-D image based on cardiac muscle, calculates blood total flow coronarius；Based on three-dimensional coronarius
Image and blood total flow coronarius calculate the blood flow of at least one branch of coronary artery；Extremely based on coronary artery
The blood flow and third pressure value of a few branch, calculate the outlet impedance of at least one branch of coronary artery.Here, third
Pressure value is to assume that coronary artery exports mean blood pressure value when lesion is not present in coronary artery.
Wherein, the myocardial volume of left ventricle is determined according to the 3-D image of cardiac muscle；According to the myocardial volume and the heart of left ventricle
Flesh density obtains the myocardial mass of left ventricle；Myocardial mass and blood flow coefficient of discharge based on left ventricle, obtain blood coronarius
Liquid total flow.
Based on 3-D image coronarius and blood total flow coronarius, at least one branch of coronary artery is calculated
Blood flow, comprising: be based on 3-D image coronarius, obtain at least one branch inlet information of coronary artery；It is based on
At least one branch inlet information of coronary artery distributes blood total flow coronarius, obtain entering coronary artery at least one
The blood flow of branch.Here, branch inlet information can be the inlet diameter of branch, and hat is specifically defined using hydraulic diameter
The inlet diameter of each branch of shape artery.
Specifically, myocardium of left ventricle volume V can be calculated according to the 3 d image data of cardiac muscle, the left ventricle heart is then taken
Myocardium of left ventricle quality can be calculated according to formula m=ρ V in flesh averag density ρ；And enter total blood flow coronarius
With the relationship of myocardial mass are as follows:
Q=Q0m3/4
Wherein, Q is to enter total blood flow coronarius, Q0=5.4mL/gmin is blood flow coefficient of discharge.
According to 3-D image coronarius, each branch inlet information of coronary artery is calculated, and is believed according to each branch inlet
Breath respectively enters the blood flow of each branch of coronary artery.
Firstly, according to individual advantage type coronarius empirically pro rate or so flow coronarius.For example, hat
When shape artery is left advantage type, the empirical scalar of left and right flow coronarius is 7:3, and when being right advantage type, left and right is coronal dynamic
The empirical scalar of the flow of arteries and veins is 3:7, and when being balanced type, the empirical scalar of left and right flow coronarius is 5:5.
Then, it according to the ratio of each branch inlet diameter of coronary artery, is calculated separately step by step into each branch of coronary artery
Blood flow.For example, the ratio of the inlet diameter of coronary artery first order arteria coroaria sinistra and arteria coronaria dextra is 7:3, the
The ratio of the inlet diameter of the descending anterior branch and left hand of second level arteria coroaria sinistra is 4:6.
It should be noted that circle due to cross section coronarius and non-critical, main root in practical application
Cross-sectional area S and perimeter C is obtained according to 3 d image data coronarius, and defines hat using hydraulic diameter D=4S/C
The inlet diameter of shape artery；
Since each branch's blood flow and the cube of vascular entrance diameter are proportional, enter each point of coronary artery
The blood flow of branch is just allocated according to each branch inlet diameter proportion, herein by taking descending anterior branch and Circumflex branch as an example, if Zuo Guanzhuan
Arterial inlet flow is QL, descending anterior branch inlet diameter is DLAD, Circumflex branch inlet diameter is DLCX, then enter the blood stream of descending anterior branch
Measure QLADAre as follows:
The theorem of characterization
Correspondingly, into the blood flow Q of Circumflex branchLCXAre as follows:
QLCX=QL-QLAD
Other are at different levels also to be distributed with this step by step, until obtaining whole branch flows.Here, LAD (left
Anterior descending artery) refer to that left anterior descending artery, LCX (left circumflex artery) refer to left hand
Artery
In one embodiment, according to the myocardium 3 d image data of sufferer, myocardium of left ventricle volume V=is obtained
165.25mL, then take empirical mean density p=1050kg/m of myocardium of left ventricle3, myocardium of left ventricle quality m=ρ V is calculated
=173.51g.
Then corresponding total blood flow coronarius are as follows:
Q=Q0m3/4=5.4 × 173.510.75=4.30 × 10-6m3/s
When determining that coronary artery is left advantage type according to 3 d image data coronarius, 70% is taken according to empirical scalar
As arteria coroaria sinistra inlet flow rate, 30% is taken to be used as arteria coronaria dextra inlet flow rate.
