Computer-implemented method for simulating myocardial blood flow under stress conditions - Patents.com

Abstract

The computer-implemented method for simulating myocardial blood flow under stress conditions includes generating (2) a simulated multiphysics model of myocardial perfusion, the generating step (2) further includes generating (21) a simulated model of epicardial blood vessels using a three-dimensional fluid dynamics description; generating (22) a simulated model of intramural blood vessels using a multi-compartment porous medium; coupling (23) the simulated model of epicardial blood vessels with the simulated model of intramural blood vessels; and automatically calibrating (3) physical parameters of the simulated multiphysics model of myocardial perfusion under stress conditions, the calibrated physical parameters being the permeability tensor (K, i=1, 2, 3), the conductance between the epicardial coronary artery and the intramural blood vessel (α, j=1, ..., J), and the conductance between compartments (i, k) (β, k, i, k=1, 2, 3).

Description

[Technical field]

[0001] The present invention relates to a computer-implemented method for simulating myocardial blood flow under stress conditions. [Background technology]

[0002] Myocardial perfusion, also known as myocardial blood flow (MBF), is the supply of blood to the heart muscle, called the myocardium, which is supplied by the coronary circulation.

[0003] Quantification of MBF and functional assessment of coronary artery disease (CAD) can be achieved by stress myocardial computed tomography perfusion (stress-CTP).

[0004] This technique requires an additional scan after resting coronary computed tomography angiography (cCTA) and administration of an intravenous stressor, which increases the patient's radiation exposure and potentially leads to stressor-related side effects.

[0005] Computational methods may enable completely non-invasive diagnostic techniques for the quantification of myocardial perfusion and the detection of coronary artery stenosis and may prove to be effective tools as a concrete support for the clinician.

[0006] To this end, the document "A computational model applied to myocardial perfusion in the human heart: From large coronaries to microvasculature" (Journal of Computational Physics, 424:109836, 2021) proposes a multiphysics mathematical and numerical model of myocardial perfusion to quantify MBF, thereby avoiding stress protocols and their associated potential side effects and reducing radiation exposure.

[0007] However, mathematical and numerical models in themselves are not sufficient to quantify MBF under stress conditions and in fact require a suitable set of patient-specific parameters that allow the numerical simulation to calculate MBF under stress conditions. Summary of the Invention [Problem to be solved by the invention]

[0008] It is therefore a primary object of the present invention to provide a computer-implemented method for simulating myocardial blood flow under stress conditions, which allows for the calculation of MBF under stress conditions in an efficient and accurate manner for a particular patient. [Means for solving the problem]

[0009] The above object is achieved by the inventive computer-implemented method for simulating myocardial blood flow under stress conditions according to the features of claim 1.

[0010] Other features and advantages of the present invention will become more apparent from the following non-exclusive description of a preferred embodiment of a computer-implemented method for simulating myocardial blood flow under stress conditions, as illustrated in the accompanying drawings, by way of non-limiting example. [Brief description of the drawings]

[0011] [Figure 1] FIG. 2 is a block diagram of a computer-implemented method in accordance with the present invention. [Diagram 2] 4A-4C show schematic diagrams of vasodilation under simulated stress conditions for the physical parameter adjustment step of the computer-implemented method according to the present invention; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] With particular reference to FIG. 1, indicated generally by the reference numeral 1 is a computer-implemented method for simulating myocardial blood flow under stress conditions.

[0013] The computer-implemented method 1 according to the invention comprises a first step 2 of generating a simulated multiphysics model of myocardial perfusion.

[0014] In particular, in the coronary artery tree, a clear separation of scales can be observed between the epicardial vessels, which are the main vessels located on the epicardium, and the intramural vessels, which are the smaller vessels that penetrate the tissue (The multi-scale modelling of coronary blood flow. Annals of Biomedical Engineering, 40(11):2399-2413, 2012).

[0015] Thus, with such separation of scales, step 2 of generating a simulated multiphysics model of myocardial perfusion includes: - Step 21: Generate a simulation model of the epicardial vessels with a three-dimensional fluid dynamics description; Step 22: Creating a simulation model of an intramural blood vessel with a multicompartment porous medium.

