Method and system for calculating forces exchanged between a fluid and a surrounding container, in particular in cardiovascular imaging

Abstract

The invention relates to a method for determining one or more parameters related to forces exchanged between a fluid and a surrounding container from a sequence of images of a boundary surface of the container, the method comprising: a) representing the boundary surface S(t) of the container as a series of meshes s, each mesh being identified by a position vector x(s,t); b) computing or receiving at input an instantaneous velocity vector v(s,t) at each position x(s,t); c) computing or receiving at input a vector n(s,t) normal to the surface at each position x(s,t); d) computing at each position x(s,t) a surface parameter f(s,t) as a function of the velocity vector v(s,t), the position vector x(s,t) and the normal vector n(s,t); e) deriving from the surface parameter f(s,t) one or more parameters related to forces exchanged between the fluid and the surrounding container. A corresponding system and computer program are also disclosed.

Description

Technical Field

[0001] The present disclosure relates to a method, computer program, and system for determining the forces exchanged between fluids flowing within a vessel, particularly blood in a heart chamber. Background Art

[0002] A fluid moving within a solid deformable container, and possibly moving in and out of such a container, exchanges forces with the surrounding boundaries. Such forces can have a significant impact on the resistance and long-term deformation of the container.

[0003] Of particular relevance is the flow of blood within blood vessels, such as the chambers of the heart. Blood is moved by the ability of a chamber, such as the left ventricle (LV) or right ventricle (RV), to generate the appropriate intraventricular pressure gradients (IVPG) that drive blood movement during ejection and filling.

[0004] Many studies have recognized the relevance of IVPG in cardiology, or equivalently the relevance of the total hemodynamic force (HDF) vector, which is the IVPG field integrated over the entire cavity. Clinical studies on base-apex IVPG are based on catheterization in animal models (Courtois et al., 1988; Guerra et al., 2013). The results showed that the dynamic rhythm of the base-apex IVPG is a clear marker of normal function, which is altered in systolic or diastolic dysfunction and is lost during heart failure. Despite the obvious importance of IVPG, it has been rarely used in clinical cardiology in the past due to the invasive nature of its acquisition, which requires a catheter or a force measuring element.

[0005] Advances in cardiovascular imaging, echocardiography, and magnetic resonance imaging (MRI) have made it possible to measure the blood flow field within the cardiac chambers and, based on post-processing, to non-invasively calculate the corresponding pressure field. Using the law of conservation of momentum, we can obtain:

[0006]

[0007] where F(t) is the hemodynamic vector, ρ is the fluid density, and v(x, t) is the fluid velocity vector field at all points x within the chamber volume V(t) measured at time t. The integral is taken over the moving volume of the fluid, so these points are assumed to be moving fluid particles. Because measurements of fluid velocity are usually more feasible at fixed points than at moving particles, it is often convenient to describe the same calculation using a spatially fixed volume of fluid. Using the Reynolds transport theorem, the integral (1) can be rewritten as:

[0008]

[0009] where the integral over a fixed point x within the volume V(t) is now assumed to be instantaneously fixed, S(t) is the closed surface bounding the volume, and n is the exterior unit normal vector.

[0010] Considering that blood is an incompressible medium, equation (2) is usually rewritten as a single integral over the volume:

[0011]

[0012] Because it enables the calculation of the hemodynamic vector based on the velocity vector field measured within the volume, the concept of hemodynamic forces (HDF) is then introduced as a mathematically well-defined global metric based on formula (2) or (3), which corresponds to the integrated IVPG within the LV and represents the forces exchanged between blood and surrounding tissues (Cimino et al., 2012; Pedrizzetti et al., 2015).

[0013] Using formula (3), HDF can be calculated noninvasively in echocardiography using methods that can assess blood flow velocity, such as Echo-PIV (Pedrizzetti et al., 2016), Doppler-VFM (Mete et al., 2018), or color Doppler M-mode echocardiography (Firstenberg et al., 2000; Greenberg et al., 2001). Recently, three-dimensional / three-dimensional phase-contrast magnetic resonance imaging (MRI), often referred to as 4D flow MRI, has been used to assess HDF in the LV of normal and diseased subjects (Arvidsson et al., 2016; Eriksson et al., 2016). Based on these techniques, the assessment of HDF is becoming an important marker of cardiovascular function.

[0014] However, these methods suffer from technical difficulties.