Wherein, as arteria coroaria sinistra inlet flow rate are as follows: QL=Q × 70%=3.01 × 10-6m3/s；
Arteria coronaria dextra inlet flow rate are as follows: QR=Q × 30%=1.29 × 10-6m3/s。
When coronary artery pathological changes occur in arteria coroaria sinistra, according to the 3 d image data of arteria coroaria sinistra, before measuring
Descending branch entrance hydraulic diameter is 5.393mm, and Circumflex branch entrance hydraulic diameter is 5.729mm, then, into the blood flow of descending anterior branch
Are as follows:
Into the blood flow of Circumflex branch are as follows:
QLCX=QL-QLAD=1.64 × 10-6m3/s。
The assignment of traffic of other each secondary branch is similarly.
Further, it according to each branch's blood flow of coronary artery and third pressure value, calculates each artery of coronary artery and goes out
Mouth impedance.Here, third pressure value is to assume that coronary artery exports mean blood pressure value when lesion is not present in coronary artery.
Calculate the formula of coronary arterial tree outlet impedance are as follows: P3=QOUTi×Ri, here, RiIt is hindered for the outlet of the i-th branch
It is anti-, QOUTiFor the exit blood flow amount of the i-th branch, P3For third pressure value.Therefore, according to each branch outlet blood flow, each point is determined
The outlet impedance R of branchi=P3/QOUTi。
Step 904: curve reestablishing CPR image information coronarius is obtained from the CTA image information of heart；From coronal
The characteristic parameter of coronary artery pathological changes is obtained in the CPR image information of artery；
Specifically, quantify to CPR image information coronarius, by software measurement obtain such as length of lesion,
Blood vessel diameter, the series of parameters such as patch sectional area, and convert and corresponding characteristic parameter is calculated.
The CTA image of the embodiment of the present application cardiac from the CTA image information of heart as shown in Fig. 2, obtain coronal dynamic
The curve reestablishing CPR image information of arteries and veins, to obtain and corresponding to by surface reconstruction algorithm according to the second order greyscale image data of CTA
The projected image of different perspectives coronarius is as shown in Figure 3.
Step 905: being based on corrected parameter and hemodynamics viscosity coronarius, obtain the source item of Fluid Control Equation；
Source item is added in Fluid Control Equation, revised Fluid Control Equation is obtained；
Blood is medically typically considered incompressible fluid, then its Fluid Control Equation can indicate are as follows:
WhereinFor blood flow velocity, t is the time, and ▽ is divergence (divergence), and ρ is density of blood, and p is pressure, and μ is
Hemodynamics viscosity (dynamic viscosity),For kinematic viscosity (kinematic viscosity), SiFor source
, SiA kind of constraint condition of Fluid Control Equation can be regarded as.
Illustratively, when lesion occurs for coronary artery, such as diffusivity lesion, due to the Partial Feature of diffusivity lesion
It is difficult to reappear by three-dimensionalreconstruction coronarius, in order to make up the missing for the feature that these influence FFR, in Fluid Control Equation
It is middle to be introduced into additional source item as in amendment addition CFD calculating:
Wherein v is blood flow velocity, C1、C2It is constant.
Constant C in blood vessel laminar flow, in above formula2It can be considered 0, being then based on correction model that corrected parameter obtains (can
To be interpreted as source item) it can simplify are as follows:
Therefore, the pressure loss of blood flow in all directions is decomposed in CFD calculating are as follows:
Wherein, vjFor x, y, the velocity component on the direction z, Δ nx, Δ nyWith Δ nzIt is diffusivity lesion in x, y, the direction z
On length, corrected parameter C1For the relationship with diffusivity lesion characteristics parameter are as follows:
C1=A (DSa·Lb·MLDc·VLd)e+B(DSa·Lb·MLDc·VLd)+C
Wherein, A, B, C and a, b, c, d, e are to return to obtain constant by mathematical method, and DS is that Coronary Artery Width is narrow
Rate, L are diffusivity length of lesion, and MLD is coronary artery pathological changes minimum diameter, and VL is Volume Loss rate.Here, joined by amendment
Number C1Correction model is obtained, and correction model is added in the source item of Fluid Control Equation.
Here, Fluid Control Equation can be the Navier Stokes equation (N-S in conventional computational fluid Mechanics Calculation
Equation), it is also possible to calculate the fluid flowing controlling party of used simplification or deformation when dimensionality reduction model or approximate simplified model
Journey.Correction model as source item when being added in these Fluid Control Equations, according to the form of expression of specific governing equation, table
Existing form may also be slightly different.