[0016] According to a preferred embodiment, the step of generating a simulation model of the epicardial vessels using a three-dimensional fluid dynamics description is performed using the incompressible Navier-Stokes equations.

[0017] Furthermore, according to a preferred embodiment, the step of generating a simulation model of an intramural vessel by a multicompartment porous medium is carried out using Darcy's law (Multi-scale parameterisation of a myocardial perfusion model using whole-organ arterial networks. Annals of Biomedical Engineering, 42(4):797-811, 2014).

[0018] Furthermore, step 2 of generating a multiphysics simulation model of myocardial perfusion includes step 23 of coupling a simulation model of the epicardial vessels with a simulation model of the intramural vessels of the myocardium using an interface condition based on the continuity of mass and momentum in each perfusion region, where each perfusion region is a specific myocardial region perfused by a separate epicardial vessel (Visualisation of intramural coronary vasculature by an imaging cryomicrotome suggests compartmentalization of myocardial perfusion areas. Medical and Biological Engineering and Computing, 43(4):431-435, 2005).

[0019] In particular, for the three compartment case, step 2 of generating a multiphysics simulation model of myocardial perfusion can be implemented by executing the following equation:

[0020]

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[0021] Finally, the notation χ A represents the characteristic function of domain A.

[0022] In particular, to enforce conservation of mass between compartments, β i,k =β k,i ,

[0023]

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[0024] Furthermore, since compartment i only exchanges mass with neighboring compartments, βi,k ≠ 0 whenever k = i ± 1 for 2 ≤ i ≤ N-1, k = 2 for i = 1, and k = N-1 for i = N. In particular, only the first compartment is involved in the coupling condition, and the homogenization property of the Darcy equation means that the average pressure across the compartment, Ω j is taken into consideration.

[0025] As disclosed in "A computational model applied to myocardial perfusion in the human heart: From large coronaries to microvasculature (Journal of Computational Physics, 424:109836, 2021)," it is pointed out that, in particular, step 2 of generating a multiphysics simulation model can be implemented.

[0026] In order to reproduce clinical data of myocardial blood flow (MBF) maps, the simulation performed by the computer-implemented method 1 according to the invention requires an appropriate set of specific physical parameters of the simulated multiphysics model of myocardial perfusion.

[0027] Advantageously, the computer-implemented method 1 according to the invention comprises a step 3 of automatic calibration of the physical parameters of the multiphysics simulation model of myocardial perfusion in stress conditions.

[0028] In particular, the calibrated physical parameters are: Permeability tensor K i , i=1, 2, 3; Conductance α between epicardial coronary arteries and intramural vessels j , j=1, ..., J, and The intercompartmental conductance β between compartments i and k i,k , i, k=1, 2, 3.

[0029] Suitable values ​​for such parameters are estimated for each patient and are expected to differ between different perfusion regions.

[0030] As shown diagrammatically in FIG. 1, the automatic calibration step 3 of the physical parameters under stress conditions comprises the following steps: - a step 31 of estimating rest-state physical parameters by utilizing the geometrical and hydrodynamic properties of the intramural vessels in the resting state; - Step 32 of adjusting physical parameters, taking into account vasodilation under stress conditions; - A step 33 of modifying a physical parameter in the partition, in particular by increasing the physical parameter within the partition.

[0031] According to an estimation step 31, the intramural vascular network is used to estimate the first possible values ​​of the physical parameters in the resting state.

[0032] Permeability tensor K i , i=1,2,3, are initialized based on a geometric problem, and in particular for each compartment and perfusion region, it is given by the ratio of the intramural vessel volume of that region to the total region volume.

[0033] The first step is to separate the intramural vascular network into two groups of vessels using a specific metric, based on which it is possible to associate the largest vessels with the first compartment and the smallest with the second compartment.

[0034] In particular, the surrogate intramural vascular network, generated according to the paper "A computational model applied to myocardial perfusion in the human heart: From large coronaries to microvasculature" (Journal of Computational Physics, 424:109836, 2021), does not include microvessels that are part of the network modeled with a third Darcy compartment.