[0015] Fluid velocity assessed by ultrasound is approximate when using echo-PIV, which also preferably requires the injection of contrast agent, and is essentially unidirectional and has limited accuracy when using Doppler-based methods. The use of 4D flow MRI is more reliable and accurate; however, this requires expensive equipment in a fixed setup and time-consuming procedures for acquisition and post-processing. It produces a large amount of information, with three-dimensional velocity vectors measured at all points in three-dimensional space, and it may not be recommended for estimating a single HDF parameter. Recently, a simplified method was introduced to estimate the HDF based on the motion of the surrounding boundaries, which can be relatively easily recorded in echocardiography or obtained from simple cine cardiac MRI (Pedrizzetti et al., 2017). However, this method is mathematically complex and approximate and is only applicable to LVs with sufficiently regular geometry. Summary of the Invention

[0016] It is therefore an object of the present disclosure to provide methods and systems for determining one or more parameters related to the forces exchanged between a fluid and a surrounding container, in particular blood in a cardiac chamber, which methods and systems are simple and easy to apply, in particular in clinical practice.

[0017] This object is achieved by a computer-implemented method comprising:

[0018] a) providing an image sequence of the boundary surface S(t) of the container;

[0019] b) Representing the container's boundary surface S(t) as a series of grids, each identified by a position vector X(s, t). Such grids may be geometric shapes, such as polygons, particularly triangles, circles, or ellipses, wherein the position vector x(s, t) identifies such a shape;

[0020] c) calculating or receiving at the input the instantaneous velocity vector v(s, t) at each position x(s, t);

[0021] d) calculating or receiving as input a vector n(s, t) perpendicular to the surface at each position x(s, t);

[0022] e) At each position x(s,t), calculate the surface parameters f(s,t) as a function of the velocity vector v(s,t), the position vector x(s,t), and the normal vector n(s,t), specifically:

[0023] f) deriving parameters related to the forces exchanged between the fluid and the surrounding container from the surface parameters f(s,t), in particular by integrating such surface parameters f(s,t) over the surface boundary S(t) and / or determining the projection of such surface parameters f(s,t) onto the normal n(s,t) of the surface at each position x(s,t).

[0024] If the vessel is the heart, specifically the chambers of the heart, the fluid is blood, and the forces exchanged between the fluid and the vessel are the intracardiac hemodynamic forces.

[0025] Therefore, by considering only information related to the boundary surfaces, the intraventricular pressure gradient (IVPG) or equivalently the total hemodynamic vector (HDF) that drives blood motion during ejection and filling, or parameters related thereto, can be estimated.

[0026] This has surprising consequences since fluid dynamics provides well-known formulas and calculations for obtaining this information only if the spatial fluid velocity within the heart is known.

[0027] The parameters related to the local force vector f(x, t) can advantageously be calculated as:

[0028]

[0029] Where ρ is the density of the fluid. From these parameters, the global force vector F(t) can be derived as:

[0030]

[0031] Alternatively, the normal component of the local force vector associated with the pressure distribution p(x, t) in an integral sense can be calculated as:

[0032]

[0033] As another option, the norm or tangential component of the local force vector f(x, t) can be considered as the output parameter.

[0034] According to an improvement, one or more parameters may be normalized on the volume of the container V(t), for example, the volume of the container V(t) is calculated as:

[0035]

[0036] In the case of a container like a heart with a hole, let S1 denote the surface of the real part and S2 denote the surface of at least one hole. The instantaneous velocity of the fluid passing through the opening boundary surface S2 can be received at the input or the average normal velocity through the hole ∫ S v·ndS is calculated as:

[0037] -∫ S v·ndS

[0038] In the case of a heart, the opening boundary surface is a valve which is advantageously segmented into individual circular or polygonal meshes.

[0039] According to an embodiment, the sequence of images of the container boundary surface is obtained by operating a three-dimensional reconstruction of the container boundary surface based on a two-dimensional or three-dimensional image dataset.

[0040] An embodiment relates to a computer product directly loadable into a memory of a digital computer and comprising software code portions for performing the method according to the embodiments herein, when the product runs on the computer.

[0041] According to another embodiment, a system for determining one or more parameters related to forces exchanged between a fluid and a surrounding container is provided. The system includes a graphical user interface (GUI) configured to receive user input, a memory storing program instructions, an input for receiving one or more sequences of two-dimensional or three-dimensional images of the container, and an output for outputting force-related parameters in a numerical and / or graphical format. A processor is configured to execute the program instructions to perform the steps of a method according to an embodiment of the present invention.