Illustratively, according to the diffusivity lesion characteristics parameter extracted, corrected parameter can be calculated are as follows:
C1=232133 × (DSLMLD1.8·VL)2-3×106×(DS·L·MLD1.8·VL)+2×107=
2.98×107
Then it is added correction model as the source item of Fluid Control Equation, obtains revised Fluid Control Equation, and
Solve revised Fluid Control Equation.
Step 906: the CFD model that can be used for calculating being generated based on grid data coronarius and boundary condition, in CFD
Revised Fluid Control Equation is solved on model, obtains the pressure value inside coronary artery；
Here, CFD model can be threedimensional model, dimensionality reduction model (such as one-dimensional or POD dimensionality reduction model) and approximation
Simplified model.For example, corresponding three-dimensional CFD model is established when grid data is three-dimensional, after three-dimensional CFD model solves amendment
Fluid Control Equation；Corresponding one-dimensional CFD model is established when using dimensionality reduction model such as one-dimensional model, in one-dimensional CFD model
It is upper to solve revised Fluid Control Equation.Which kind of model to be entangled with the requirement calculated depending on actual conditions CFD using.
Specifically, 3-D image coronarius is carried out region division, grid data coronarius is obtained, further
It is converted into the CFD model for calculating；Using outlet impedance coronarius and the second pressure value, boundary condition is set.Here,
Second pressure value is coronary artery entrance mean arterial blood pressure, herein as coronary artery entrance boundary condition, using number
Value method solves Fluid Control Equation group, can obtain the flow field parameter information of coronary artery everywhere, concern herein coronal
The pressure value P of artery everywhereCAi。
Step 907: based on the pressure value and the first pressure value inside coronary artery, obtaining blood flow reserve coronarius point
Number FFR.
In practical application, since FFR value can be approximately equal to coronary artery stenosis remote pressure PdIt is pressed with coronary artery proximal end
Power PaThe ratio between, therefore, FFR value coronarius are as follows:
Work as PCAiIt takes in lesion with remote, P can be equivalent tod, the FFR value obtained at this time is the FFR in general medicine meaning
Value.For example, PCAiTake apart from lesion locations with the pressure value inside the coronary artery at the remote position 2-3cm.
Here, the diameter stenosis rate of diffusivity lesion, length, minimum diameter, Volume Loss rate are to pass through statistical method
The effective characteristic parameters filtered out can be obtained to the severity of comprehensive characterization diffusivity lesion according to these characteristic parameters
To personalized corrected parameter, and then correction model is obtained using corrected parameter, is able to by correction model in hydrodynamics meter
Influence of the complexity of diffusivity lesion to blood flow is embodied in calculation.In this way, the method for determining FFR provided by the present application can make up
This kind of complex lesions of diffusivity lesion constantly inevitable information loss is being calculated using general CFD approach, is greatly being reduced
The calculating error of FFR.
Embodiment three
Based on the same inventive concept, the embodiment of the present application also provides a kind of dresses of determining coronary flow reserve score
It sets, as shown in Figure 10, which includes:
Image processing module 1001, for obtaining image information coronarius, from the image information coronarius
The middle characteristic parameter for obtaining coronary artery pathological changes；
Correction module 1002, for determining the amendment of coronary artery pathological changes based on the characteristic parameter of the coronary artery pathological changes
Parameter；Fluid Control Equation is modified based on the corrected parameter, obtains revised Fluid Control Equation；
Computing module 1003 obtains inside the coronary artery for solving the revised Fluid Control Equation
Pressure value；Based on the pressure value and the first pressure value inside the coronary artery, the blood flow reserve coronarius point is obtained
Number FFR.
In some embodiments, the correction module 1002 is joined specifically for the feature based on the coronary artery pathological changes
Several and at least one constant, determines the corrected parameter of coronary artery pathological changes.Illustratively, the characteristic parameter includes at least: hat
Shape artery diameter stenosis rate, length of lesion, coronary artery pathological changes minimum diameter and Volume Loss rate.
In some embodiments, the correction module 1002 is specifically used for being based on the corrected parameter, the coronary artery
Hemodynamics viscosity, obtain the source item of the Fluid Control Equation；The source item is added in Fluid Control Equation, is obtained
Revised Fluid Control Equation.