[0035] To carry out such an operation, the estimation step 31 estimates for each node y of the intramural vascular network i This step includes the definition of the hierarchical parameters ζε[0,1] for

[0036] In particular, the definition step is to define the hierarchical parameters ζ(y i ) to y i The method includes calculating the ratio of the total length of the blood vessels distal to the network to the total length of all blood vessels in the network.

[0037] In this way, ζ will be 1 at the closest node and 0 at the farthest end node.

[0038] Next, each perfusion area Ω j M to value Z j Given ε(0,1), the estimation step 31 determines whether the average of the values ​​of ζ at the nodes of the vascular network at hand lies in the range [0,Z j ] or range [Z j , 1], sorting the vessels of the network so that they belong to the first vessel group or the second vessel group.

[0039] Z j The value of is chosen to have approximately the same number of vessels in the two groups.

[0040] In particular, the estimation step 31 estimates the global constant hydraulic conductivity tensor K as follows: i This involves calculating:

[0041]

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[0042]

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[0043]

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[0044]

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[0045]

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[0046] Conductance β i,k , and α j To calculate the conductance β, other information about the distribution of pressure and flow in the vascular network is also required. In particular, i,k , and α j To obtain an approximation of , the solution of the Poiseuille flow problem along the vascular network, given by the coupling of the epicardial coronary arteries with the intramural network, is considered.

[0047] To reduce the computational effort, the epicardial coronary arteries are modeled as one-dimensional tubular structures (note that this is done only for parameter estimation; in other parts of the model, the coronary arteries are three-dimensional).

[0048] The boundary conditions are an inlet pressure of 109 mmHg and an outlet pressure that depends on the radius of the peripheral blood vessel.

[0049] To obtain the physiological flow rate starting from this pressure gradient, it is the case that a constant multiplicative correction factor η is applied for all vessel radii.

[0050] Referring to this Poiseuille solution, Q j i,k =Q j k,i , i, k=1, 2, 3 is the perfusion area Ω at the interface between compartment i and compartment k. j M is the total flow rate exchanged between

[0051] The third compartment does not have any blood vessels, so Q j 2,3 is Ω j M is set equal to the total flow rate at the outlet of the second compartment.

[0052] Also, p j i,n , i=1,2 is the perfusion area Ω j M is the pressure in the nth vessel of compartment i at

[0053]

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[0054] In particular, the estimation step 31 estimates the global piecewise constant intercompartmental conductance β i,k This involves calculating:

[0055]

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[0056] In particular, the perfusion area Ωj M The local coupling coefficient β in j i,k is defined as follows:

[0057]

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[0058]

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[0059]

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[0060]

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[0061]

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[0062]

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[0063]

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[0064] In a similar manner, the estimation step 31 estimates the conductance coefficient α j This involves calculating:

[0065]

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[0066] After calculating the physical parameters in the resting state, the effect of stress factors on the coronary arteries needs to be considered. For this purpose, the epicardial coronary artery domain Ω reconstructed from the resting CT images is C was post-processed to account for vasodilation.

[0067] In particular, the physical parameter adjustment step 32 includes carrying out the following steps: - selecting a sample of epicardial coronary arteries visible on axial scans obtained in the resting and stress states; - the resting radius value R of the sample epicardial coronary artery rest-sample and the stress radius value R stress-sample and measuring; - Vasodilator index V str and calculating:

[0068]

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[0069]

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[0070] Furthermore, physiological findings indicate that adenosine injection results in an approximately 10-fold increase in vascular resistance. Therefore, to account for vasodilation within the intramural vascular network, the physical resistance parameter β of the multicompartment Darcy model was modified. 1,2 , and β 2,3 , K1 and K2 are increased by a factor of 10 relative to the baseline parameters estimated for the resting state in the estimation step above.

[0071] The final adjustment is the β 1,2 and β 2,3 This is performed based on the observation that the value of is lower in the whole body than in other myocardial regions, which results in an underestimation of the MBF calculated by numerical simulation relative to the MBF estimated by stress CTP.