[0042] Further developments of the invention form the subject matter of the dependent claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The characteristics of the invention and the advantages resulting therefrom will become more apparent from the following description of a non-limiting embodiment thereof shown in the accompanying drawings, in which:

[0044] Figure 1 An exemplary block diagram of a first embodiment of the apparatus is shown;

[0045] Figure 2 An exemplary block diagram of a second embodiment of the apparatus is shown;

[0046] Figures 3 and 4 A flowchart illustrating the operation of a method according to an embodiment of the present invention;

[0047] Figure 5 An example of a right ventricular (RV) surface made of triangular elements is shown;

[0048] Figure 6 shows the surface of a child's RV extracted using semi-automatic segmentation shown at end-systole (smaller darker RV) and end-diastole (wider semi-transparent surface);

[0049] Figure 7A mesh in the form of triangular elements described by the 3D position vectors of the vertices is shown.

[0050] Figure 8 Figure 2 shows the calculated hemodynamic forces during one heartbeat in the RV. Comparison between the results from computational fluid dynamics (solid line) and the results obtained by the method disclosed herein (black dots). The three components of force are reported separately. DETAILED DESCRIPTION

[0051] The present invention will be described primarily with reference to applications for measuring hemodynamic parameters and therefore with the heart as the target of analysis. However, this should not be considered as limiting the scope of protection, as the same considerations discussed in detail below can be readily extended to any fluid in any deformable container, with or without inlet / outlet apertures.

[0052] refer to Figure 1 According to one embodiment, a system includes: a graphical user interface (GUI) 401 for receiving user input; a memory 201 for storing program instructions; and a processing unit 301 for reading input data 101 and processing the input data to estimate hemodynamic parameters in a patient's heart by executing the program instructions to perform one or more steps of a method according to an embodiment of the present invention. An output, such as a monitor 501, can display the results of the analysis in graphical and / or numerical form. Processing unit 301 can be a dedicated microprocessor system or, more commonly, a general-purpose personal computer. The characteristics of unit 301 will be significantly reflected in the processing speed.

[0053] The input data may be in the form of an image of the heart's boundary surface or a sequence of two-dimensional or three-dimensional images of the entire heart. In this case, the processing unit 301 is configured to perform a three-dimensional reconstruction of the heart's boundary surface based on an imaging dataset received from, for example, an imaging device such as that shown in the figure of Reference 2. Examples include ultrasound, MRI, computed tomography (CT), and optical or laser-based devices known in the art. In one embodiment, the system may also be integrated into one of these devices to achieve a very compact configuration.

[0054] like Figure 2 In the example shown, the system may also comprise a further input 601 for receiving a value of the velocity of the fluid at a hole through a boundary surface of the container, wherein the processing unit 301 is advantageously configured to use such a value as the velocity of a grid covering such a hole.

[0055] Advantageously, an ultrasound device with Doppler capability or a phase contrast MRI device 3 may be provided in combination to obtain velocity values ​​of the fluid passing through the aperture of the container, which is then delivered to the second input 601 of the system. In one embodiment, this device is the same as the device providing the imaging dataset at input 101, which offers significant advantages in terms of compactness and reduced cost.

[0056] Depending on the type of data available at the input, the processing unit 301 is configured to process the data by executing Figures 3 and 4 The operations in the flowchart are shown to describe in detail data information about the subject's heart to estimate hemodynamic parameters.

[0057] Reference Figure 3 The flowchart of one embodiment includes two basic operations:

[0058] (A) Non-invasively obtain the three-dimensional (3D) motion geometry of the vessel boundary;

[0059] (B) Hemodynamic forces are calculated from this geometry based on the original mathematical solution.

[0060] (A) Non-invasively obtain the three-dimensional (3D) moving geometry of the container boundary

[0061] The internal geometry of a cardiovascular region such as the LV or RV can be visualized by existing imaging techniques such as conventional ultrasound or MRI or CT. Other techniques such as those based on optics or lasers can be used in different environments when appropriate. The moving geometry can then be identified by manual delineation or by applying automated segmentation methods, many of which are based on edge detection, pattern recognition, neural networks, atlas matching, active deformation or other techniques that end with the identification of boundaries, margins, edges. The movement is given by applying the segmentation method at different times, and can also be estimated by applying optical flow methods that can track the movement of the boundaries of the segmentation at one or some times (for example, as disclosed in Seo et al., 2014, and Muraro et al., 2016, which will be considered incorporated herein by reference).