In some embodiments, image processing module 1001, specifically for obtaining the computed tomography blood vessel of heart
Radiography CTA image information；
The 3-D image that the heart is reconstructed based on the CTA image information of the heart obtains the three-dimensional figure of the heart
Picture；
The 3-D image and 3-D image coronarius of cardiac muscle are isolated from the 3-D image of the heart；
3-D image and 3-D image coronarius based on the cardiac muscle calculate the outlet resistance coronarius
It is anti-；Wherein, the outlet impedance coronarius is for solving the revised Fluid Control Equation；
The curve reestablishing CPR image information coronarius is obtained from the CTA image information of the heart；
The characteristic parameter of coronary artery pathological changes is obtained from the CPR image information coronarius.
In some embodiments, image processing module 1001 are also used to be repaired out with the plane perpendicular to blood flow direction and are preced with
The inlet and outlet face of shape artery is as corresponding boundary coronarius.
In some embodiments, the computing module 1003 is specifically used for carrying out the 3-D image coronarius
Region division obtains the grid data coronarius；
Using the outlet impedance coronarius and the second pressure value, boundary condition is set；
Based on the grid data coronarius and boundary condition, revised Fluid Control Equation is solved, obtains institute
State the pressure value inside coronary artery.
In some embodiments, described image processing module 1001, specifically for the 3-D image based on the cardiac muscle, meter
Calculate blood total flow coronarius；Based on the 3-D image coronarius and the blood total flow coronarius,
Calculate the blood flow of at least one branch of coronary artery；Blood flow based at least one branch of coronary artery
With third pressure value, the outlet impedance of at least one branch of coronary artery is calculated.
In some embodiments, described image processing module 1001, it is true specifically for the 3-D image according to the cardiac muscle
Determine the myocardial volume of left ventricle；According to the myocardial volume and cardiac texture of the left ventricle, the myocardium matter of the left ventricle is obtained
Amount；Myocardial mass and blood flow coefficient of discharge based on the left ventricle obtain the blood total flow coronarius；
Described image processing module 1001 is specifically used for being based on the 3-D image coronarius, obtain described coronal
At least one branch inlet information of artery；The coronary artery is distributed based at least one branch inlet information of the coronary artery
Blood total flow, obtain the blood flow at least one branch of coronary artery.
In practical applications, above-mentioned memory can be volatile memory (volatile memory), such as deposit at random
Access to memory (RAM, Random-Access Memory)；Or nonvolatile memory (non-volatile memory), example
Such as read-only memory (ROM, Read-Only Memory), flash memory (flash memory), hard disk (HDD, Hard
Disk Drive) or solid state hard disk (SSD, Solid-State Drive)；Or the combination of the memory of mentioned kind, and to
Processor provides instruction and data.
Above-mentioned processor can be application-specific IC (ASIC, Application Specific Integrated
Circuit), digital signal processing device (DSPD, Digital Signal Processing Device), programmable logic dress
Set (PLD, Programmable Logic Device), field programmable gate array (Field-Programmable Gate
Array, FPGA), controller, at least one of microcontroller, microprocessor.It is to be appreciated that being used for different equipment
In realize the electronic device of above-mentioned processor function can also be it is other, the embodiment of the present application is not especially limited.
By adopting the above technical scheme, after coronary artery pathological changes, without intrusive Operations Research, but the coronal of individual is utilized
The characteristic parameter of arterial disease is obtained personalized corrected parameter, and then is repaired using corrected parameter to Fluid Control Equation
Just, make influence of the complexity to blood flow that coronary artery pathological changes are emerged from hydrodynamics method, to make up using general
CFD approach inevitable information loss when calculating the FFR of complicated coronary lesion, reduces the calculating error of FFR.
Based on the hardware realization of each unit in above-mentioned apparatus, the embodiment of the present application also provides another kinds to determine coronary artery
The device of blood flow reserve score, as shown in figure 11, the device 110 include: processor 1101 and are configured to store and can handle
The memory 1102 of the computer program run on device；
Wherein, when processor 1101 is configured to operation computer program, the method and step in previous embodiment is executed.
Certainly, when practical application, as shown in figure 11, the various components in the device 110 are coupled by bus system 1103
Together.It is understood that bus system 1103 is for realizing the connection communication between these components.It includes number that bus system 1103, which is removed,
It further include power bus, control bus and status signal bus in addition except bus.But for the sake of clear explanation, in Figure 11
It is middle that various buses are all designated as bus system 1103.
In practical applications, above-mentioned processor can be application-specific IC (ASIC, Application
Specific Integrated Circuit), digital signal processing device (DSPD, Digital Signal Processing
Device), programmable logic device (PLD, Programmable Logic Device), field programmable gate array
At least one of (Field-Programmable Gate Array, FPGA), controller, microcontroller, microprocessor.It can
To understand ground, for different equipment, the electronic device for realizing above-mentioned processor function can also be other, the application reality
Example is applied to be not especially limited.