[0072] To overcome this, the correction step 33 adjusts the intercompartmental pressure coupling coefficient β in the perfusion region located in the interventricular septum. 1,2 and β 2,3 This involves multiplying by a factor of 5.

[0073] The present invention also relates to an apparatus for rest coronary computed tomography angiography (cCTA) configured to perform the steps of the computer-implemented method 1 disclosed above.

[0074] The device according to the invention therefore comprises all the hardware and software conventionally required for rest coronary computed tomography angiography (cCTA) and a further elaboration unit configured to execute the computer-implemented method 1.

Claims

1. 1. A computer-implemented method for simulating myocardial blood flow under stress conditions, performed on a resting coronary computed tomography angiography device, comprising the step (2) of generating a simulated multi-physics model of myocardial perfusion, said generating step (2) further comprising: - generating (21) a simulation model of the epicardial vessels with a three-dimensional fluid dynamics description; - generating (22) a simulation model of an intramural blood vessel by a multicompartment porous medium; - coupling (23) said simulation model of said epicardial vessels and said simulation model of said intramural vessels; and (3) automatically calibrating physical parameters of the simulated multiphysics model of the myocardial perfusion under stress conditions, wherein the calibrated physical parameters include: - Permeability tensor (K ｉ , i=1, 2, 3); - Conductance between the epicardial coronary artery and the intramural vessel (α ｊ , j=1, . . . , J); and - Conductance between compartments (i, k) (β ｉ，ｋ , i ， k=1, 2, 3), where: Here, the automatic calibration step (3) includes the following steps: - a step (31) of estimating said physical parameters in a resting state by utilizing the geometrical and hydrodynamic properties of said intramural vessels in a resting state; - adjusting (32) said physical parameters to take into account vasodilation under stress conditions; - modifying (33) a physical parameter in the partition, in particular by increasing the physical parameter in the partition; wherein said adjusting step (32) of said physical parameters comprises carrying out the following steps: - selecting a sample of epicardial coronary arteries visible on axial scans obtained in the resting and stress states; the resting state radius value R of said sample epicardial coronary artery ｒｅｓｔ－ｓａｍｐｌｅ and the value of the radius in the stress state R ｓｔｒｅｓｓ－ｓａｍｐｌｅ and measuring; - the vasodilatation coefficient v ｓｔｒ and calculating [0010] - calculating the centerline of said epicardial coronary artery reconstructed from a resting computed tomography angiogram (CTA) and calculating the radius of said vessel at each point of said centerline; - Generating a new epicardial coronary artery surface by extruding tubular surfaces from said centerline, the radius of each tube being calculated as follows: [0025] where s is the curvilinear abscissa along the centerline.

2. The estimation step (31) includes estimating a global constant permeability tensor K ｉ 2. The computer-implemented method of claim 1 , comprising: [0030]

3. The permeability tensor K ｊ ｉ 3. The computer-implemented method of claim 2, wherein is defined as follows: [0045]

4. The steady porosity Φ ｊ ｉ 4. The computer-implemented method of claim 3, wherein is defined as follows: [0050] During the ceremony, [006] [0070]

5. The estimation step (31) includes estimating a global piecewise constant intercompartmental conductance β ｉ，ｋ A computer-implemented method according to any one of claims 1 to 4, comprising calculating: [0080]

6. The perfusion area Ω ｊ Ｍ The local coupling coefficient β ｊ ｉ，ｋ 6. The computer-implemented method of claim 5, wherein is defined as follows: [0097] [0010] (Other than that) ##EQU00011## ##EQU00012## (Other than that), ##EQU00013## (Other locations) ##EQU14## and ##EQU00015## It is.

7. The estimation step (31) is performed by determining the conductance coefficient α ｊ A computer-implemented method according to any one of claims 1 to 6, comprising calculating: ##EQU00016##

8. The modifying step (33) adjusts the intercompartmental pressure coupling coefficient (β １，２ , β ２，３ 8. The method of claim 1, further comprising multiplying the first signal by a predetermined factor.

9. An apparatus for rest coronary computed tomography angiography (cCTA) configured to perform the steps of the computer-implemented method (1) for simulating myocardial blood flow under stress conditions according to any one of claims 1 to 8.

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