[0062] When using 3D imaging techniques, 3D geometry can be obtained by applying these methods for directly estimating the boundaries of 3D images or data sets. See, for example, the literature incorporated by reference (Satriano et al. 2017; Pedrizzetti et al. 2014; Zheng 2018; Satriano et al. 2019) for examples of available applications. 3D geometry can also be reconstructed by estimating the boundaries from one or more 2D images, and then appropriately recombining these 2D images in 3D space. Similar to the 3 longitudinal slices, or multiple short axis slices, commonly used for imaging in the LV. See, for example, 3D reconstructions from simple cine cardiac MRI (Pedrizzetti et al. 2017; Biffi 2019), which are incorporated by reference. There are also many solutions available on the market for this purpose, and some examples are reported here and incorporated into this article by reference (“4D LV-Analysis” and “4D RV-Function”, TOMTEC Imaging Systems GmbH, Germany; “Medis Suite MR”, Medis Medical Imaging Systems, Leidan, The Netherlands; “Segment CMR” and “Segment CT”, Medviso AB, Lund, Sweden).

[0063] The result of this step will be a three-dimensional reconstruction of the vessel boundary surface S(t), which will consist of a solid boundary S1(t) (such as the endocardium of the LV) and an opening boundary S2(t) (such as the valve of the left ventricle) from which fluid can enter or leave the vessel. The surface will be described by a series of position vectors x(s, t) on the surface. These position vectors change their coordinate values ​​during time t according to the motion of the surface. These positions are marked by an identifier or index, usually denoted by s; this identification makes it possible to draw a connected structure describing the surface as triangles, rectangles or other types of surface elements, each element being identified by the corresponding position vectors of its vertices.

[0064] Figure 5 An example of the surface of an RV made of triangular elements is shown. Figure 6 It is shown that each individual triangle element is described by the 3D position vectors of the element's vertices.

[0065] (B) Calculation of hemodynamic HDF based on the geometry of the vessel boundary

[0066] First, the instantaneous velocity of each single position is calculated by time-differentiating the boundary position

[0067]

[0068] This time derivative can be calculated numerically using the formula for numerical derivatives based on the known positions at a series of moments. In the case of a boundary describing a solid impermeable boundary, the velocity (4) corresponds to the velocity of the viscous fluid. For open parts of the boundary, the velocity must be obtained by direct measurement from other information or additional considerations.

[0069] Equations (1), (2), or (3) involve volume integrals that require knowledge of the interior of the fluid domain and cannot be evaluated by knowledge of the surface alone. However, careful inspection shows that the first term in (2) can be rewritten in terms of a surface integral as follows:

[0070]

[0071] This is achieved by a crude application of Gauss's theorem (also known as the divergence theorem), which takes advantage of the fact that the fluid is incompressible. This can be verified for a general component i, assuming that the velocity is divergence-free and considering that the integral is over a fixed point in space, we can write:

[0072]

[0073] where the last equation uses Gauss's theorem and implicitly assumes summation over a repetition index (here k) (Einstein notation).

[0074] Therefore, combining Equation (5) into Equation (2) provides a way to calculate the hemodynamics based on surface integrals, and therefore only based on knowledge of the values ​​at the boundaries. The complete result can be written in a single formula as:

[0075]

[0076] It can be immediately verified that similar results can be obtained by combining the same steps with different combinations of formulas (1) or (3), with minor formal differences and equivalent results, paying special attention to the difference between the volume described by fixed positions in (2) and (3) and the volume consisting of moving fluid particles in (1).

[0077] The hemodynamic forces are usually normalized by the volume V(t) of the analyzed chamber, which can be calculated in various ways and, for example, by applying Gauss's theorem:

[0078]

[0079] The process formally synthesized in equation (7) is an exact result never before published that enables the calculation of the HDF vector from the knowledge of the moving boundary as obtained in the previous step (A). The surface integral present therein can be estimated by many numerical methods. A simple approach is to transform the integral into a function of the integral over all individual surface elements (e.g., Figure 5 Any quadrature formula or numerical integration method can be used as per your convenience.