Above-mentioned memory can be volatile memory (volatile memory), such as random access memory (RAM,
Random-Access Memory)；Or nonvolatile memory (non-volatile memory), such as read-only memory
(ROM, Read-Only Memory), flash memory (flash memory), hard disk (HDD, Hard Disk Drive) or solid
State hard disk (SSD, Solid-State Drive)；Or the combination of the memory of mentioned kind, and to processor provide instruction and
Data.
In the exemplary embodiment, the embodiment of the present application also provides a kind of computer readable storage medium, for example including
The memory 1102 of computer program, above-mentioned computer program can be executed by the processor 1101 of device 110, to complete aforementioned side
Method step.
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer program
Product.Therefore, the shape of hardware embodiment, software implementation or embodiment combining software and hardware aspects can be used in the application
Formula.Moreover, it wherein includes the computer-readable storage of computer usable program code that the application, which can be used in one or more,
The form for the computer program product implemented on medium (including but not limited to magnetic disk storage and optical memory etc.).
The application is referring to according to the method, apparatus of the embodiment of the present application and the flow diagram of computer program product
And/or block diagram describes.It should be understood that can be realized by computer program instructions each in flow diagram and/or block diagram
The combination of process and/or process and/or box in box and flow diagram and/or block diagram.It can provide these calculating
Processing of the machine program instruction to general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices
Device is to generate a machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute
For realizing the function specified in flow diagram one process or multiple processes and/or block diagrams one box or multiple boxes
The device of energy.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
The manufacture of device is enabled, which realizes in one side of flow diagram one process or multiple processes and/or block diagrams
The function of being specified in frame or multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one process of flow diagram or multiple processes and/or box
The step of function of being specified in figure one box or multiple boxes.
The above, the only preferred embodiment of the application, are not intended to limit the protection scope of the application.
Claims (14)
1. a kind of method of determining coronary flow reserve score, which is characterized in that the described method includes:
Image information coronarius is obtained, the feature ginseng of coronary artery pathological changes is obtained from the image information coronarius
Number；
The corrected parameter of coronary artery pathological changes is determined based on the characteristic parameter of the coronary artery pathological changes；
Fluid Control Equation is modified based on the corrected parameter, obtains revised Fluid Control Equation；
The revised Fluid Control Equation is solved, the pressure value inside the coronary artery is obtained；
Based on the pressure value and the first pressure value inside the coronary artery, the blood flow reserve score coronarius is obtained
FFR。
2. the method according to claim 1, wherein the characteristic parameter based on the coronary artery pathological changes is true
Determine the corrected parameter of coronary artery pathological changes, comprising:
Characteristic parameter and at least one constant based on the coronary artery pathological changes, determine the corrected parameter of coronary artery pathological changes.
3. the method according to claim 1, wherein it is described based on the corrected parameter to Fluid Control Equation into
Row amendment, obtains revised Fluid Control Equation, comprising:
Based on the corrected parameter, the hemodynamics viscosity coronarius, the source item of the Fluid Control Equation is obtained；
The source item is added in Fluid Control Equation, revised Fluid Control Equation is obtained.
4. the method according to claim 1, wherein the method also includes:
Obtain the computed tomography angiography CTA image information of heart；
The 3-D image that the heart is reconstructed based on the CTA image information of the heart obtains the 3-D image of the heart；
The 3-D image and 3-D image coronarius of cardiac muscle are isolated from the 3-D image of the heart；
3-D image and 3-D image coronarius based on the cardiac muscle calculate the outlet impedance coronarius；Its
In, the outlet impedance coronarius is for solving the revised Fluid Control Equation；
It is described to obtain image information coronarius, the spy of coronary artery pathological changes is obtained from the image information coronarius
Levy parameter, comprising:
The curve reestablishing CPR image information coronarius is obtained from the CTA image information of the heart；
The characteristic parameter of coronary artery pathological changes is obtained from the CPR image information coronarius.
5. according to the method described in claim 4, it is characterized in that, the solution revised Fluid Control Equation, obtains
Pressure value to inside the coronary artery, comprising:
The 3-D image coronarius is subjected to region division, obtains the grid data coronarius；
Using the outlet impedance coronarius and the second pressure value, boundary condition is set；
Based on the grid data coronarius and boundary condition, revised Fluid Control Equation is solved, obtains the hat
Pressure value inside shape artery.