[0080] The surface integral (such as that in equations (2), (5), (7), and (8)) consists of the integral over the closed real part S1 of the container boundary and the integral over the open part S2 through which the fluid can flow. Although the fluid velocity over the solid part corresponds to the boundary velocity and is usually obtained directly from the image, the fluid velocity over the open part may not be directly available after differentiation (4). Sometimes it can be provided directly by imaging techniques, such as in some applications of Doppler ultrasound or by phase contrast MRI, which is often used to measure out-of-plane velocity components. When these measurements are not available, the conservation of mass can be used

[0081]

[0082] to estimate the average normal velocity across the opening. Furthermore, the fluid velocity can be assumed to be approximately uniform across the entire orifice and primarily unidirectional, giving the velocity v = v(v·n)n. The same arguments apply to a single orifice or multiple openings.

[0083] In general, the existence of a formula similar to (7) allows the estimation of the distribution of forces on the boundary surface with respect to a time-varying constant value. Recall that the total force can be calculated by definition, and neglecting the viscous forces which are essentially negligible in the cardiac chambers (Domenichinie and Pedrizzetti 2015), as the integral of the pressure p(x, t) on the surface as follows:

[0084]

[0085] The formal similarity between (7) and (9) suggests that there is a distribution of local force terms as follows,

[0086]

[0087] It plays a role similar to pressure, where (7) and (9) illustrate that the analogy is valid at the level of integration, not punctuality. The pressure distribution (10) can represent an indicator for revealing local functional differences of the cardiac chambers. Other indicators based on (10) are the normal component of the local force vector, emphasizing the analogy with pressure based on (9); the tangential component, emphasizing the analogy with wall shear stress; or the magnitude of the local force vector expressed as a norm:

[0088]

[0089] or other combinations may also be used as indicators of specific types of disorders or indicators of cardiac remodeling.

[0090] The complete process (A) + (B) has been validated by calculating the hemodynamic forces in complex RV geometries during heartbeats and comparing the results obtained by the method disclosed in this article with those obtained by applying equation (3) to the full three-dimensional three-dimensional velocity vector field calculated by computational fluid dynamics (CFD).

[0091] The RV was recorded by echocardiographic imaging, and segmentation was performed by a semi-automated algorithm of the type described in (Seo et al., 2014; Muraro et al., 2016). Figure 7 The geometry of the RV segmentation surface at two moments in time is shown. The same geometry is used to perform a CFD study at high resolution in order to obtain the velocity vector field inside the moving RV volume at all moments during one heartbeat. To this end, CFD solves the fluid dynamics equations governing an incompressible Newtonian fluid inside the geometry immersed in the domain. All details of the CFD technique are reported in (Mangual et al., 2012). Based on the CFD results (which takes about 40 hours in the workstation), the hemodynamic forces are calculated by volume integration (3), a step that requires attention in the internal volume segmentation based on a known surface. The same results are obtained by applying formula (7) directly from the previously segmented surface (in less than 1 second in the same workstation). Figure 8 Comparative results are reported because they are expected to be very comparable, with minor differences due to the different time resolutions used when computing the time derivatives, differences in the numerical integration of space and volume, and differences in the separation of the internal volume with a fixed grid in CFD.

[0092] The forces exchanged between fluids flowing within a vessel are an important measure of the interaction between the fluid and surrounding structures. In particular, in the cardiovascular system, hemodynamic forces, or equivalently, pressure gradients, are considered fundamental to describing the function of cardiovascular regions.

[0093] The methods used to calculate them are approximate or exhibit significant complexity (4D flow MRI). A method to accurately calculate them in a simple and fast manner would be beneficial in many aspects. In particular, a method to estimate them from routine, frequently used cardiovascular imaging would enable their application in medicine.

[0094] References:

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[0104]

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Claims

1. A computer-implemented method for estimating hemodynamic forces between blood and surrounding cardiac chambers based on a sequence of images of a boundary surface of a cardiac chamber, the method comprising: a) representing the boundary surface S(t) of the cardiac chamber as a series of grids s as a function of time t, each grid being identified by a position vector x(s,t); b) calculating or receiving at the input the instantaneous velocity vector v(s, t) of the blood at each position vector x(s, t); c) calculating or receiving at input a normal vector n(s, t) perpendicular to the boundary surface at each position vector x(s, t); d) calculating at each position vector x(s,t) a surface parameter f(s,t) as a function of said velocity vector v(s,t), said position vector x(s,t) and a normal vector n(s,t); and e) deriving a force vector from the surface parameters f(s,t) as an estimate of the hemodynamic force.

2. The method according to claim 1, wherein Step e) comprises integrating said surface parameter f(s, t) over said boundary surface S(t).

3. The method according to claim 1 or 2, wherein: Step e) comprises determining the projection of said surface parameters f(s, t) onto the normal vector n(s, t) of the surface at each position vector x(s, t).

4. The method according to claim 1, wherein Step d) comprises calculating the surface parameter f(s, t) as:

5. The method according to claim 1, wherein Step e) comprises deriving a local force vector f(x, t) as an estimate of said hemodynamic force: Wherein, ρ is the density of the blood.

6. The method according to claim 1, wherein Step e) comprises calculating the force vector F(t) as: Here, ρ is the density of the blood.

7. The method according to claim 1, wherein Step e) comprises calculating the normal component of the local force vector associated with the pressure distribution p(x, t) in an integral sense as a parameter: Here, ρ is the density of the blood.

8. The method according to claim 1, wherein Step e) comprises calculating the norm or tangential component of the local force vector f(x, t) as a parameter.

9. The method according to claim 1, wherein: Step e) comprises normalizing the estimated hemodynamic forces on the volume V(t) of said cardiac chamber.

10. The method according to claim 9, wherein: The volume V(t) of the heart chamber is calculated as:

11. The method according to claim 1, wherein Step a) comprises representing the boundary surface S(t) of the cardiac chamber as a series of geometric figures, wherein the position vector x(s, t) identifies the center of the figures.

12. The method according to claim 1, wherein The heart chamber has a real part and at least one hole, wherein the real part has a surface S1; the at least one hole has an open boundary surface S2, step b) comprises: receiving at the input the velocity of the blood passing through the open boundary surface S2 or the average normal velocity passing through the hole as the velocity vector v Calculated as:

13. The method according to claim 1, wherein A sequence of images of the boundary surface of the heart chamber is obtained by performing a three-dimensional reconstruction of the boundary surface of the heart chamber based on a two-dimensional or three-dimensional image dataset.

14. The method according to claim 13, wherein A portion of the boundary surface corresponding to at least one heart valve is segmented into a single circular or polygonal mesh.

15. A computer product directly loadable into the memory of a digital computer and comprising software code portions for performing the method according to any one of the preceding claims when said product is run on said digital computer.

16. A system (1) for estimating hemodynamic forces between blood and surrounding cardiac chambers, the system comprising: a) a first input (101) for receiving one or more sequences of two-dimensional or three-dimensional images of the heart chamber; b) a memory (201) for storing program instructions; c) a processing unit (301); d) a graphical user interface (401) configured to receive user input; e) an output terminal (501) for outputting force-related parameters in digital and / or graphical format; Characterized in that the processing unit (301) is configured to execute program instructions to perform the following steps: a) performing three-dimensional reconstruction of the boundary surface S(t) of the cardiac chamber; b) dividing the boundary surface S(t) of the cardiac chamber into a series of grids s; c) associate a position vector x(s, t) with each grid; d) Calculate the instantaneous velocity vector v(s, t) at each position vector x(s, t); e) calculating a normal vector n(s, t) perpendicular to the boundary surface at each position vector x(s, t); f) calculating, at each position vector x(s,t), surface parameters f(s,t) as a function of the velocity vector v(s,t), said position vector x(s,t) and the normal vector n(s,t); g) deriving a force vector from said surface parameters f(s,t) as an estimate of said hemodynamic force; h) Outputting a value of the force vector as an estimate of the hemodynamic force based on the surface parameters f(s,t).

17. The system (1) according to claim 16, characterized in that The system is arranged in combination with an ultrasound device, a computed tomography (CT) device or a magnetic resonance imaging (MRI) device (2) for acquiring a sequence of two-dimensional or three-dimensional images of the heart chambers to be transmitted to the first input (101) of the system (1).

18. The system (1) according to claim 17 further comprises a second input terminal (601) for receiving a value of the velocity of the blood at a hole passing through the boundary surface of the heart chamber, the processing unit (301) being configured to use the value as the velocity of a grid covering the hole.

19. The system (1) according to claim 18, characterized in that The system is combined with an ultrasound imaging device or a phase contrast magnetic resonance imaging device (3) with Doppler capability, which is used to obtain the value of the velocity of the blood at the hole through the boundary surface of the heart chamber to be transmitted to the second input end (601).

20. System (1) according to any one of claims 16 to 19, characterized in that The system is configured to interface with or be combined with an imaging device (2) for acquiring two-dimensional or three-dimensional images of a subject's heart, and the processing unit (301) is configured to estimate the geometry of the endocardial border and, optionally, the velocity of blood passing through the subject's mitral valve and aortic valve.

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