6. according to the method described in claim 4, it is characterized in that, the 3-D image and coronary artery based on the cardiac muscle
3-D image, calculate the outlet impedance coronarius, comprising:
Based on the 3-D image of the cardiac muscle, blood total flow coronarius is calculated；
Based on the 3-D image coronarius and the blood total flow coronarius, the coronary artery is calculated at least
The blood flow of one branch；
Blood flow and third pressure value based at least one branch of coronary artery, calculate the coronary artery at least one
The outlet impedance of a branch.
7. according to the method described in claim 6, it is characterized in that, the 3-D image based on the cardiac muscle, calculates coronal
The blood total flow of artery, comprising:
The myocardial volume of left ventricle is determined according to the 3-D image of the cardiac muscle；
According to the myocardial volume and cardiac texture of the left ventricle, the myocardial mass of the left ventricle is obtained；
Myocardial mass and blood flow coefficient of discharge based on the left ventricle obtain the blood total flow coronarius；
It is described to be based on the 3-D image coronarius and the blood total flow coronarius, calculate the coronary artery
The blood flow of at least one branch, comprising:
Based on the 3-D image coronarius, at least one branch inlet information of the coronary artery is obtained；
The blood total flow coronarius is distributed based at least one branch inlet information of the coronary artery, is entered
The blood flow of at least one branch of coronary artery.
8. a kind of device of determining coronary flow reserve score, which is characterized in that described device includes:
Image processing module obtains hat for obtaining image information coronarius from the image information coronarius
The characteristic parameter of shape arterial disease；
Correction module, for determining the corrected parameter of coronary artery pathological changes based on the characteristic parameter of the coronary artery pathological changes；Base
Fluid Control Equation is modified in the corrected parameter, obtains revised Fluid Control Equation；
Computing module obtains the pressure value inside the coronary artery for solving the revised Fluid Control Equation；Base
Pressure value and the first pressure value inside the coronary artery obtain the blood flow reserve score FFR coronarius.
9. device according to claim 8, which is characterized in that
The correction module determines hat specifically for characteristic parameter and at least one constant based on the coronary artery pathological changes
The corrected parameter of shape arterial disease.
10. device according to claim 8, which is characterized in that the correction module is specifically used for joining based on the amendment
Several, the described hemodynamics viscosity coronarius, obtains the source item of the Fluid Control Equation；The source item is added to flowing
In governing equation, revised Fluid Control Equation is obtained.
11. device according to claim 8, which is characterized in that described image processing module, specifically for obtaining heart
Computed tomography angiography CTA image information；
The 3-D image that the heart is reconstructed based on the CTA image information of the heart obtains the 3-D image of the heart；
The 3-D image and 3-D image coronarius of cardiac muscle are isolated from the 3-D image of the heart；
3-D image and 3-D image coronarius based on the cardiac muscle calculate the outlet impedance coronarius；Its
In, the outlet impedance coronarius is for solving the revised Fluid Control Equation；
The curve reestablishing CPR image information coronarius is obtained from the CTA image information of the heart；
The characteristic parameter of coronary artery pathological changes is obtained from the CPR image information coronarius.
12. device according to claim 11, which is characterized in that the computing module, being specifically used for will be described coronal dynamic
The 3-D image of arteries and veins carries out region division, obtains the grid data coronarius；
Using the outlet impedance coronarius and the second pressure value, boundary condition is set；
Based on the grid data coronarius and boundary condition, revised Fluid Control Equation is solved, obtains the hat
Pressure value inside shape artery.
13. a kind of device of determining coronary flow reserve score, described device include: processor and be configured to storage can
The memory of the computer program run on a processor,
Wherein, when the processor is configured to run the computer program, perform claim requires any one of 1 to 7 the method
The step of.
14. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that the computer program quilt
The step of any one of claim 1 to 7 the method is realized when processor executes.
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| CN113995388A (en) * | 2021-12-13 | 2022-02-01 | 数坤(北京)网络科技股份有限公司 | Fractional flow reserve calculation method and device, electronic equipment and readable storage medium |
| WO2022160973A1 (en) * | 2021-01-26 | 2022-08-04 | 上海杏脉信息科技有限公司 | Coronary fractional flow reserve obtaining system and method, and medium |
| CN117462156A (en) * | 2023-10-08 | 2024-01-30 | 中国人民解放军陆军军医大学第一附属医院 | A method for non-invasive calculation of IMR based on physiologically specific coronary blood flow model |
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